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https://www.hackmath.net/en/word-math-problems/expression-of-a-variable-from-the-formula?page_num=36
[ "# Expression of a variable from the formula - math word problems\n\n#### Number of examples found: 808\n\n• The ball", null, "The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?\n• Exponential warm", null, "Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degr\n• Telegraph poles", null, "The bases of two adjacent telegraph poles have a height difference of 10.5 m. How long do the wires connect the two poles if the slope is 39° 30´?\n• Klara", null, "Klara and Jitka went on a hiking trip at 13 o'clock at speed 5km/h. At 14 o'clock, Tomas ride on the bike at an average speed of 28 km/h. How many hours and at what distance from the beginning of the road Tomáš caught the two girls?\n• Equilateral triangle", null, "A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.\n• Orchard", null, "One-eighth of the trees in the fruit plant in winter froze and one-twelfth of damaged disease and pests. Healthy trees remained 152. Is it enough to supply 35 trees to restore the original number of trees in the orchard?\n• Painting rooms", null, "If Dano paint three hours daily given work he complete in 7.5 days. How many hours a day would have to work to finish the job 1.5 days earlier?\n• An observer", null, "An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?\n• Hexagonal pyramid", null, "Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.\n• The wellbore", null, "The wellbore has a tributary of 2 m3 per hour. When there is no tapping, there are a stable 28 liters of water in the well. The pump suction basket is at the bottom of the well. At 14.00, the water was pumped out at a rate of 0.5 liters of water every se\n• Right triangle", null, "Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.\n• Between two bus stops", null, "Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that whether he was running to one or the other stop, he would have arrived at the bus stop. The average bus speed is 60 km/h. What is the average\n• Two pipes", null, "How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?\n• A map", null, "A map with a scale of 1: 5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field?\n• The diagram 2", null, "The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone\n• Two ships", null, "The distance from A to B is 300km. At 7 am started from A to B a ferry with speed higher by 20 km/h than a ship that leaves at 8 o'clock from B to A. Both met at 10h 24min. Determine how far they will meet from A and when they reach the destination.\n• A kite", null, "Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain?\n• Fire tank", null, "Whole fire tank was discharged once in 5 days by first out by second in \\$n days. Once firefighters pumped out 6/13 of water out from the tank and then let the water flow out both drain. How long take empty the tank?", null, "The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.", null, "Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?" ]
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https://unitconversion.io/25-ppb-to-ppm
[ "#### Convert 25 Parts-Per-Billion (ppb) to Parts-Per-Million (ppm)\n\nThis is our conversion tool for converting parts-per-billion to parts-per-million.\nTo use the tool, simply enter a number in any of the inputs and the converted value will automatically appear in the opposite box.\n\nppb\n\n### =\n\nppm\n\n##### How to convert Parts-Per-Billion (ppb) to Parts-Per-Million (ppm)\n\nConverting Parts-Per-Billion (ppb) to Parts-Per-Million (ppm) is simple. Why is it simple? Because it only requires one basic operation: multiplication. The same is true for many types of unit conversion (there are some expections, such as temperature). To convert Parts-Per-Billion (ppb) to Parts-Per-Million (ppm), you just need to know that 1ppb is equal to ppm. With that knowledge, you can solve any other similar conversion problem by multiplying the number of Parts-Per-Billion (ppb) by . For example, 4ppb multiplied by is equal to ppm.\n\n#### Best conversion unit for 25 Parts-Per-Billion (ppb)\n\nWe define the \"best\" unit to convert a number as the unit that is the lowest without going lower than 1. For 25 parts-per-billion, the best unit to convert to is .\n\n#### Fast Conversions\n\n 1 ppb = ppm 5 ppb = ppm 10 ppb = ppm 15 ppb = ppm 25 ppb = ppm 100 ppb = ppm 1000 ppb = ppm 1 ppm = ppb 5 ppm = ppb 10 ppm = ppb 15 ppm = ppb 25 ppm = ppb 100 ppm = ppb 1000 ppm = ppb" ]
[ null ]
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https://open.library.ubc.ca/cIRcle/collections/ubctheses/831/items/1.0095634
[ "# Open Collections\n\n## UBC Theses and Dissertations", null, "## UBC Theses and Dissertations\n\n### Wilson Harris and the experimental novel Sealy, I. Allan 1982\n\nMedia\n831-UBC_1982_A1 S43.pdf [ 12.32MB ]\nJSON: 831-1.0095634.json\nJSON-LD: 831-1.0095634-ld.json\nRDF/XML (Pretty): 831-1.0095634-rdf.xml\nRDF/JSON: 831-1.0095634-rdf.json\nTurtle: 831-1.0095634-turtle.txt\nN-Triples: 831-1.0095634-rdf-ntriples.txt\nOriginal Record: 831-1.0095634-source.json\nFull Text\n831-1.0095634-fulltext.txt\nCitation\n831-1.0095634.ris\n\n#### Full Text\n\n`WILSON HARRIS AND THE EXPERIMENTAL NOVEL by ALLAN SEALY B.A. (Hons.) U n i v e r s i t y of D e l h i , 1971 B.A. (Hons.) Western Michigan U n i v e r s i t y , 1972 M.A. Western Michigan U n i v e r s i t y , 1974 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES Department of E n g l i s h We accept t h i s t h e s i s as conforming to the re q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA February, 1982 0 A l l a n Sealy, 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the head of my department or by h i s or her representatives. It i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date , f 9 & 2 -i i . Abstract Wilson Harris i s the author of fourteen novels and two books of shorter f i c t i o n . His work, c r y p t i c and yet urgent, checks the widespread b e l i e f that experimental w r i t i n g today i s condemned to parody and s e l f -r e f e r e n t i a l performance. Located at the crossroads of numerous c u l t u r a l t r a d i t i o n s , A f r i c a n , Amerindian, and European, h i s novels evolve a complex language well suited to the a r t i c u l a t i o n of marginal needs i n an increasingly polarized world. The novels are d i f f i c u l t , and to examine the grounds of t h e i r d i f f i c u l t y , I rehearse at the outset a general theory of experiment in f i c t i o n , before reviewing .Harris's own remarks on the subject, gleaned from h i s c r i t i c a l essays. Harris's d i s t o r t i o n s appear f i r s t at the l e v e l of the l i n e ; the oddity of h i s s t y l e , and' i t s attendant vexations, are the subject of my next chapter, \"Experiment and Language.\" Here I consider the techniques and uses of s t y l i s t i c f r a c t u r e and surreal montage, showing how Harris undoes the t r a d i t i o n a l concept of r h e t o r i c by working an amalgam of the extraordinary and the commonplace. The r h e t o r i c of unrhetoric has i t s s t r u c t u r a l equivalent i n an unmaking of na r r a t i v e sequence and causation. \"Experiment and Narrative\" examines the devices by which these s e c u r i t i e s are f o i l e d , time by space, presence by absence. \"Experiment and the I n d i v i d u a l \" considers the fate of character i n f i c t i o n s set at the ragged edges of the modern world. Harris refuses the holographic i l l u s i o n of conventional i d e n t i t y , depicting instead those i n d i v i d u a l s whose resources are so slender as to have become i n v i s i b l e . F i n a l l y , \"Experiment and Tradition\"attempts to show how the dispossessed begin to f i n d a v o i c e i n the experimental language of a w r i t e r whose very o b s c u r i t y allows him to perplex the ideology of c i v i l d i s c o u r s e . H a r r i s has developed a s t y l e which i s r e p r e s e n t a t i v e but not mimetic; h i s marginal discourse adds a new dimension to the \"blank s l a t e \" of the avantgarde. i v . Table of Contents Page Ab s t r a c t i i I n t r o d u c t i o n 1 I. Experiment. i ) On Experiment 4 i i ) H a r r i s on Experiment 19 I I . Experiment and Language 33 I I I . Experiment and N a r r a t i v e 71 IV. Experiment and the I n d i v i d u a l 110 V. Experiment and T r a d i t i o n 148 Conclusion 181 Notes 190 B i b l i o g r a p h y 213 Ab b r e v i a t i o n s 226 1. I n t r o d u c t i o n The case of Wilson H a r r i s i s a c o n t r a d i c t o r y one. That a w r i t e r of h i s genius should have to wait h i s due i n an age when l i t e r a r y c r i t i c i s m i s nowhere i n short supply, i s the l e a s t of the c o n t r a d i c t i o n s that I propose to explore i n the pages that f o l l o w . Some of h i s o b s c u r i t y r e f l e c t s the d i s t r i b u t i o n of other kinds of power than l i t e r a r y power i n the world of l e t t e r s , but a p o r t i o n i s of h i s own making, and i t i s t h i s c o n t r a d i c t i o n which I w i l l c h i e f l y address. H a r r i s i s a d i f f i c u l t n o v e l i s t , and h i s work wants c a r e f u l reading. The d i f f i c u l t y i s not g r a t u i t o u s ; i t has a purpose, and to discover that purpose i s a task as rewarding as i t i s s u f f i c i e n t . My p o l i c y w i l l not be to s i m p l i f y , but to map, from v a r i o u s angles, the grounds of H a r r i s ' s d i f f i c u l t y . To do t h i s , I must c l e a r away at the outset c e r t a i n misconceptions which hedge about the author. H a r r i s i s f i r s t a n o v e l i s t and only then any of the other things he has been taken to be, whether mystic or shaman, anthroposophist or mytho-grapher, poet or psychodramatist. That he could come to be so v a r i o u s l y construed, speaks an enigma i n the man and h i s work, but i t i s a l s o the product of a taxonomic impulse i n l i t e r a r y s t u d i e s which begins by plunging the man i n t o a bath marked \"Guyanese\" or \"West In d i a n \" or \"Caribbean,\" and thereby s h i f t s the reader's i n t e r e s t from what the n o v e l i s t w r i t e s to what he represents. Once t h i s elementary displacement (but one of Archimidean p r o p o r t i o n s f o r the novels) has been e f f e c t e d , the c r i t i c may dart unabashed i n t o the s t r e e t p r o c l a i m i n g h i s d i s c o v e r y of the r e a l H a r r i s , who w i l l u s u a l l y prove a n a t i o n a l myth-maker, a r e g i o n a l voodooist, an e x o t i c geomancer, or e l s e a chimera formed of these p a r t s . Lost i n the 2. press of claimants i s u s u a l l y H a r r i s the experimental n o v e l i s t , and i t i s he who i s the object of my study. Theodore Wilson H a r r i s was born on 24 March, 1921, i n New Amsterdam, B r i t i s h Guiana (now the independent r e p u b l i c of Guyana). He was educated at Queen's Co l l e g e , Georgetown, and t r a i n e d as a land surveyor, i n which p r o f e s s i o n he advanced to the o f f i c e of Senior Surveyor. During the 1940s and e a r l y 1950s, he traversed the i n t e r i o r of Guyana on v a r i o u s mapping e x p e d i t i o n s , developing an intimacy w i t h the landscape that would f e a t u r e so prominently i n h i s work, i n c l u d i n g h i s short s t o r i e s and poems which began to appear at the time. His knowledge of the many faces of the land (a knowledge most Guyanese l a c k , l i v i n g as they do along the coast) H a r r i s took w i t h him to B r i t a i n when he emigrated there i n 1959. A year l a t e r , h i s f i r s t n o v e l , Palace of the Peacock, appeared. Since then, he has l i v e d i n London, producing a steady flow of f i c t i o n published by the house of Faber and Faber. His fourteenth and most recent novel i s The Tree of the Sun (1978). A book of c r i t i c a l essays, The Womb of Space, w i l l mark h i s North American debut, and a new n o v e l , The Angel at the Gate, i s due i n 1982. I t would be i d l e to deny that H a r r i s ' s novels are scored by t h e i r author's o r i g i n s , and that the s e n s i b i l i t y which informs them, e s p e c i a l l y i n the period p r i o r to 1970, i s a West Indian one. The reader who i s u n f a m i l i a r w i t h the West Indies or w i t h i t s l i t e r a t u r e , w i l l f i n d a b r i e f l i t e r a r y h i s t o r y of the region i n my f i n a l chapter, but since the account given there i s scant and moreover that of an o u t s i d e r , he would be b e t t e r advised to go to Michael G i l k e s ' s Wilson H a r r i s and the Caribbean N o v e l , 1 or to any of the small but growing number of West Indian l i t e r a r y h i s t o r i e s w r i t t e n or e d i t e d by v a r i o u s hands. To some degree, then, a formal approach i s enjoined on an o u t s i d e r , who i s b e t t e r q u a l i f i e d to t r e a t the novels as novels than to judge t h e i r t r u t h to a l i f e he has not known. This i s no e s p e c i a l misfortune, since the most a r r e s t i n g f e a t u r e of H a r r i s ' s novels i s not t h e i r s e t t i n g but t h e i r experimental s u r f a c e , an assumption which has determined the course of my t h e s i s from i t s t i t l e onward. I have chosen i n what f o l l o w s to preserve an overarching chronology w i t h respect to the p u b l i c a t i o n of the novels, w h i l e b r i n g i n g to bear at d i f f e r e n t stages a schematic c r o s s - s e c t i o n of concerns ranging from s t y l e and s t r u c t u r e to i n d i v i d u a l character and s o c i a l h i s t o r y . In t h i s way, a sense of the progress of H a r r i s ' s work i s combined w i t h successive i n q u i r i e s i n t o a v a r i e t y of experimental modes. So \"Experiment and Language, \"Experiment and N a r r a t i v e , \" \"Experiment and the I n d i v i d u a l , \" and \"Experiment and T r a d i t i o n \" s t r a d d l e s e q u e n t i a l stages of H a r r i s ' s canon, covering i n each case novels most appropriate to the moment's i n q u i r y . Such an approach w i l l mean that c e r t a i n aspects of c e r t a i n novels get short s h r i f t , but I have p r e f e r r e d t h i s method to the a l t e r n a t i v e and greater s i n of examining every one of the novels four times over. At the same time, i n order to compare developments of technique, I have i n each chapter introduced a r e l e v a n t novel from outside the period under c o n s i -d e r a t i o n , an i n t r u s i o n a l t o g e t h e r i n keeping w i t h H a r r i s ' s own d i s r u p t i v e p r a c t i c e . 4. I. Experiment i ) On Experiment Two decades a f t e r the p u b l i c a t i o n of Palace of the Peacock, Wilson H a r r i s stands i n the f r o n t rank of contemporary experimental n o v e l i s t s . During the years since that beginning, he has worked h i s l i t e r a r y s k i l l s w i t h an independence that has won him admiration even as i t has caused h i s p a r t i a l e c l i p s e . U n w i l l i n g to couple experiment w i t h prudence, he has f o r f e i t e d a wide readership, but then out of h i s p a t i e n t p r a c t i c e has come a new w r i t i n g that could not have been won without t h i s r i s k . C e r t a i n l y , prudence i s not the most evident q u a l i t y of the f i r s t paragraphs of h i s f i r s t n o vel: A horseman appeared on the road coming at a breakneck s t r i d e . A shot rang out suddenly, near and f a r as i f the wind had been st r e t c h e d and t o r n and had s t a r t e d c o i l i n g and running i n an i n s t a n t . The horseman s t i f f e n e d w i t h a d e v i l ' s s m i l e , and the horse reared, g r i n n i n g f i e n d i s h l y and snapping at the r e i n s . The horseman gave a bow to heaven l i k e a hanging man to h i s executioner, and r o l l e d from h i s saddle to the ground. The shot had p u l l e d me up and s t i f l e d my own heart i n heaven. I s t a r t e d walking suddenly and approached the man on the ground. His h a i r l a y on h i s forehead. Someone was watching us from the trees and bushes that c l u s t e r e d the s i d e of the road. Watching me as I bent down and looked at the man whose open eyes stared at the sky through h i s long hanging h a i r . The sun b l i n d e d and r u l e d my l i v i n g s i g h t but the dead man's eye remained open and o b s t i n a t e and c l e a r . Here i s no conventional entry i n t o the sublunary world of f i c t i o n any more than i t i s a safe beginning to a novel. Yet i t s very a b o l i t i o n of s e c u r i t y , i t s t e a s i n g a m b i g u i t i e s , and i t s u n s e t t l i n g syntax, l i n k i t w i t h a t r a d i t i o n of experiment which renders i t i n t e l l i g i b l e . This \" t r a d i t i o n of experiment\" i s not so improbable a beast as might f i r s t appear. The contradiction lodged i n i t s heart i s both the motor force and the m o r t a l i t y of a l l avantgardism: the new needs what i t despises i n the old. \"Modernity,\" says Paul de Man, \"which i s fundamentally a f a l l i n g away from l i t e r a t u r e and a r e j e c t i o n of h i s t o r y also acts as the p r i n c i p l e that gives l i t e r a t u r e duration and h i s t o r i c a l existence.\"''\" The new, moreover, not only needs the old; i t becomes the old. No sooner does the c r i t i c discover and anatomize modernism than he i s compelled to create a space marked \"postmodernism.\" Whereupon one gains the uneasy l i b e r t y to drive a \"post\" before what the world had taken to be contemporary, or else to create a new word whose hoary fate i s sealed i n i t s conception. The novel i s a singular v i c t i m of t h i s passion: embarrassed by i t s generic name, which w i l l draw such unseemly advances as \"New New Novel,\" i t prefers to go abroad disguised as \" f i c t i o n . \" In i t s track we f i n d innumerable tokens of the old anxiety: metafiction, k a t a f i c t i o n , p a r a f i c t i o n , 2 s u r f i c t i o n , s u p e r f i c t i o n , even postcontemporary f i c t i o n . There i s , then, no esp e c i a l urgency for the reader of Harris to j o i n the fray, and c e r t a i n l y no excuse for him to swell the progress of i t s bloodied nominalism. \"Postmodernism\" w i l l serve most purposes quite s a t i s f a c t o r i l y , since there i s t o l e r a b l y common consent as to what and when modernism was, and f o r the innovative impulse I w i l l be content with \"experiment\" and i t s d e r i v a t i v e s . Since, however, a rea c t i o n to experiment i n the novel i s now underway, i t i s worth pausing to measure Harris's achievements i n that mode before a springtide of neo-conservative pro-nouncements engulfs them. Reaction i s perhaps too strong a word to describe the present impatience with formal innovation, since the movement, for a l l i t s r e v i v a l i s t i n t e n s i t i e s , lacks conviction and wears an a i r of having been 6. w i t h us before. Among c r i t i c s , i t may be no more than a motion of censure hatched to outwit the t h e o r e t i c i a n s of the avantgarde, and i n s o f a r as i t s n o v e l i s t s seek to unmask the po s t u r i n g that much experimental w r i t i n g has become, i t i s i n f a c t j u s t i f i e d . There are, however, the usu a l i n d i c a t i o n s that the movement would p r e f e r to oust form a l t o g e t h e r and create a new orthodoxy of noble content. I t i s true that experimentalism had created an orthodoxy of i t s own (and i t w i l l be one of my c h i e f concerns to d i s t i n g u i s h the work of Wilson H a r r i s from that orthodoxy) by enshrining formal i n n o v a t i o n i n a sanctum which fewer and fewer could penetrate. Inasmuch as i t d i d , i t was i t s e l f a r e a c t i o n , or the l a t e phase of a r e a c t i o n , to conventional r e a l i s m . There i s no surer s i g n of t h i s than that even i t s mannered flamboyancies had d e c l i n e d i n t o a kind of i l l - M a n n e r i s m , .a A f e b r i l e mimicry of innovat i o n condemned to rehearse forever i t s r e p e r t o r y of one t r i c k . I t would be a mistake, however to assume that because, f a i r l y e a r l y i n the spree, John 3 Barth declared a l l f i c t i o n a l forms exhausted, t h i s was i n f a c t the case. Nor need one devalue the achievement of a Borges (whom Barth was concerned to honour i n h i s a r t i c l e ) i n order to suggest that even at t h i s stage experimental w r i t i n g had come to be boxed r a t h e r too r e a d i l y i n t o the parodic mode. At any r a t e , ever since that time, c r i t i c a l w r i t i n g has dwelt on t h i s aspect of experimentalism, i t s d e s i r e to parody eve r y t h i n g , i n c l u d i n g i t s e l f . The self - c o n s c i o u s n e s s which such a d e s i r e must e n t a i l i s a c c o r d i n g l y transformed from the a e s t h e t i c s i n i t was under the o l d d i s p e n s a t i o n , i n t o a muscular v i r t u e , f o r as Richard P o i r i e r pointed out i n h i s e x c e l l e n t book on t h i s f i c t i o n , \" L i f e i n l i t e r a t u r e i s e x h i b i t e d by the a c t s of performance that make i t i n t e r e s t i n g , not by the act s of 4 r e n d i t i o n that make i t r e a l . \" 7. One might, nonetheless, ask whether t h i s energetic parodying was ever q u i t e so f a r removed from a heavy-lidded a e s t h e t i c i s m as i t l i k e d to imagine. There i s , a f t e r a l l , something c l o s e about the a i r i n a novel whose charac-t e r s are f o r e v e r announcing that they are aware of t h e i r f i c t i o n a l i t y , whose m u l t i p l e n a r r a t o r s look d i r e c t l y at the reader and f o r c e him to c a l l the f i c t i o n a l b l u f f . Moreover, the n o v e l i s t whose e n t i r e c o n s t r u c t i s an elaborate hoax wants a reader who w i l l not only a l l o w but connive i n h i s own d i s c o m f i t u r e . Which i s to say, the s e l f - c o n s c i o u s author begets, by c l o s e inbreeding, the s e l f - c o n s c i o u s reader. Extreme s o p h i s t i c a t i o n i n the one w i l l t o l e r a t e no d u l l a r d r y i n the other: you cannot c a l l i n question a l l the forms of yesterday nor advance brav e l y i n t o tomorrow's w i t h a s u l l e n or l a g g a r d l y audience. And where the parody of others once demanded a p a r t i c u l a r o u t s i d e knowledge, the parody of oneself and one's audience c r i e s out f o r a c o t e r i e . Now there might be no end to these steamy i n t i m a c i e s but f o r the s t r i c t l i m i t s which l i t e r a r y i n v o l u t i o n must confront. The parody of a parody undoes i t s e l f ; even l e s s credence can be given the parody which begins to take i t s e l f s e r i o u s l y . I t w i l l be remembered t h a t , very e a r l y i n the h i s t o r y of the E n g l i s h n o v e l , when F i e l d i n g began to do j u s t that i n Shamela, he w i s e l y abandoned h i s p r o j e c t and got on w i t h Joseph Andrews i n s t e a d . Contemporary p a r o d i s t s and s e l f -p a r o d i s t s have ignored t h i s precedent to t h e i r own c o s t . There i s none of t h i s s e l f - c o n s c i o u s n e s s i n H a r r i s . His novels are not about other novels, and when they are about themselves they are not c l o y i n g l y so. At the same time, they are unmistakably experimental i n t h e i r technique, bearing a c e r t a i n (and confusing) resemblance to another strand of a v a n t g a r d i s t f i c t i o n , one which has been c a l l e d apocalyptic.\"' Where p a r o d i s t s f i n d cause f o r despair and the d a r k l y comic, apocalypts 8. see grounds f o r hope and c h a o t i c c e l e b r a t i o n . Antonin Artaud spoke f o r the mode when he declared: \"The highest a r t i s that which b r i n g s us nearest chaos.\" Whether t h e i r conjectures are founded on transcendental notions or not, apocalypts make no secret of t h e i r energetic engagement w i t h the unknown. I t i s sometimes suggested that t h e i r w r i t i n g , d e s p i t e i t s energy (or because of i t ) i s untroubled, that they have not heard the bad news about the death of meaning, the death of God, the death of man, death i t s e l f . Yet, such a charge i s w i t h greater j u s t i c e brought against paro-d i s t s , whose mocking laughter must always hover on the b r i n k of angst but never q u i t e go over or e l s e the charade i s s p o i l t . A more t e l l i n g c r i t i q u e of the l i t e r a t u r e of i n s p i r e d madness, Eros unbound, mysticism, and the v a r i o u s c u l t s of p o e t i c dementia, i s that which demonstrates how e a s i l y these forms of p r o t e s t and a s p i r a t i o n can be contained. The p o i n t has been o f t e n made, as i n Gerald G r a f f ' s a r t i c l e , \"The Myth of the Post-modernist Breakthrough,\" where i t assumes a s p e c i a l trenchancy.^ Graff goes on to p r e d i c t an i d e n t i c a l f a t e f o r p a r o d i s t s , but, being k i n d l y disposed towards \"Western r a t i o n a l humanism,\" he tends to p r e f e r t h e i r sombre s t r a t e g y , i f only because of t h e i r honest bafflement before a r e a l i t y emptied of meaning. The s u s p i c i o n that the v i s i o n a r y company tend to cheat a l i t t l e d i e s hard. I am not disposed to plead e i t h e r cause, though I w i l l suggest that l i t e r a r y experiment goes more r e a d i l y w i t h s e r e n d i p i t y than w i t h suasion. Harris's i s i n any case a s p e c i f i c experimentalism, n e i t h e r parodic nor a p o c a l y p t i c . In order to s i t u a t e what might be c a l l e d h i s symbolic experimentation, I would l i k e to r e t u r n to the question of experiment i n the a b s t r a c t to s i f t c e r t a i n elementary words i n i t s p o e t i c s , words such as \"symbolism,\" \" r e a l i s m , \" and \"experiment\" i t s e l f , s i n c e they are 9. each s u s c e p t i b l e to d i v e r s e and not always d e f e n s i b l e i n t e r p r e t a t i o n s . I t has been customary i n the c r i t i c i s m of f i c t i o n to speak of r e a l i s m and experimentalism as a n t i t h e t i c a l c a t e g o r i e s . The r e a l i s t w r i t e r , i t i s s a i d , copies the world, and the experimental w r i t e r d i s t o r t s i t . Now t h i s may be a s a t i s f a c t o r y account of the case, and even where i t i s not, l i t t l e i s to be gained by c a l l i n g i n question words which have i n t h e i r commonly accepted usages served admirably to s u s t a i n a v a l u a b l e i f yet unresolved debate. I do not propose, t h e r e f o r e , anything so d r a s t i c as a s c u t t l i n g of t h i s terminology. I w i l l , however, suggest that there are c e r t a i n a m b i g u i t i e s , c o n t r a d i c t i o n s even, which have come to lodge i n these words, and which, perhaps because of t h e i r c o n t r a d i c t o r y nature, can be coaxed i n t o e x t r a o r d i n a r y meanings. Before the heyday of the r e a l i s t - f o r m a l i s t debate, the p a i r to r e a l i s m was not experiment but symbolism. That symbolism has f a l l e n out of favour, that there i s today no f l o u r i s h i n g school of sym b o l i s t s , r e f l e c t s our growing impatience w i t h e x a l t e d given meanings, whether personal or t r a d i t i o n a l , and perhaps a l s o our contempt f o r the conjurings of i n t e r e s t e d commentators. I t i s not, however, the method of meaning but a f a i t h i n i t s immanence that I am concerned w i t h , and i n t h i s r e s p e c t , as has o f t e n been pointed out, the symbolist movement was not a r e a c t i o n to but a c o n t i n u a t i o n of romanticism. Realism, on the other hand, was committed from the s t a r t to a simple documentation of r e a l i t y , to the recording of meanings but not to the di s c o v e r y or i m p o s i t i o n of transcendent meaning. Ac c o r d i n g l y , i t d e a l t w i t h a v a i l a b l e s i g n i f i c a t i o n s u n t i l that pass i n December 1910, when immanent meaning was found to be hollow. Realism's commitment to documentation now re q u i r e d i t to record meaninglessness (or e l s e to continue an a n a c h r o n i s t i c r e f l e c t i o n of nineteenth century meanings, which l a s t i t has c o n t r i v e d to do w i t h great success to t h i s day), and by t h i s token, much modern experimentalism can be shown to be r e a l i s t i c . The French New Novel i s a case i n p o i n t . I t s chosisme, i t s d e s i r e to record without romancing or r o m a n t i c i z i n g , to describe objects without bestowing on them the t e l e o l o g y of human metaphor, c o n s t i t u t e s nothing l e s s than r e a l i s m , only, the terms of the r e a l are now r e v i s e d . A l l that the New Novel r e j e c t e d i n the o l d r e a l i s m were i t s s u b j e c t i v e , p s y c h o l o g i c a l elements, and t h i s i n a b i d to ensure that i t s d e s c r i p t i o n not appear to be an imposed one (as f a r as t h i s was p o s s i b l e — w h i c h i s not very f a r , and which i s why the whole e n t e r p r i s e has f a l l e n f o u l of a c e r t a i n v u l g a r and healthy s c e p t i c i s m ) . Even taken on i t s own terms, as an attempt at s t r i c t placement of the observable world without the p r o j e c t i o n of any human emotions, t h i s act i s a mimetic one and so f a l l s w i t h i n the province of r e a l i s m , however newly d e f i n e d . And as with chosisme, so w i t h the parodic mode we have glanced a t , since the l a t t e r e i t h e r r e p o r t s on the a b s u r d i t y of the r e a l or enacts that a b s u r d i t y ad i n f i n i t u m . The p o i n t of t h i s excursus i s , as I have suggested, that r e a l i s m and experiment are not i n v a r i a b l y and e a s i l y the a n t i t h e t i c a l c a t e g o r i e s they are taken to be, sin c e the one represents a view and the other an a c t i o n . I t i s a poin t worth making, because when we come upon the symbolic experimentation of a w r i t e r l i k e H a r r i s , which an attempt to challenge the mimetic view of the world, we might be tempted i n t o an opposite funda-mentalism, d e c l a r i n g symbolic w r i t e r s the only e x p e r i m e n t a l i s t s . And the c o r o l l a r y of t h i s b e l i e f would be that the ruck of e x p e r i m e n t a l i s t s are p r o d u c i n g ' r e a l i s t t e x t s , w h i l e a great many r e a l i s t w r i t e r s are i n f a c t symbolists s i n c e they continue to t r a f f i c i n meaning. In f a c t a l l I am suggesting i s that the a c t i o n of experimentalism can have as i t s object e q u a l l y a r e a l i s t or a symbolist view of t h i n g s . I do not wish to defend the value that i s t r a d i t i o n a l l y attached to symbols and symbolism. That t h e i r powers have been both rhapsodized and berated i s a matter more to do w i t h the h a b i t s of i n t e r p r e t e r s than w i t h the performance of w r i t e r s . I have summoned them up simply to c l a r i f y the concept of experiment, and to d i s t i n g u i s h H a r r i s ' s symbolic p e r s p e c t i v e from h i s experimental p r a c t i c e . Nevertheless, the r e t u r n to meaning— a meaning no longer deemed immanent i n things but one created by an i n d i v i d u a l i n h i s sensuous mediation w i t h the w o r l d — i s a minimal r e q u i r e -ment f o r those engaged i n the w r i t i n g and reading of t e x t s , not to speak of other p u r s u i t s . In a p l u r a l i s t u n i v e r s e , symbolic experimentalism might be f a i r l y c h a r a c t e r i z e d as the naive counterpart of a sentimental avantgardism committed to the c e l e b r a t i o n of meaninglessness. But i f the parodic v e r s i o n of the r e a l were i t s e l f subverted, one might begin to speak of a symbolic r e a l i s m . Here i s that \"new form of ' c l a s s i c a l ' animation r a t h e r than 'romantic' escape or s e l f - d e l u s i o n \" H a r r i s foreshadows. This r e a l i s m i s not the subject of experimental a c t i o n but i t s o b j e c t . I t i s the product of that e x p l o r a t o r y impulse i n the a r t s and sciences of which i n t u r n H a r r i s ' s marginal f i c t i o n i s an exemplar. The r e j e c t i o n of the parodic \" r e a l , \" then, does not imply an i n e l u c t a b l e r e t u r n to nineteenth century r e a l i s m , and the symbolic experimentation of w r i t e r s such as H a r r i s p o i n t s a way out of t h i s f a l s e impasse. I t i s here that we may r e l i n q u i s h any p r o v i s i o n a l sense l e n t these elementary words. There i s another, graver problem w i t h t r a d i t i o n a l r e a l i s m . I t has to do w i t h c e r t a i n r i p p l e s i n the face of the r e a l which vex the conven-t i o n a l category of r e a l i t y and the customary manner of i t s r e p r e s e n t a t i o n . An a e s t h e t i c s of t h i s disturbance would have to consider the modernist 12. p r a c t i c e of rupture as more than simply a r e f l e c t i o n i n i t s t u r n of the growing complexity of modern l i f e . I t would a l s o need to show that the r e a l i s t e n t e r p r i s e i s no securer than that modernist p r a c t i c e , f o r a l l that the former appeals to common sense. Such a system does e x i s t , f o r there has grown up beside experimentalism an a n t i - o r g a n i c i s t p o e t i c s of considerable i n f l u e n c e and explanatory power. I am t h i n k i n g of the a e s t h e t i c s of f r a c t u r e which draws on the M a r x i s t theory of ideology. I f r e a l i s m seeks to show the world as i t i s , i t s task i s immediately complicated by the f a c t that the world i s not a v a i l a b l e f o r t r a n s c r i p t i o n i n i t s e l f but only as an ensemble of p r e v a i l i n g ideas about i t , that i s , 9 as \"ideology.\" Realism confronts, then, not the world, but a p i c t u r e of the world. Nor i s the p i c t u r e a complete one, f o r ideology i s always a s e l e c t i v e account of the r e a l , a r e a l destined to elude t h i s and every other form of r e p r e s e n t a t i o n . Ideology resembles, or perhaps dissembles, the r e a l by r e f l e c t i n g only those of i t s features that are consonant w i t h the m a t e r i a l i n t e r e s t s of the power e l i t e (whether of c l a s s , gender, or race) i n a p a r t i c u l a r economic and s o c i a l formation. This sense of ideology as an e n t i r e mode of production's r e p r e s e n t a t i o n of i t s e l f , i s c l e a r l y not the common c o n s t r u c t i o n put upon the word, that of any system of ideas p e c u l i a r to an a r t i c u l a t e group. So f a r from being the w i l l e d f o r m u l a t i o n of a d o c t r i n e , i t i s i n f a c t an i n v o l u n t a r y r e p r o d u c t i o n i n the realm of ideas, of the d i s p o s i t i o n of s o c i a l f o r c e s i n the m a t e r i a l world. Ideology, then, i s not to be confused w i t h dogma, though i t s e l a b o r a t i o n i s a form of dogmatism. I t s f i x i t y i s nevertheless amenable to manipulation i n the i n t e r e s t of c o n t r o l , even as i t i s to d i s t o r t i o n f o r the purpose of r e s i s t a n c e , and t h i s d i s t o r t i o n of the supposedly r e a l r e t u r n s us to the i s s u e of experimentalism i n the a r t s . I f ideology i s i t s e l f a k i n d of r e a l i s m , a f u n c t i o n a l reproduction of the r e a l , then f i c t i o n a l r e a l i s m i s a mimeticism twice removed. Looked at i n t h i s l i g h t , r e a l i s m i s not simply a p r e f e r r e d manner of d e s c r i p t i o n but an o b l i g i n g r e - p r e s e n t a t i o n of a r e i f i e d or u n r e a l r e a l i t y : the more f a i t h f u l that r e p r e s e n t a t i o n , the more specious i t i s l i k e l y to be. And s i n c e the s t y l e of t h i s r e p r e s e n t a t i o n i s i n s e p a r a b l e from i t s i d e a s , i t s knowledge, i t copies along w i t h the shape of that world, i t s r u l i n g p r e j u d i c e s . Committed to r e a l i s m , the s t e r n e s t c r i t i q u e of s o c i e t y comes to be couched i n terms that are already chosen f o r i t and t h e r e f o r e denatured, and i t i s compromised not d e s p i t e i t s r e a l i s t i c exposures but because of them. Thus i t has become a commonplace of l i t e r a r y c r i t i c i s m that a work may be more e f f e c t i v e through i t s s i l e n c e s , the gaps i n i t s r e p r e s e n t a t i o n , than i n the d e t a i l s i t c a r e f u l l y reproduces. I t f o l l o w s that a work which e x p e r i -mentally de-forms the world s t r a y s no f u r t h e r from the r e a l than one which simply, or not so simply, r e f l e c t s i t ; i n f a c t , i t s d i s t o r t i o n s , f o r a l l t h e i r seeming u n r e a l i t y , may t e l l us more (or more that i s u s e f u l ) about a c o n t r a d i c t o r y world. I t i s not long s i n c e , i n l i b e r a l as w e l l as M a r x i s t theory, t h i s view was a s o r t of heresy. In the eyes of both a Lubbock and a Lukacs, i f f o r d i f f e r e n t reasons, those novels were most s u c c e s s f u l which seemed of a piece w i t h r e a l i t y . With Lubbock, the motive f o r t h i s requirement was an a e s t h e t i c one: that a n o v e l r e c o n s t i t u t e i t s world without a u t h o r i a l r e f r a c t i o n ; f o r Lukacs, the c o n s i d e r a t i o n s were s o c i a l : that a novel a c c u r a t e l y embody the c o n t r a d i c t i o n s of the s o c i e t y which i t s t r i v e s to r e p r e s e n t . ^ I n e v i t a b l y , then, content was to take precedence over form, and q u i t e as i n e v i t a b l y the r e a c t i o n to t h i s p r i n c i p l e would take on a f o r m a l i s t c o l o u r , one which i t i s only now beginning to l o s e . I t i s 14. f i t t i n g that Lukacs's i n s i s t e n c e on the c o r r e c t d e p i c t i o n of human a l i e n a t i o n should be met by Brecht's experiments w i t h an \" a l i e n a t i o n e f f e c t , \" a l a r g e l y formal gesture. For, as Brecht, h i m s e l f no f o r m a l i s t , pointed out, r e a l i s m and a n t i - r e a l i s m are e q u a l l y formal, that i s , \"on paper.\" For t h i s very reason, t h e i r p o l i t i c i z i n g \"does not i n v o l v e undoing techniques, but developing them. That the t e c h n i c a l i t y of n o v e l i s t i c experiment came at l a s t to construct a monad i s part of the f u r t h e r adventures of a f o r m a l i s t d i a l e c t i c , and need not d e t a i n us here. Of greater i n t e r e s t i s the process by which i a \"bourgeois bohemianism,\" . i t s e l f . . . \"The Ideology of the Modern,\" could be transformed i n t o an a n t i - d d e o l o g i c a l charm. This r e v o l u t i o n may be traced i n the passage from a conception of the l i t e r a r y work as an embodi-ment of c o n t r a d i c t i o n s to that of the work as i t s e l f c o n t r a d i c t o r y . Where the r e a l i s t n o v e l sought to p u r i f y i t s e l f of i n c o n s i s t e n c i e s , the modernist novel and i t s successors r e v e l l e d i n formal c o n t r a d i c t i o n s . In t h i s , l i t e r a r y experimentalism has commonly t r a c e d i t s l i n e a g e to V i c t o r Shklovsky, whose twin dictums of \"making strange\" and \" l a y i n g bare\" may 12 serve as mottoes of the mode. By these p r i n c i p l e s a novel was not simply to \" d e f a m i l i a r i z e \" i t s subject but to r e v e a l at the same time the workings of that d e f a m i l i a r i z a t i o n . So where a t r a d i t i o n a l n o v e l i s t might, having already r e s o l v e d any i n c o n s i s t e n c i e s i n h i s book, seek to erase s c r u p u l o u s l y a l l marks of labour from i t s s u r f a c e , the experimental n o v e l i s t would not only generate c o n t r a d i c t i o n s w i t h i n h i s n o v e l , but put the generative mechanism on d i s p l a y . The f i r s t of these impulses has been described 13 as the commodification of the l i t e r a r y product: every e f f o r t the author makes to render h i s work b e l i e v a b l e ensures i t s ready consumption along w i t h the i d e o l o g i c a l \" r e a l i t y \" i t embodies. The second impulse i s , a c c o r d i n g l y , a r e f u s a l of commodification, and the notorious \" d i f f i c u l t y \" of modernist and postmodernist works, which i s an instance of making strange even as t h e i r s e l f - c o n s c i o u s n e s s i s a way of l a y i n g bare, ensures that ideology does not go down e a s i l y . Indeed, a great p o r t i o n of the charge of o b s c u r i t y that has been brought against H a r r i s may be l a i d at the door of t h i s t e x t u a l n e gation, a r e f u t a t i o n of the given by a d e n i a l of i t s terms. \"Demonic, t e r r i b l e and negative: t h i s i s the Modern Muse,\" wrote 14 L e s l i e F i e d l e r . And from Jung's d e s c r i p t i o n of Ulysses as \"sheer negation to Marcuse's n o t i o n of the \"Great R e f u s a l , \" c r i t i c s have seen i n modernist a r t a c o n t r a d i c t i o n . Now, t h i s p erception has i t s e l f been roundly c r i t i -c i z e d f o r i t s wish to place l i t e r a t u r e i n a s h e l t e r outside ideology where i t s c r i t i c a l resources remain f r e e from contamination. The c r i t i c i s m i s a j u s t one w i t h i n i t s l i m i t s ; l i t e r a r y works do not transcend ideology: they give i t shape, a l l o w i n g i t to be read. But i t i s a l s o worth asking whether an a l l too esemplastic conception of ideology i s not i t s e l f s u s c e p t i b l e to rupture, whether one might not speak of p e r i p h e r i e s to ideology. In the f i r s t p l a c e , a symbolic experimentation such as H a r r i s ' s operates on the edge of consciousness as w e l l as on the f r i n g e of p r e d i c t a -b i l i t y : i t s deformations are wrought as much by random j u x t a p o s i t i o n as by a u t h o r i a l n e c e s s i t y . In the second, ide o l o g y , w h i l e encompassing s p e c i f i c orders of s o c i a l r e l a t i o n s , i s not yet g l o b a l . I t may be s a i d to have margins where one mode of production meets another and where i t i s more r e a d i l y breached than at i t s centres. This i s where H a r r i s ' s novels are l o c a t e d : here i s a n o v e l i s t from a former colony w r i t i n g at the m e t r o p o l i t a n centre works which do not s p r i n g wholly from the ideology of e i t h e r of the worlds they s t r a d d l e . The very m a r g i n a l i t y of these works serves to warp the i d e o l o g i e s of both c o l o n i z e r and c o l o n i z e d when they concur, f o r i n s t a n c e , i n producing a \" h i s t o r y l e s s \" West Indian past. Out of t h i s supposed barrenness, H a r r i s i s able to develop a m i n i m a l i s t e x p e r i -ment which i s r a t h e r more convincing than the endless s e l f - p a r o d y of much Northern postmodernism. While H a r r i s c e r t a i n l y i n h a b i t s a European l i t e r a r y t r a d i t i o n , which might i n c l u d e C o n t i n e n t a l symbolists and B r i t i s h romantics and modernists, he shapes t h i s t r a d i t i o n to h i s own needs, and w h i l e he i s i n e v i t a b l y l e d i n t o i d e o l o g i c a l r e s o l u t i o n s of r e a l c o n t r a d i c t i o n s , h i s own c o n t r a d i c t o r y works mix the t r a d i t i o n s of a l i e n c u l t u r e s w i t h r e s u l t s that i l l u m i n e as o f t e n as they m y s t i f y . This r a i s e s once more the question of d i f f i c u l t y , which I have suggested i s a species of working c o n t r a d i c t i o n . To describe i t so i s to e l u c i d a t e d i f f i c u l t y , not the d i f f i c u l t ; the task of i n t e r p r e t a t i o n remains. I t i s an i d l e pretence which declares that c r i t i c i s m deals not w i t h meaning but w i t h the production of meaning; the one, i n f a c t , derives from the other. The conceptual d i v i s i o n i s a u s e f u l one, however, f o r i f the c r i t i c can d i s c o v e r i n the mechanism of the book a method which l i n k s the production to the product, h i s task of i n t e r p r e t a t i o n i s f a c i l i t a t e d . In t h i s , H a r r i s ' s n o v e l s , f a r from being the r i d d l e s they are commonly taken to be, go a long way to meeting the c r i t i c . For c o n t r a d i c t i o n i s at the heart of H a r r i s ' s w r i t i n g : i t obtains i n the shape and movement of h i s t y p i c a l sentence; i t i s generated by h i s s w i f t and u n p r e d i c t a b l e conjunc-t i o n of d i s p a r a t e elements, by the b r i s k s h u t t l e of h i s n a r r a t i v e , and by the masking and unmasking of h i s c h a r a c t e r s ; i t i s , f i n a l l y , the s t u f f of the l a r g e r r e b u t t a l of r e a l i s m which h i s e n t i r e oeuvre represents. In f a c t , the c r i t i c concerned w i t h H a r r i s ' s experimentalism could h a r d l y do other than f i r s t come to terms w i t h the most s i g n i f i c a n t f e a t u r e of the prose and the ideas that prose experimentally advances. I have sought, then, to di s c o v e r i n H a r r i s ' s s t y l e a general p r i n c i p l e f o r the i n t e r -p r e t a t i o n of h i s novels. Since I have taken t h i s p r i n c i p l e to be c o n t r a -d i c t i o n , i t w i l l be necessary i n the chapters which f o l l o w to elaborate a grammar of d i s s e n t by which these t e x t s may be parsed. C o n t r a d i c t i o n i s i n the f i r s t place a saying no. I t i s true that s i l e n c e w i l l pronounce q u i t e as eloquent a negat i v e , but then s i l e n c e , despite the a b s u r d i s t experiment, i s not a l i t e r a r y form. Besides, i t in v o l v e s a c e r t a i n s o l i p s i s t i c r e t r e a t , and c o n t r a d i c t i o n i s a l s o a form of advance. So, i t i s necessary to go beyond t h i s elementary l e v e l of c o n t r a d i c t i o n , to which an odour of the querulous c l i n g s , and enter at once i n t o the realm of the p o l y s y l l a b i c , i n t o l i t e r a r y c o n s t r u c t i o n s which r e t u r n a more complex negative. I do not wish to imply that a s u c c e s s f u l experimentation must employ c o n t r a d i c t i o n , o r , even more r e d u c t i v e l y , that the more c o n t r a d i c t o r y a nov e l the greater i t s v a l u e . What I am suggesting, i s that the t e x t u r e of H a r r i s ' s l i t e r a r y m a t e r i a l agrees w i t h the a c t i o n of a l a r g e r d i a l e c t i c . I t i s a concept to which H a r r i s h i m s e l f makes e x p l i c i t recourse, so the c o n t r a d i c t i o n s I w i l l t r e a t a r i s e out of h i s c r i t i c i s m as w e l l as h i s novels. I choose c o n t r a -d i c t i o n not because H a r r i s ' s t e x t i l l u s t r a t e s the concept or advances i t s theory, but because the concept serves to e l u c i d a t e much that i s otherwise obscure i n H a r r i s . I wish to give the word \" c o n t r a d i c t i o n \" an i d i o s y n c r a t i c scope which w i l l not always agree w i t h the t r a d i t i o n of negative d i a l e c t i c s from which i t s p r i n g s . When I de a l w i t h H a r r i s ' s s t y l e , I w i l l take r h e t o r i c a l c o n t r a d i c t i o n to be s u f f i c i e n t l y capacious to admit the v a r i e t i e s of p a r a t a x i s which he employs. In c o n s i d e r i n g H a r r i s ' s n a r r a t i v e , I w i l l put an even more strenuous c o n s t r u c t i o n on the word, seeing i t s presence i n the movement between s t a t e s of dream and waking, death and l i f e , oppression and r e s i s t a n c e , r u i n and o r i g i n . I t i s there a l s o i n the antinomies e s t a b l i s h e d between the v a r i o u s stages of journeying by which H a r r i s enacts the d i a l o g i c h i s t o r y of the peoples he d e s c r i b e s . So, too, i n the chapters on character and on community, I w i l l examine H a r r i s ' s e x p e r i -mental treatment of the i n d i v i d u a l and s o c i e t y , both i n and out of the Caribbean, through c o n t r a d i c t i o n s which may have no name or f u n c t i o n i n the t h e o r i e s which contemporary r e c e i v e d wisdom has devised f o r the study of marginal c u l t u r e s . One of my c h i e f claims f o r H a r r i s ' s importance w i l l r e s t upon h i s development of a unique v o i c e by which he a r t i c u l a t e s the c o n t r a d i c t i o n s of a d i v i d e d world by making small or e l s e subversive recourse to t r a d i t i o n s which have been r e s p o n s i b l e f o r that d i v i s i o n . Having once developed t h i s v o i c e , H a r r i s begins, i n h i s more recent n o v e l s , to t u r n i t upon a l i e n landscapes to produce a new and r i c h resonance. I w i l l argue that he has been able to do t h i s only through h i s commitment to experimentation and despite the d i f f i c u l t i e s that commitment has n e c e s s a r i l y generated. I f H a r r i s i s d i f f i c u l t , i t i s because he has found simple reportage wanting; i f he i s obscure, i t i s because the l u c i d i t y which other w r i t e r s have brought to bear on the problems he confronts has been unequal to the task of addressing the c o n t r a d i c t i o n s of m a r g i n a l i t y . I f c o n t r a d i c t i o n generates d i f f i c u l t y , i t a l s o generates meaning. This i s why—and not only because he deals i n s y m b o l s — I have chosen to speak of H a r r i s ' s \"symbolic\" experimentation. I f I have laboured the i s s u e of c o n t r a d i c t i o n i t i s because the paradoxes which r e s i d e i n that theory bear a s i g n i f i c a n t r e l a t i o n to H a r r i s ' s own t h e o r i e s of experiment i n f i c t i o n . I speak a d v i s e d l y of h i s t h e o r i e s , s i n c e he has nowhere advanced a_ s y n o p t i c a l p o e t i c s of the genre, having chosen, as w i t h h i s n o v e l s , to show himse l f by degrees. I t i s to these t h e o r i e s that we may now t u r n , bearing i n mind that although t h e i r sources are statements H a r r i s has made i n c r i t i c a l essays, addresses and i n t e r v i e w s , they form only the s c a f f o l d i n g of the novels. The present chapter, t h e r e f o r e , i s a p r e p a r a t i o n f o r those which f o l l o w , chapters i n which t h i s s c a f f o l d i n g w i l l be assumed to have been dismantled but not f o r g o t t e n . This i s perhaps a p e r i l o u s assumption, because H a r r i s has developed over the years an i d i o s y n c r a t i c vocabulary of d e s c r i p t i o n and a n a l y s i s , a vocabulary i t s e l f r e s p o n s i b l e on occasion f o r a l l e g a t i o n s of o b s c u r i t y . In f a c t , the reader armed w i t h patience and memory w i l l f i n d that i t s c o n s t r u c t i o n admirably serves H a r r i s ' s purpose of b r i n g i n g to l i g h t resources concealed w i t h i n the f o l d s of conventional d i s c o u r s e . i i ) H a r r i s on Experiment An e a r l y essay, \"Art and C r i t i c i s m , \" w i l l serve to introduce H a r r i s ' s 16 fragmentary a e s t h e t i c . Published i n 1951 i n the Guyanese j o u r n a l , K yk-over-al, i t i s a s l i g h t piece of some f i v e pages, but c o n t a i n i n g as i t does the seeds of ideas H a r r i s was to develop l a t e r i n more substan-t i a l essays, i t may be taken as a k i n d of exemplar. The essay begins by r e c a l l i n g a \"very important c o n t r i b u t i o n to c r i t i c i s m of a r t \" made by Engels and l a t e r r e a f f i r m e d by Georg .Lukacs. 1^ Before we are served the c o n t r i b u t i o n , H a r r i s , i n a c h a r a c t e r i s t i c and i l l u s t r a t i v e gesture, has already dug i n h i s h e e l s . The c o n t r i b u t i o n , he reminds us, \"reacts w i t h p o e t i c j u s t i c e on many of the t h e o r i e s of Luk&cs h i m s e l f \" (p. 7). Then he proceeds once more: the c o n t r i b u t i o n \" i s that c r e a t i v e work may, and o f t e n does, have e n t i r e l y d i f f e r e n t meanings to what the author hopes, and may be the exact opposite of h i s s u b j e c t i v e i d e a l i s m or the mechanical i d e a l i s m of h i s time.\" Nevertheless, beside these i d e a l i s m s , \"an o b j e c t i v e process e x i s t s , a se c r e t form or t r a d i t i o n , which y i e l d s i t s e l f , f r a g -m e n t a r i l y perhaps, but d e c i s i v e l y as time goes on.\" Already the H a r r i s i a n hermetic caveat has come to be i n s c r i b e d i n the m a t e r i a l , not i n o p p o s i t i o n to that m a t e r i a l i s m , but r a t h e r as a reminder that the o b j e c t i v e i s not to be taken as only the outward. A \"new a r c h i t e c t u r e \" (p. 8) i s needed, H a r r i s maintains, to supplant the p i t i f u l c l a s s i c a l order of t h i n g s ; between human passion and the given order and m o r a l i t y , a great g u l f i s f i x e d . Marxism and e x i s t e n -t i a l i s m are attempts to bridge t h i s g u l f , \"the f i r s t concerning i t s e l f w i t h mechanical n e c e s s i t y , the second w i t h s u b j e c t i v e f a t e , \" but the i d e n t i t y they seek, that o b j e c t i v e process, c o n s t a n t l y eludes them. For t h i s process i s i n f a c t a d i s r u p t i o n of the pure l y \" s u b j e c t i v e \" and the purel y \"mechanical\": i t e x i s t s i n the space where t h e i r separate forces meet, \" i n the a s s o c i a t i o n of l i f e and environment\" (p. 9 ) . This asso-c i a t i o n i s a \"deep process immensely a l t e r i n g or breaking the shape of t h i n g s . . . \" f o r , the impact of the human mind and body on the hard w o r l d , i n c o n s t r u c t i n g something and des t r o y i n g something has a u n i t y or combination that i s both s e c r e t and p l a i n , immaterial and m a t e r i a l , showing f o r t h the power of pas s i o n , the l i m i t s and order of being. There f o l l o w s a g l a n c i n g treatment of American poetry, chosen because of i t s \" n a t u r a l daring beyond the s t a t i s t i c a l r e c t i t u d e of exhausted or bl o o d l e s s passions\" (pp. 9-10), at the s t a r t of which H a r r i s i s once more detained. He i s reminded of a school of West Indian a r t which i d e a l i z e s the sun. This he f i n d s c u r i o u s , \"an American a t t i t u d e , American i d e a l i s m . \" The surveyor i n him responds: I have l i v e d f o r long periods i n savannahs so much exposed to heat and f i r e , t hat the sun has become an a d v e r s a r y — o n e of two a n t a g o n i s t i c p r i n c i p l e s - — n i g h t and day—and only an assoc-i a t i o n of these two p r i n c i p l e s provides r e l e a s e ; What i s needed, H a r r i s contends, i s an \" a r c h i t e c t u r e of r e l e a s e , \" and i n the American poets he has chosen, he f i n d s \"an overwhelming or d e a l without r e l e a s e . \" He concludes that although t h i s poetry i s \"one of the a r t s where America has c o n s c i o u s l y and unconsciously h e l d a m i r r o r to the c o n t r a d i c t i o n s of s o c i e t y and the i n d i v i d u a l , \" i t i s s t i l l \"burdened by the c o n t i n u a t i o n of c l a s s i c a l i d e a l i s m s \" (p. 12). I t has not l e a r n t the p r i n c i p l e s of the new a r c h i t e c t u r e , one of which i s that \" l i f e i n i t s e s s e n t i a l c o n t r a d i c t i o n i s a r t : i t i s the deep unconscious humour of c a r n i v a l . \" The reader who f i n d s t h i s b r i e f essay burdened, through some c r i t i c a l e q u i valent of Engels's wisdom, by a c o n t i n u a t i o n of romantic i d e a l i s m s , i s b a r k i n g up the wrong t r e e . For, what i s of i n t e r e s t here i s not a r e s i d u a l n o s t a l g i a f o r meaning at the heart of things but the p o s i t i n g : . of an o b j e c t i v e i d e n t i t y i n the i n t e r e s t s of heterogeneity. This otherness d e f l a t e s the t o t a l i t i e s of the \" s u b j e c t i v e \" as w e l l as the \"mechanical,\" even as i t s a e s t h e t i c extension denies the value of endless o b l a t i o n s at the s h r i n e of the whole, or e l s e repeated testimonies to the o r d e a l of s o c i e t y ' s c o n t r a d i c t i o n s . The new a r c h i t e c t u r e i s not one which mimes the given or \" c l a s s i c a l \" order of thi n g s or e l s e parodies the hollowness of that order, but one which experimentally d i s r u p t s that order through constant reminders of i t s inherent f r i a b i l i t y . Only by t h i s assumption does H a r r i s speak of an emerging c l a s s i c i s m , one w i t h i t s roots i n a c a r n i v a l which does m i s c h i e f to solemn order. Not the overt but the underground c o n t r a d i c t i o n s of l i f e are the model of t h i s a r t . H a r r i s ' s metaphor i s a t e l l i n g one: the new a r c h i t e c t u r e which would b r i n g the forms that are bound i n a p r i n c i p l e of s u b j e c t i o n , genuinely i n t o the l i g h t of day, without c r u e l s u f f e r i n g , must f i n d t r u l y that the sun has no s t a t i o n a r y hold over i t s subjects l i k e a fe d u a l l o r d over h i s s e r f s (p. 10). The language of these statements i s n e c e s s a r i l y p r i v a t e , but i t c l o t h e s i n t u rn a d e s i r e to make i t s workings p u b l i c . \"Each one of us, I b e l i e v e , \" says H a r r i s i n a gesture of l a y i n g bare, \"has to expose h i s personal method, to challenge the o r i g i n a l i t y of other minds\" (FR p. 14). H a r r i s ' s own o r i g i n a l i t y begins w i t h the assumption of o r i g i n a l i t y i n others; to r e t u r n t h i s courtesy might seem incumbent on us. Moreover, to take h i s e x p e r i -mentalism f o r granted i s to avoid rehearsing the customary d i s t i n c t i o n s between the o l d and the \"new\" n o v e l , d i s t i n c t i o n s which are hardly p e c u l i a r to H a r r i s , and to concentrate on the more important task of d i s c r i m i n a t i n g between the conventional new and H a r r i s ' s own work. Nevertheless, i t must 18 be s a i d that H a r r i s ' s b a t t l e w i t h the \"demon of r e a l i s m \" amounts to something of an obsession, i f c l e a r l y not a possession. I f H a r r i s and h i s e a r l y i n t e r p r e t e r s tended to harp on t h i s anti-mimetic theme, they were r i g h t to do so i n a c r i t i c a l (and B r i t i s h ) c l i m a t e l a r g e l y h o s t i l e 19 to formal experimentation. For my part I have wished, i n a chapter on experiment, to i s o l a t e a s u f f i c i e n t though not necessary c o n t r a d i c t i o n to symbolism upon which H a r r i s ' s own t h e o r i e s might r e a c t . H a r r i s ' s c l a s s i c statement of h i s p o s i t i o n i s h i s l e c t u r e , \" T r a d i t i o n and the West Indian Novel,\" d e l i v e r e d before the London West Indian 20 Students' Union i n 1964. In t h i s remarkable address, to which I w i l l r e t u r n more than once i n the chapters which f o l l o w , he d i s t i n g u i s h e s the \"novel of persuasion\" from the \"epic and r e v o l u t i o n a r y n o v e l of a s s o c i a t i o n s , and sees the former as r e s t i n g \"on grounds of apparent common sense\" and a c e r t a i n c o n s o l i d a t i n g \" s e l e c t i o n of items, manners, uniform conv e r s a t i o n , 23. h i s t o r i c a l s i t u a t i o n s , e t c . \" (p. 29). This s e l e c t i o n i s j u s t i f i a b l e i n the nineteenth century n o v e l , where i t c o i n c i d e s w i t h \" s t a t e s of s o c i e t y which were i n v o l v e d i n c o n s o l i d a t i n g t h e i r c l a s s and other vested i n t e r e s t s , \" but to the pale l i t e r a r y successors of that novel H a r r i s seeks to counterpose 21 a \" n a t i v e t r a d i t i o n of depth\" (p. 31). The c o n s o l i d a t i n g d r i v e wants f o r i t s l i t e r a r y r e c o n s t i t u t i o n a r e f l e c t i v e t i s s u e which the n a t i v e t r a d i t i o n of \"landscape-in-depth\" r e j e c t s . R e f l e c t i o n , says H a r r i s i n another p l a c e , \" i s b u i l t i n t o a passive order of the imagination which possesses i t s own marvels of e x a c t i t u d e though to r e i f y i t a b s o l u t e l y i s to submit to a s t r a i t j a c k e t of t r a d i t i o n . . . \" (RV p. 15). The n a t i v e t r a d i t i o n w i l l not make t h i s mistake, and once again H a r r i s c i t e s Luk£cs, who p o i n t s out that a simple a f f i r m a t i o n of c l a s s i c a l t r a d i t i o n i s not enough. And he says a renewal of the c l a s s i c a l form can only come by r e p u d i a t i n g much i n the h i s t o r i c a l apparatus of the novel or as he puts i t i n Hegel's words ' i n the form of a negation of a negation' (TW p. 42). H a r r i s ' s own negation i s h i s experimentation (a matter i n which he i s more c o n s i s t e n t than LukScs), and he takes h i s f e l l o w w r i t e r s to task f o r t h e i r formal t i m i d i t y : i t i s one of the i r o n i c things w i t h West Indians of my generation that they may conceive of themselves i n the most r a d i c a l p o l i t i c a l l i g h t but t h e i r approach to a r t and l i t e r a t u r e i s one which c o n s o l i d a t e s the most conven-t i o n a l and documentary techniques i n the novel. In f a c t many of the great V i c t o r i a n s — R u s k i n , Gerard Manley Hopkins, Dickens i n Bleak House, f o r example, where a strange k i n s h i p emerges w i t h the symbolism of both Poe and K a f k a — are r e v o l u t i o n a r i e s who make the p r o t e s t a t i o n s of many a contemporary r a d i c a l look l i k e a sham and a pose. The f a c t i s — e v e n when s i n c e r e l y h e l d p o l i t i c a l r a d i c a l i s m i s merely a f a s h i o n a b l e a t t i t u d e unless i t i s accompanied by profound i n s i g h t s i n t o the experimental nature of the a r t s and the sciences (p. 46). So H a r r i s f i n d s that the work of a w r i t e r l i k e V.S. Naipaul \"serves u l t i m a t e l y to c o n s o l i d a t e one's preconceptions of humanity, the comedy of pathos and the pathos of comedy,\" thus remaining \"a persuasion of s i n g u l a r and p a t h e t i c enlightenment r a t h e r than a t r a g i c c e n t r a l i t y or a c a p a c i t y f o r p l u r a l forms of a profound i d e n t i t y \" (p. 40). In a recent i n t e r v i e w , he a s c r i b e s t h i s to Naipaul's i r o n i c detachment: Naipaul i t would seem to me i s a b r i l l i a n t w r i t e r whose p o s i t i o n i s that of a s p e c t a t o r . I don't sense i n h i s work a profound immersion i n the elements he des c r i b e s . Thus h i s work seems to me to conform much more to a k i n d of b r i l l i a n t j o u r n a l i s m . And towards the end of the same i n t e r v i e w , he remarks that very many novels which c l a i m to be r e a l i s t f a s t e n on catastrophe, they see only t h a t . They're pu r e l y s p e c t a t o r i a l n o v e l s , and they simply i n s p e c t the catastrophe and they have no sense of the l i f e running through i t , or of the regenerative seed that can come out of i t (WH p. 29). When he turns to George Lamming, H a r r i s i s again d i s s a t i s f i e d , though he recognizes Lamming's own growing impatience w i t h conventional forms. These forms are a k i n d of tyranny, but one which the e a r l y Lamming has chosen: i n terms of the r u l i n g framework he accepts, the i n d i v i d u a l -i t y of character, the d i s t i n c t i o n s of st a t u s and p r i v i l e g e which mark one i n d i v i d u a l from another, must be maintained. This i s the k i n d of r e a l i s m , the r e a l i s m of c l a s s e s and c l a s s i f i c a t i o n s . . . the n o v e l , i n i t s orthodox mould, demands (TW p. 38). More r e c e n t l y , i n the same i n t e r v i e w from which I have j u s t quoted, H a r r i s f i n d s that Lamming q u i t e c l e a r l y . . . i s not content w i t h the shape of the n o v e l , the E n g l i s h shape of the nov e l . And thus you see v a r i o u s t h r u s t s and perspectives coming i n which would suggest that the s o r t of d i s i n t e g r a t i o n s which occur i n the novel are themselves the th r e s h o l d f o r something e l s e (WH p. 23). This \"something e l s e \" i s the l i t e r a r y f i g u r a t i o n , through \"apparent gaps, a n g u l a r i t i e s , turbulences, o p a c i t i e s \" (CP p. 143), of that p r i n c i p l e of heterogeneity, that o b j e c t i v e i d e n t i t y at the i n t e r s e c t i o n of the s u b j e c t i v e and the mechanical, whose exi s t e n c e the H a r r i s i a n n o v e l c e l e b r a t e s . Since the d i s i n t e g r a t i o n s H a r r i s speaks of do not c o n s t i t u t e t h i s otherness so much as form i t s p r e c o n d i t i o n , the l a r g e r claims of formalism c o l l a p s e . For i f simple r e a l i s m w i l l not wash, mere \"extravagance of p a t t e r n \" washes perhaps too r e a d i l y . I t i s here that we begin to see H a r r i s d i s c r i m i n a t e among experimentalisms. In the same way as r e a l i s m the s t y l e e n t a i l s r e a l i s m the p o s i t i v i s t world view, experimentalism the a c t i o n must modify i t s object by p e r c e i v i n g i t anew i n and through i t s e x p l o r a t i o n . Without t h i s always fragmentary production of i t s \"knowledge,\" experimentation can s l i p a l l too e a s i l y i n t o the parodic mode, which, anti-mimetic as i t may w e l l be, \"represents\" a c e r t a i n v i c a r i o u s n e s s whose q u a l i t y i s caught by H a r r i s when, quoting d e f t l y , he suggests that \"the p r a c t i t i o n e r s of the a r t of the absurd...may themselves merely ' s t i f f e n i n a rented room'\" (B p. 26). Parodic experimentalism, f o r a l l i t s sombre—or e l s e f r i v o l o u s — s t r a t e g i e s of disavowal, becomes an escape route which may w e l l prove the best of two worlds and permit a s k i l f u l s h o r t c i r c u i t i n g of a r e a l c r i s i s or c o n f r o n t a t i o n i n depth. The a r t i n short not of a l i e n a t i o n as i t i s p o p u l a r l y c a l l e d but of i n s u l a t i o n (UC p. 44). To t h i s pretence, even the ambiguous c i v i l i t i e s of r e a l i s m are p r e f e r a b l e , and i n f a c t H a r r i s ' s c r i t i c i s m shows him q u i t e as a p p r e c i a t i v e of r e a l i s t i c n o v e l s , so long as t h e i r mimeticism i s not the product of an obssessive i r o n i c detachment, as he i s of t h e i r anti-mimetic counter-p a r t s . So, h i s t a s t e i n f i c t i o n runs to n o v e l i s t s as w i d e l y removed as a measured P a t r i c k White and a \"problematic\" Amos Tutuola, w i t h a d i v e r s i t y of experimental w r i t e r s i n between, from L a t i n American magic r e a l i s t s such as Marquez, Carpentier and A s t u r i a s , to French or E n g l i s h new n o v e l i s t s such as Claude Simon and B.S. Johnson. In none of these w r i t e r s i s e i t h e r the conservation or the d i s r u p t i o n of form canonized. For H a r r i s , then a w i l f u l f r a c t u r i n g of language i s not experiment enough; i t must consort w i t h \"a c e r t a i n e x p l o s i o n of a s u b j e c t i v e order of experience...which u n s e t t l e s to an extent the s t a b l e or o b j e c t i v e i l l u s i o n of the world...\" (SM p. 68). His r e j e c t i o n of both f o r m a l i s t and r e a l i s t e x c l u s i v i t i e s i s e x p l i c i t : the breakthrough of the 'experimental' w r i t e r . . . w i l l i n s t i n c t i v e l y d i v e s t i t s e l f not only of ' i n t e l l e c t u a l pastime' or ' s e l f - i n d u l g e n c e ' but of every k i n d of e x c l u s i v e and one-sided c o n s o l i d a t i o n , though i n t h i s element of freedom there may w e l l be i n t r u s i o n s of o b s c u r i t y l i k e c o n s t r u c t i v e but hidden agents i n a d i s ^ mantling process (SM p. 66). The o b s c u r i t y H a r r i s a l l o w s , i n h i s theory as i n h i s p r a c t i c e , now comes to show i t s f e t t l e . I t i s a p r o d u c t i v e , not a perverse, d i s t o r t i o n of language which f i g u r a t i v e l y deploys the experience of the unconscious against the given order of t h i n g s whose outer armour i s a given order of language. N e i t h e r order i s sacrosanct: t h i s was Nietzsche's p o i n t 23 when he s c o f f e d that we have l o s t God but s t i l l b e l i e v e i n grammar. I f H a r r i s ' s o b s c u r i t y i s not perverse, n e i t h e r are h i s c l a r i t i e s portentous. The symbolic dissonance which i d e n t i f i e s h i s score i s a reminder that what these symbols do matters more than what they t r a d i -t i o n a l l y mean. So f a r from conveying one s w i f t l y to a realm of unchanging meaning, they serve, by t h e i r s u r r e a l yokings and unyokings, to budge o l d meanings and s u b s t i t u t e experimental ones. Confronted w i t h an ideology of barrenness, symbolic experimentation demonstrates through i t s c o n t r a d i c t o r y techniques that p s y c h o l o g i c a l and c u l t u r a l d i s i n t e g r a t -i o n do not s i g n i f y an end to meaning. H a r r i s o f f e r s an example: I could i l l u s t r a t e t h i s best by r e f e r r i n g to a novel by Juan R u l f o c a l l e d Pedro Paramo i n which you do have a world that i s c o l l a p s i n g , d i s i n t e g r a t i n g , but what i s strange about that novel i s that the l i f e of the psyche i s so intense that i t moves through that s h e l l of a w o r l d — i n other words the stubborn s t r u c t u r e i s cloven. And the psyche t h e r e f o r e moves so that even though the world that has been depicted remains bleak, there i s a curious power there, a wildness that witnesses to the p o s s i b i l i t i e s of l i f e , , and the whole s t r u c t u r e of the f i c t i o n i s t h e r e f o r e q u i t e d i f f e r e n t (WH p. 23). Instead of c e a s e l e s s l y lamenting, or d r i l y s a t i r i z i n g , the oppression and the barrenness of the Caribbean past and present, and the havoc these have wrought on the i n d i v i d u a l consciousness, one must \" c r e a t i v e l y descend i n t o the d i s o r d e r of i t , s u f f e r c r e a t i v e l y the d i s o r d e r of i t \" (UC p. 44). A resource the experimental n o v e l i s t shares w i t h the i n a r t i c u l a t e i n d i v i d u a l i n the face of the ideology of h i s t o r y l e s s n e s s i s that c a r n i v a l undercurrent to d e v a s t a t i o n which we heard H a r r i s speak of e a r l i e r . Against the \"homogeneous comedy\"—or indeed the homogeneous tragedy, the \"monolith of c o n q u e s t \" — o f the given, an order l e n t credence by the \" s o - c a l l e d l u c i d and documentary t a c t i c of the t y r a n t or demagogue\" (NP p. 146), are discharged \"clowns of broken r e a l i s m \" (BC p. 45). What i s more, such a disturbance can erupt even w i t h i n the r e a l i s t novel (and here we see the demon l a i d ) : because language i t s e l f . . . c a r r i e s an i n v e r s e f a c t o r , an unsuspected r e v o l u t i o n a r y pressure which stands i n i n v e r s e p r o p o r t i o n to obsessive c e n t r a l i t y (obsessive animism): thus one may f i n d oneself p i c k i n g up i n f i c t i o n — a t the heart of sovereign r e a l i s m i t s e l f — a d e c e n t r a l i z i n g , d e - e s c a l a t i n g t a b u l a rasa i r o n y as the s e r i a l p l a y , the s e r i a l d e a t h s / s e r i a l r e b i r t h s of a c h i l d (the h a l f god, h a l f monster i n ourselves) (FP pp. 9-10). This i s H a r r i s ' s r i d d l i n g expression of h i s d e n i a l of pure or organic i d e n t i t y to the i n d i v i d u a l or to h i s t o r y , a d e n i a l which subverts not only the l i b e r a l or c l a s s i c a l conception of e i t h e r of these e n t i t i e s but a l s o t h e i r romantic v e r s i o n s , v e s t i g e s of which may seem to rec u r i n h i s own work. We begin to grasp h i s meaning when he declares t h a t \"an uncon-scious p o l i t i c a l i r o n y i s i n the process of being born w i t h i n the t e l l i n g s i l e n c e s of the f a m i l y of the Word\" (RV p. 19). The r i t u a l syntax (and r i t u a l i s one of H a r r i s ' s synonyms f o r a s p e c t r a l r e a l i s m , a spurious r e a l i t y ) of absolute power i s being f i g u r a t i v e l y undone, the grammar of h a b i t u a l p e r c e p t i o n going the way of God. The new grammar i s not an escape from h i s t o r y , though i t i s a d e n i a l of the numb, wholly conditioned s u b j e c t , which i s an escape i n t o h i s t o r y . The calamitous past and i t s debris are a v a i l a b l e as hollow forms. They e x i s t , says H a r r i s , i n a v o i d and t h e r e f o r e one needs to p a r t i c i p a t e i n i t . . . w i t h an a r t of f i c t i o n , an imaginative f l u i d i t y that i s as c l o s e as one can p o s s i b l y come to e x i s t i n g now, w i t h immed-i a c y , i n a form that has already been broken i n the past (PL p. 3 ) . The broken r e a l i s m of H a r r i s ' s f i c t i o n i s the a e s t h e t i c equivalent of continuous h i s t o r i c a l rupture; i t i s an attempt to capture the s t y l e of h i s t o r y by approaching and yet scrambling i t s c o n t r a d i c t i o n s . I t i s i n t h i s extreme r e a l i s a t i o n of the c o n t r a d i c t o r y and sometimes t e r r i f y i n g p r o p e r t i e s of consciousness that one begins to enter a phenomenal t r a d i t i o n which...may a f f e c t our approaches to the media of p a i n t i n g , a r c h i t e c t u r e , and s c u l p t u r e as w e l l as l i t e r a t u r e (PL p. 1). Moreover, once one recognizes the c o n t r a d i c t o r y \"substance\" of r e a l i t y , one begins to v i s u a l i s e , n e g a t i v e l y as i t were, heterogeneous forms of s o c i a l as w e l l as l i t e r a r y a s s o c i a t i o n , \"one s t a r t s to concede, and enter upon those a l t e r n a t i v e r e a l i t i e s ('phenomenal legacy') which may lead to a new s c a l e or i l l u m i n a t i o n of the meaning of 'community'\" (PL p. 3). Realism, w r i t e s H a r r i s , l i v e s by \" s i m p l i f i c a t i o n s of experience.\" I t s converse form, a s e l f - r e f e r e n t i a l experimentalism, and e s p e c i a l l y the theory of that form, stand i n constant danger of e r r i n g on the other s i d e . The e x t r a o r d i n a r y s e l f - c o n s c i o u s n e s s of the one and the h i g h l y t h e o r e t i c a l a n t i - e m p i r i c i s m of the other are fraught w i t h the p e r i l of a l l d e s a n c t i f i c a t i o n : they r e i f y themselves i n t o a new s u f f i c i e n c y , a s u b s t i -t u t e v i r t u a l i t y . So, the l i t e r a t u r e desirous of re-forming r e a l i s m and the theory designed to c r i t i c i z e r e i f i c a t i o n become i n t h e i r t u rn a s i n g l e f o r m a l i s t e f f i g y by something l i k e that \" t a c t i c of fascism which battens on f e a r of c o n t r a s t s \" (NP p. 144). Against t h i s u n i f o r m i t y there endures the heterogeneity of experience, and not l e a s t the \" l i v e d otherness\" of c u l t u r a l l y d i s s i m i l a r experience. Of t h i s experience, H a r r i s ' s \"landscape i s a model, j u s t as h i s \"imagination\" i s a metaphor not of a r e t u r n to some romantic c a p i t a l i z a t i o n of the Subject but of the i n d i v i d u a l ' s experience of that landscape. H a r r i s ' s experimentalism r e s i d e s i n h i s readiness to j o i n the one to the other. The s e l f - r e f e r e n t i a l e x p e r i m e n t a l i s t w i l l court and at length c a p i -t u l a t e to theory; examples of t h i s melancholy f a t e abound. H a r r i s has had the good sense to s k i r t the t h e o r e t i c snare; indeed, i t i s e x h i l a r a t i n to f i n d i n h i s f i c t i o n d i s c o v e r i e s or at l e a s t assumptions which t h e o r i s t s d i d not come upon f o r themselves u n t i l another season. His advances are the product of a great experimental v i r t u e , namely, r i s k : the experimental n o v e l i s t i s u n a f r a i d of saying the wrong t h i n g . In t h i s he i s an example to the c r i t i c who l i v e s i n constant t e r r o r of f a l l i n g v i c t i m to the very c u t t i n g edge he so keenly hones. No contemporary c r i t i c would a l l o w h i m s e l f to speak i n these \" n o s t a l g i c \" tones: One could t h i n k of the i n s t i n c t of a b i r d , a b i r d that f l i e s w i t h uncanny o r i e n t a t i o n from one area of the world to another. On a higher l e v e l you begin to see an element of f a i t h , and f a i t h can mutate at a higher l e v e l i n t o what one c a l l s r i s k . These are a l l i r r a t i o n a l formations. But once one can sense that one's reason and one's l o g i c have t h e i r roots i n such l a y e r s of i r r a t i o n a l i t y , one i s c o n s t a n t l y aware that the g i f t s of nature are g i f t s which one must accept, and which one must p r i z e . One must have the f a i t h 30. to accept what one i s given i n the midst of a world that may seem shattered and dangerous. And those g i f t s a l l the time r e l a t e to the continu i n g act of c r e a t i o n , which goes through the obstacles that surround us (WH p. 25). I t i s p r e c i s e l y H a r r i s ' s w i l l i n g n e s s to take r i s k s that i s r e s p o n s i b l e f o r h i s a s t o n i s h i n g power as a n o v e l i s t . The c r i t i c ' s p r e s c r i p t i o n s , then, are a k i n d of i m p o s i t i o n , and one which the experimental w r i t e r p r o p e r l y r e s e n t s , i f he i s l i s t e n i n g at a l l . Here l i e s the paradox of w r i t i n g about such f i c t i o n : f o r even when one describes r a t h e r than p r e s c r i b i n g , one i s s e t t i n g up expectat-i o n s , and the experimental novel l i v e s by u p s e t t i n g e x p e c t a t i o n s . More hopeless s t i l l i s p r o s c r i p t i o n . When B.S. Johnson declared p a s s i o n a t e l y that \" t e l l i n g s t o r i e s i s t e l l i n g l i e s , \" and set up t r u t h over against 24 f i c t i o n , he was c a l l i n g d e s p i t e himself f o r a neo-realism, that i s , the c o u p l i n g of an experimental technique w i t h a f a c t i c i t y that takes the r e a l , or v e r i f i a b l e \" t r u t h , \" on i t s own terms. More than t h i s , he would have d i s q u a l i f i e d those f i c t i o n s which might i n c l u d e s t o r i e s as part of t h e i r experimental stategy from i n c l u s i o n i n the novel canon, whose very concept he was at pains to sp i k e . To al l o w s t o r y - t e l l i n g i s not to embrace u n c r i t i c a l l y a l l the i m p l i c a t i o n s of F o r s t e r ' s c e l e b r a t e d \"oh dear, yes,\" but simply to r e f r a i n from s e t t i n g boundaries to w r i t i n g . Such s t o r i e s do f i g u r e i n H a r r i s ' s novels; to speak c l a s s i c a l l y , there i s ^ the i m i t a t i o n of an a c t i o n , though i t s u n i t i e s are seve r e l y v i o l a t e d . Experiment i s by i t s nature a breaking of r u l e s , and Johnson's own novels are f i n e examples of t h i s r e c a l c i t r a n c e . I t i s now n e a r l y ten years s i n c e Johnson published h i s short l i s t of n o v e l i s t s — i n c l u d i n g Harris—whom he saw as mattering on the B r i t i s h scene. While i t i s dangerous to make d i s c r i m i n a t i o n s w i t h i n d i s c r i m i n a t -i o n s , one may hazard the opi n i o n that w h i l e the recent work of many of these w r i t e r s r e v e a l s an en v i a b l e amplitude, few of them have experimented w i t h H a r r i s ' s l i n g u i s t i c d a r i n g , and c e r t a i n l y none has evolved so o r i g i n a l and s t r i k i n g a s t y l e . I w i l l t u rn to an examination of t h i s s t y l e i n the f o l l o w i n g chapter; f o r the present i t remains to scotch a non s e q u i t u r . Formalism may w e l l have overreached i t s e l f : the p a r o d i s t has become a k i n d of p l a t i t u d i n a r i a n , and d e f a m i l i a r i z a t i o n has become so f a m i l i a r ( i f not p l a i n ) that Pound's o l d cry of \"Make i t New\" has met i t s echo i n 25 John Gardner's \"Postmodernism means New! Improved!\" To the extent that Gardner's moral r e a c t i o n i s a reproof d e l i v e r e d to the i n t r a n s i t i v e , monadic avantgarde, i t i s j u s t i f i e d . But t h i s should give no handle to contemporary t r a d i t i o n a l i s t s who wish to dodge a l l experiment and malinger amid the a r t s of a V i c t o r i a n f i c t i o n which served i t s own pe r i o d without : anachronism. The c a l l f o r a r e t u r n to e s t a b l i s h e d values i s r a r e l y d i s i n t e r e s t e d , and i t r i n g s loudest i n high p l a c e s : What i s 'Modernism'? The barbarous L a t i n word modernus (from modo, ' j u s t now') occurs f i r s t i n the s i x t h century.... In a r t we a l l know what 'Modernism' means. I t p r i d e s i t s e l f on a r e p u d i a t i o n of a l l t r a d i t i o n s and a l l accepted canons of beauty, and shows an a f f i n i t y both w i t h the naive a r t i s t i c attempts of savages, and w i t h the newest p r o l e t a r i a n i s m i n R ussia. A modernist p a i n t e r w i l l cover h i s canvas w i t h zigzags or dep i c t a woman w i t h green hair...These phenomena are c l e a r l y p a t h o l o g i c a l . . . . How e a s i l y our contemporaries a l l o w themselves to be brow-beaten by t h i s puppyism!.... I have not read Ulysses or any of the works of D.H. Lawrence, so I must not speak of them; but there are others who seem to take a pleasure i n t e a r i n g away a l l v e i l s . I confess that I copied the bishop whom I r e f e r r e d to j u s t now, and threw my copy of one of them i n t o the A d r i a t i c . . . I f the matter were not so t r a g i c , one might smile at the not i o n that the most deeply-rooted r a c i a l h a b i t s — r e l i g i o n , p r i v a t e ownership, the f a m i l y and p a t r i o t i s m — c a n be uprooted i n one generation by a gang of r e v o l u t i o n a r i e s . R u s s i a , i f I am not mistaken, has been through the f e v e r , and i s coming out i n t o something more l i k e her o l d s e l f . I have no doubt that cubism and f u t u r i s m and most of vers l i b r e w i l l soon pass i n t o limbo.2° The v o i c e i s that of the Very Reverend W.R. Inge, d e l i v e r i n g h i s p r e s i -d e n t i a l address before the E n g l i s h A s s o c i a t i o n i n 1937. I t i s easy to smile at past v e x a t i o n s ; i f those who i n v e i g h against postmodernism today are l e s s s h r i l l , i t i s because a c e r t a i n s o p h i s t i c a t i o n i n matters of newness prevents them, and indeed permits yet another c a l l f o r a r e t u r n to \" r e a l i s t i c \" meaning. As I have argued, the c u l t u r a l and c r i t i c a l e v o l u t i o n of these words has rendered them adaptable, so that a l i t t l e bending w i l l a l l o w \" r e a l i s m \" versus \"experiment\" to s i g n i f y an o p p o s i t i o n between meaning and unmeaning, and to obscure the f a c t that the p u r s u i t of meaning i s i n t i m a t e l y bound up w i t h experiment. H a r r i s has spoken of the k i n d of w r i t e r who \"sets out again and again across a c e r t a i n t e r r i t o r y of p r i m o r d i a l but broken r e c o l l e c t i o n i n search of a community or species of f i c t i o n whose ex i s t e n c e he begins to d i s c e r n \" (TW p. 48). We may see i n t h i s metaphor tra c e s of H a r r i s ' s experience as a surveyor during the years he spent mapping parts of the i n t e r i o r of Guyana, but i t i s p r i m a r i l y the statement of a n o v e l i s t ' s f a i t h , f o r a l l novels worth the name are e x p l o r a t i o n s . I I . Experiment and Language The reader who takes up one of H a r r i s ' s novels f o r the f i r s t time w i l l not go f a r before being s t r u c k by a c e r t a i n p e c u l i a r i t y i n the shape of the sentences. I t i s t h i s p e c u l i a r i t y and i t s attendant complications which I wish to examine here. So, i f I speak of \"Experiment and Language,\" i t i s not because I propose elsewhere to consider H a r r i s ' s experiments i n any other medium. I t i s simply that I w i l l t r e a t here the lower reaches of the f i c t i o n , those narrower orders of i t s w r i t i n g which are part of, but do not i n themselves c o n s t i t u t e , form. I might e q u a l l y have spoken of \"Experiment and S t y l e , \" but s t y l e i s a vexed i s s u e . 1 There i s b e t t e r agreement about the nature of language; besides, H a r r i s has some i n t e r e s t i n g t h i n g s to say of i t and very l i t t l e except rudeness f o r \" s t y l e . \" \" L i t e r a r y s t y l e \" even today evokes w r i t i n g w i t h a \" f i n i s h , \" i n more than one sense of the word. The t r a d i t i o n a l complaint against s t y l e f i n d s the l u s t r e of i t s surface a d i s t r a c t i o n from the meaning beneath, the manner from the matter. The p r o p o s i t i o n s of contemporary semiology have s i l e n c e d t h i s p a r t i c u l a r grievance by c a l l i n g i n t o question the d i s t i n c t i o n 2 between form and content, though i n p r a c t i c e the couple l i v e h a p p i l y on. The other sense of \" f i n i s h , \" that of completeness, meets a l i k e o b j e c t i o n . The l i t e r a r y t e x t , so f a r from being s u f f i c i e n t unto i t s e l f i s , a f t e r a l l (and t h i s i s not an i n s i g h t which wanted s e m i o t i c s ) 3 an i n e r t q u a n t i t y r e q u i r i n g a reader f o r i t s r e a l i s a t i o n . E x i s t i n g as a v i r t u a l i t y , i t must be produced anew each time. So, although s t y l e would seem to be v i n d i c a t e d by the judgement that there i s nothing but s t y l e , i t s popular reading i s one that cannot seem to a d j u s t to the incompleteness of \"language\" without a l o s s of face. I f , however, we can b r i n g ourselves to see s t y l e as the production of language i n the same way that reading i s a production of the t e x t , we have no reason to abandon the concept on such t r i v i a l grounds. For i f w r i t i n g i s a m a t e r i a l p r a c t i c e , then to confront s t y l e i s to confront the p h y s i c a l i t y of language. I t i s part of the l e s s o n that we l e a r n from t h i s encounter that the a c t i o n of language may be q u i t e as i n t r i g u i n g as i t s meaning, and indeed ij3 the meaning. Read c o r r e c t l y , s t y l e i s the p r o f i l e of language i n a c t i o n , and the e f f e c t s of t h i s a c t i o n need be no l e s s s i g n i f i c a n t than i t s motives. These are some f a c e t s of H a r r i s ' s language that I w i l l examine: the work of h i s works. Such an approach has i t s l i m i t a t i o n s , and i t may be that our present a b s o r p t i o n i n the mechanism of meaning r e f l e c t s a r e v u l s i o n against an endless supply of commodities, not excluding l i t e r a r y commodities, and an a r c h a i c longing to grasp once more the 4 f u n c t i o n i n g of t h i n g s . The r e l a t i o n s h i p between the how of a work and i t s what or why, then, w i l l not here be one of s u b o r d i n a t i o n or e x c l u s i o n : i t i s a poor wisdom which knows the clockwork but cannot t e l l the time. But t h i s r e a l i s a t i o n i n no way diminishes the p e r i l s of a p u r e l y e x p l i c a t o r y approach which e i t h e r advances e m p i r i c a l l y or, e n t e r t a i n i n g l o f t i e r s c i e n t i f i c ambitions, hopes to f a s h i o n a Casaubonish Key by which a d i f f i c u l t s t y l e may be opened and a l l p e r p l e x i t i e s resolved To proceed so, by e f f u s i o n s or by g r i d s , i s i n a sense to betray the t e x t . To render i t i n t o e x p o s i t o r y prose by a n t i c i p a t i n g i t s p a t t e r n s r e s t o r i n g i t s rhythms to n o r m a l i t y , t a k i n g stock of i t s s u r p r i s e s , i n s h o r t , n a t u r a l i s i n g i t , i s to n u l l i f y i t s challenge to our h a b i t s of reading. I f , instead of thus t r a n s l a t i n g the s t y l e , we learn i t s language, we may extend our s t y l e of knowing as well as our knowledge of s t y l e , for Harris's s y n t a c t i c a l strategies are often also h e u r i s t i c ones. Further, by refusing to transpose h i s t o n a l i t i e s into a simpler key, we respect the o r i g i n a l by never seeming to excuse what we would explain. We also secure our apprehension of the text i n the mode of the text's apprehension of the world. In Harris's f i c t i o n s , t h i s knowledge i s one of strange and sometimes savage complexity; to tame i t would be to do i t harm. In the f i r s t place, i t i s not, or not p r i n c i p a l l y , a question of grammatical complexity. Unlike the Proustian sentence, which i s endlessly p r o l i f e r a t e d but always accessible, Harris's sentences are usu a l l y \"simple\" and yet semantically d i f f i c u l t . Theirs i s a state which w i l l sometimes approach that fourth and l a s t type of d i f f i c u l t y which George Steiner has distinguished,^ where \"the contract of ultimate or preponderant i n t e l l i g i b i l i t y between poet and reader, between text and meaning\" i s breached. This d i f f i c u l t y i s evident i n a great deal of modernist and postmodernist w r i t i n g , though i t s seductions are neither u n i v e r s a l l y entertained nor altogether new. Besieged by such d i f f i c u l t y , \"we bear witness,\" says Steiner, \"to the precarious p o s s i b i l i t y of existence i n an 'open' space of c o l l i s i o n s , or momentary fusions between word and re f e r e n t . \" In t h i s f r a g i l e moment, one may f i n d pleasure of another order and duration, but no les s r e a l than that which the Proustian sentence y i e l d s . There may be pleasure i n d i f f i c u l t y ; more often there i s displeasure. We do not as a r u l e r e l i s h bafflement, although i f t h i s i s true there i s an element of masochism i n our remorseless and conspicuous consumption of much postmodern l i t e r a t u r e . C e r t a i n l y , there i s no v i r t u e i n d i f f i c u l t y . To admire H a r r i s because he i s d i f f i c u l t would be a s i n g u l a r piece of c h i l d i s h n e s s , but to r e v i l e him because he i s d i f f i c u l t i s no m a t u r i t y . Unreserved p r a i s e may w e l l have given r e a c t i o n a cause: the c r i t i c who professes to be unmoved by such devotion i s always at hand w i t h a trump card of unspeakable s i m p l i c i t y , and such contests are i n v a r i a b l y d u l l . On one of h i s e a r l i e s t appearances i n p r i n t , H a r r i s was reproached f o r i n h a b i t i n g \"a wordy metaphysical world of h i s own making.\"'7 We s h a l l have to examine the j u s t i c e of t h i s charge (and there i s some) to see whether part of i t s impatience does not d e r i v e from a f a i l u r e to grasp the s t r a t e g i e s of H a r r i s ' s prose. In f a c t , d i f f i c u l t y i s simply a t a c t i c a l weapon i n H a r r i s ' s work; i t s deployment represents a k i n d of mining of the f i c t i o n a l t e r r a i n . Nor i s t h i s deployment u n r e l e n t i n g , f o r the decorum of a c o n t r a d i c t o r y s t y l e i s p r e c i s e l y i t s r e f u s a l of the wholly obscure along w i t h the u t t e r l y p l a i n . I t i s no coincidence that the informing p r i n c i p l e of H a r r i s ' s \"new a r c h i t e c t u r e \" i s asymmetry, a p r i n c i p l e whose contours appear f i r s t a t the l e v e l of the l i n e . The decorum of asymmetry g i s a curious paradox, but not one without precedence. I t ends, as we s h a l l see, by undoing the very concept of decorum. In a review of H a r r i s ' s n o v e l , Companions of the Day and Night, the B r i t i s h poet, M a r t i n Seymour-Smith, has made a c r i s p assessment of the 9 novelist!'s s t y l e . \"There i s , \" he s t a t e s simply, \"no r h e t o r i c . \" The i m p l i c a t i o n s of t h i s l a c o n i c judgement are immense and i t s f u n c t i o n p i v o t a l . With one stroke i t l a y s bare the workings of H a r r i s ' s experimen-t a l i s m and d i s t i n g u i s h e s h i s p r a c t i c e from that w r i t i n g which p r a c t i s e s e i t h e r on the reader or on i t s e l f . Yet, as a judgement i t must immediately q u a l i f i e d . S t r i c t l y , the only novel which i s u n r h e t o r i c a l i s the a l e a t o r y one which comes to i t s reader loose-leaved i n a box, and even there one i s hostage to the page. A l l w r i t i n g , even the most formless, shows a minimum of a u t h o r i a l c o n t r o l , and we would do w e l l to guard against immaculate conceptions of l i t e r a r y s t y l e . H a r r i s ' s novels have, of course, a r h e t o r i -c a l q u o t i e n t , to the degree that any work may be s a i d to have a design, that i s , a shape and purpose. I t i s when shape bows to purpose that a novel becomes u n e q u i v o c a l l y r h e t o r i c a l . For i t i s then that the author's sel f - c o n s c i o u s n e s s becomes acute and e v e n t u a l l y coy. And s i n c e the knowing s e l f i s here wholly i n c o n t r o l , r h e t o r i c a l experimentation i s s c a r c e l y experimentation at a l l . I t knows i t s e f f e c t s before they are caused, or, to put i t another way, i t i s c e r t a i n of the causes of i t s e f f e c t s . By \" r h e t o r i c , \" t h e r e f o r e , I intend an excessive designing i n the use of language, a meaning which Seymour-Smith doubtless had i n mind. Where t h i s designing i s e i t h e r s e v e r e l y reduced or d e l i b e r a t e l y thwarted, i t becomes p o s s i b l e to speak of a r h e t o r i c of u n r h e t o r i c , a w r i t i n g that i s worked and yet unwrought. \"^ I t i s true that w r i t i n g represents a d e c i s i v e a c t i o n , that s t y l e i s , i n Susan Sontag's words, \"the signature of the a r t i s t ' s w i l l . \" \" ' \" 1 Even so, there i s room f o r an unconsciousness i n the c r e a t i v e use of language which does not a d v e r t i s e i t s e l f as auto-matic handwriting. As Sontag goes on to remark, t h i s a r b i t r a r i n e s s dogs the c r i t i c who i n s i s t s that a work of a r t could not have been other than i t i s : \"every a r t i s t , when i t comes to h i s own work, remembering the r o l e of chance, f a t i g u e , e x t e r n a l d i s t r a c t i o n s , knows what the c r i t i c says to be a l i e . . . \" (p. 33). To t h i s company of men from P o r l o c k one might add randomness and happenstance, i f no longer d i v i n e a f f l a t u s . H a r r i s himself i n s i s t s on the i n t u i t i v e as e x i s t i n g alongside the conscious: My approaches to such a residue of experience [as we a l l share] — I cannot overemphasise t h i s — a r e not i n t e l l e c t u a l , but r a t h e r p a r t of a hard and continuous w r e s t l i n g w i t h i n the medium of my own work, a process more a k i n to something a c t i v e and unpre-d i c t a b l e r a t h e r than planned and t h e o r e t i c a l (PL pp. 1-2).12 Not s u r p r i s i n g l y , when H a r r i s does mention r h e t o r i c , i t i s u s u a l l y coupled w i t h a p e j o r a t i v e : \"nightmare r h e t o r i c \" (FJ p. 41), \" r h e t o r i c and s t e r i l i t y \" (SL p. 206), \" r u i n and r h e t o r i c \" (AO p. 124). In a d e c l a r a t i v e mood he w i l l p i n h i s f a i t h on \"an a r t of the imagination based on concen-t r a t i o n and i n t u i t i o n r a t h e r than formula or r h e t o r i c \" (MT p. 39). This co n c e n t r a t i o n must be recognized, f o r i t i s easy to misread H a r r i s ' s r e f u s a l of r h e t o r i c as an excuse f o r ca r e l e s s n e s s . Among the conscious ways i n which t r a d i t i o n a l r h e t o r i c i s f l o u t e d are the obvious admission of 13 inelegance or the d e l i b e r a t e use of c l i c h e , not to speak of those spontaneous i r r e l e v a n c i e s which appear from time to time and whose f u n c t i o n we s h a l l examine i n due course. F i n a l l y , there i s the notorious opacity of the language, i t s ambiguities ranged i n the f a r t h e r reaches of Empson's schema, but s e r v i n g to complicate r a t h e r than to m y s t i f y . For t h i s reason, complexity i s perhaps a b e t t e r word than the o b s c u r i t y sometimes imputed to H a r r i s , s i n c e i t w i l l admit of an urge to communicate, i f not always i n the language of the t r i b e . Language, H a r r i s seems to say, already has i t s own r h e t o r i c besides and other than the \"persuasions\" of the author's a u t h o r i t y . But the laws of t h i s r h e t o r i c are of a v o l a t i l e nature, t h e i r r u l e a kind of m i s r u l e because the concept of language i s one which c o n t i n u a l l y transforms inner and outer formal c a t e g o r i e s of experience, e a r l i e r and r e p r e s e n t a t i v e modes of speech i t s e l f , the s t i l l l i f e r e s i d e n t i n p a i n t i n g and s c u l p t u r e as such, even music which one ceases to ' h e a r ' — t h e peculiar: - r e a l i t y of language provides a medium to see i n consciousness the ' f r e e ' motion and to hear w i t h consciousness the ' s i l e n t ' f l o o d of sound by a continuous inward r e v i s i o n a r y and momentous l o g i c of potent e x p l o s i v e images evoked i n the mind (TW p. 32). We may now observe t h i s language at work i n H a r r i s ' s f i r s t n o v e l , Palace of the Peacock (1960). The novel i s a v a r i a t i o n on the quest f o r E l Dorado, i t s p r i n c i p a l s a crew of dead men, the motley p i c k i n g s of race and time. Captain to t h i s crew i s a rancher of \" t e r r i b l e stamping\" energy, the horseman of that opening fragment w i t h which we saw H a r r i s begin h i s n o v e l i s t i c career. Deserted by h i s Amerindian workers and shot by the m i s t r e s s he c r u e l l y used, h i s ghost now leads an e x p e d i t i o n u p r i v e r i n p u r s u i t of the f u g i t i v e f o l k . But the woman, M a r i e l l a , has become an enigma, both a place and a people, and p r e s s i n g beyond the M i s s i o n , the crew l e a r n some t r u t h s about the nature of d e s i r e and power before r e l i v i n g t h e i r former deaths. I m p e r i l l e d by rocks and r a p i d s , and musing on t h e i r sundry obsessions, the men come f i n a l l y to a w a t e r f a l l which overhangs t h e i r graves on Sorrow H i l l . Mounting ladders set i n the face of the c l i f f , they climb past windows which open onto a b e a t i f i c v i s i o n . They have reached the Palace of the Peacock, Then they f a l l to deaths which no longer matter, f o r a l l are caught up i n the music of the peacock's dance. This i s the \"dreaming s k e l e t o n \" of the s t o r y t o l d by Donne's broth e r , who stands w i t h i n him and r e l i v e s the e n t i r e e x p e d i t i o n as he pores over the map of the savannahs. His r o l l - c a l l of the men as they set out i s a good example of H a r r i s ' s supple and yet q u i c k s i l v e r prose: The crew swarmed l i k e u p r i g h t s p i d e r s , half-naked, scrambling under a burden of cargo they were c a r r y i n g ashore. F i r s t I picked and counted the d a S i l v a twins of Sorrow H i l l , t h i n , long-legged, f a i r - s k i n n e d , of Portuguese e x t r a c t i o n . Then I spotted o l d Schomburgh, a l s o of Sorrow H i l l , a g i l e and s w i f t as a monkey f o r a l l h i s seasoned years. Donne p r i z e d Schom-burgh as a bowman, the best i n a l l the world h i s epitaph boasted and read. There was V i g i l a n c e , b l a c k - h a i r e d , Indian, s p a r k l i n g and shrewd of eye, reading the r i v e r ' s mysterious book. V i g i l a n c e had recommended C a r r o l l , h i s c o u s i n , a t h i c k - s e t young Negro boy g i f t e d w i t h h i s paddle as i f i t were a v i o l i n and a sword together i n paradise. My eye f e l l on Cameron, b r i c k - r e d face, slow f e e t , f a s t e r than a snake i n the f o r e s t w i t h h i s hands; and Jennings, the mechanic, young solemn-featured, carved out of s t i l l wood i t seemed, sweating the s t i l l dew of h i s t e a r s , c u r s i n g and reproving h i s w h i r l i n g engine and toy i n the u n e a r t h l y t e r r i f y i n g g r i p i n the water. Last I counted Wishrop, a s s i s t a n t bowman and captain's understudy (PP pp. 22-23). When they have l i f t e d t h e i r c r a f t out of the water, the crew arm themselves w i t h prospecting knives to cut a l i n e of portage through the f o r e s t . A w i l d v i s i o n a r y prospect. The sun glowed upon a mass of v e g e t a t i o n that swarmed i n c r e v i c e s of rocky nature u n t i l the stone y i e l d e d and turned a green spongy carpet out of which emerged enormous trunks and trees from the hidden dark earth beneath and beyond the sun. The s o l i d w a l l of t r e e s was f i l l e d w i t h ancient blocks of shadow and w i t h gleaming hinges of l i g h t . Wind r u s t l e d the l e a f y c u r t a i n s through which masks of l i v i n g beard dangled as low as the water and the sun. My l i v i n g eye was stunned by i n v e r s i o n s of the b r i l l i a n c y and the gloom of the f o r e s t i n a deception and hollow and socket (p. 26). Already the reader w i l l have become aware of the c o n t r a d i c t o r y , o s c i l l a t i n g q u a l i t y of t h i s prose: i t s frequent recourse to a n t i t h e s i s (Schomburgh's age yet h i s monkey's a g i l i t y , Cameron's slow f e e t yet h i s snaking hands, Jennings, carved out of s t i l l wood, reproving h i s w h i r l i n g engine); i t s Metaphysical c o u p l i n g s , as w i t h C a r r o l l ' s paddle or Jenning's \"engine and toy\"; i t s s t a r t l i n g i n v e r s i o n s of darkness and l i g h t , bulk and c a v i t y , up and down. The topography of the language shapes by \"hinge\" and \"mask,\" 14 those deceptions of landscape and human presence the dreamer senses. With equal d i s d a i n , i t s t a c t i l e and v i s u a l p r o d i g a l i t y ( n o t i c e the r e c u r r -ence of \"swarmed\" and \"swarming\" i n the two passages) gives and takes away. For a l l t h e i r c l a r i t y , the images t h i s poet-turned-novelist\"'\"\"' deploys do not f u n c t i o n to c o n s o l i d a t e or r e f l e c t or even to represent, f o r each e x i s t s by v i r t u e of that to which i t i s j o i n e d . The poet H a r r i s had explained i t i n t h i s way: \"We might juxtapose 'heaven' w i t h 'roots' or 'jungles'—TROPIC OF HEAVEN...to b r i n g i n t o sharp focus the disturbance created by opposing c o n d i t i o n s \" (FR p. 15). And many years l a t e r , the n o v e l i s t r e t a i n e d t h i s c o n v i c t i o n : the convolutions of image, whether c l e a r or grotesque, are r e l a t e d as d i v e r s e rooms, c a p a c i t i e s expanding or c o n t r a c t i n g w i t h i n one f i e l d of consciousness. To p r i s e these images apart i s i n f a c t to l o s e the d i a l e c t i c a l f i e l d i n which they stand or move (WS p. 55). The e f f e c t of these laminations of image i s a d e n s i t y that one o r d i n a r i l y 16 a s s o c i a t e s w i t h concrete poetry, but i t s f u n c t i o n goes beyond what Shklovsky c a l l e d \"making the stone stony.\" To say t h i s i s not to shrug away the experience of Shklovsky's (or indeed Dr. Johnson's) stone i n the name of a n t i - e m p i r i c i s m , but to preserve a c e r t a i n s k e p t i c i s m about the formal completeness of the world. The compaction H a r r i s repeatedly invokes i s a k i n d of searching out of the \" p e c u l i a r gaps or holes i n the s o l i d m a t e r i a l \" \" ^ c o n s i s t e n t w i t h a \" f i c t i o n of i m p l o s i o n \" (WS p. 49). And s i n c e there i s no way by which the resources discovered there can be described except by analogy w i t h the images that are cast up out of the 18 unconscious, the w r i t e r seeks to capture these p r i o r to t h e i r domesti-c a t i o n by r h e t o r i c . What iss u e s from t h i s \" e x p r e s s i o n i s t i c v o i d of place and time\" (SI p. 38), i s a prose of n e i t h e r absences nor o b j e c t s but of objects i n motion. Not s u r p r i s i n g l y , t h e i r s t a t e i s expressed i n the language of mysticism: \"The sun r o l l e d i n the grasses waving i n the wind and grew on the s o l i t a r y t r e e \" (p. 144). Even when the prose i s s t i l l , i t s s t i l l n e s s i s charged w i t h an energy which d e r i v e s from i t s adjacencies. The image i s no longer simply the r e p r e s e n t a t i o n of something i n the world but of a space surrounding that t h i n g and of the r e l a t i o n s h i p of that t h i n g to another. Seeking, as so o f t e n , to e x p l a i n t h i s r e l a t i o n s h i p i n l o c a l terms, H a r r i s a l i g h t s on the Arawak zemi or i c o n , which he takes to designate p e r s p e c t i v e s e c l i p s e d by the d e b r i s of conventional West Indian \" h i s t o r y \" and ideology. Seen i n 19 t h i s l i g h t , the zemi comes to challenge the category of simple i d e n t i t y and to \"image\" a network of r e l a t i o n s h i p s about that seeming s u f f i c i e n c y . The r e s u l t i s a prose of continuous f l u x which seeks to convey not so much the shape as the process of a nature whose constant i s change. This becomes p a r t i c u l a r l y n o t i c e a b l e when the pace of H a r r i s ' s prose a c c e l e r a t e s In the f o l l o w i n g passage, the crew d r i v e on above M a r i e l l a , having found i t deserted except f o r an ancient Arawak woman they press i n t o s e r v i c e as a guide. Her race was a v a n i s h i n g one overpowered by the fantasy of a C a t h o l i c as w e l l as a P r o t e s t a n t i n v a s i o n . This cross she had f o r g i v e n and f o r g o t t e n i n an e a r l i e r dream of d i s t a n t c e n t u r i e s and a r e t u r n i n g to the S i b e r i a n unconscious p i l g r i m a g e i n the s t r a i t s where l i f e had possessed and abandoned at the same time the apprehension of a f a c i l e beginning and ending. An unearthly p o i n t l e s s n e s s was her true manner, an a l l - i n c l u s i v e manner that s t i l l c o n t r i v e d to b e — a s a duck sheds water from i t s w i n g s — t h e negation of every t h r e a t of conquest and of f e a r — e v e r y shade of p e r s e c u t i o n wherein was drawn and mingled the pursuer and pursued a l i k e , separate and yet one and the same person. I t was a v a n i s h i n g and yet a s t a r t i n g race i n which long e t e r n a l malice and w r i n k l e d s e l f - d e f e n c e and the c r u e l p u r s u i t of t h e . f o l k were tu r n i n g i n t o u n i v e r s a l p r o t e c t i o n and i n t u i t i o n and that harmonious rounded m i r a c l e of s p i r i t which the world of appearances had never t r u l y known. Before the sun was much higher we were i n the g r i p of the s t r a i t s of memory. The sudden dreaming f u r y of the stream was naught e l s e but the ancient s p i t of a l l f l y i n g i n s o lence i n the v o i c e l e s s and t e r r i b l e h u m i l i t y of the f o l k . Tiny embroideries resembling the handwork on the Arawak woman's k e r c h i e f and the w r i n k l e s on her brow turned to i n c r e d i b l e and f a s t breakers of foam. Her crumpled bosom and r i v e r grew a g i t a t e d w i t h d e s i r e , b o t t l i n g and shaking every f e a r and i n h i b i t a t i o n and outcry. The r u f f l e s i n the water were her dress r o l l i n g and r i s i n g to embrace the crew. This sudden .insolence of s o u l rose and'caught them from the powder of her eyes and the age of her smile and the dust i n her h a i r a l l f l o w i n g back upon them w i t h s i l e n t streaming majesty and abnormal youth and i n a wave of freedom and str e n g t h . The crew were transformed by the awesome spe c t a c l e of a v o i c e l e s s soundless motion, the purest appearance of v i s i o n i n the chaos of emotional sense. Earthquake and v o l c a n i c water appeared to s e i z e them and stop t h e i r ears dashing the s c a l e s only from t h e i r eyes. They saw the naked unequivocal f l o w i n g p e r i l and beauty and s o u l of the pursuer and the pursued a l l together, and they knew they' would p e r i s h i f they dreamed to t u r n back (pp. 72-73). Here we begin to see H a r r i s ' s prose enact the c o n t r a d i c t i o n s i t seeks;,to convey. F i r s t , i t roundly declares c o n q u i s t a d o r i a l adventures, o l d and new, a \" f a n t a s y . \" Then i t s e t s up a s e r i e s of paradoxes: an apprehension \"possessed and abandoned\"; pursuer and pursued as \"separate and yet one and the same person\"; a race \"vanishing and yet s t a r t i n g . \" Having c a l l e d i n t o question time (\"beginning and end\") and space (\"the world of appearances\") and absorbed both of these i n an \"unearthly p o i n t l e s s n e s s \" and \" a l l - i n c l u s i v e manner\" born of the Arawak woman's dream memory of the Amerindians' f i r s t coming, the w r i t i n g proceeds to demonstrate the s t r a t e g i e s of t h i s p r oductive remembering. Immediately the boat i s swept i n t o \"the s t r a i t s of memory,\" o u t l i n e s begin to l o s e t h e i r v a l u e . An i m a g e — t h a t of a h a n d k e r c h i e f — i s r e c a l l e d from the past ( i t and i t s a s s o c i a t i o n s have f i g u r e d i n the two previous pages), and \" s p i t , \" \"handwork,\" \"embroideries,\" \"crumpled,\" \" r u f f l e s , \" \"powder,\" and \"dust\" are threaded at random i n t o the prose u n t i l r i v e r and woman are i n d i s t i n g u i s h a b l e . In t h i s way, not only does the flow of the language match that of the r i v e r (the crew have entered the War O f f i c e r a p i d s ) , i t c o n s t i t u t e s the mnemonic l e s s o n which i s \"the negation of every t h r e a t of conquest and f e a r . \" Once again, the language of mysticism i s put to work against the r i t u a l p e rception of absolute d e s p o l i a t i o n . I t r e c a l l s H a r r i s ' s l a n d s c a p e - i n - d e p t h — t h e shock of great r a p i d s and complex landscapes and f o r e s t s — p l a y i n g through memory to confirm p e r s p e c t i v e s of i m p e r i l l e d community and c r e a t i v i t y reach-ing back i n t o the Pre-Columbian mists of time (NP p. 149) and warns against simple documentary readings of h i s t o r y : conquest, we remember, was a \"berserk and c a n n i b a l r e a l i s m \" (NP p. 148). The image takes i t s p l a c e , then, w i t h i n a grammar of disturbance. I t s deployment i n t h i s way i s the r u l e , not the exception: i n each of H a r r i s ' s novels there i s t h i s constant and u n p r e d i c t a b l e s u r f a c i n g of fragments from another context, so that the reader's a t t e n t i o n i s wrenched 20 backwards and forwards through the t e x t . C l e a r l y a r h e t o r i c of s o r t s i s at. work here, but i f the s c a t t e r i n g of the image i s not a c c i d e n t a l , n e i t h e r i s i t a c o n t r o l l e d a f f a i r , and i t s haphazard nature serves to d i s o r d e r the uniform ideology of absolute power. In seeding h i s e a r l y novels w i t h Jungian symbols of transformation, H a r r i s i s again r h e t o r i c a l , t h i s time i n a more d e l i b e r a t e way, but 21 f a s c i n a t i n g as the tracing;.o.f these symbols may w e l l be, one must not a l l o w the e x e g e t i c a l impulse to obscure t h e i r t e x t u a l f u n c t i o n . I t i s t r u e that M a r t i n C a r t e r , the Guyanese poet, wrote of H a r r i s that \" i n h i s work no r i v e r i s simply a r i v e r , no t r e e merely a tree...Everything i s a 22 symbol,\" but once these r i v e r s and t r e e s have been t a l l i e d w i t h t h e i r i n e f f a b l e s i g n i f i e d s , i t i s s t i l l a task to elaborate a theory of t h e i r a c t i o n i n the novels. Nor would t h i s work be divorced from meaning; i t would, i n f a c t , d e s c r i b e the mechanism of meaning, though perhaps i n ways which might modify our conception of the s i g n i f i e d . The v ery concept of \"symbol\" might take on a r a t h e r d i f f e r e n t complexion i n the West Indian context from that i t o r d i n a r i l y wears i f we see i n i t not a s t a b l e e i d o l o n of p l e n i t u d e but a strategem of c a r n i v a l deception and u n p r e d i c t a b l e i n g e n u i t y . At the c l o s e of one of h i s essays, H a r r i s introduces what could be the germ of such an a e s t h e t i c i n a curious passage lodged between two parables: 'What man i s there of you, whom i f h i s son ask bread, w i l l g i ve him a stone? Or i f he ask a f i s h , w i l l he give him a serpent?' The e l u s i v e question of man's nature, man's inhumanity to man, remains unsolved, symbolic of f l e s h as w e l l as of stone. The d i v i s i o n between man and man i s the momentous c o n c e i t , the t r a g i c c o n c e i t , the tragi-comic c o n c e i t which provides l i f e blood to the th e a t r e . We are h e a v i l y indebted to t h i s i n v i s i b l e , world-wide c a p i t a l f o r a magical economics— the knife-edge of humanity on which we bargain s t i l l . In The Black Jacobins, by C.L.R. James, a sla v e i s accused of s t e a l i n g a pigeon. He denies i t . The pigeon i s discovered hidden i n h i s s h i r t . 'Well, w e l l , look at that pigeon. I t takes my s h i r t f o r a nest.' Through the s h i r t of another, a master can f e e l the potatoes which he denies he has s t o l e n . They are not potatoes, he says, they are stones. He i s undressed and the potatoes f a l l to the ground. 'Eh! master. The d e v i l i s wicked. Put stones, and look, you f i n d potatoes' (B pp. 26-27). By t h i s view, the r e f e r e n t of a symbol i s n e i t h e r absent nor brimming w i t h meaning: i t i s o f t e n simply obvious. What i s of i n t e r e s t i s the r e l a t i o n between i t s bald r e a l i t y and the magical, but e q u a l l y r e a l , l i n e of s h i f t s and ploys which t r a c e s i t . I t i s no a c c i d e n t , then,that when H a r r i s speaks of the epic stratagems a v a i l a b l e to Caribbean a r t i s t s , he invokes the t r i c k s t e r f i g u r e , Anancy: the r i s e of the poet or a r t i s t i n c u r s a gamble of the s o u l which i s symbolised i n the West Indian t r i c k s t e r (the spider of anancy c o n f i g u r a t i o n ) . I t i s t h i s element of t r i c k s t e r d o m that creates an i n d i v i d u a l and personal r i s k a b s o l u t e l y f o r e i g n to the conventional s a n c t i o n of an Old T r i b a l World: a r i s k which i d e n t i f i e s him (the a r t i s t ) w i t h the submerged a u t h o r i t y of dispossessed peoples but r e q u i r e s of him, i n the same token, a l c h e m i c a l resources to conceal, as w e l l as el a b o r a t e , a f a r - r e a c h i n g order of the imagination which, being suspect, could draw down upon him a crushing burden of censorship i n economic or p o l i t i c a l terms. He stands t h e r e f o r e at the heart of the l i e of community and the t r u t h of community (HFM p. 17). The symbol, which preserved u n s u l l i e d i t s c a p a c i t y to s i g n i f y a s t a b l e and s i n g l e meaning, i s now contaminated by the paradox of l i e s i n t r u t h and t r u t h i n l i e s , so that i t s f u n c t i o n may q u i t e as r e a d i l y 23 be to d e f l e c t as to conceal. And since i t s d e f l e c t i o n s may be a s s i s t e d by the immediate presence of others, i t i s the concatenation of these, the c l a s h of symbols, as i t were, which commands our a t t e n t i o n and works on the subconscious, that i s , i s read, before we can reach f o r our 24 d i c t i o n a r i e s of hermetic wisdom. Consider t h i s passage which occurs i n the f i n a l pages of Palace of the Peacock: I saw the tre e i n the d i s t a n c e wave i t s arms and walk when I looked at i t through the s p i r i t u a l eye of the s o u l . F i r s t i t shed i t s leaves sudden and s w i f t as i f the gust of the wind that blew had ripped i t almost bare. The bark and wood turned to l i g h t n i n g f l e s h and the sun which had been suspended from i t s head r i p p l e d and broke i n t o s t a r s that stood where the shattered leaves had been i n the l i v i n g wake of the storm. The enormous s t a r r y dress i t now wore spread i t s e l f a l l around i n t o a f u l l m a j e s t i c gown from which emerged the i n t i m a t e column of a neck, face and hands, and t w i n k l i n g f e e t . The s t a r s became peacock's eyes, and the great tree of f l e s h and blood s w i r l e d i n t o another stream that sparkled w i t h d i v i n e feathers where the neck and the hands and the f e e t had been n a i l e d (p. 146). The t r e e here would seem to bear out Ca r t e r ' s c l a i m : i t i s more than a t r e e . The n a i l e d hands and f e e t make that p l a i n , and indeed one might, i f i n c l i n e d , f i n d other s i g n i f i c a n c e s i n the passage which do not appear w i t h i n the t e x t . But s u r e l y the most zealous of d i v i n e r s and the most spartan of b i n a r i s t s might be persuaded that the w r i t i n g i s i n the f i r s t 25 place pleasurable? To begin at once to hunt f o r nodules of wisdom cunningly sown i n the furrows of the t e x t i s to seek examples of i t s c r a f t r a t h e r than i t s craftsmanship. This i s not to ignore the f a c t that one i n e v i t a b l y b r i n g s to a book systems of knowledge that are e x t r i n s i c to i t , or even to f o r g e t that there are l i m i t s ( u s u a l l y of world enough and time) to one's ra p t u r e . I t i s simply to r e q u i r e that we attend f i r s t to the w r i t i n g , upon which we discover that a good measure of our d e l i g h t s prings from those metamorphoses which the language undergoes before our eyes, from i t s c o l l i s i o n s , d i s i n t e g r a t i o n s and remakings, i n short from i t s surfaces r a t h e r than from i t s depths. This a c t i o n i s even more g r a p h i c a l l y rendered by the next two para-graphs . C a r r o l l was w h i s t l i n g . A solemn and b e a u t i f u l c r y — u n l i k e a w h i s t l e I r e f l e c t e d — d e e p e r and mature. Nevertheless h i s l i p s were framed to w h i s t l e and I could only e x p l a i n the d i f f e r e n c e by assuming the sound from h i s l i p s was changed when i t s t r u c k the window and issued i n t o the world. I t was an organ c r y almost and yet q u i t e d i f f e r e n t I r e f l e c t e d again. I t seemed to break and mend i t s e l f a l ways—tremulous, f o r l o r n , d i s t a n t , triumphant, the echo of sound so pure and o u t l i n e d i n space i t broke again i n t o a mass of music. The dark notes rose everywhere, so dark, so sombre, they broke i n t o a f o u n t a i n — l i g h t as the r a i n b o w — s p a r k l i n g and immaterial as i n v i s i b l e sources and echoes. The savannahs grew l o n e l y as the sea and broke again i n t o a wave and f o r e s t . T a l l t r e e s w i t h b l a c k marching boots and f e e t were c l a d i n the spurs and sharp wings of a b u t t e r f l y . They fle w and vanished i n the sky w i t h a sound that was t e r r i b l e and wonderful; i t was s o r r o w f u l and i t was m y s t i c a l (pp. 147-48). Here again, our pleasure i n the language deri v e s i n l a r g e p a r t from the 26 \"dance of words,\" from i t s h a r l e q u i n o p p o s i t i o n s which enact that \"deep unconscious humour of c a r n i v a l \" (AC p. 12) we saw the e a r l y H a r r i s foreshadow. The passage has a t t r a c t e d , and j u s t l y , a good d e a l of 27 commentary, so I w i l l have l i t t l e to say of i t except to repeat that there i s enough o c c u r r i n g at the phenomenal l e v e l to render deep soundings u n p r o f i t a b l e . More important, i t i s p r e c i s e l y t h i s s u p e r f i c i a l i t y which s h i e l d s us from o v e r i n t e r p r e t a t i o n or m i s i n t e r p r e t a t i o n ; and here we see that our a t t e n t i o n to the language c o n s t i t u t e s the meaning of the passage as w e l l as that of the n o v e l . For i f we examine what Gerald Moore has 28 c a l l e d i t s \" d i s s o l v i n g s t y l e \" i n i t s own r i g h t , we are prevented from a t t r i b u t i n g a t e l e o l o g y to what i s i n f a c t a technique. The f u n c t i o n of the c o n t r a d i c t o r y images and indeed of a l l the s h i f t s and changes of the prose i s to operate w i t h i n and e s t a b l i s h the conventions of a l a r g e r form, so that we read i t not as mysticism but as a m y s t i c a l n o v e l . This might seem a s c h o l a s t i c q u i d d i t y , but a great many of H a r r i s ' s readers have indeed taken Palace of the Peacock as a piece of naked 29 mysticism, and what i s more, f e l t moved to apologise f o r t h i s aspect 30 of the novel. I f i n s t e a d , we begin by assuming that the novel's m y s t i -cism i s a l i n g u i s t i c means of o r g a n i s i n g i t s a s s a u l t on s e t t l e d conceptions of the nature of power, we cannot mistake what i s a convention f o r the trappings of a transcendental S i g n i f i e d . To d e c l a r e that i n the l a t e r novels H a r r i s w i l l not come by h i s v i s i o n of e c s t a t i c u n i t y q u i t e so e a s i l y , i s to undervalue the primary q u a l i t y of t h i s n o v e l : i t s e x t r a -o r d i n a r y w r i t i n g . I t i s e x a c t l y because of i t s untrammelled use of the m y s t i c a l mode that Palace of the Peacock i s a b e t t e r novel than any of the others i n the s o - c a l l e d Guyana Quartet. To f i n d the mysticism of the novel on the one hand embarrassing, and on the -'other e l e v a t i n g , i s to d i s c o v e r e i t h e r too l i t t l e or too much. H a r r i s i s , of course, not w r i t i n g a theosophical t r a c t : by reading h i s work as such, whether u n c h a r i t a b l y (as quackery) or w i t h devotion (as a r e p a i r manual f o r the broken i n d i v i d u a l or the wasted country) we miss i t s primary i n t e n t , which i s a l i t e r a r y one. The manuscript of Palace of the Peacock was, a f t e r a l l , sent to Faber and Faber, not to the Rudolf S t e i n e r S o c i e t y . I f H a r r i s ' s e x p l i c i t warnings against f a i t h i n hidden 31 f o r c e s were not s u f f i c i e n t , the vigorous tugs of h i s language would s u f f i c e to d i s t r a c t the reader from the charms of the Absolute. One of the lessons we l e a r n i n the course of our reading i s that the s i g n i f i e d e x i s t s p r e c i s e l y as an unmaker of a b s o l u t e s , p o i n t i n g s t r a t e g i c a l l y back to the c o n t r a d i c t o r y surface of the t e x t . 32 The novel i s , then, not so much an abacus of symbols as an a l l e g o r y of the nature of power and d e s i r e i n the world. This theme i s present from the s t a r t i n the shooting of the dream horseman, f o r no sooner does the dreamer awake ( s t r i c t l y , he dreams he awakes), than he remembers having once been rocked by \"the o l d e s t u n c e r t a i n t y and d e s i r e i n the world, the d e s i r e to govern or be governed, r u l e or be r u l e d f o r ever\" (p. 14). Immediately, there i s a knock on the door and the dream horseman e n t e r s , greeted as \"gaoler and r u l e r . \" This i s Donne, who, even as he governs h i s brother's imagination, dominates h i s m i s t r e s s M a r i e l l a ' s body: as she bends to feed the chickens, he looks at her \"as at a l a r g e r and e q u a l l y senseless c r e a t u r e whom he governed and r u l e d l i k e a f o w l \" (p. 15). At the c l o s e of the f i r s t chapter, we hear him counsel h i s brother i n the l o r e of power: 'Rule the land,' he s a i d , 'while you s t i l l have the ghost of a chance. And you r u l e the world. Look at the sun.' His dead eye b l i n d e d mine. 'Look at the sun,' he c r i e d i n a stamping t e r r i b l e v o i c e (p. 19). The scene i s now set f o r a c o u n t e r v a i l i n g f o r c e which, i n c o n j u n c t i o n w i t h the f i r s t , w i l l f u r n i s h that \" a r c h i t e c t u r e of r e l e a s e \" we saw H a r r i s foreshadow i n h i s homily on the f e u d a l o v e r l o r d s h i p of the sun. Nor are we kept w a i t i n g , f o r Chapter Two opens w i t h the u n r o l l i n g of a dream map that i s both \"an a c t u a l stage,\" and an a l l e g o r i c a l one: \" I saw t h i s kingdom of man turned i n t o a colony and battleground of s p i r i t , a p r i c e l e s s tempting jewel I dreamed I possessed\" (p. 20). This d u a l i t y gives H a r r i s a purchase, a \"necessary stone and f o o t i n g , \" of which he makes splendid concrete use i n the course of h i s s w i r l i n g m y s t i c a l c u r r e n t of prose. From t h i s p o i n t on, dream works i t s way towards v i s i o n as each member of the crew d i s c o v e r s f o r himself what the dreamer at one pass s t r u g g l e s to express, that \"nothing e x i s t e d to f o o l and t e r r o r i z e anybody unless one chose to imagine one was bewitched and a f o o l a l l one's l i f e \" (p. 96). The l i e u t e n a n t of power i s f e a r , a f e a r which b l i n d s one to resources which become v i s i b l e only when t h i s apprehension i s turned i n s i d e out i n t o a knowledge which l i b e r a t e s one from f e a r and ther e f o r e from power. C e r t a i n of death, even the most abject of the dispossessed l e a r n that \" f e a r i s nothing but a dream\" (p. 59). This i s the substance of the Arawak woman's \"inso l e n c e of s o u l , \" and once the sca l e s are dashed from the crew's eyes, they are \"on the threshold of the f o l k . \" Under the guidance now of V i g i l a n c e , the Indian i n t h e i r midst, the men are brought to .their journey's end and to the r e a l i s a t i o n that not t h e i r obsessions but the e x t i n c t i o n of d e s i r e , not t h e i r scheming l i v e s but \"death and nothingness\" (p. 130) are t h e i r support. The same d e s i r e that Donne had turned i n t o \"a compulsive design and a b l i n d engine of war\" (p. 150), i s now transformed i n t o the outspread fan of the peacock. Wi t h i n the m y s t i c a l convention of the n a r r a t i v e , the c o n t r a d i c t i o n s of power and powerlessness are re s o l v e d i n a u n i v e r s a l dance to the music of the peacock, a dance i n which pursued and pursuer are no longer d i s -t i n g u i s h a b l e , s i n c e both stand f i r m l y i n the palace, \" f r e e from the chains of i l l u s i o n we had made without...\" (p. 151). Such r e s o l u t i o n s can be subjected to the c r i t i q u e of any mysticism, but to mount t h i s c r i t i q u e here would be to evince an unfortunate l i t e r a l - m i n d e d n e s s . I t i s obvious that the p o l a r i z a t i o n s of c o n f l i c t are here d i s s o l v e d only because they come to be immersed i n a plenum whose boundaries are not boundaries at a l l . The v i t a l i s t conception of the whole ensures that a l l antagonisms are defused, a l l opposites i n t e r p e n e t r a t e . But read on i t s own terms, the a l l e g o r y presents a c o n s i s t e n t i f unconventional c r i t i q u e of power and not simply another t e x t f o r d e c o n s t r u c t i o n . To designate the argument of the novel as, say, \"fea r i s the only s u b j e c t i o n , \" or \"power i s an i l l u s i o n , \" i s not to have f i n a l l y d i s t i l l e d a content from i t s s p i r i t e d extravagance of words. Otherwise one could argue that t h i s message might e q u a l l y have been clothed i n a. form which showed, r e a l i s t i c a l l y and by the cumulation of d e t a i l , the sorrows of young M a r i e l l a and the botched tyranny of a rancher, Donne. Yet there i s no guarantee t h a t , had t h i s been managed, the meaning would have remained the same: the message of Palace of the Peacock i s inseparable from i t s form, and the d i s m a n t l i n g of power i s conducted as much by the language as through i t . I f power seeks above a l l t hings s t a b i l i t y to ensure i t s dominance, t h i s i s the one e s t a t e which the \"melting essence\" of the language withholds from i t . W i t h i n the conventions of the novel's mysticism, the undoing of power must take the form of the undoing of every \" m a t e r i a l hoax\" (p. 83). This then i s the f u n c t i o n of a sentence such as the f o l l o w i n g : The fowls of the a i r danced and wheeled on i n v i s i b l e l i n e s that s t r e t c h e d taut between the ages of l i g h t and snapped every now and then i n t o l i g h t n i n g executions of dreaming men when each i n s t a n t ghost r e p a i r e d the wires again i n the form of an i n q u i s i t i v e hanging eye and b i r d (p. 108). The \" i n v e r s e stream\" and \" i n v e r s e c r a f t \" which the dreamer speaks of might e q u a l l y apply to the language and a r t which produce r i v e r and boat. And even as the language, l i k e C a r r o l l ' s c r y , seems \"to break and mend i t s e l f always,\" so the s t r u c t u r e of the novel w i t h i t s \"mixed f u t u r i s t i c order of memory and event\" (p. 53), m i l i t a t e s against the l i n e a r order of a h i s t o r y which seems to r a t i f y d i s p o s s e s s i o n by i t s p l a c i d r e f l e c t i o n of the past. The present i s , l i k e w i s e , amenable to m i s r e p r e s e n t a t i o n by documentary renderings. At the c l o s e of the book e n t i t l e d \"The Second Death,\" one of the d a S i l v a twins who had dropped out of s i g h t , reappears. His presence had been not so much f o r g o t t e n as obscured by the prose, and now we see why. His bones were s p l i n t e r s and p o i n t s V i g i l a n c e saw and h i s f l e s h was newspaper, drab, wet u n t i l the l i n e s and markings had run f a n t a s t i c a l l y together. His h a i r stood f l a t on h i s brow l i k e i n k . He nodded p r e c a r i o u s l y and one marvelled how he preserved h i s appearance without d i s i n t e g r a t i n g i n t o soggy lumps and patches when the wind blew and rocked the pins of h i s bones a l i t t l e . He shook h i s head again but not a word blew from h i s l i p s . D a S i l v a s t a r e d . at the a p p a r i t i o n h i s brother presented as a man would s t a r e at a r e p o r t e r who had returned from the grave w i t h no news whatsoever of a l i v i n g r e t u r n (pp. 122-23). In the terms of the a l l e g o r y , not death's s t i n g but absolute death, s l a v i s h l y rendered, i s the u l t i m a t e v i c t o r y of power. The a p p a r i t i o n , t h e r e f o r e , p l a y s a dual r o l e : as an a l l e g o r i c a l v e c t o r , the d a S i l v a twin i s a poor r e p r e s e n t a t i v e of h i s a b s o l u t i s t ideology; as a newspaper man, h i s s o r r y c o n d i t i o n mutely t e s t i f i e s to the power of the s u r r e a l to 34 confound r e a l i s t i c reportage. Both the ideology and i t s mode of pro-j e c t i o n are r e f u t e d by the only means a n o v e l i s t has to make such r e f u t a t -i o n s : the a l l e g o r y puts absolute power i n t o doubt even as the language puts r e a l i s m i n t o d i s a r r a y . The d i s l o c a t i o n of Harrises language i s i t s most evident f e a t u r e , and now we r e a l i s e i t i s not the product of whimsy. To be sure, the fragmen-t a t i o n i s n e i t h e r unique nor e s p e c i a l l y r a d i c a l : aside from the more common typ o g r a p h i c a l v a r i a t i o n s , there are none of the s p l i t t e x t s , f r a c t u r e d columns, s c a t t e r e d words, blank or s o l i d or f e n e s t r a t e d pages, v a n i s h i n g m a r g i n a l i a , or any of the numerous v i s u a l i r r u p t i o n s which have been the stock i n trade of the p l a y f u l n o v e l i s t since Sterne or the dedicated f o r m a l i s t s i n c e f u t u r i s m . At most, the l a t e r novels admit one or two r a t h e r schematized diagrams, which are n e i t h e r l u d i c nor earnest but simply f o r l o r n . They do, however, continue w i t h i n t h e i r graphic parameters those op p o s i t i o n s whose presence i n the body of the t e x t takes the shape of imaged c o n t r a d i c t i o n s : p h y s i c a l t a r g e t s are set over against mental t a r g e t s , s o l u b l e uniform against i n s o l u b l e d e i t y , tone against non-tone, f o s s i l w a l l s of time punctured by c a n n i b a l bone f l u t e . Always the d i s t i n c t i o n between.apparent and r e a l , always the suggestion of untapped energies. The cumulative e f f e c t of these antinomies i s not that of a Ye a t s i a n cosmogony but simply a sense of the f r a g i l i t y of the recei v e d t e x t of the world. I f what we take to be r e a l i t y i s indeed such a t e x t , a s t y l e of r e p r e s e n t a t i o n as much as an ontology, then a language which d i s t o r t s t h i s s t y l e i s some short way advanced towards f i g u r i n g an a l t e r n a t i v e r e a l i t y . This i s the substance of H a r r i s ' s \"mimetic crash or crack or bone,\" h i s \"breaking down things i n order to sense a v i s i o n through t h i n g s \" (KK p. 52) In one of h i s Amerindian t a l e s , \"Yurokon,\" we f i n d t h i s passage: Break the land. Break the sea. Break the savannah. Break the f o r e s t . Break the twig. Break the bough. The un w r i t t e n symphony of the wind, unwritten spark of the wind, made him b a r k — a sudden bark. [The Carib boy, Yurokon's, uncle] stared a t the b r i s t l i n g dog of the f i r e , f i r e break, f i r e bark, d e l i c a c y , magic; he smacked h i s l i p s and the ro a s t of Yurokon's bark subsided i n t o the s i l e n t bay of conscience l i k e an i n v o c a t i o n at the heart of the f e a s t : man's best enemy or f r i e n d . Was i t the immortal dog of war and peace that sang i n the break of the f i r e , shadowy t a i l or bone? (SR p. 69). H a r r i s glosses the piece i n t h i s way: The .'breaking of the land, sea, savannah e t c ' i s an inner perception or a n t i c i p a t i o n of cleavage i n the persona of conquest—mimetic crash or crack or bone of a n a t i v e / u n i v e r s a l symphony w i t h i n which image and imagelessness are orches t r a t e d i n t o a metaphor which i m p l i e s that the very ruined w a l l s of time may provide an aperture or organ.or f l u t e through which the theme of community i s r e s t a t e d as a ca p a c i t y to s u s t a i n inner and outer overlapping p e r s p e c t i v e s . Thus 'the breaking of the sea, l a n d , e t c ' i n the Yurokon symphony stands i n parenthesis to C a r r o l l ' s crew and the 'cloudy s c a l e of incenstuous c r u e l t y which tumbled from t h e i r eye' (NP p. 150). The shock troops of t h i s a c t i o n are H a r r i s ' s images, but the breakage goes beyond t h i s atomic, sensory l e v e l to that of the l i n e . Hence the tropes of r e v e r s a l and overturning omnipresent i n the H a r r i s i a n grapholect. Next i n the Guyana Quartet, The Far Journey of Oudin (1961) opens so: The s t a r s shone f a i n t i n the stream on the windy night and they penetrated a f l y i n g cloud. The l i g h t s s h i n i n g f a r across the r i v e r were u n c e r t a i n and d i s t a n t , c l o s e to the ground and one w i t h glimmering heaven. The shape of a cow loomed on the opposite bank, so enormous i t b l o t t e d out the l i g h t s and i n v i s i b l e windows of the f a r s c a t t e r e d settlements: i t loomed l i k e a cloud, shapeless and massive i n the dreaming f a i n t l i g h t , s l i t h e r i n g down the bank and suddenly i n t o the water, washing the s t a r s away as i t swam across the n i g h t (FJ p. 11). The continuous s h i f t s of p e r s p e c t i v e i n t h i s opening paragraph prepare the reader once more f o r a t a l e of d u p l i c i t y and s e l f - d e c e p t i o n . And indeed, the s t o r y about to u n f o l d i s that of a t r i c k s t e r , Oudin, who becomes the w i l l i n g t o o l of a grasping moneylender, Ram, and p l a y s t h i s r o l e w e l l u n t i l he d i s c o v e r s the v i r t u e of freedom i n r e s p o n s i b i l i t y . Awakening to t h i s knowledge, he marries the g i r l he has been set to abduct f o r Ram, o u t w i t t i n g h i s master both now and on the day of h i s death, t h i r t e e n years l a t e r . The g i r l , B e t i , i l l i t e r a t e daughter of one of Ram's scheming v i c t i m s , i s l e f t pregnant, but suspecting a p l o t by which her f u t u r e c h i l d w i l l now become Ram's i n exchange f o r a f r e e -h o l d , she f i n d s the v i t a l scrap of deed paper i n her dead husband's hands and eats i t . To t h i s s t o r y , H a r r i s b r i n g s h i s apparatus of disturbance, r i p p l i n g the surface of t h i n g s i n a way that i s w e l l i l l u s t r a t e d by the passage below. Ram, who i s spying on B e t i , has come upon her washing c l o t h e s at the r i v e r ' s s i d e . He hopes to observe her s e c r e t i n g the scrap of deed paper i n some \"empty rum b o t t l e or j u g \" ; i n s t e a d he sees only h i m s e l f , waving up and down as he t r o d on the shaking planks, s l i c i n g and waving almost e n d l e s s l y u n t i l the s l i c e s and fragments were drawn together on a loose s a i l i n g thread. He could make out very l i t t l e as he peered i n t o the r i v e r ' s obsession and depth, save that a banner had been u n f u r l e d over the grave of Oudin, one of those waving f l a g s anonymous processions hold over t h e i r head when they c e l e b r a t e a v i c t o r y or r e s o l u t i o n and triumph. A p u b l i c banner and epitaph everyone knows i t i s , and yet a most p r i v a t e symbol of r e b i r t h and death, since the face on the banner represents an absent hero whose s l i d i n g p r o p o r t i o n s are the mask of t i m e l e s s s p i r i t r a t h e r than Ram's fading p e r s o n a l i t y (p. 25). The ''slices and fragments\" we are now accustomed t o , but the l a r g e r a n t i -t h e s i s of p u b l i c \"and y e t \" p r i v a t e sets up a new c o n t r a d i c t i o n , and one which l i e s at the root of the f a b l e . A n t i t h e s i s i s , of course, a r e c u r r i n g f e a t u r e i n the s t y l e of a great many w r i t e r s , not a l l of them modern, yet where o r d i n a r i l y i t represents a l o g i c a l p l a y between conceptual opposites, here i t s \" s l i d i n g p r o p o r t i o n s \" s t r e s s not a brace of i d e n t i t i e s but the r e l a t i o n which connects them. When, much l a t e r , Ram i s d i s c o u r s i n g l a r g e l y on p o l i t i c s before h i s l a s t v i c t i m , Mohammed, we are expected to remember t h i s r e l a t i o n s h i p between p u b l i c and p r i v a t e . ' Korea—a country j u s t l i k e t h i s I would s a y ' — h e waved h i s hand g e n e r o u s l y — ' s p l i t ' i n h a l f , man. What a mix-up f a m i l y s t o r y . God know who i s k i l l i n g who. You i s not the only one i n t h i s new f a m i l y t r o u b l e . And what happening to you i s p r i v a t e , p l a i n AND o r d i n a r y compared to t h a t ' (p. 98). 35 The p o i n t of the analogy and indeed of the e n t i r e parable of Oudin i s that the d i s t i n c t i o n s customarily made between power on a grand scale and that which operates between i n d i v i d u a l s are n u l l : the very cate g o r i e s of p u b l i c and p r i v a t e c o l l a p s e . This i s both a bad and a good t h i n g . On the one hand, i t allows H a r r i s to mock the p u b l i c sphere and to m y s t i f y the sources of s o c i a l power by p e r s o n a l i s i n g them; on the other, i t r a i s e s important i s s u e s of i n d i v i d u a l e x p l o i t a t i o n and r e s i s t a n c e that commonly go unnoticed. An t i t h e s e s of t h i s k i n d f a s t e n on c o n t r a d i c t i o n s not so much i n the body p o l i t i c as i n i t s members. In the same way as the crew of Palace of the Peacock have the s c a l e s dashed from t h e i r eyes, so the v a r i o u s characters of t h i s novel have t h e i r moments of c r i s i s and self-knowledge. At the end of the n o v e l , a f i s s u r e begins to open i n Ram, \"the t h i e f who had s t o l e n from h i m s e l f . \" But as he scans \"the new b i t t e r wastes of water over which a blue window i n the clouds had opened,\" he remains a \"seemingly s e l f - c o n t a i n e d man,\" p l o t t i n g to create \"an unassailable\" appearance.\" He i s not cured of h i s obsession w i t h \"a son who would be the acknowledged c h i l d of h i s l i f e to f i l l the widening blue crack i n heaven l i k e a p i c t u r e \" (p. 134-135). Even t h i s mimetic d i s t r a c t i o n w i l l be denied him, f o r the novel has opened w i t h Oudin's death and B e t i ' s e a t i n g of the \"covenant.\" Oudin, we are t o l d , \"embarked on t h i s fabulous dying journey\" when, t h i r t e e n years before, he \" c a n c e l l e d out Ram's command.\" He f e l t i n a s t u b l i n g i n t u i t i o n of s e l f , that the p a t t e r n of a l i f e t i m e of migrating from province to province was now being s e t , and the coming journey was a c r u c i a l r e h e a r s a l , a r e h e a r s a l that would be repeated once again over t h i r t e e n dreaming years of h i s marriage to B e t i . He foresaw i n the f i r e and smoke of fantasy, the running abduction, and the dim uncomprehending married years that would f o l l o w , ushering i n — o n the midnight morning that he d i e d — t h e f a r journey outward, i n t o the land that was nowhere. This dark, i n t u i t i v e thought-sun was both an opportunity and a stumbling-block (p. 100). By f o l l o w i n g t h i s i n t u i t i o n , Oudin outwits Ram and f r e e s h i m s e l f . This equation of independence w i t h self-knowledge i s c o n s t a n t l y i t e r a t e d through such s t y l i s t i c devices as the oxymora \"midnight morning\" and \"dark, i n t u i t i v e thought-sun\" here lodged among l a r g e r a n t i t h e s e s . The l i n k i s even more p l a i n l y conveyed by a H a r r i s i a n d e v i c e , that of m u l t i p l e co n j u n c t i o n . Where once Oudin had been Ram's \" l i s t e n e r and s l a v e , \" t u r n i n g every \" p i l l a r and p r o p r i e t o r \" i n t o the money-lender's \" l a s t i n g fence and world and market,\" now he i s i n t e n t on overthrowing \"every misconception and i n f e r i o r r e l a t i o n s h i p . \" A s t r i n g of \"ands\" i s no doubt a kind of r h e t o r i c , but only m a r g i n a l l y so. I t i s the rag-and-bone r h e t o r i c of b r i c o l a g e , or making do w i t h 3 6 a v a i l a b l e m a t e r i a l s . \"But i s who f a u l t i f the only language we got i s a breaking-up or making-up language?\" Mohammed asks. The-.question i s one which West Indian w r i t e r s have voiced i n many and ingenious ways. H a r r i s turns to r i c h account the l a c k i t addresses, d i s d a i n i n g no source and rummaging through every midden he comes upon to piece together the creature we might c a l l h i s crooked s t y l e . His t h i r d n o v e l , The Whole 37 Armour (1962), begins w i t h two epigraphs, one of which, from Hopkins, reads: This Jack, j o k e , poor potsherd, patch, matchwood, immortal diamond, Is immortal diamond. And t a k i n g t h i s t e x t to h e a r t , H a r r i s has w r i t t e n a hard and\" b r i l l i a n t novel which once more grapples w i t h \"the ancient jaguar of death\" as i t marauds \"on the f r o n t i e r between changing fantasy and the growth of a new settlement\" (WA p. 37). Again we begin w i t h a dream, one that fades on a parody of a hut on a s p i t of land that looked u n y i e l d i n g and hard amidst the trenches that had been t o r n and eroded on e i t h e r s i d e , u n t i l they were crowded w i t h a gnarled husk and mask and a twist e d alphabet of timber. Every p r i v a t e n o t i c e and f a b l e and boundary against the sea stood i n the t u r m o i l of the foreshore as i n a graveyard of sculptured h i s t o r y and misadventure (p. 17). Out of the twist e d m a t e r i a l s of t h i s wasteland—Book One i s c a l l e d \"Jigsaw B a y \" — a new h i s t o r y i s to be pieced together, though i t i s not before a lengthy v i g i l , and one that w i l l probably end i n h i s death, that the hero, C r i s t o , can c l a i m h i s ordeal has remade him. \" F i t t e d me together again,\" he says of the \"Garibs\" he imagines he met i n h i s f o r t y days and n i g h t s i n the j u n g l e . The son of a Pomeroon whore, C r i s t o i s i n h i d i n g , wrongly suspected of murder. Magda, h i s mother p r e v a i l s on one of her long-time customers, Abram, to hide C r i s t o i n h i s remote hut, but Abram d i e s two months a f t e r t a k i n g the young man i n . While C r i s t o ventures out to r e p o r t t h i s death to h i s mother, a jaguar c a r r i e s away the body, so that when mother and son r e t u r n , a column of crows i s hovering over the remains. B e l i e v i n g t h i s to be C r i s t o ' s second murder, but d r i v e n nonetheless by a d e s i r e to p r o t e c t the son she has scrimped f o r , Magda for c e s him at gunpoint to dress the corpse i n h i s own c l o t h e s . F o r t y days a f t e r the \"death\" or her son, Magda holds a wake to which the e n t i r e community i s i n v i t e d , i n c l u d i n g the g i r l Sharon, whose f i r s t s u i t o r C r i s t o was b e l i e v e d to have k i l l e d . Sharon comes escorted by her new s u i t o r , M a t t i a s , but he too i s a c c i d e n t a l l y k i l l e d i n a s c u f f l e w i t h her drunken f a t h e r . Meanwhile, Sharon l e a r n s from Magda that C r i s t o i s a l i v e , and some n i g h t s l a t e r she goes to him i n the f o r e s t . The next morning C r i s t o decides that he w i l l g i ve himself up. His o r d e a l has taught him that to f l y from a mistaken j u s t i c e i s to perpetuate a l i e . He knows that i t w i l l go hard by him: the recent rash of v i o l e n c e i n the d i s t r i c t has l e f t the community nervous and ready f o r a scapegoat. At the c l o s e of the n o v e l , he i s observed, and as the p o l i c e net c l o s e s i n on Sharon's house, he dreams of the c h i l d who w i l l s u r v i v e him. I f E t e r n i t y to Season was H a r r i s ' s p o e t i c a l Book of Genesis, and Palace of the Peacock a k i n d of R e v e l a t i o n s , The Whole Armour a s p i r e s , w i t h an audacity that compels admiration, to be the Guyanese New Testament. Even as \"every p r i v a t e n o t i c e and f a b l e and boundary\" of the o l d covenant i s demolished, we may pass from techniques of breaking to those of j o i n i n g , and observe at work the second part of that question l e f t hanging i n The Far Journey of Oudin: \" I s who f a u l t i f the only language we got i s a breaking-up or a making-up language?\" An equal p o r t i o n of the \"making-up w i l l f a l l to the reader. So, i f the burden of the novel i s that i t i s imperative to recognise a primeval chaos i n the i n d i v i d u a l and to f a b r i c a t e out of t h i s s t a t e a new meaning to community, t h i s process i s c l o s e l y r e p l i c a t e d i n that by which meaning i s produced from the c h a o t i c language of the t e x t . Indeed the stages by which the i d e n t i t y of the c e n t r a l characters i s broken down from a s t r i c t \" s e l f - p o s s e s s i o n \" i n t o \"a strange and blundering excitement and p a r t i c i p a t i o n \" (p. 70), might be shown to have t h e i r e q uivalent i n the process by which the reader l e a r n s to r e s i s t the s t r i c t i d e n t i t y of a word or image and to make sense of the f a r - f l u n g network of r e l a t i o n s h i p s between words and images. The yoking together of heterogeneous ideas i s not a device of recent o r i g i n , but where i n the Metaphysical c o n c e i t a l o g i c of d i s t a n t resem-blances, once e s t a b l i s h e d , i s worked out w i t h a p r e c i s i o n that appeals to p a i r e d sequences w i t h i n a universe of i d e n t i t y , i n the s u r r e a l i s t p r a c t i c e of H a r r i s ' s w r i t i n g t h i s machinery i s d i s r u p t e d . In making up \" n o t i c e and f a b l e and boundary',\" the prose appeals not to p a i r s of resemblances or even to homologies of these ( f o r there i s l i t t l e that the three elements d i r e c t l y share) but to a f o u r t h and absent q u a n t i t y whose o u t l i n e s are formed by a coalescence of the given three. I t i s not so much that the i d e n t i t i e s of the superimposed words are shaken, as that the r e l a t i o n s h i p between them produces, by a transference among metonymies, a new id e a . In the sentence which ends the paragraph d e s c r i b i n g Abram's \"parody of a hut,\" the chimera compounded of p e t r i -f i e d l i m i t s (\"boundary\") and posted sanctions (\"notice\") i s one whose i d e n t i t y the subsequent \"graveyard of sculptured h i s t o r y \" would seem to confirm, were i t not f o r the troublesome \" f a b l e . \" By i t s very insub-s t a n t i a l i t y i n t h i s s o l i d company, f a b l e r e c a l l s one's a t t e n t i o n from graveyard and misadventure, p u t t i n g t h e i r f i n a l i t y i n doubt, or at l e a s t s e t t i n g up an expectation that they w i l l be overturned. This message i s , i n f a c t , the novel w r i t s m a l l : h i s t o r y i s not a closed chapter, nor i s i t hallowed ground, graven and daunting as i t s authorized v e r s i o n may w e l l be. To be sure, the reader does not s e i z e a l l t h i s i n some b l i s t e r i n g epiphany, or even i n the e l a s t i c moment of h i s t r a v e l l i n g eye; he may 39 w e l l have to stop and go back a short way. I t may even be that h i s reading w i l l not match the one given here (or f o r that matter h i s l a s t or h i s next reading of the same passage) but the process of i t s c o n s t r u c t -i o n w i l l have re q u i r e d him to r e v i s e h i s h a b i t u a l s t r a t e g i e s of reading. This i s a l s o what i s asked of the Pomeroon community, who have, as i t were, put on the wrong armour, r a l l y i n g . . . a l l t h e i r f o r c e s i n t o an incestuous persona and image and a l l i a n c e — t h e very a n t i t h e s i s of t h e i r dark t r u t h and h i s t o r y , w r i t t e n i n the v i o l e n t mixture of races that had bred them as though t h e i r t r u e mother was a wanton on the face of the e a r t h and t h e i r true f a t h e r a vagrant and a rogue.from every continent (p. 4 9 ) . Assembled at the wake, they remain \" b l i n d to each other\"; they \" l o s e each other i n the midst of t h e i r chronic d e n s i t y and i d e n t i t y \" (p. 68). I t i s p a l e , u n c e r t a i n M a t t i a s , Sharon's e s c o r t , whose \" t e r r i b l e honour\" i t i s to be \"chosen by the shattered medium of the wake to redeem the r e l i c s of c r i p p l e d p e r s p e c t i v e . \" As he stands, on \"the threshold of a profound p a r t i c i p a t i o n , \" every d i s j o i n t e d p i c t u r e and impression revolved i n h i s m i n d — a s e r i e s of r e v e l a t i o n s , engagements and disengagements, each p a t t e r n appearing the very unstable a n t i t h e s i s of another and undermining even i t s e l f as i t dawned (pp. 7 3 - 7 4 ) . Instead of shrugging o f f the \"most t r o u b l i n g question of a l l mankind— the meaning of i n d i v i d u a l innocence and g u i l t , \" he remains to r e s o l v e i t over a t r i f l i n g a c c u s a t i o n and f o r f e i t s h i s l i f e . I t i s p o s s i b l e t h a t , as w i t h another young man's tragedy, the emotion generated here i s i n excess of the a c t i o n , but H a r r i s i s t r y i n g to c a r r y o f f two things at one time: to poin t h i s t h e s i s that a closed i d e n t i t y , whether of i n d i v i d u a l or group, i s a f a i l u r e of communal r e s p o n s i b i l i t y , and to i l l u s t r a t e t h i s need f o r p a r t i c i p a t i o n by w r i t i n g i t out. As he faces Sharon's drunken f a t h e r , M a t t i a s sees a beast he recognizes w i t h a primeval s t a r t from the moment one f i n d s one has crawled out of the ancient egg of the sea i n t o a new b r u t i s h s h e l l and hatching f a m i l y t r e e and camouflage. A l l hunted and hunting sensation was d r a i n i n g from Peet's c r e a t u r e l y face so that i t turned h a l f -woman, half-man, t u r n i n g i n s t a n t l y again on i t s e l f i n order to b i t e i t s e l f . He grabbed a k n i f e and l i f t e d i t h i g h i n the a i r to s t r i k e the nearest v i s i o n a r y one. M a t t i a s caught the r a i s e d arm j u s t i n time, t w i s t i n g the w r i s t and e x t r a c t i n g the k n i f e . The crowd went mad. A l i t t l e harmless blood must s p i l l i n the foreday morning, they began to chant. M a t t i a s t r i e d to push h i s way back. Someone pushed him forward. He f e l l upon Peet who pushed him from him as a b a l l jumps from foo t to hand and hand to f o o t . M a t t i a s bounced forward again and t r i p p e d on the l e g of a c h a i r . He was i n a s t a t e of curio u s i n t o x i c a t i o n . He thought he was f a l l i n g on the i r o n trunk of Abram's tree and he st r e t c h e d h i s hands out to save himself from being t e r r i b l y b r u i s e d , l o s i n g s i g h t of the k n i f e , he s t i l l grasped. A scream bu r s t from h i s l i p s , so c l e a r and d i s c e r n i n g , there was a dead s i l e n c e a l l around. No one t r u s t e d t h e i r eye as i t beheld the d r i p p i n g treasury of blood (p. 94). Having already declared that \"Mankind i t s e l f was the t i g e r \" (p. 78), the t e x t now creates something of the ju n g l e which i t contends i s to be faced before a community of r e s p o n s i b l e persons can be born. The c l u s t e r of images which f o l l o w s the f i r s t c r a w l i n g does not make s t r i c t sense; a progression of s o r t s i s a l l that can be made out at once, and then perhaps the n o t i o n of each s t a t e encapsulating the next. Any f u t h e r advance i n the reader's understanding of t h i s c l u s t e r w i l l not be a l i n e a r one, and w i l l i n f a c t devolve upon a r e c o g n i t i o n of the u n d i f f e r e n t i a t e d nature of the words so brought together. The s e v e r a l elements, which H a r r i s would c a l l a. \" c o n s t e l l a t i o n \" (SI p. 40), c o n s t i t u t e a k i n d of m u l t i p l e c o n t r a - -d i c t i o n : they remain suspended s y n c h r o n i c a l l y , as i t were i n a s o l u t i o n of consciousness, without any a u t h o r i a l attempt to r e s o l v e or tame them r h e t o r i c a l l y . I f the t e x t works by suggestion, the reader p e r f o r c e f a l l s back from time to time on impressions. This i s why the p e j o r a t i v e \" i m p r e s s i o n i s t i c , \" wants to be s p a r i n g l y used, f o r i n cases such as t h i s (and, f o r that matter, others where the reader might suppose himself to be proceeding w i t h the a n a l y t i c r i g o u r of a s c i e n t i s t ) our responses occur i n p r e c i s e l y t h i s domain. The job i s a t a x i n g one, and i t i s w i t h a sense of r e l i e f that the reader f i n d s the deceptions of \" s h e l l \" and \" t r e e \" and \"camouflage\" to g i v e onto a more t r a c t a b l e s e r i e s of c o n t r a d i c t i o n s . H a r r i s has himself remarked, i n a preface to the paperback e d i t i o n of The Whole Armour and The Secret Ladder, that the \" f a n t a s t i c a t i o n of imagery\" i n the f i r s t novel has been \"a source of d i f f i c u l t y f o r some readers\": I can only say i t i s intended not as an e x o t i c device but as a s u b j e c t i v e a l t e r a t i o n of form i n order to r e l a t e new content or new existences to a r e v i s e d canvas of community (p. 9 ). The f a n t i s t i c a t i o n , then, i s not \"surplusage\"; moreover i t has i t s 41 own c o n t r a d i c t i o n i n a s t y l e of nothingness. At the end of the n o v e l , C r i s t o dreams i t i s f i v e minutes to the ten o'clock of h i s execution: h i s mind was so empty i t had become a frame f o r the f u t u r e , almost as though he had stopped e x i s t i n g a l r e a d y , i n f a c t no one e x i s t e d , a hundred s e r i a l years had passed, and they were a l l dead fused p o r t r a i t s on the w a l l f o r anyone to recognize and l e a r n whatever they wished they understood (p. 129). Here again, the w r i t i n g produces the r e q u i r e d d i s s o l u t i o n of s e l f : the v i t a l images of that ungoverned chaos M a t t i a s recognized, now give way to \"dead fused p o r t r a i t s , \" s e r i a l l y interchangeable w i t h i n the empty frame of C r i s t o ' s mind. The s e r i a l deaths of the novel attempt to express t h i s conception of h i s t o r y s t r u c t u r a l l y : they are i n a sense the formal equivalent of the s t y l e of nothingness, d e l i n e a t i n g the space where the hollow subject touches h i s t o r y . C r i s t o ' s r e a l i s a t i o n that \"nothing always contained e v e r y t h i n g \" i s not a mysticism or the s e l f ' s f i n a l a b s o r p t i o n of the other, but a r e c o g n i t i o n that the two are locked i n a ceaseless exchange of i d e n t i t i e s . The t h i r d epigraph of H a r r i s ' s next novel,The Secret Ladder, reads: I t i s indeed an i n t e g r a t i o n of the movements of the agent w i t h the movements of the Other, so that i n a c t i o n the s e l f and the Other form a u n i t y . MACMURRAY The s e l f i n t h i s f i c t i o n i s that of R u s s e l l Fenwick, a young surveyor; the Other takes the shape of Poseidon, venerable leader of a group of bush negroes, the descendants of runaway slaves s e t t l e d i n the barren r e g i o n Fenwick and h i s party have come to survey. F r i c t i o n between the o u t s i d e r s and the r i v e r people i s not long developing. Word has got about that the survey party i s preparing :the way f o r an i r r i g a t i o n scheme that w i l l drown the catchment of the Canje r i v e r and \"everybody's land w i l l duck f o r good\". The c o n f l i c t d i v i d e s the team and t r i g g e r s a c r i s i s w i t h i n Fenwick, who f i n d s himself drawn, against the wishes of h i s foreman (a man of power) and h i s storeman (a man of prudence), to sympathise w i t h the r i v e r f o l k and t h e i r ancient c h i e f . Nevertheless, the work must go on, and as i t does, the threatened i n h a b i t a n t s r e s o r t to sabotage. The h a r d l i n e r s i n the survey p a r t y press f o r r e p r i s a l s , e s p e c i a l l y when one of t h e i r number, Chiung, i s attacked at n i g h t . But Fenwick r e s i s t s , and Chiung himself confesses he had t r i e d to cheat the men who s t r u c k him down. Matters come to a head when Poseidon meets an a c c i d e n t a l death, seemingly at the hands of Fenwick's boatman, Bryant, the man who loved him best. In d i s a r r a y , Poseidon's f o l l o w e r s are about to wreak t h e i r revenge, when the two bushmen who b e l i e v e they have k i l l e d Chiung come running with t h e i r t a l e of fear, and cause a general panic. Poseidon's body i s abandoned, but t h i s i s no ignominy, for i t i s the husk of a purpose already served. Compared to the other novels of the Quartet, The Secret Ladder i s a sluggish stream; the rapids of Palace of the Peacock would seem to have debouched onto a sudden p l a i n . This e f f e c t i s p a r t l y that of the physical t e r r a i n which the novel evokes, the f l a t s of the Canje headwaters. The novel i s also the darkest of the four, the greater part of i t s a c t i o n unravelling i n the t w i l i g h t of the jungle or at night. I t i s as i f the underworld so often lurki n g at the fringes of the previous novels were now at l a s t penetrated. The t r a n s i t i o n occurs at the very s t a r t of the novel: a hundred yards from where Fenwick stands by the s t e l l i n g , i n the \"exposure and defeat\" of the noonday sun, \"the jungle turned b l i n d as a shuttered place and the eye learnt to r e l i n q u i s h the neighbouring sun for a tenebrous, almost e l e c t r i c a l gloom\" (p. 143, paper edn.). But i f the sensation of s t i l l n e s s and gloom i s conveyed by the landscape and atmosphere of the novel, i t derives also from a modulation i n the shape and pace of Harris's w r i t i n g . And t h i s i n turn i s traceable to the novel's scheme, or rather i t s scheming. Despite i t s r e l a t i v e l y conventional surface, The Secret Ladder i s a highly wrought novel. Certain resemblances l i n k i t with Harris's f i r s t , and round o f f the Quartet: i t s action spans the seven days that Donne's crew journey beyond M a r i e l l a , and Fenwick c a l l s h i s boat Palace of the Peacock. But where i n the e a r l i e r novel the writing and the design were always one, so that the form was the content, here there are occasions when the two come apart and the content appears to tyrannize the form. \"Intent\" i s perhaps a more accurate word than \"content,\" for where the design becomes most designing the phrasing s a t i s f i e s l e a s t . The n a r r a t i v e u s u a l l y redresses t h i s imbalance, but whenever i t i s invested w i t h a greater s i g n i f i c a n c e than i t s frame w i l l bear, the novel becomes unf o r -t u n a t e l y r h e t o r i c a l . C u r i o u s l y , i t i s the s i g n i f i c a n c e and not the frame which s u f f e r s , and c h i e f l y i n those passages where a h i g h l y c o n t r i v e d s e r i e s of hermetic connections overpowers the n a r r a t i v e and proceeds to r a r e f y i t . H a r r i s i s himself conscious of t h i s ; danger, one which springs as much from the i n t a n g i b i l i t y of h i s subject as from h i s penchant f o r Jungian symbology. I t i s because h i s theme can so e a s i l y be taken as hackneyed— the need to u n i t e head and h e a r t , science and modes of f e e l i n g — t h a t he chooses i n d i r e c t i o n , and yet t h i s very i n d i r e c t i o n commits him to a p r e c i o s i t y which renders h i s i n t e n t the more palpable. L i k e Chiung, who s t r u g g l e s to t e l l a t r u t h which w i l l i n c r i m i n a t e h i m s e l f , he grows \" d e s p a i r i n g l y c r a f t y , the vaguest h i n t of a parable i n h i s f l a t i n s e n s i b l e v o i c e \" (p. 234). He i s d r i v e n to a p o l o g i s e : Dead easy to j o i n i n p o i n t i n g a f a c i l e f i n g e r at the mocking portentous l e t t e r s of an age and to acquiesce i n misreading i t s true meaning and s p i r i t (p. 193). Or again, \" A l l was an a r t i f i c e of mystery to which one addressed oneself o f t e n w i t h i d l e and p r e t e n t i o u s words\" (p. 195). P r o t e s t i n g too much, H a r r i s would seem to condemn h i m s e l f : the seven days of d e c r e a t i o n , the secret ladder, the cross r h a t i s Poseidon's house, the v e s s e l that i s the woman Catalena, these perhaps weigh h e a v i l y on the w r i t e r who has coupled \" r h e t o r i c and s t e r i l i t y \" (p. 206). But H a r r i s i s not blaming h i s t o o l s ; they are, he i n s i s t s , a l l that i s a v a i l a b l e to him and at the l a s t , expendable. I f we take him at h i s word, we f i n d that the \"true meaning and s p i r i t \" of the novel do not i n f a c t l i e i n those accoutrements of myth which the contemporary s e n s i b i l i t y f i n d s i m p l a u s i b l e and even fatuous. A good example i s Poseidon him s e l f . On each of h i s appearances, he i s described w i t h an imagery t h a t b e f i t s h i s m y t h i c a l c h a r a c t e r : the \" f l a p p i n g ragged f i n s of trousers on h i s l e g s \" (p. 155), h i s \"ancient f e e t webbed w i t h grass and muck,\" h i s hands \"wreathed i n a fisherman's w r i t h i n g net of cord\" (p. 181), but when Bryant declares that the o l d man i s \" f r e e r than you and me...\" Fenwick r e t o r t s , \"look at him, man, he's l i k e a f i s h i n a net.\" And to himself he c r i e s , Yes, I confess I owe a l l e g i a n c e to him because of h i s c o n d i t i o n , a l l e g i a n c e of an important k i n d , that of conscience, of the r e b i r t h of humanity...But s u r e l y t h i s does not mean I must reduce myself to h i s trapped c o n d i t i o n , become even l e s s human than he, a mere symbol and nothing more... Then, speaking openly again: P l a i n wholesome understanding of h i s t o r y and f a c t s and p o s s i b i l i t i e s i s important, Bryant. Take the unadorned f a c t s of s c i e n c e , the p l a i n economic s t r u c t u r e of s o c i e t y shorn of w o r s h i p f u l emotion, shorn of t h i s f i c t i o n of freedom you c l a i m Poseidon alone possesses. I am glad we can see him as he i s so that we can know what t h i s l i f e i s , the hard business of t h i s l i f e , here and now (do you f o l l o w me?) and indeed we can see—beyond a shadow of d o u b t — t h e n e c e s s i t y f o r human freedom (pp. 182-83). So, at the end, when Poseidon d i e s , Fenwick marvels that the two who have brought the news are i n t e a r s , f o r what has died i s merely the symbol, 42 the god that was: \"An angel of polemic and a b s u r d i t y would have shouted f o r j o y \" (p. 246). This knowledge, Fenwick immediately r e f l e c t s , i s always \" i n s t a n t l y p l a s t e r e d w i t h the slime of s p i r i t u a l parody, the parody of a u n i v e r s a l and uncapturable essence\"; p r o p e r l y regarded, the symbolic s t y l e i s a p i s a l l e r which i n v i t e s d i s b e l i e f because i t a d v e r t i s e s a nothingness which makes meaning p o s s i b l e . The symbol, then, i s always an unfortunate parody: i t i s not a s i g n concealing an absence, but a r i c h , even p r o f l i g a t e , excuse f o r a bare p o s s i b i l i t y that cannot be explained i n any s a t i s f a c t o r y way. I t has i t s p u b l i c equivalent i n s o c i e t i e s that are compelled to s t a r t w i t h nothing, or very l i t t l e . The potatoes are there, the pigeon discovered, but the s t o r y i s an i n v e n t i o n ex n i h i l o , snatched out of the a i r and run up, l i k e Abram's parody of a hut, w i t h the m a t e r i a l s to hand. The much-vaunted empty s i g n , the exhaustion of meaning, and so on, assume a new s i g n i f i c a n c e when viewed i n the context of t h i s marginalism: t h e i r emptiness i s cause f o r c e l e b r a t i o n , t h e i r s t o r y - t e l l i n g , t h e i r pretence, even when these i n c l u d e a measure of mimicry, speak an i n v e n t i v e n e s s . They are what make both l i f e and e x i s t e n c e bearable; not any supposed p l e n i t u d e behind t h e i r language, but the work (and the play) of the language i t s e l f i s of i n t e r e s t . One might have wished f o r greater invention or a wider ransacking here, but H a r r i s has not chosen to spurn a ready-made symbolic system. As f o r the s t y l e i n t o which i t i s worked, that i s h i s own, and i n i t s f a b r i c not u n l i k e Poseidon's home: \"created e q u a l l y by d e s t i n y and a c c i d e n t . \" Musing on i t s \"sacred comedy of m a t e r i a l s , \" which have been tra n s p l a n t e d from a Roman C a t h o l i c M i s s i o n u p r i v e r , Fenwick asks To what and whose s p i r i t d i d the house belong? Had i t been g r a f t e d from above (unconscious of i t s e l f ) on to the l a n d , or d i d i t possess a s e l f - c o n s c i o u s k i n s h i p and i d e n t i t y beneath? I t had an a i r both f o r e i g n and n a t i v e , i d e a l and p r i m i t i v e , at one and the same time; and yet i t seemed so p r e c a r i o u s l y and a b s o l u t e l y r i g h t , belonging so t r u l y i n t h i s n a t u r a l or unnatural context of landscape, that the thought of an i m p o s i t i o n , of pretentiousness of' a b s u r d i t y i n the l i f e of the crumbling b u i l d i n g , seemed e q u a l l y r i d i c u l o u s and impossible. In f a c t — i f i t had been the g i f t of an imposing high d i v i n i t y — i t bore a c e r t a i n generous conception, economic and s t i l l humane. There were no marks of exclusiveness--rather a s p i r i t of a l l -i n c l u s i v e p r i v a c y , the most welcome a r t i f i c e of humanity. What was at stake here was not the i n e v i t a b l e r u i n of an o l d house, but a p e r c e p t i o n of depth more l a s t i n g than time, the moral p r i v i l e g e and r i g h t of place. This was Poseidon's asylum and home. I t had acquired a s p e c i a l s e a l and p r i v i l e g e , the stamp of a m u l t i p l e t r a d i t i o n and h e r i t a g e (pp. 199-200). This \"most s o l i d (though d i s i n t e g r a t i n g ) \" house i s the forge and the emblem of H a r r i s ' s c o n t r a d i c t o r y s t y l e , a s t y l e which e f f e c t s what he c a l l s \"the p r i m i t i v e j u x t a p o s i t i o n of the unclean\" w i t h the c l e a n , of the f a n t a s t i c and the everyday, of ornament and breakage, of r e a l and s u r r e a l . The a l t e r n a t i o n between r e a l i s t i c and symbolic w r i t i n g i n The Secret Ladder i s a case i n p o i n t , and.it i s t h i s which repeatedly rescues passages of metaphysical f l o u n d e r i n g . At the very moment where d i f f i c u l t y would seem to have been enthroned, a t h r u s t of s t a r t l i n g l u c i d i t y w i l l 43 unseat i t . D i a l e c t o f t e n f u n c t i o n s i n t h i s way. In every one of the Guyana novels i t i s put to remarkable use, r e l i e v i n g or i n t e n s i f y i n g , d e f l a t i n g or d i s r u p t i n g , c a r r y i n g the n a r r a t i v e forward or back. The 44 \"many a gipsy phrase\" which Pater would hay.e.purged from good s t y l e i s e x a c t l y what H a r r i s , who e a r l y approved of \"doing v i o l e n c e to Standard E n g l i s h \" (SM p. 65), introduces to great e f f e c t . These are, of course, a l l r h e t o r i c a l d e v i c e s , but along w i t h the numerous other c o n t r a d i c t o r y i n t r u s i o n s and s p l i c i n g s , they c o n s t i t u t e an indecorous decorum, a mixture 45 of r h e t o r i c a l r e g i s t e r s which may w e l l offend readers of a p u r i s t kidney, not l e a s t those who p r e f e r t h e i r postmodernism unadulterated w i t h metaphor and meaning. H a r r i s i s e x p l i c i t : The p o i n t I want to make i n regard to the West Indies i s that the p u r s u i t of a strange and s u b t l e g o a l , m e l t i n g pot, c a l l i t what you l i k e , i s the mainstream (though unacknowledged) t r a d i t i o n i n the Americas. And the s i g n i f i c a n c e of t h i s i s a k i n to the European preoccupation w i t h alchemy, w i t h the growth of experimental s c i e n c e , the poetry of science as w e l l as of e x p l o s i v e nature which i s informed by a s o l u t i o n of images, agnostic h u m i l i t y and e s s e n t i a l beauty, r a t h e r than vested i n t e r e s t i n a f i x e d assumption and c l a s s i f i c a t i o n of things (TW pp. 32-33). I f there are moments i n The Secret Ladder when H a r r i s seems to have y i e l d e d to \"a f i x e d assumption and c l a s s i f i c a t i o n \" o f symbols borrowed a l l together, t h i s f i x i t y i s l e f t behind i n the l a t e r novels. One such, which represents a r e t u r n to Guyana unusual i n the more recent H a r r i s , i s Genesis of the Clowns (1977). The novel bears a c e r t a i n resemblance to The Secret Ladder, concerning as i t does the r e l a t i o n s h i p of a young surveyor to h i s crew, but there the resemblance ends. Lacking the c a r e f u l p l o t of the e a r l i e r n o v e l , i t l a c k s a l s o the t a i l o r e d and l a r g e l y d e r i v a -t i v e set of symbols. Here, the random s p e c u l a t i o n s of surveyor Frank W e l l i n g t o n f i n d t h e i r images i n a f a r more mundane sphere: homunculi and Gorgon's heads g i v e way to (or take t h e i r place among) a paytable, a market s t a l l , a dumpy l e v e l , a surveyor's p o l e . One noonday, W e l l i n g t o n meditates on h i s mechanic's w i f e , Ada. Hope had already eaten and stood l o o k i n g out to the l i n e of the t i d e . He held an umbrella over my dumpy l e v e l to preserve the bubble on. the instrument from s h r i n k i n g e x c e s s i v e l y under the f i r e of the sun. Cummings Day stood beside her w i t h a twelve-foot t a l l s t a f f , b l a c k and red decimal numbers on a white background; he leaned h i s forehead upon i t so that i t possessed him l i k e an elongated mask, a v e r t i c a l p o l e , a science.... 'I wonder,' I thought to myself as broad d a y l i g h t dreamed of M i s t r e s s Ada's naked f l e s h , 'how deeply rooted are we i n a datum l i n e of space to which we remain i n part unconscious w i t h i n the b l a c k / r ed land and the sea's h a r l e q u i n f i r e ' (p. 94). At sunset, a f t e r the day's work, he sees her again i n the crowded v i l l a g e market; then, h i s a t t e n t i o n i s caught by h i s surroundings: The marketplace was crowded. The v o i c e of the sea stood at my back l i k e a rough crowd.on the coast threatening w a l l and defences. The ground i t s e l f moved u n t i l the market swam. Then as I looked away from b l a c k / r e d s t a l l s w i t h h a r l e q u i n meat and f r u i t l i k e a harvest of the sea I was s t r u c k by an absolute p r i n t of s t i l l n e s s i n the vacant evening overhead. The leaves on the t r e e s were extended i n t o the palm of sunset. Not a f e a t h e r , not a f i n moved. A d e n s i t y of creatures seemed bound there i n space as i f the globe i t s e l f had moved to stand on t i p t o e w i t h i n the heterogenous body of f i s h , b i r d , gods, goddesses f o r s a l e a l l r e i n e d to an impulsive root f o r r e d r e s s , undress of f a t e s (pp. 95-96). M i s t r e s s Ada i s indeed a \" f e r t i l i t y goddess,\" but i t i s what the language does r a t h e r than what she represents which matters. By i t s \" s o l u t i o n of images,\" t h i s language produces that f e c u n d i t y of \" e x p l o s i v e nature\" which H a r r i s invokes. Hence the bounty of the marketplace, the \" d e n s i t y of c r e a t u r e s \" and t h e i r heterogeneity. In t h i s process, the metaphoring i s as o f t e n that of mute nature as i t i s anthropomorphic. On the one hand, there i s the n e u t r a l t r a n s f e r of category a t t r i b u t e s at work i n the \"palm of sunset,\" or the c o l l a p s e of i d e n t i t i e s by which Day's s t a f f possesses him as mask, pole and s c i e n c e . On the other, there i s the unpredictable recurrence of the decimal benchmarks i n the evening, l i k e spots imprinted on the r e t i n a by the f i e r c e l i g h t of noon, an endless peopling of the landscape by the h a r l e q u i n congress of b l a c k \" M i s t r e s s Ada's naked f l e s h \" and the \" f i r e of the sun.\" Both courses are p o s s i b l e because the n a r r a t i v e i s n e i t h e r e x c l u s i v e l y n a t u r a l i s t i c nor r e l e n t l e s s l y symbolic, a c o n t r a -d i c t i o n epitomised i n the p r o l i f e r a t i o n of the oblique (\"black/red\") as a s t y l i s t i c f e a t u r e of the l a t e r H a r r i s . In t h i s way, what might seem to be an overt d e n i a l of r h e t o r i c which admits i t a l l the same by some tradesman's entrance, i s i n f a c t n e i t h e r indulgence nor abstinence. I t i s r a t h e r a kind of c a r n i v a l l i c e n s e , a tumbling i n which the concept of r h e t o r i c comes to be deflowered. I I I . Experiment and N a r r a t i v e I am not a P l a t o n i s t . But I was reminded r e c e n t l y of that most enigmatic work of P l a t o The Timaeus w i t h i n which a S e n i o r i t y of Forms i s propounded as antecedent to the d i v i n e w i l l — a n enigmatic s e n i o r i t y which defeated C h r i s t i a n P l a t o n i s t s i n t h e i r attempt to modify i t i n accordance w i t h t h e i r b a s i c dogma. The cu r i o u s p r i o r i t y of Forms to the mind and w i l l of God i n The Timaeus (regarded as h e r e t i c a l by the Church Fathers) may be i n t e r p r e t e d , no doubt, i n s e v e r a l ways but I would suggest our v i s u a l i z i n g i t . . . a s a p o e t i c warning to look through the r i t u a l p r o p r i e t o r s of the Universe f o r .a s c a l e of s e l f - d e c e p t i o n i n s e l f - d e f i n i t i o n — a s c a l e that a s s i s t s us to bind h u m i l i t y and c r e a t i v i t y together i n t o an e s s e n t i a l caveat of the imagination (NP p. 150). These cautionary words, which appear at the c l o s e of H a r r i s ' s esaay, \"The N a t i v e Phenomenon,\" can be pressed to serve more than t h e i r immediate purpose. In t h e i r c o ntext, they embody what might p r o p e r l y have been c a l l e d H a r r i s ' s f i r s t p r i n c i p l e were not the d o c t r i n e of primacy i t s e l f i n q uestion. That p r i n c i p l e i s stated f o r t h r i g h t l y both here and e a r l i e r i n the same essay. Taken out of context, as s u r e l y i t begs to be taken, the S e n i o r i t y of Forms performs another task, and t h i s without et y m o l o g i c a l s t r a i n , that of f u r n i s h i n g a formal paradigm of the n a r r a t i v e s t r u c t u r e of H a r r i s ' s novels. By such a paradigm, the method of these novels i s . one where the n a r r a t i v e proceeds through a s e r i e s of t e n t a t i v e t h r u s t s i n the v o i d , w i t h m a t e r i a l a s s i s t a n c e from a past which may d e l i m i t but never determine present forms. But i f these present c o n s t r u c t s do not have a s i n g l e and e x c l u s i v e o r i g i n , whether i n the author or i n h i s fund of pa t t e r n s s o c i a l or l i t e r a r y , n e i t h e r are they s u f f i c i e n t i n themselves, being at every stage q u a l i f i e d by one another. In terms of the metaphor, i f not s t r i c t l y of the Timaeus, there i s always an unmaking s t r u c t u r e of otherness, a margin of indeterminacy, a sen i o r form. This i s the sum., of H a r r i s ' s Platonism; i n f i n d i n g more we misread the caveat. We begin w i t h a r e v e r s a l . Where i n the previous chapter we c o n s i -dered the surface of language, here we w i l l examine the innards of the t e x t , those s t r u c t u r e s which run as i t were crosswise to the prose, r e g u l a t i n g i t s advance and guiding i t s d i r e c t i o n . In passing from s t y l e to s t r u c t u r e , we may r e h a b i l i t a t e along the way the concept of r h e t o r i c : not the r h e t o r i c of language but the r h e t o r i c of the t e x t i s now intended by that word, and where we saw H a r r i s f l o u t the one, we now see him f l a u n t the other. We w i l l leave language behind, then, though i t w i l l not be easy or even at a l l times p o s s i b l e , i n order to consider the l a r g e r u n i t s of n o v e l - w r i t i n g , those which have come, s i n c e Wayne Booth, to be c a l l e d 2 the r h e t o r i c of f i c t i o n . I t i s t h i s r h e t o r i c which H a r r i s l a y s bare through a v a r i e t y of asymmetrical devices, i n the i n t e r e s t of that l a r g e r a n t e r i o r i t y whose v i r t u e we have j u s t heard him expound. The r h e t o r i c of f i c t i o n s has, of course, been much di s p l a y e d of l a t e , so much so that a mass r e t u r n to d i s c r e e t n a r r a t i v e \"showing\" i s d a i l y expected. H a r r i s ' s n a r r a t i v e s t r i v e s f o r n e i t h e r pure mimesis nor pure d i e g e s i s , n e i t h e r f a i t h f u l i m i t a t i o n nor u n d i l u t e d r e c i t a t i o n . His l a y i n g bare of the t e x t ' s r h e t o r i c proceeds not through a brazen \" t e l l i n g \" but almost i n a d v e r t e n t l y , as i f declamation mattered even l e s s than the s u r r e p t i t i o u s p u l l i n g of s t r i n g s . This inadvertency should not be misread as insouciance: r a t h e r , i t springs from an awareness that absolute s t r u c t u r e can masquerade e q u a l l y as i l l u s i o n and v e r i s i m i l i t u d e or as s e l f -consciousness and performance. At the same time, the novels' a f f i n i t i e s are decidedly modernist, and i t i s by means of a modernist a e s t h e t i c that t h e i r n a r r a t i v e method deserves to be analysed. There i s now no dearth of grammars of n a r r a t i v e by which t e x t s ancient and modern may be parsed. The best known among these draw t h e i r i n s p i r a t -i o n from e a r l i e r f o r m a l i s t morphologies of d i v e r s e c u l t u r a l o b j e c t s from the f o l k t a l e to k i n groups, and seek by c o r o l l a r y to reduce complex l i t e r a r y systems to t h e i r f u n c t i o n a l u n i t s , u n i t s which i n many cases are d i v i s i o n s of apparently i r r e d u c i b l e e n t i t i e s i n the o r i g i n a l . Hence the rococo taxonomies and e n d l e s s l y r a m i f i e d stemmata of much recent 3 n a r r a t i v e a n a l y s i s . Hence a l s o the p r o l i f e r a t i o n of terminologies by which these newly discovered n a r r a t i v e c e l l s are described, terminologies which, however s a l u t a r y t h e i r i n t e n t , by t h e i r sheer m u l t i p l i c i t y begin i n competition and end i n confusion. So we w i l l shut .. anachronies and ani s o c h r o n i e s , o b l i g a t i v e s and o p t a t i v e s , f u n c t i o n s and i n d i c e s i n a box, there to await the Pandoras of another age, and make do w i t h c e r t a i n b a s i c m a t e r i a l s : s t o r y , n a r r a t i v e , and n a r r a t i n g , though f o r the most 4 part we w i l l d eal w i t h the middle item, n a r r a t i v e proper. The d i s t i n c t i o n between s t o r y and n a r r a t i v e i s p l a i n l y put by C h r i s t i a n Metz: \"There i s the time of the thi n g t o l d and the time of the n a r r a t i v e (the time of the s i g n i f i e d and the time of the s i g n i f i e r ) . \" ' A s t o r y , that i s to say, f o l l o w s a causal sequence such as i t s s i g n i f i e d might i n the r e a l world, w h i l e a n a r r a t i v e guards i t s own order. A n a r r a t i v e , f o r example, may w e l l begin w i t h the execution of i t s hero, but i t i s a r a r e man, be he never so h e r o i c , who begins h i s adventures i n t h i s way. So much i s unremarkable; what Metz goes on to say i s of greater i n t e r e s t . The d u a l i t y between the time of the s t o r y and time of the n a r r a t -i v e , he continues, \" i n v i t e s us to invent one time scheme i n terms of another time scheme.\" Metz i s speaking of f i l m , but e q u a l l y i n f i c t i o n i t i s the t e n s i o n between the two schemes which generates much of the reader's i n t e r e s t i n a novel and indeed makes p l a u s i b l e the category of n a r r a t i v e i t s e l f . F i n a l l y , there i s the time of the n a r r a t i v e u t t e r a n c e , the n a r r a t i n g , a f u r t h e r source of t e n s i o n , f o r now a t h i r d conceptual surface presents i t s e l f , though one whose precarious l i f e , eked out at a bare remove from the n a r r a t i v e , reminds us of the f r a g i l i t y of a l l our f i c t i o n a l c a t e g o r i e s . N a r r a t i v e , l i k e s t o r y , i m p l i e s a succession, but where a s t o r y i s bound to a f i x e d l i n e a r i t y , n a r r a t i v e may do as i t pleases w i t h the a c t i o n i t s i g n i f i e s . I t i s a matter of p r e s e n t a t i o n , and though i t may choose to reproduce a sequence of events, i t may e q u a l l y produce that sequence anew. So where we saw s t y l e produce the surface of an event or gesture i n such a way as to d e f a m i l i a r i s e i t so that i t i s experienced as i f f o r the f i r s t time, we now expect to see n a r r a t i v e produce a sequence of events and gestures i n such a way as to d i s o r d e r them and prevent our being l u l l e d i n t o a secure f o u r - d i m e n s i o n a l i t y . To t h i s end the modern n o v e l i s t has deployed i r r e g u l a r blocks of a c t i o n , s h i f t i n g p e r s p e c t i v e s , m u l t i p l e l e v e l s of n a r r a t i o n , a v a r i a b l e locus of n a r r a t i n g , and so on, a l l of which devices occur as planes whose surface l i e s against the g r a i n of s e q u e n t i a l i t y . Now the u n f o l d i n g of a s t o r y i s o r d i n a r i l y a matter of t i m e — t h e and then of the a c t i o n — b u t time i s not a l l of n a r r a t i v e , s i n c e a c t i o n occurs i n space and t h i s a p p l i e s not only to the realm of the s i g n i f i e d but that of the n a r r a t i n g i t s e l f . A l l of the metaphors we have used h e r e — b l o c k , p e r s p e c t i v e , l e v e l , l o c u s , p l a n e — w i l l be seen to evoke s p a t i a l i t y , and t h i s not because time i s made v i s i b l e by these means alone but because any attempt to examine a m o b i l i t y must stop i t i n i t s t r a c k s or despair of an exact d e s c r i p t i o n . Northrop Frye's o p p o s i t i o n of d l a n o i a or meaning and s i m u l t a n e i t y to mythos or n a r r a t i v e and movement i s u n h e l p f u l here f o r we need a theory which does not put n a r r a t i v e and s i m u l t a n e i t y i n opposite camps. Nor i s the concept of s p a t i a l form an answer, though i t comes c l o s e , f o r the numerous c r i t i c i s m s of a h i s t o r i c i t y which have been brought against i t do have some b a s i s . ^ We are saved the t r o u b l e of l o o k i n g outside f i c t i o n f o r a model by the f a c t that much contemporary f i c t i o n has i t s e l f turned away from the evocation of tempora-l i t y c h a r a c t e r i s e d , f o r example, by stream-of-consciousness w r i t i n g . \" I t h i n k , \" says W i l l i a m Burroughs, i n a remark which sums up the present g r e a c t i o n , \"the f u t u r e of f i c t i o n i s i n space, not time.\" Space i s indeed the content, or b e t t e r , the subject of H a r r i s ' s f i c t i o n s . I r e j e c t \"content\" because the word suggests a r e c o g n i z a b l e r e a l i t y worked by some mimetic i l l u s i o n i n t o a formal frame. Quite the opposite i s intended by H a r r i s ' s usage, f o r the s i g n i f i e d space of the novels i s a matter so dense as to always conceal some i n t r a n s i g e n t p e r s p e c t i v e behind i t s e m p i r i c a l surface. We s h a l l see that t h i s i s not a f l i g h t from experience, but f o r the moment we must r e t u r n to the use of t h i s space as a model. The s e n i o r i t y of forms now takes on a f u t h e r s i g n i f i c a n c e , f o r i t becomes an emblem of the way i n which there i s always a s t r u c t u r e of space p o s i t e d around the given. The s t r u c t u r a l p r i n c i p l e of the novels i s one of a n t e r i o r i t y r a t h e r than simple s e q u e n t i a l i t y , an a n t e r i o r i t y to be thought of as s p a t i a l r a t h e r than temporal, beyond r a t h e r than before, i n s h o r t , an a l t e r i t y . This continuous p o s i t i n g of an otherness which unmakes the whole, i s enacted i n the machinery of the novels and i s i n i m i c a l to both s t r u c t u r e and a n t i s t r u c t u r e . Hence H a r r i s ' s warning that we \"see through the v a r i o u s dogmatic p r o p r i e t o r s of the globe w i t h i n a p l a y of c o n t r a s t i n g s t r u c t u r e s and a n t i - s t r u c t u r e s \" (NP p. 148). The s p a t i a l i t y of the novels, then, i n v i t e s a kind of g e o l o g i c a l c r o s s -s e c t i o n , only t h i s cut must t r a v e r s e more than one plane so as to s a t i s f y the requirements of a n t i - s t r u c t u r e as w e l l as s t r u c t u r e . Where synchronic s t r u c t u r e attempts to c o l l a p s e time i n t o a s i n g l e s u r f a c e , a m u l t i p l i c i t y of planes preserves something of the b e w i l d e r i n g m u l t i - d i m e n s i o n a l i t y of a s t r u c t u r e i n motion. A m u l t i p l e synchrony cannot, i t i s t r u e , be s a i d to have access to \" h i s t o r y \" but then n e i t h e r does a diachrony, whose s t r u c t u r e s are no more a genuine rendering of time than i t s f i g u r a l r e p r e s e n t a t i o n s are an a u t h e n t i c rendering of space. We d e a l always, that i s to say, w i t h conventions, j u s t as the l i n e a r i t y of the t e x t i s always w i t h us, and as Gerard Genette remarks, \" e a s i e r to deny i n theory 9 than e l i m i n a t e i n f a c t . \" To t h i s degree even the most r a d i c a l of experimentalisms are confined by circumstance and dependent on r h e t o r i c , a s t a t e which the post-Boothian reader w i l l recognise but not scorn. I f the l a r g e r u n i t s of n a r r a t i v e are s t r u c t u r a l l y juggled and yet bound by the tyranny of the l i n e , the reader p e r f o r c e experiences them s e q u e n t i a l l y . His next r e s o r t must be to d i s c o v e r how these u n i t s r e act upon each other, whether by reinforcement or by negation, and h i s i n v e s t i -g a t i o n i s advanced i f he r e c a l l s the f u n c t i o n of images i n the H a r r i s i a n t e x t . The image, we remember, was a creature of i n t e r i o r space, the token of e c l i p s e d p e r s p e c t i v e s which i t served to disclose.\"*\"'\"1 So conceived, i t was an agent of d e s t a b i l i z a t i o n : \"an asymmetrical power of images,\" H a r r i s wrote, \" i s one which cannot be sustained by the conventional n o v e l \" (IN p. 142). In the same way as the image reacted w i t h and upon i t s c o n t r a d i c t o r y neighbours, the l a r g e r s t r u c t u r e s of the f i c t i o n c o n t i n u a l l y make and unmake each other i n a discontinuous s e r i a l i t y which d i s r u p t s the i l l u s i o n of a whole present or past and leaves a way open f o r a form to come. As H a r r i s puts i t i n another, and t h i s time h i s t o r i c a l context, the \" d i s l o c a t i o n or i n t e r i o r space serves t h e r e f o r e as a c o r r e c t i v e to a uniform cloak or documentary status of i m p e r i a l i s m \" (HFM p. 11). We w i l l come to the h i s t o r i c a l use of t h i s mode i n due time; f o r the present the d i s l o c a t i o n must be seen to serve a s t r u c t u r a l (or a n t i - s t r u c t u r a l ) purpose by c o r r e c t i n g the uniform and c o n s o l i d a t i n g a c c r e t i o n s of r e a l i s t i c n a r r a t i v e . The p l a y of forms, that i s , creates the f u t u r e of the t e x t , and t h i s not by a studied and cumulative o r c h e s t r a t i o n of s t r u c t u r e b u i l d i n g upon s t r u c t u r e , but out of a 'vacancy' i n nature w i t h i n which agents appear who are t r a n s l a t e d one by the other and who ( i n a k i n d of s e r i a l i l l u m i n a t i o n — i f ' s e r i a l ' i s the r i g h t word) reappear through each other, i n h a b i t each other, r e f l e c t a burden of n e c e s s i t y , push one another to plunge i n t o the unknown, i n t o the t r a n s l a t a b l e , transmutable l e g a c i e s of h i s t o r y . Their uniqueness l i e s i n t h i s c u r i o u s openness to o r i g i n -a l i t y as w e l l as change... (IN p. 146). :. I t i s ' i n this.jsense that the l i n e a r i t y of n a r r a t i v e i s overcome: s t r u c t u r e s are q u a l i f i e d and even negated by those that surround them, each i n s t a l l m e n t already f o r e s t a l l e d . But might i t be that what was won from l i n e a r i t y has been surrendered to c i r c u l a r i t y ? The Secret Ladder, i t w i l l be r e c a l l e d , ended w i t h the E l i o t i c r e f r a i n : \"In our end...our end...our end i s our beginning...beginning...beginning\": a r e f r a i n which rounded o f f not only the novel but the t e t r a l o g y which has come to be c a l l e d the Guyana Quartet. Lest the whole too r e a d i l y round upon i t s e l f , H a r r i s ' s next novel,Heartland, extends and asymmetrically breaks the p a t t e r n , as the f i f t h i n a quartet. I t stands i n r e l a t i o n to the preceding novels as a se n i o r form, at times e x p l i c i t l y c a l l i n g i n t o question t h e i r 11 claims to the t r u t h . We must not, however, make too much of t h i s metaphor u n t i l we have seen i t at work. \" I t i s easy to make propaganda of i d e a s , \" H a r r i s warns. \"One may c l a i m a n o v e l i s t i s doing t h i s , doing t h a t , doing the other, when i n f a c t he may not be doing what i s claimed f o r him at a l l w i t h i n the n a r r a t i v e p a t t e r n he uses\" (SI p. 45). With t h i s i n mind we may turn to the n a r r a t i v e p a t t e r n of H a r r i s ' s f i f t h n o vel. In a canon of short works, Heartland i s one of the^shorter;: . i t also..'\" has one of the smallest c a s t s . Four f i g u r e s make t h e i r appearance on i t s stage (although others are a l l u d e d t o ) : Stevenson, a watchman on a wood grant above a w a t e r f a l l ; K a i s e r , a l o r r y d r i v e r (who looks l i k e both h i s namesakes from The Far Journey of Oudin); a pork-knocker or lone prospector, d a S i l v a (one of the twins from Palace of the Peacock); and an Amerindian woman, Pet r a (who i s the M a r i e l l a of H a r r i s ' s f i r s t n o v e l ) . The f a t e s of these characters are played out on a s i g n i f i c a n t landscape whose power, amounting to dominance, commands the very t i t l e of the novel. Palace of the Peacock had had an indeterminate s e t t i n g , but one perhaps not f a r from that which we are about to enter, w h i l e the three subsequent novels of the Quartet showed r e p r e s e n t a t i v e areas and communities of Guyana: the c e n t r a l croplands, the Pomeroon of the west, and the Canje headwaters i n the east. Heartland i s set at the gateway to the i n t e r i o r ; i n l a t e r novels H a r r i s w i l l penetrate deeper i n t o Guyana, but f o r the present t h i s i s the farthest., i d e n t i f i a b l e p o i n t . I t i s here that \"the sl e e p i n g [Cuyuni] r i v e r l o s e s i t s poise and drops l i k e a smoking breath down the face of the Kaieteuran escarpment\" (p. 70). This escarpment i s a d i v i d e and a poi n t of departure, j u s t as Kartabo P o i n t , downstream from the f a l l s , marks \"the beginnings of a new legendary c o n t i n e n t a l o f f s p r i n g born of 12 many ra c e s \" (p. 66). The s t o r y of the novel i s e a s i l y t o l d . Zechariah Stevenson, j n r . , i s i n self-imposed e x i l e from the c i t y f o l l o w i n g a f i n a n c i a l scandal that involved h i s f a t h e r ' s company, h i s m i s t r e s s , M a r i a , and her husband, the company's accountant. Stevenson b a r e l y has time to d i g e s t the news of h i s f a t h e r ' s unexplained death, when the scandal breaks. Stunned, he nonetheless refuses to c r e d i t Maria's involvement i n the f r a u d , and b e l i e v e s she w i l l r e t u r n to him from B r a z i l , where she and her husband have f l e d . Only a f t e r a year i n h i s f o r e s t r e t r e a t does he come to s t r i p himself down to a knowledge of h i s own timorous s e l f - d e c e p t i o n and i r r e s p o n s i b i l i t y . In t h i s process he i s a s s i s t e d by another pawn of fortune who i s \" t r y i n g to f i n d me s e l f - p o r t r a i t \" (p. 20), the l o r r y d r i v e r K a i s e r . One morning, K a i s e r , whose job i t i s to b r i n g s u p p l i e s from Lower Kamaria to the depot at Upper Kamaria, leaves some r a t i o n boxes f o r a d a S i l v a , \" f u n n i e s t pork-knocking guy i n the world\" (p. 16). Stevenson i s s c e p t i c a l when he le a r n s that the boxes are under l o c k and key, but a f t e r d a S i l v a has passed by h i s l a n d i n g , stopping f o r a cup of co f f e e and a mocking sermon, he f i n d s t h a t the pre c a u t i o n was necessary but f u t i l e : the r a t i o n s are gone. Where he had l e f t a note f o r d a S i l v a to f i n d on h i s way back from the depot, d a S i l v a i n turn has l e f t a note at the depot to say that he has gone to rep o r t the t h e f t . Stevenson sets out a f t e r him, f o l l o w i n g the l i n e of portage around the f a l l s . Half way down he n o t i c e s the body of a man lodged i n the depths of a r a v i n e . I t i s d a S i l v a . The t h i e f , i t turns out, was P e t r a , who i s f a r gone i n pregnancy, got w i t h c h i l d i t i s rumoured by d a S i l v a h i m s e l f . D i s c o v e r i n g t h i s , her t r i b e have ejected her and ambushed d a S i l v a . Reaching K a i s e r ' s depot at the foo t of the f a l l s , Stevenson f i n d s P e t r a i n labour and t r i e s to help d e l i v e r her c h i l d . Afterwards, he takes a f i s h i n g l i n e down to the r i v e r ; when he r e t u r n s , mother and c h i l d have vanished. Stung, he sets once more upon a course of r e c r i m i n a t i o n and se l f - e x a m i n a t i o n u n t i l he a r r i v e s at l a s t a t the beginning of understanding. Now he sets out on a road which leads f a r t h e r and f a r t h e r i n t o the i n t e r i o r u n t i l he disappears i n the j u n g l e s of the h e a r t l a n d , l e a v i n g only fragments of l e t t e r s to Maria and three scorched poems. This i s s t o r y of Heartland; by way of passing to i t s n a r r a t i v e , we may note that the predominant a c t i o n of the novel i s a journey, or many journeys, and may be summed up simply as \" l o o k i n g f o r . \" Indeed at one p o i n t we f i n d Stevenson l o o k i n g f o r d a S i l v a who i s l o o k i n g f o r K a i s e r who i s l o o k i n g f o r s u p p l i e s . Hence t h i s s e r i e s of notes: SHALL TRY TO FOLLOW ANCIENT LINE TO DEPOT. HOPE TO MAKE IT AND BACK BY NOON. DINGHY GONE FROM LANDING (p. 51). SOMEBODY STEAL MY RATIONS. WHO? GONE TO TELL KAISER (p. 55). CLOSED, GONE TO COLLECT SUPPLIES (p. 61). Gone. The word t o l l s through the t a l e u n t i l we can almost p r e d i c t the i s s u e when Stevenson r e t u r n s to K a i s e r ' s house to f i n d P e t r a : gone. F i n a l l y , Stevenson himself vanishes. Doubtless, i n the t h i n l y populated i n t e r i o r such absences are to be expected, and one might f i n d sound reasons f o r them w i t h i n the universe of the s t o r y . But the p a t t e r n of f l i g h t and e x i l e has been set up and r e q u i r e s a c l o s e r s c r u t i n y at the l e v e l of the n a r r a t i v e . Where the s t o r y began i n the c i t y a year and more before the main body of the a c t i o n , the n a r r a t i v e begins and ends i n the f o r e s t . I t s antecedents are not recounted u n t i l one m orning—the f i r s t day of the n a r r a t i v e — Stevenson has paddled downstream from h i s post to the depot at the top of the f a l l s where he meets K a i s e r and l e a r n s that d a S i l v a i s to pass that way. When Kai s e r has gone, Stevenson begins to r e f l e c t on the events 'which l e d him t o \" t h i s outpost and a seam i s opened between the present of the n a r r a t i v e , i n d i c a t e d by a s t r i n g of i t a l i c i s e d nows, and and the past of the s t o r y , a n ' ; i t a l i c i s e d then. What i s of i n t e r e s t i s of course not the existence of t h i s o p p o s i t i o n , which few novels exclude, but the frequency of the s h i f t s and the urgency of the d i s t i n c t i o n . C l e a r l y the n a r r a t i v e now i s more important than the s t o r y ' s then, even though the l a t t e r included most of Stevenson's residence i n the f o r e s t : Indeed the choice of the heartland had not been h i s . . . u n t i l now...for what had r e a l l y s t a r t e d i n an accident and the p u r s u i t of mere expediency was only now, today, i n process of confirming i t s e l f i n retrospect as h i s own grave stake and risk...Would he be confronted f i n a l l y by an i m p o s s i b i l i t y of escaping from h i m s e l f , l i v i n g or dead, or would he discover an i d e n t i t y of abandonment which would inform him and some-times lead him l i k e h i s own shadow i n t o the s u b t l e s t r e a l -i z a t i o n of time? (p. 21). \"Retrospect\" and \" r i s k , \" \" i d e n t i t y \" and \"time\" we w i l l d i s c o v e r to be s i g n a l words, even key words, f o r Stevenson has now been launched upon an e n t e r p r i s e of memory and i d e n t i t y on t h i s f i r s t day. K a i s e r ' s f a r e w e l l was loaded: \"Why, beggars and pork-knockers l i k e d a S i l v a ! You need them and they need you l i k e s k i n need bone. Man need man, Mr. Stevenson.\" K a i s e r ' s eyes opened and f l a r e d and surveyed the f l a g of grass behind which the p a r a d o x i c a l key of a l l substance he guarded was hidden (pp. 20-21). Stevenson's ruminations begin immediately upon the n a r r a t i v e space which f o l l o w s K a i s e r ' s departure, and continue interwoven w i t h the present (set p a r e n t h e t i c a l l y o f f ) u n t i l he i s drawn i n t o the woods f o r a k i n d of i n i t i a t i o n by which the temporal i s given substance. He i s about to reach f o r the key to the depot when he hears \"a sharp s p l i n t e r i n g crack l i k e a dry branch underfoot\" (p. 29) and springs about. Deciding to i n v e s t i g a t e , he f o l l o w s a f r e s h t r a i l along which K a i s e r has been hunting, and i s l e d by \"the mood of the p l a c e \" to r e f l e c t on those who have been there before him. Nothing had changed over the c e n t u r i e s . Long before European c o l o n i z e r — P o r t u g u e s e , Spanish, French, Dutch, E n g l i s h — a n d A f r i c a n c o l o n i z e d a r r i v e d and ventured i n t o nameless t r i b u t a r i e s , t h e i r pre-Columbian s p i r i t u a l ancestors had been on the selfsame ground, To l t e c or Peruvian adminis-t r a t o r s or merchants w i t h t h e i r attendants and middlemen. They had apparently f a i l e d i n t h e i r m i s s i o n to catch the u n r e a l i t y of themselves which they encountered i n the rude nomadic t r i b e s they came to rescue and c i v i l i z e , who f l i t t e d l i k e ghosts under a more compulsive baton, born of the s p i r i t of p l a c e , than any human conqueror could devise (p. 30). He imagines the shamanistic r i t e s by which these predecessors sought to discover t h e i r heartland,but r e a l i s e s that to experience t h e i r heights of i n t o x i c a t e d limbs was to s u f f e r as w e l l an acute f a l l i n t o the v o i d . The golden age they wished to f i n d — t h e Palace of the Peacock—may never have e x i s t e d f o r a l l anyone knew. Existence now was what counted. And t h i s e x i s t e n c e was becoming r e a l f o r Stevenson...(p. 31) Brought up short by these r e f l e c t i o n s Stevenson experiences h i s own f a l l i n t o the v o i d : he f i n d s he has l o s t h i s way. A \"panic of a s s o c i a t i o n s \" g r i p s h i s mind and he s u f f e r s a s e i z u r e i n which h i s body i s contorted \"Into every alarming shape, snake and man and beast\" and h i s c l o t h e s are \"ripped to s c a l e s . \" Afterwards, he has the sensation that time has been \" r e t r i e v e d . \" In d i s c o v e r i n g \"existence now\" Stevenson has had to brush w i t h the here of t h i n g s ; he must s t i l l t a c k l e the not here before f i n d i n g h i s \" i d e n t i t y of abandonment.\" In order to \"catch the u n r e a l i t y \" of h i m s e l f , he must discover a v a l i d otherness, even when the l o o k i n g f o r means f i n d i n g nothing: the journey i t s e l f i s a motion away from s e l f - a b s o r p t i o n and nothingness i s p r e c i s e l y the g o a l , or one p o l e , of the quest. This i s the p a t t e r n we have seen the n a r r a t i v e produce by i t s successive \"gones, and i n the same way suspense (and even mystery) f u n c t i o n to d i s p l a c e time by w i t h h o l d i n g knowledge of what i s now or next. At the l e v e l of s t o r y or event, the crack of the branch i s probably caused by P e t r a , who i s watching the depot f o r her chance. But t h i s i s concealed (and even r a r e f i e d ) by the n a r r a t i v e : P e t r a i s not introduced u n t i l Book Three, where she i s described as \"the muse of the j u n g l e \" (p. 62). For the moment, Stevenson i s v i s i t e d only by the \" s p i r i t of p l a c e , \" and the f o l l o w i n g day at h i s own landing he has \"the dark impression of someone walking across the c l e a r i n g \" (p. 45). While he dozes, a shadow f a l l s on the j u n g l e and h i s dinghy i s freed from i t s moorings by \"an arm of spray.\" This s t r u c t u r e of displacement a l s o g i v e s form to the c o n s o l a t i o n s which the s t o r y p r o v i d e s , and the f i r s t of these i s s e r i a l i t y . Recognizing now \"the genuine human i m p o s s i b i l i t y of breaking through beyond o n e s e l f \" (p. 48), Stevenson f e e l s compelled to abandon a l e t t e r he has been w r i t i n g to M aria, motivated, he sees, by a k i n d of s e l f - g r a t i f i c a t i o n . In place of t h i s d e s i r e there comes by degrees a sense of the i n t r i c a t e web of d i s i n t e r e s t e d n e s s which binds him to others: Who was i t that fed one (the anonymous midwife and middleman of the ages) and who the person one helped, i n t u r n , to feed, possessed an answer e q u a l l y i n the s p i r i t of the jung l e as i n the spectre of d i s m a n t l i n g a rose (p. 50). Stevenson's l e t t e r r o t s at the bottom of the dinghy that w i l l now be used by someone he does not know. \"Man need man,\" as K a i s e r s a i d , but i t i s not always c l e a r j u s t whom one i s bound t o , and by what t i e s of debt. The message was d r i v e n home by d a S i l v a : \"everybody's death belong to everybody's l i f e \" (p. 43), so that innocence and g u i l t become c u r i o u s l y enmeshed. In these circumstances, s a c r i f i c e assumes a c e r t a i n s i g n i f i c a n c e , but a s a c r i f i c e emptied of sentiment and s a t i s f a c t i o n , f o r the web of dependence i s spun upon anonymity. One dies i n another's p l a c e , as the d a S i l v a whose twin k i l l e d Cameron i n Palace of the Peacock, d i s c o v e r s here. When Stevenson f i n d s h i s corpse at the bottom of the r a v i n e , pinned between two boulders, \" s t a r i n g , suspended between d r e a d f u l compassion and c u r i o s i t y , half-monkey, half-man,\" i t i s some moments before he r e a l i s e s that the body i s indeed the pork-knocker's: \" I t was d a S i l v a a f t e r a l l who stood s t a r k and dead ..though so changed i n twenty-four hours he could have been K a i s e r or Cameron or Stevenson h i m s e l f \" (p. 58). But the moment and the mode of d a S i l v a ' s death are not described u n t i l the l a s t quarter of the n o v e l , and then i n an extended parenthesis spanning seven pages (73-79). W i t h i n t h i s loop, the blow i s a r e c u r r i n g one; i n the course of i t s many nows i t t r i g g e r s i n d a S i l v a a r e c o l l e c t i o n of h i s mongrel dog which died the day of h i s own recovery from a deathly f e v e r , \" d i g e s t i n g h i s mortal ailment.\" The n a r r a t i v e ' s f a r - f l u n g network of connections has come to r e f l e c t those correspondences which the s t o r y d e s i r e s f o r i t s f u l f i l m e n t . There i s another plane upon which t h i s web of indebtedness may be traced i n the n a r r a t i v e , and t h i s i s h i n t e d at the primary d i v i s i o n s of the n o v e l , i t s three books, e n t i t l e d \"The Watchers,\" \"The Watched,\" and \"Cre a t i o n of the Watch.\" Pe r s p e c t i v e i s already b u i l t i n t o these headings-,-but we s h a l l see that the problem i s more complicated than the t r i p a r t i t e s t r u c t u r e suggests. Although the poin t of view or \" f o c a l i z a t i o n \" of the n a r r a t i v e i s l a r g e l y Stevenson's, we have from time to time seen him and the other watchers watched i n t h e i r t u r n . Again, although we have marked a d r i f t towards \"pl a c e \" i n the n o v e l , i t i s s t i l l w i t h the landscape's surface r a t h e r than i t s depths that we d e a l . This being so, any unmaking of s t r u c t u r e must proceed h o r i z o n t a l l y , d e a l i n g w i t h angles r a t h e r than l e v e l s . And i t i s here that we f i n d the l i m i t e d cast of Heartland begin to widen, f o r i t i s as i f the play of pe r s p e c t i v e s i n t h i s novel were not bound by the four characters at a l l but extended beyond the species to a l l nature. This i s to be expected of a novel set i n a s o l i t u d e of bush, but there are other reasons why we should not too q u i c k l y diagnose a p a t h e t i c f a l l a c y at work. I t i s i n f a c t q u i t e the reverse: the p r o l i f e r a t i o n of p e r s p e c t i v e s suggests a r e a l i t y that i s never to be wholly grasped by an i n d i v i d u a l p e r c e i v i n g s u b j e c t , a r e a l i t y which so f a r from r e f l e c t i n g h i s p e c u l i a r needs, makes i t s own i n s c r u t a b l e demands. So, w h i l e the watchman Stevenson i s asleep, i t i s not an omniscient A n a r r a t o r who s t e a l s away from him to report the t h e f t of the dinghy. The l i n e attached to the bow appeared to s t i f f e n i t s h o l d , r e l u c t a n t l y g i v i n g way i n the end to the p u l l of the frame as an arm of spray mounted and descended, s p r i n k l i n g the passage of a minute spider c r a w l i n g i n the hammock of the v e s s e l ' s i n t e r i o r : i t grew d i f f i c u l t to t e l l where the veined grassroot of one's l i f e commenced and the r o c k i n g c l i f f of i l l u s i o n ended as::the: world, halfstufned, o n . i t s ^ , . . . . . . s i d e e c l i p s i n g the n a t i v e eye of the spider t r a i n e d on the circumstance of space. A swallow darted from loops of a i r and f l e w s t r a i g h t to the boat to a l i g h t on the s t e r n . I t f l e w nervously o f f as the dinghy, which was running backside foremost, s t r u c k a rock. The v e s s e l bounced o f f and t h i s time when the swallow returned, i t chose to f a l l back upon the bow. The animalcule gaze of the b i r d crossed the web the s p i d e r had spun, as though the f r a i l e s t r e f r a c t i o n of v i s i o n occurred, s w i f t as a g l i s t e n i n g bead of water on d i s p e r s i n g and immaterial f a b r i c . I t was a f l e e t i n g coincidence e s t a b l i s h e d out of s p i r a l l i n g v i s i o n a r y moments; i n the s p i d e r ' s t e r r e s t r i a l universe the sky was p r e c a r i o u s l y r e v o l v i n g around the e a r t h , a sky whose s i l k e n broken t e x t u r e one could conceivably have b u i l t ; i n ,the swallow's f l y i n g i n s t i n c t the earth was l e a n i n g upwards condensed out of every shattered cobweb which he l d a running stream together l i k e an i n s t i n c t u a l b a l l one could n e v e r — i n one's w i l d e s t i m a g i n a t i o n — have invented or made....(pp. 46-47) The world i s seen here by animate and inanimate a l i k e : by s p i d e r , swallow, even boat and bead J. of water. What s u f f e r s , a c c o r d i n g l y , i s the supremacy of the c o n s t i t u t i n g s u b j e c t , of that c l a s s i c a l i n d i v i d u a l who makes absolute sense of the world, drawing a l l p e r s p e c t i v e s together i n t o a s i n g l e i n t e l l i g i b l e t o t a l i t y . The d i f f i c u l t y of expressing a p r e v a i l i n g otherness i s f e l t by those who have experienced long periods of s o l i t u d e . As he t a l k s to Stevenson, K a i s e r ' s v o i c e grates \"with the mournful rhythm the body of a t r e e makes when i t cracks w i t h the wind, seeming to deplore the inadequacy of language i t s e l f \" (pp. 16-17). Time and again i n t h i s n ovel ( s u r e l y the l a r g e s t menagerie i n a l l H a r r i s ' s f i c t i o n ) p e r s p e c t i v e w i l l s t r a y from the c h a r a c t e r s to a dog, a r a b b i t , a f i s h , a f l y , a b e e t l e , an ant, a t r e e , a rock. I t i s true that a t e l e o l o g y i s affirmed beneath t h i s \"jigsaw of i n t a n g i b l e resources\" and man i s effaced only to be r e s t o r e d , but the new meaning which the i n v e n t i o n of i d e n t i t y i m p l i e s , i s achieved not through a u n i t y but a m u l t i p l i c i t y of p e r s p e c t i v e . In f i c t i o n a l terms t h i s means a check upon the p r i v i l e g e d i n s i g h t of the n a r r a t o r who from a p o s i t i o n of s e c u r i t y manipulates i r o n i c d i s t a n c e and p e r s p e c t i v e to c o n s o l i d a t e a standard v e r s i o n of the world. As each p e r s p e c t i v e i s challenged by another, the o l d i r o n y and \"absolute rage f o r good\" (p. 84) succumbs to a p r i n c i p l e of displacement and what H a r r i s has c a l l e d \"a new unconscious p o l i t i c a l i r o n y \" (RV p. 19). In t h i s way the order of things i s shaken and i t i s through the c o n t r a s t s b u i l t i n t o the n a r r a t i v e that another order i s f i g u r e d . To extend Metz's d e s c r i p t i o n , n a r r a t i v e i s a matter of i n v e n t i n g not only one time scheme i n terms of 13 another, but as w e l l one s p a t i a l i t y i n place of another... The \" e c l i p s e of time\" (p. 66) i s b e t t e r i l l u s t r a t e d i f we reduce the n a r r a t i v e to a s k e l e t o n and i t s characters to t h e i r f u n c t i o n s , a device by which the small human cast w i l l be seen to s h r i n k even f u r t h e r , to three. Reduced to t h i s frame, the a c t i o n of the novel f o l l o w s a sequence not u n l i k e that of a f o l k t a l e . In such a schema, the most obvious p a i r s are r e a d i l y c o n f l a t e d ; as the novel repeatedly suggests, P e t r a i s to d a S i l v a as Maria i s to Stevenson. The s i g n i f i c a n t merger, however, i s Stevenson-daSilva, d a S i l v a being Stevenson's other, that n o t - s e l f whose discov e r y i s i n f a c t the hero's m i s s i o n . D a S i l v a says so q u i t e openly: \" I t u r n i n g i n t o the ghost of a r e p o r t e r of the one court of conscience a f t e r a l l — c o m p r i s i n g nobody e l s e but the mystery of me (or y o u ) — i n s p i t e of the f c o n t r a d i c t i o n on every crowded conventional body's l i p s . D a S i l v a . D a S i l v a , \" he confessed. \"Stevenson. Stevenson,\" he e j a c u l a t e d , g i v i n g Stevenson an i r o n i c a l , almost unholy, look. \"Somebody or other always addressing me as a f l e s h -and-barebones s e d u c e r — f u l l of t r i c k s — a n d you f o r the Jeky11-and-Hyde d e v i l i n your name (p. 44). With Stevenson and d a S i l v a become one, Petra's s t r u c t u r a l p o s i t i o n as heroine i s f u r t h e r strengthened, not l e a s t because Maria i s an absent heroine w h i l e P e t r a i s i n d u b i t a b l y and s o l i d l y present. I t i s she who gets the d r i f t i n g l e t t e r from the hero which was cast away before being sent to the absent heroine. The t h i r d i r r e d u c i b l e character i s K a i s e r , who may be described as the absent midwife, f o r although i t i s the hero who i s present at the c r i t i c a l moment, he i s h e l p l e s s , and i t i s i n K a i s e r ' s bed that Petra's i n f a n t i s born. Kaiser, i s ' i n more ways than t h i s the middleman, f o r he i s the go-between of f o l k - t a l e (he d r i v e s a l o r r y between Lower and Upper Kamaria) and moreover the c l a s s i c mentor who guards the \"key to a l l substance\" and sets the hero upon h i s quest. I t i s he who, as i t were, introduces Stevenson to himself by f i r s t t e l l i n g him of d a S i l v a . This done, he withdraws, and Stevenson undergoes h i s ordea of i n i t i a t i o n (the s e i z u r e ) before s t a r t i n g out on h i s m i s s i o n of f i n d i n g another place. The knowledge he i s l o o k i n g f o r does not come at once (hence the gones, the empty chambers) but h i s encounter w i t h d a S i l v a i s a beginning. His next \" o r d e a l \" — s o d e s c r i b e d — i s h i s presence at Petra's c h i l d i n g , followed by another disappointment. A sentence midway i n the novel c r y s t a l l i z e d h i s task: I t was the s e l f i s h f e a r of experiencing f e a r , the s e l f i s h l ove of the possession of love one was being summoned to transcend or see through by a b i d i n g to a s t e a d f a s t covenant and r e f u s a l to s h r i n k from the extremity and volume of the demoralizing contact and content of death (p. 48). D a S i l v a and P e t r a have cured him of s e l f i s h f e a r and i n t e r e s t e d l o v e ; now Stevenson must not s h r i n k from h i s l a s t o r d e a l . He sets out upon \"the longest crumbling b l a c k road\" by which he comes f i n a l l y to merge w i t h the h e a r t l a n d . The t a l e i s not q u i t e t o l d . A p o s t s c r i p t remains, which t e l l s of Stevenson's disappearance and i n c l u d e s the fragments of three poems he l e f t behind. But before we look at these, there remains another vacancy i n the morphology of t h i s n a r r a t i v e . We have encountered i n our schema a hero, a heroine, and a go-between: we have not met a v i l l a i n . He i s of course an absent v i l l a i n , but only because Time cannot p r o p e r l y be counted a character. Time i t i s which evokes i n Stevenson \"the g r e a t e s t fe a r of a l l , the f e a r that every elaborate means however v a r i e d and admirable i n encompassing distances i n space, always accomplished the same end i n time\" (p. 49). But there i s a way i n which the v i l l a i n can 14 be c o l l a r e d , and to i l l u s t r a t e i t we w i l l e f f e c t a f i n a l merger. We have seen Stevenson disappear i n t o the j u n g l e s , thus meeting h i s match i n time and becoming one w i t h space. S u r v i v i n g him, w i t h her c h i l d , i s \"the muse of the j u n g l e , \" the \" s p i r i t of p l a c e , \" P e t r a , who h e r s e l f has pronounced s p a t i a l q u a l i t i e s . When b i g w i t h c h i l d , she was \" l i k e a numinous boulder informed by arms and l e g s \" (p. 71), and her name i s , a f t e r a l l , P e t r a . L i k e the M a r i e l l a of Palace of the Peacock, she has become both person and place. Together, the dead hero and the s u r v i v i n g heroine come at l a s t to forge an equal a l l i a n c e against time, namely 15 space. Space w i l l assume l a r g e r p r o p o r t i o n s , or a greater d e n s i t y , i n H a r r i s ' s next n o v e l , The Eye of the Scarecrow, but we may pause on our way there to observe that the \" e c l i p s e of time\" by the \" d i s c of p l a c e \" (p. 80) i s never t o t a l . Nor i s space a l t o g e t h e r benign, since i t must i n turn be f i s s u r e d . Although the poems which c l o s e Heartland are poems of p l a c e : \"Troy,\" \"Behring S t r a i t s , \" and \"Amazon,\" they are each a m e d i t a t i o n e q u a l l y on 16 \"the c o n t r o v e r s i a l t r e e of time.\" Taken together, the fragments (damaged by f i r e , and so incomplete) are a k i n d of sunken bridge from Old World to New, and i n t h i s way preserve the p a t t e r n of m i g r a t i o n or journeying of \" l o o k i n g f o r \" which the main body of the novel set i n motion. I t i s t h i s movement which tr a c e s the i n t e r s e c t i o n of the two dimensions, and as \"Hector/hero of time\" and Stevenson, hero of space d i s c o v e r , there i s no escaping that nexus: \"man must d i e f i r s t to be f r e e \" (p. 93). P e t r a responds to the \" l o s s e s , r a i d s and d e p r i v a t i o n s \" of h i s t o r y w i t h a mute a s s e r t i o n of i d e n t i t y which enables her \"to i n c o r p o r a t e the f l i g h t of time and draw a s s i s t a n c e out of g r a n i t e \" (p. 71). Stevenson's more r a t i o c i n a t i v e response i s to elaborate a philosophy of u n i f o r m i t y and d i v e r s i t y which leads him i n t o a d u a l i t y whose consequences we w i l l examine s h o r t l y . Here i t allows him to master or r e g a i n time: he p i c k s up and w i n d s — o r dreams he d o e s — K a i s e r ' s c l o c k , and sets i t going again. I t i s an o l d dream. The Eye of the Scarecrow does not abandon t h i s hope. Endeavouring to \" r e t r a c e my own steps i n time\" (p. 21), the n a r r a t o r remembers a dream i n which as a boy he saw a b a l l o o n , \" h a l f - c a r r i a g e , h a l f - b i r d f l o a t i n g above the housetops\" and c a r r y i n g \" o f f i c i a l s and d i r e c t o r s of church and s t a t e , by whom I was employed i n an obscure al c h e m i c a l c a p a c i t y \" (p. 22). The b a l l o o n comes down next door, and wishing to elude h i s employers, the n a r r a t o r climbs to an u p s t a i r s room furnish e d w i t h \" r o y a l l y made beds.\" Undeceived and s i c k at h e a r t , he sees a door i n the w a l l which he had not noticed e a r l i e r , and enters by i t a secret apartment devoid of every f i l m or integument of a window. Nevertheless however c l o i s t e r e d i t f i r s t a p p e a r e d — i t was f i l l e d w i t h a r u s t - c o l o u r e d l i g h t l i k e ammunition f i r e d from d i s t a n t s t a r s , naked m e t a l l i c r ose, n e i t h e r i r o n nor bronze nor gold: the sleep of an immaterial unsupported element: the armour of the poor, and I knew then how dread and necessary i t was to dream to enter the s t r i k i n g innermost chemistry of l o v e , transcending every proud chamber i n the i n e x o r a b l e b a l l o o n of time (pp. 22-23). There i s much of the H a r r i s i a n p r o j e c t here: the dream i t s e l f , the c o n j u n c t i v e impulse ( \" h a l f - c a r r i a g e , h a l f - b i r d \" ) , the \"obscure\" alchemical c a l l i n g , the v i s i o n a r y l i g h t , the mystic l o v e , the hermetic chamber. The l e s s o n i s p l a i n enough: p o l i t i c i a n s and d i v i n e s promise a spurious heaven; t r u t h l i e s a step beyond. But we may take the movement of the dream as an exemplum a l s o of the n a r r a t i v e p a t t e r n of t h i s novel. Where the f l i g h t from time i n Heartland found refuge i n a p l e t h o r a of surface p e r s p e c t i v e s , that i n The Eye of the Scarecrow seeks to penetrate r a t h e r than m u l t i p l y space. In the e a r l i e r n o v e l , the i n t e r i o r was a r e t r e a t , a p l a teau of s e c l u s i o n crossed by a road along which the hero pressed f a r t h e r and f a r t h e r ; the i n t e r i o r , that i s to say, was l a r g e l y e x t e r i o r i n i t s c o n c e p t i o n . 1 ^ The l a t e r novel i s r i d d l e d from s t a r t to f i n i s h w i t h sockets of space and time; i t s i n t e r i o r i s no longer a matter of journeying f a r t h e r , but deeper, tunnel and grave having replaced road and depot. Of a l l H a r r i s ' s novels to date, The Eye of the Scarecrow i s , perhaps f or these reasons, the most impenetrable, the most obscure, meta-phors which w i l l be seen to share a subterranean dimension. I t i s as i f H a r r i s had vowed, f o l l o w i n g Lawrence, to reach \"a stratum deeper than... 18 anybody has ever gone, i n a n o v e l \" Recognizing the problems which such an endeavour must pose f o r the reader, he added an author's note to the paperback e d i t i o n of the novel, i n which he addressed the issue of d i f f i c u l t y as i t concerned what he c a l l e d \"pace and new dimension i n a c e r t a i n kind of imaginative f i c t i o n \" (n.p.). The two terms should not automatically be reduced to private time and inner space, but the imaginative h i s t o r y Harris proposes does indeed seek to capture the essence of the one and the substance of the other. Some of the d i f f i c u l t y of t h i s novel stems from the f a c t that what l i t t l e there i s i n the way of a d i s c e r n i b l e story, even one so slender as that of Heartland's emerges i n d i s l o c a t e d fragments at the whim of the narrator. Instead of a p l o t , there are scattered vignettes from the narrator's past, a number of which concern L , h i s f r i e n d from boyhood, whom he l a t e r accompanied on an expedition to a remote mining town. Another pair had already made t h i s nine months' journey to Raven's Head: the narrator's father and h i s f r i e n d and engineering colleague. This f r i e n d was to become the narrator's stepfather a f t e r the r e a l father was executed for murder when the narrator, i t was said, was l e s s than a minute old. The stepfather was i n turn drowned when he returned to Raven's Head to t r y to prove h i s friend's innocence. Now the narrator (who signs himself Idiot Nameless) makes the same journey with L , again an engineer. In the i n t e r i o r , they send for a p r o s t i t u t e named Hebra (but also Raven's Head) and come to quarrel over her. They are involved i n a crash of car or plane i n which both survive but are separated, Nameless being found and cared for by a shepherd. Nine months l a t e r , he wanders out of the jungle j u s t i n time to save L from being executed on a charge of having murdered h i s missing f r i e n d . The story i s further complicated by the d e l i b e r a t e confusion of L _'s and Nameless's i d e n t i t i e s ; moreover, i t transpires that the actual v i c t i m i s Hebra, h e r s e l f much the same woman as she whom Nameless's f a t h e r had s t r a n g l e d . The murder charge, which now inclu d e s Nameless as w e l l , i s dropped only when a pork-knocker, Scarecrow, confesses to the deed. L i k e Palace of the Peacock, The Eye of the Scarecrow i s an account of a journey r e l i v e d . The overt doubling i n the f i r s t n o v e l , by which the names of the two crews match man f o r man, i s not here repeated, f o r the n a r r a t o r ' s f a t h e r and ste p - f a t h e r remain anonymous, but then so do the ch i e f c h a r a c t e r s , w h i l e i t i s c l e a r that Nameless stands f o r h i s f a t h e r w h i l e L stands f o r the f a t h e r ' s f r i e n d . The phrase \"parent s c a f f o l d , \" which rec u r s i n the t e x t , may thus be read as something of a pun, f o r whi l e Nameless recovers h i s f a t h e r ' s execution, the p r i o r s e r i e s of events not only overhangs but e n c i r c l e s and forms the frame of that which repeats i t . There i s a l s o a resemblance to Heartland. L i k e Nameless, Stevenson 19 embarked on an e x p e d i t i o n i n t o \"an i n t e r i o r where one saw oneself turned i n s i d e out\" (p. 48), but where Stevenson was l o s t , Nameless l i v e s to repor t back from \"the f i n a l s t a t i o n . . . o f ourselves i n time and space\" (p. 76). His c l o s i n g communications are dated \"Night's Bridge.\" I t i s a r e p o r t i n g of t h i s k i n d which c o n s t i t u t e s the bulk of the n a r r a t i v e , so that the s t o r y f i l t e r s through o b l i q u e l y and almost by accident. Yet even without t h i s supervention of n a r r a t i v e , the s t o r y would be a d i s j o i n t e d one, a f a c t which suggests that here s t o r y i s of i t s own accord approaching the c o n d i t i o n of n a r r a t i v e , and on n a r r a t i v e ' s terms. In the course of s t o r y ' s becoming n a r r a t i v e , n a r r a t i v e uses the st o r y ' s a c t i o n f o r i t s own r h e t o r i c u n t i l the n a r r a t i n g i t s e l f becomes, i f not the subject of the no v e l , then the enabling process of that s u b j e c t . The novel becomes a me d i t a t i o n on n a r r a t i v e c o n s t r u c t i o n and r e c o n s t r u c t i o n . Having f i n i s h e d an asymmetrical qu a r t e t , f o r the most part f i c t i o n a l , the n o v e l i s t now allows himself to r e f l e c t on h i s f a c t u a l past. Yet the s p e c i a l i n t e n s i t y of t h i s novel i s not wholly to be explained by the n a r r a t i v e \" I \" and c e r t a i n t h i n l y v e i l e d passages of autobiography. What i s of essence i s l e s s the author's past than the a r t of i t s recapture and, more, the f a c t that what i s l a i d bare i n the s t r u c t u r e of the n a r r a t i v e i s h i s p r i v a t e philosophy and the s t a t e s of i t s e v o l u t i o n , i n f i n e , the growth of a n a r r a t i v e poet's mind. In a p u b l i c l e t t e r e n t i t l e d \" K i t h and K i n , \" i n which he l a t e r t r e a t e d once more c e r t a i n i n c i d e n t s a s s o c i a t e d w i t h L , H a r r i s spoke of v i s u a l i z -20 ing \"one or two c o n t r a d i c t i o n s of memory.\" This phrase h a p p i l y sums up the method of The Eye of the Scarecrow as w e l l : i f the past sleeps i n disordered memory, i t i s woken i n a language no l e s s c o n t r a d i c t o r y . One mode i n which these c o n t r a d i c t i o n s o r d i n a r i l y appear i s the j o u r n a l , and i t i s as a j o u r n a l that t h i s novel begins. Such a genre wants no p l o t ( u n t i l one a r r i v e s and begins by degrees to manipulate the w r i t i n g ) ; i t i s i n f a c t n o n - f i c t i o n , and i s moreover a way of beginning when the past o f f e r s no other handle. \" K i t h and K i n \" plunged, as i s so f r e q u e n t l y the case w i t h l e t t e r s , i n t o a s a l u t a t i o n and then at once found i t s e l f i n t r o u b l e : My Dear L , Now that I am embarked on t h i s l e t t e r I f i n d myself involved i n the most curious d i f f i c u l t i e s . Memories that I have c a r r i e d around (and taken f o r granted) since c h i l d -hood suddenly seem more r e t i c e n t , more withdrawn, than ever. And yet i n that r e t i c e n c e p a r a d o x i c a l l y more a c t i v e , w i t h a deep inwardness to r e s i s t or s c r u t i n i z e from t h e i r s i d e any k i n d of f a c i l e p o r t r a i t or summary on my s i d e (p. 1). H a r r i s i s having problems s t a r t i n g , and t h i s not from any l a c k of n a t i v e i n v e n t i o n or t e c h n i c a l s k i l l , but because the past i s to be more than regained; i t i s to be remade i n the moment of i t s d i s c o v e r y , worked out, given shape, q u i t e l i t e r a l l y f a b r i c a t e d . In The Eye of the Scarecrow, the contradictions begin with the organ of inner v i s u a l i z a t i o n i t s e l f : i t i s both \"the explosive t r a i n of memory\" (p. 21) and the \" f r a i l v i s i o n a r y organization of memory—one thing against another\" (p. 16). Recognizing that he cannot \" r e c a l l — l i k e a ghost returning to the p a s t — t h e i d e n t i c a l map of place,\" the narrator, who i s perhaps not yet Nameless, finds himself \"conferring the curious baptism of l i v i n g imagination upon helpless r e l i c s \" (p. 15). To attempt exactitude, he declares, would be to succumb to the dead t i d e of self-indulgent realism. On the other hand, to t r a v e l with the flood of animated wreckage that followed a f t e r , i s a d i f f e r e n t matter, a t r u s t i n g matter i n which I am involved (p. 15). Harris w i l l t r u s t to the contradictions of memory, \"one thing against another,\" and i n order that h i s r h e t o r i c be l a i d bare, he works the poles of past and present into the text. Hence the a l t e r n a t i n g time-scheme: the present of the narrating, 1963-1964, and the rescued presents of the past, 1929, 1932, 1948, those spots i n time which inhabit the ea r l y n a r r a t i v e space of the novel. Once the cross-play of t h i s s e r i e s has been set i n motion, i t gathers momentum and a f i c t i o n generated by c o l l i s i o n s of f a c t takes over the text. Writing elsewhere of an attempt \"to fuse the actua l and f i c t i t i o u s within an asymmetrical l o c a t i o n , \" Harris remarks that resort must be made to \"an art of memory which d i s l o c a t e s , i n some i measure, an idolatrous plane of realism by immersing us i n a peculiar kind of ruined f a b r i c \" (IN p. 142). \"Ruined f a b r i c , \" \"animated wreckage,\" \"Is i t that within the rubble of oneself s t i l l l i e s the key?\" (p. 27): a l l of these images i l l u s t r a t e the e x t r a o r d i n a r i l y f i s s u r e d form of The Eye of the Scarecrow, marking a seismic a c t i v i t y equalled so far i n Harris's canon only by the \"mixed f u t u r i s t i c order\" of Palace of the Peacock. With i t s t a l e s of innocence and experience which undermine cause and e f f e c t (as i n an account of the n a r r a t o r ' s pushing L i n t o a canal) and supplant i d e n t i t y w i t h r e l a t i o n (as i n the confusion which f o l l o w s the crash of car or p l a n e ) , the t e x t s e t s out to question the s e q u e n t i a l i t y of time and the s o l i d i t y of space. I t s chosen techniques of rupture and e l l i p s i s are c l o s e to those of f i l m , w i t h i t s jump-cut and montage, but a cinematics which, having combed the \"rubbish heap of memory\" (p. 56), recognizes that m a t e r i a l s are scarce and shots not to be squandered. Hence an a r t that i s both dense and fragmented, whose b r i c o l e u r i s Nameless h i m s e l f . The Eye of the Scarecrow would seem almost a casebook of that b r i c o l a g e 21 described i n L e v i - S t r a u s s ' s c l a s s i c o p p o s i t i o n of engineer and b r i c o l e u r . The two c e n t r a l characters f i t t h i s mould p r e c i s e l y , the engineer L w i t h a r e p u t a t i o n f o r \"sober and matchless good sense, judgement, r e s p o n s i b i l i t y , \" w h i l e Nameless i s \"the s t r i k i n g , u n p r e d i c t a b l e one\" (p. 40). Together they stand on a suspension bridge that i s to one a t e c h n i c a l f e a t and f o r the other \"a trapdoor and a poem,\" and while L d i s c o u r s e s on t e n s i o n and load, Nameless sees \"the most f r a g i l e and b e a u t i f u l web against the sky,\" and i s possessed by the \"muse of p l a c e . \" L has been commissioned to r e l o c a t e Raven's Head f o r the \" f a n t a s t i c gold d e p o s i t s \" s a i d to l i e thereabouts; \"an astronomical investment, labour, machinery, a new township\" hang on h i s success. For Nameless, t h i s i s a s h o e s t r i n g adventure i n t o h i s own obsessions; the t r a i l s to h i s ghost town s t r a d d l e the mnemonic past. A passage from one of H a r r i s ' s e a r l y essays developed t h i s same o p p o s i t i o n of \"masses and m a t e r i a l s \" to the \"bareness of the West Indian world,\" a bareness whose \"symbol i s man, the human person.\" The West Indian has most s i g n i f i c a n t l y to i n f l u e n c e the a r c h i t e c t u r a l problem of h i s time, s i n c e though he may work p r i n c i p a l l y i n terms of values i n h i s bare world, the e f f e c t s w i l l be f e l t soon or l a t e i n terms of masses and s t r u c t u r a l o r g a n i z a t i o n . Now, i t i s not an easy matter to see the human being today. So many w a l l s f a l l between us and our f e l l o w s . Money, myth, and numerous obsessions. Yet when we look at the human we must be prepared not to overlook these obsessions but to work them i n t o the s t r u c t u r e of art...(FR p. 14). As a poet, H a r r i s was quick to apply h i s p h i l o s o p h i c marginalism, which might have taken many d i r e c t i o n s , to \"the s t r u c t u r e of a r t , \" and t h i s i s what concerns us here. An a e s t h e t i c s t r u c t u r e based on \"masses and m a t e r i a l would be none other than what H a r r i s was l a t e r to c a l l the novel of \"persuasion\" or \" c o n s o l i d a t i o n \" (TW p. 29). Such a s t r u c t u r e could not t o l e r a t e rupture and d i s e q u i l i b r i u m , or the r a p i d and i l l o g i c a l leaps of memory which scorn i t s order and mock i t s seamlessness. On the other hand, an a r t of marginal experiment, confronted w i t h sparse but d i v e r s e resources, must employ p r e c i s e l y such techniques, l a y i n g bare t h e i r bareness and f i n d i n g v i r t u e i n t h e i r u n s t r u c t u r a t i o n . The r e s u l t i n g d i f f i c u l t i e s , as H a r r i s warns i n h i s preface, cannot be smoothed over; they have been worked i n t o the n a r r a t i v e w i t h a purpose w h i c h — a t the l e v e l of the l i n e — w e examined i n some d e t a i l i n the chapter on language. In The Eye of the Scarecrow, language now o f f e r s , i n i t s zany patchwork (the image of s t i t c h i n g occurs again and again) a s t r i k i n g p a t t e r n of the l a r g e r n a r r a t i v e counterpoint. Racking h i s memory f o r a p i c t u r e of the o l d shepherd and h i s grandson who found and cared f o r him a f t e r the crash, Nameless wonders: How d i d I c o n t r i v e — i n the v o i d of the mind which seems so long a g o — t o s t i t c h a w i l d apprehension of them together? G l a r i n g touch of c o n c e i t : f a l l a c y . Needless to say i t was they who obscurely measured and needled me when they found me l y i n g on the ground. R u m p e l s t i l t s k i n threads b r i s t l e d l i k e the wisest whiskers. A s t i c h i n time saves nine. Cat's eyes f a b r i c . B a l l o o n s k i n p a t t e r n . Skyscraper t a p e s t r y . The toy cow jumped over the toy moon (p. 79). This passage i s not to be mistaken f o r a stream-of-consciousness rendering of the dazed Nameless's thoughts as he l i e s on the b r i n k of unconsciousness. Or i f i t i s t h a t , i t i s more, f o r i t works i n m i n i a t u r e the s t r u c t u r e of that \"epic and r e v o l u t i o n a r y novel of a s s o c i a t i o n s \" which H a r r i s opposed to the novel of persuasion. A l l of the m o t i f s sewn i n t o t h i s passage are t r a c e a b l e across v a r y i n g d i s t a n c e s of n a r r a t i v e to elements i n the t e x t ; at the same time, they appear to be generated out of each other, i n a random progression. T h i s , as we have seen, i s the method by which the novel got underway. The b r i c o l e u r ' s a c t i v i t y , L e v i - S t r a u s s holds, w h i l e comprising a \" c o n t i n u a l r e c o n s t r u c t i o n from the same m a t e r i a l s , \" has t h i s d i s t i n c t i v e f e a t u r e that \" i t i s always e a r l i e r ends which are c a l l e d upon to p l a y the part of means: the s i g n i f i e d changes i n t o the s i g n i f y i n g and 22 v i c e v e r s a . \" The a e s t h e t i c moral of t h i s formula (which L e v i - S t r a u s s d e c l a r e s \"could serve as a d e f i n i t i o n of ' b r i c o l a g e ' \" ) i s that i n a passage such as H a r r i s ' s s t i t c h e r y above, language i s guiding r a t h e r than i m i t a t i n g consciousness, the images have become s i g n i f i e r s r a t h e r than passive s i g n i f i e d s . In i t s turn,' the passage expresses or s i g n i f i e s 23 the s t r u c t u r e of the novel; the l a r g e r n a r r a t i v e u n i t s , d e b r i s i n t h e i r own way of past experience,are played o f f one against the other: 1928 against 1963 against 1948, even \"2048.\" The \"toy cow\" fragment, f o r example, gives d i r e c t l y (but not c h r o n o l o g i c a l l y ) onto the subterranean v i s i o n which c o n s t i t u t e s the t u r n i n g point of the novel: \"THE FIRST BURNED r IMAGES which returned to me (long before I a c t u a l l y saw the face of grandfather or grandson) were the womb and c a r r i a g e of a dream I had f o r g o t t e n \" (p. 79). Inventing as i t goes, language helps memory take on form and d i r e c t i o n . By r e t u r n i n g b r i e f l y to the l e v e l of the sentence, which was our h o r i z o n i n Chapter Two, we have glimpsed the n a r r a t i v e counterpoint w r i t . small. The nar r a t i v e \"sentence\" i s subject to the same disordering, and for the same purpose, as that of the novel's language, i t s parts of speech juggled, i t s i n f l e x i o n s deflected, i t s syntax unbound. Such procedures, common enough i n modernist f i c t i o n s , disorder not only the time of the story but also the h i s t o r y of the time i n which the events are set. Thus they serve Nameless's express purpose of exercising an \"open memory\" the better \"to escape from the prison of past knowledge\" (p. 46). The dream l o g i c of the nar r a t i v e structure i s one more attempt by Harris to disrupt • What i n h i s preface he c a l l s the \"nightmare of h i s t o r y , \" but unlike Joyce, who wished to wake from the nightmare, Harris wishes to pass to another mode of dreaming. Reviewing i n h i s author's note the events of the f o r t y years covered by the novel, he denies \"the claims of h i s t o r i c a l n arrative to be i d e n t i c a l with u n i v e r s a l i t y , \" to be at once a general framework of expression bound up with the i n s t i t u t i o n s of the day; to be at the same time a general framework of protest bound up with the i n s t i t u t i o n s of the day (n.p.) It should be clear from t h i s that Harris i s here concerned with h i s t o r y as discourse: not the events themselves but a version, the standard version, of the events i s i n dispute. Hence the vehemence of h i s attack on the received account: \"history (as un i v e r s a l given tool) was both c u l p r i t and nightmare.\" The imaginative h i s t o r y offered i n The Eye of the Scarecrow no more than glances at the public events of the day, but i t s f i r s t foot i n the past i s planted i n 1948, \"year of the Guiana S t r i k e . \" The s t r i k e i s not sympathetically portrayed: i t a r i s e s out of an \"irony and n i h i l i s m of s p i r i t , \" and the unity of the workers involves the hideous and l o g i c a l denigration of every person, high and low, i n the horror of a progressive realism which was far more dangerous, because i t seemed p o l i t i c and necessary however aimless and subversive, than the most f e r t i l e incestuous fantasy. I t was the d e v i l ' s abyss b l o c k i n g the way, I dreamt...(p. 18). The i d e o l o g i c a l content of H a r r i s ' s own account i s s p e l t out here. I f ideology i n e v i t a b l y takes the form of n a r r a t i v e , t h i s n a r r a t i v e o b l i g i n g l y gives the i d e o l o g i c a l i t s f i c t i v e nomenclature: \" i r o n y \" and \" r e a l i s m \" versus \" f a n t a s y \" and dream. In the teeth of h i s t o r i c a l r e a l i s m , the n a r r a t o r proposes to f o l l o w the v i c t i m s of the p o l i c e f i r i n g (and perhaps others i n the procession of s t r i k e r s ) to \"some f u n e r e a l c e l l a r corresponding to the burning of a l l m a t e r i a l ambition\" (p. 21). Then commences the dream of the b a l l o o n and the bedchambers and the genuine \"armour of the poor.\" I t i s to be a quest f o r i n d i v i d u a l s ; spurning the \"nightmare account\" of the mass, the n a r r a t i v e w i l l represent \"the psyche of ord i n a r y men and women,\" the \"pace\" of whose l i v e s i s d i s t i n c t from that of h i s t o r y . Herein l i e s the source of that ambition to transcend \"every proud chamber i n the i n e x o r a b l e b a l l o o n of time.\" The p r o j e c t i n v o l v e s , as any t r a n s -cendental \" h i s t o r y \" must, an e x t r a o r d i n a r y v a l u a t i o n of the i n d i v i d u a l ' s c a p a c i t y to overcome the contingent (as w i t h the f a m i l y Anthrop, who alone of a l l the tenants i n a shanty a l l e y preserve a c h e e r f u l demeanour and manage to pay t h e i r r e n t ) and e v e n t u a l l y the necessary (as w i t h the enigma of the \"poor man's hearse,\" which v e h i c l e , l a c k i n g the g l a s s sides of conventional mourning c a r r i a g e s , may w e l l be empty, i t s paupers having cheated what i s l a t e r c a l l e d \"the l i b e r a l form of death\" [p. 93] ). But \"pace\" i s only one h a l f of the proposed r e v i s i o n a r y h i s t o r y : \"new dimension\" i s the other. E a r l y i n the novel there i s a r e c o l l e c t i o n of a boyhood v i s i t to the c i t y s e awall. H a r r i s r e t u r n s to t h i s s i t e i n a l e c t u r e given f i v e years a f t e r the n o v e l , w h i l e on the subject of landscape and r e a l i s m . 100. . . . I r e c a l l e d my boyhood (before World War I I broke out) when I o f t e n swam at the Fort on the Georgetown foreshore. I r e f l e c t e d a l s o on an observation I made when I was l a s t i n Georgetown i n 1966: the sea no longer stands where i t used to be and the land has grown i n i t s p l a c e by s i x or seven f e e t . Therefore, i f I were to endow the de f a c t o mound or grave which now e x i s t s on the foreshore w i t h a f i g u r a t i v e meaning beyond the present s t a s i s of r e a l i t y I might see the ghost^ of the past (the ghost of my c h i l d -hood) swimming i n dry land (HFM p. 24). Something of t h i s i m a g i n a t i o n — w h i c h H a r r i s at once recognises as \"suspect\" — i s necessary f o r an apprehension of the space evoked i n The Eye of the Scarecrow. And sin c e t h i s space i s one which assumes ever greater r e s p o n s i -b i l i t i e s as H a r r i s ' s w r i t i n g progresses, i t i s worth quoting a passage from another essay that might f u r t h e r c l a r i f y the concept. In a piece r e v e a l i n g i y e n t l t l e d \" R e f l e c t i o n and V i s i o n , \" H a r r i s puts i t t h i s way: A Take an o b j e c t . A bridge perhaps, a bone, a f l u t e perhaps, a coat, a piece of s c u l p t u r e , a fence, a t r e e , a r i v e r , a c a n a l . Around i t may l i e deepseated r e f l e c t i o n s of a personal and/or h i s t o r i c a l nature. Indeed those r e f l e c t i o n s may be the seed of i n s t i t u t i o n s , the p s y c h o l o g i c a l t e x t u r e , the proud, implacable scars a s o c i e t y wears on i t s back as i n s t i t u t i o n , costume, r i t u a l etc...And as that texture r e i n f o r c e s i t s e l f over generations and c e n t u r i e s i n t o an im p r i n t of sovereign e a r t h . . . i t i s i n e v i t a b l e that a v u l n e r a b l e c e n t r e , an o r i g i n a l f r a i l t y (and a l l t h a t that means as marvellous s u s c e p t i b i l i t y to space and depth) i s wholly masked and f o r g o t t e n (RV p. 16). The depth intended here i s i n the f i r s t p lace not the i l l u s i o n i s m of p e r s p e c t i v e , whether i n p a i n t i n g or i n f i c t i o n , f o r H a r r i s goes on to speak of \"'black holes of g r a v i t y ' as an e x t i n c t i o n of l i g h t drawn i n t o p a r a d o x i c a l genesis of suns beyond imagined or imaginable models\" (RV p. 17). But i f i t i s not o l d - s t y l e r e a l i s m , n e i t h e r i s i t that r e a c t i v e experimen-t a l i s m which t r e a t s the world as a surface to be swept by a n e u t r a l , t r a v e l l i n g i n t e l l i g e n c e . Rather, i t looks beyond t h i s s p a t i a l i t y of s u p e r f i c e s i n t o a marginal zone of \" e c l i p s e d p e r s p e c t i v e s , \" that \" o r i g i n a l f r a i l t y \" which w h i l e e m p i r i c a l l y undemonstrable e x i s t s nonetheless as a 101. p o s i t e d s t a t e of extreme d e n s i t y . The d e n s i t y of the n o v e l , then, i s an attempt to express f o r m a l l y t h i s h y p o t h e t i c a l content. Where e a r l i e r we saw H a r r i s take the image as a k i n d of fragmenting device when juxtaposed w i t h a sharply d i f f e r i n g other, here we see him press l a y e r upon l a y e r of n a r r a t i v e to produce that \" d e n s i t y of p l a c e \" which, although an e a r l y c o n v i c t i o n , d i d not become the subject of a novel u n t i l The Eye of the Scarecrow. Although on one l e v e l the novel presents the t r a c k i n g of a murderer now dead, at another, f u r t h e r down, i t comes to prosecute the concept \"murder\" i n a way which d e t e c t i v e f i c t i o n s would consider scandalously i r r e g u l a r . I t i s only a f t e r the crash, when the \" d r i v e r \" has pie r c e d through these sedimented s t r a t a to a r e c o g n i t i o n of \"the realm of depth or p l a c e , \" that the \"framework of a parent s c a f f o l d \" begins to show i t s e l f . Now he enters \"a sphere of r e d u c t i o n , \" at which zero point i n space, \"one f r a i l body of i n s t i n c t \" may i m a g i n a t i v e l y communicate w i t h the \" i n s t a n t dust of another,\" Nameless w i t h that other who i s h i s executed f a t h e r . Having now s u f f e r e d 24 \"death,\" he begins to acknowledge and r e c o n s t r u c t the murder he has been so anxious to deny, from a m i s c o n s t r u c t i o n of h i s f a t h e r ' s innocence and g u i l t . The r e c o n s t r u c t i o n i n v o l v e s an account of death which i s as daring as the doing (or being done) to death w i l l be c o n t r o v e r s i a l . A l l of the novel's images and obsessions po i n t t h i s way: the c o f f i n s , graves, tunnels, c r a c k s , holes and f a u l t s . At l a s t , by way of a descent i n t o a JCaf.kaesque v i s i o n whose i m p l i c a t i o n s are that murder i s a pact i n which the p r i n c i p a l s act out an equal s t r u g g l e where absolute c a t e g o r i e s such as l o s s and g a i n , a c t i v e and p a s s i v e , are inadequate, Nameless imagines himself f a c i n g h i s fa t h e r \" i n the dense and transparent c e l l of h i s moveable, immoveable, deceptive p r i s o n and person\" (p. 91). The instruments of death h i s f a t h e r does not f e a r , but \"space he could not yet dream to bear\" (p. 93). Having by h i s \" a r t of murder\" invoked a l i f e i n l i f e l e s s n e s s , a somethingness i n nothingness, he now f i n d s the w a l l s of h i s c e l l c l o s e i n upon him i n t u r n , \" i n c h by w a l l , w a l l by f o o t , \" u n t i l every conventional d i s t i n c t i o n between volume and surface became i n e x t r i c a b l y c l o s e and u n r e a l . For s i n c e a cube i s subject to f i l l i n g or ho l l o w i n g , i t s u b s i s t s i n p o t e n t i a l d e p l e t i o n or r e p l e t i o n of i t s e l f ( i t s own paradox of v a i n expansion): but s i n c e the th i n n e s t f i l m or surface i n t o which i t may u l t i m a t e l y r e s o l v e i s s u s c e p t i b l e to an a b s t r a c t measurement i n depth s t i l l , however unimaginably f r a i l and i n d i s t i n c t , THIS (and no other) l i v e s i n a tru e body of d e n s i t y which demolishes at one stroke the t e c h n i c a l , s u b j e c t i v e hollow or v o i d ; but remains, as i t were, t e c h n i c a l l y f u l l s t i l l , a d r i p p i n g mist or sweat of p r o p o r t i o n , incapable NOW of being dug i n t o or dug out, inner space ( i t s true u n a s s a i l a b l e p o s s e s s i o n ) , i n d e s t r u c t i b l e , f a i n t s c a l e or measure of One universe (pp. 93-94). The u n i t y of v i c t o r and v i c t i m , the \" u n i t y of a n c e s t r a l master and s l a v e \" (p. 25), could not but s u b s i s t upon t h i s c e n t r a l Oneness. I t i s true that the novel r e s o l u t e l y i n s i s t s upon a d u a l i t y to t h i n g s ; from the moment of the crash, the d r i v e r (who i s himself both Nameless and L ) le a r n s to respect t h i s \"strange company—TWO and IT— t h o u g h who i t _ was no one could say: a crumbling scarecrow perhaps\" (p. 75). And the p o s t s c r i p t which Nameless attaches to the whole i s a catalogue which o s c i l l a t e s between the q u a l i t i e s of \"one\" and two.\" But there i s never-t h e l e s s a tendency f o r t h i s dualism to c o l l a p s e — a s i f by v i r t u e of H a r r i s ' commitment to depth, and i n v i o l a t i o n of the s e n i o r i t y of f o r m s — i n t o a prime Idea, or i n Nameless's language, \"the o r i g i n a l Word, the Well of S i l e n c e \" (p. 95). This u n i t y H a r r i s i s d r i v e n to confess d e s p i t e h i s deepest m i s t r u s t of f i n a l i t y : \" a f t e r addressing every c a u t i o n to oneself against absolutes, there i s an absolute medium of consciousness which we must l e a r n to accept as the language of a r t \" (PL p. 5). A r t , that i s to say, makes speak the o r i g i n a l s i l e n c e . 103. In Heartland, the dualism of \"two\"and 'It\" took the shape of a philosophy i n which u n i f o r m i t y and d i v e r s i t y were held i n e q u i l i b r i u m : \"The uniform burden of p l a c e was n e i t h e r nearer nor f a r t h e r from the t r u t h of being 25 than the d i v e r s e gambols of s t a t i o n \" (p. 87). In The Eye of the Scarecrow, where the p a i r have become \" c a p a c i t y \" and \" d e n s i t y , \" there i s an avowed attempt to \" f i n d i n nature an innocent array of objects and the ground, as w e l l , of c l a s s i c a l u n i t y f r e e from an a r b i t r a r y i n t e r e s t i n mood or c o l o u r \" (p. 96). The \"as w e l l \" i s s i g n i f i c a n t , f o r Nameless's p r o j e c t seems to be to f i n d r e a l i t y both dead and l i v i n g (the unmaking of murder i s part of t h i s scheme), or to a r r i v e at a p o i n t where the d i s t i n c t i o n between these s t a t e s i s n u l l and, l i t e r a l l y , v o i d . Hence those \"numinous boulders\" which strew the landscape of both Heartland (p. 71) and The Eye of the Scarecrow (p. 68). Hence a l s o the numerous c o n t r a d i c t o r y s t a t e s i n these and H a r r i s ' s other f i c t i o n s , c o n t r a d i c t i o n s undone by the u n i t y which l i e s at t h e i r heart. I t i s as i f the c o n j u n c t i o which the obscure alchemist d e s i r e d were an i n t e r p e n e t r a t i o n of opposites so complete that the marriage bed opened i n t o an \" u l t i m a t e grave of s t i l l n e s s \" (p. 43). This s t i l l p o i n t i s what H a r r i s has elsewhere c a l l e d the \"unnameable cen t r e \" (WH p. 24), and what others have c a l l e d the \"romantic heart of 2 6 t h i n g s \" (Barthes) or simply a \"suspect i n t e r i o r i t y \" ( R o b b e - G r i l l e t ) . Nameless has already declared h i s \"an unproven, even unprovable manifesto\" (p. 95), but h i s p o s t s c r i p t s t e a d f a s t l y a s s e r t s that twoness i s \"a continuous and miraculous conception of ' l i v i n g ' and 'dead' nature, r e h a b i l i t a t i o n of the l o s t One, the u n r e a l i z e d One, the i n a r t i c u l a t e One\" (p. 108). The c r i t i c must not pounce too s w i f t l y on t h i s metaphysics; h i s w i l l not be a \"groundless f a l l . \" I f there i s a logocentrism here, i t i s one 104. that w i l l be found to have a t a c t i c a l value beyond i t s o r i g i n a l s t i l l n e s s , pointing away from i t s e l f to engagement with the world. The way back to the contingent i s best shown by means of c e r t a i n remarks on language which Nameless includes i n h i s manifesto. \"Language,\" he asserts, \"because of i t s untrappable source transforms i n a t e r r i f y i n g and well-nigh unendurable p e r s p e c t i v e — e v e r y subjective block and f i x t u r e of capacity\" (p. 96); one sees inwardly by means of language and thus learns to d i s t r u s t the given order of things. But the p l a u s i b l e new language of f l u i d i t y , that \"very apparent b i r t h of a 'future' language of p o s s i b i l i t i e s \" (p. 97) which imitates the inward state and seems to replace the r h e t o r i c a l order of the old, i s i t s e l f to be dis t r u s t e d and broken down. Only out of t h i s second negation can a poetic language come, one which neither passively records nor a c t i v e l y denies because i t i s \"the l i f e b l o o d of seeing and responding without succumbing\" (p. 97). The eye of the scarecrow looks both ways. 27 At the l e v e l of the novel's story, authentic being and seeing have required a crumbling of the landscape of w i l l , of that i n v u l n e r a b i l i t y of s e l f which prevents a character from standing i n another's shoes (or space) as Nameless eventually comes to do both with h i s father and with L . It i s by way of t h i s \"'negative' i d e n t i t y , s e l f - c o n t r a d i c t i o n , even 'po s i t i v e ' loathing of the 'ground' of ' s p i r i t ' \" (p. 101), that one a r r i v e s at.a.new sense of community by which one can sympathize with \"the derangement of a l l creatures within h i s t o r y and circumstance\" (p. 102) without self-indulgence and with a genuine s o l i d a r i t y because one has i n fac t been another. The n a r r a t i v e consequences of t h i s scarecrow otherness are further testimony to the v i r t u e of i n d i r e c t i o n . Just as settlements l i k e Raven's Head \"belonged to those who v o l u n t a r i l y began to relinquish'the r i g h t they 105. deserved to a place i n them\" (p. 55), the \" o r i g i n a l w e l l of s i l e n c e \" i s tapped when one i s , as i t were, not l i s t e n i n g , the Word best read when one i s l o o k i n g the other way. S i m i l a r l y , the forms of the n a r r a t i v e ' s f u t u r e are best f i g u r e d when they are not r i g o r o u s l y determined by the author's w i l l . This i s not, as we s h a l l see, a surrender of the author's a u t h o r i t y , but r a t h e r an openness to the unconscious of language through what Nameless, 28 i n the vocabulary of. romanticism, c a l l s \"an Imagination empty of s e l f -determined forms to come, blank frames, i n d w e l l i n g non-resemblance, freedom from past, present, f u t u r e form and formlessness\" (p. 98). We have seen how the most f r e e l y a s s o c i a t i n g passage i n the n o v e l , that of the needlework, l e d s t r u c t u r a l l y i n t o the v i s i o n which completed the crumbling of the d r i v e r ' s w i l l . In 'the same way, the n a r r a t o r ' s r e c o v e r i e s of the past and the n a r r a t i v e ' s d i s c o v e r i e s of i t s f u t u r e depend on the c o l l i s i o n s of u n r e l a t e d , even i r r e l e v a n t , s t r u c t u r e s one with an-other. A novel on whose surface such words as \"crumbling,\" \"uprooting,\" and \"subduction\" f r e q u e n t l y reappear may expect to f i n d i t s n a r r a t i v e sentence shaped by t h e i r corresponding verbs and any r e s i d u a l s e c u r i t i e s of form and d i r e c t i o n i m p e r i l l e d by the v o i d i t f r e e l y invokes. There i s even a suggestion of r e l a t i v i t y to the time-scheme, as i f the n a r r a t i v e met i t s e l f r e t u r n i n g : i n choosing to give h i m s e l f up, the f a t h e r r e t r e a t s from \"the assured d i c t a t i o n of the f u t u r e \" (p. 95), w h i l e the son, i n t r a c i n g him to h i s c e l l r e t r e a t s from h i s own present, f i n d i n g that he has come \" i n t h i s backward, unexpected pregnant way to the goal of my long quest\" (p. 91). The novel c l o s e s w i t h a formal embodiment of Nameless's quest f o r \"phenomenal space r a t h e r than phenomenal time\" (p. 108). I t s f i n a l \" d i s p o s s e s s i o n of the s t r a i t - j a c k e t of time\" i s a s e r i e s of eleven s e l f -quo'tatioris of v a r y i n g lengths and s t a t i o n s i n time past and f u t u r e e n t i t l e d 106. \"THE BLACK ROOMS.\" Here The Eye of the Scarecrow provides i t s own synchronic s t r u c t u r e the b e t t e r to d i s c l o s e i t s n a r r a t i v e space. The p o s t s c r i p t i s a f i n a l asymmetry. The v o i d i n The Eye of the Scarecrow, then, has a l i t e r a r y as w e l l as a metaphysical dimension: i t serves both as a caveat i n nature and as the empty frame of the novel's d i s c o v e r y of i t s own form. Indeed, p r o p e r l y read, the unnameable centre Is a \" s t r u c t u r e \" of postponement, where u n i t y i s always i n the f u t u r e or i n some other place w h i l e the now and here of the n a r r a t i v e remain f o r m a l l y broken and o r g a n i c a l l y unredeemed. 29 Looking \"both ways i n the same blank crude i n s t a n t \" (p. 75), the scarecrow represents not a d e n i a l of the world but an \"unsleeping s i g n a l \" of t h i s u n s t r u c t u r i n g s t r u c t u r e of otherness and i t s f u n c t i o n i n the i n t e r p r e t a t i o n of that world through the i n v e n t i v e r e v i s i o n of i t s forms. The f o r c e of t h i s r e v i s i o n i s demonstrated w i t h splendid b r i o i n a l a t e r novel to which The Eye of the Scarecrow i s c l o s e l y r e l a t e d , Black Marsden (1972). Much of the s p i r i t of Black Marsden i s contained i n i t s s u b t i t l e : \"a t a b u l a rasa comedy.\" The novel i s a kind of comic p l a y , and a good deal of the wry wordplay w i t h i n the p l a y i s of the same i m p r o v i s a t i o n a l k i n d as that of the s t r u c t u r e s we have j u s t examined i n the scant l i g h t of The Eye of the Scarecrow. C l i v e Goodrich, winner of the F o o t b a l l Pools and patron of the a r t s , takes i n the vagabond impresario, Doctor Black Marsden and h i s troupe, J e n n i f e r Gorgon, K n i f e and Harp. Making themselves at home, the a c t o r s come and go, rehearsing a p l a y and d i s c u s s i n g the world and i t s contents to a l l hours w i t h t h e i r host. Then one day, Goodrich f i n d s they presume too much and turns them out. There i s no p l o t : the w r i t i n g i n s t r u c t s and e n t e r t a i n s l i k e some impromptu m o r a l i t y p l a y whose a c t o r s invent t h e i r l i n e s as they go u n t i l the f i n a l abrupt c u r t a i n . I t i s the a r t of the blank s l a t e . , L i k e a l l H a r r i s ' s work, Black Marsden i s s t o u t l y , even o b s e s s i v e l y a n t i - r e a l i s t i c . E a r l y i n the p i e c e , Goodrich dreams he sees K n i f e s l a s h 30 Marsden who i s dressed as Deacon Camera; r e l i e f i s i n s t a n t . There f o l l o w s a n a r r a t i v e of continuous s h i f t s and s u r p r i s e s , w i t h a b e w i l d e r i n g \" r a i n of p e r s p e c t i v e s \" and tense. Once again, there i s a d i a r y , and although i t s form i s not imposed on the n o v e l , i t i s an instrument of d i s c o v e r y . The morning a f t e r h i s dream of the slashed photographer's \"wig of c l o t h , \" Goodrich's entry i s e n t i t l e d \"COMEDY OF FREEDOM\" and begins i n a s i n i s t e r v o i d : LEFT HAND: Tunnel/garment. Doodles of i n k . When my doodling tunnel i s b l a c k e s t I move towards a p i n p r i c k of l i g h t at the f a r end which grows b r i g h t e r u n t i l the p i n p r i c k becomes a s k y l i g h t (p. 24). And so on. Relieved of the .necessity to i m i t a t e , Goodrich w r i t e s out of nothing, f e e l i n g h i s way as he progresses. The elements of the world are preserved; what i s changed i s t h e i r order, f o r the d i a r y entry i s the i s s u e of a dream. Goodrich's \"deep d i a r y , \" as Marsen mockingly c a l l s i t , i s not the only element t h i s novel shares w i t h The Eye of the Scarecrow. The n a r r a t i v e of the e a r l i e r novel began w i t h a r e c o l l e c t i o n of Edinburgh; Black Marsden i s set i n that c i t y . The c o n f l i c t between Nameless and L has some resemblance to that between Marsden and Goodrich, and J e n n i f e r Gorgon, whom host wishes to wrest from guest, has an u g l i n e s s to her beauty even as Hebra had a beauty to her u g l i n e s s . Goodrich hims e l f has a \"scarecrow eye\" (p. 42), but must l e a r n to use i t , and i t i s as i f he were pushed by Marsden (who i s i n f a c t a \" p r o j e c t i o n \" [p. 32] of h i s h o s t ) , as L was pushed, i n t o d i s c o v e r i n g h i m s e l f . What then has become of Nameless? L i k e M a r i e l l a , l i k e P e t r a , l i k e Hebra, 108. he has become a place: the desert town of .Namless [ s i c ] , scene of the novel's most b i z a r r e fantasy. In a sustained piece of s u r r e a l w r i t i n g , Goodrich r e c o n s t r u c t s a journey to h i s childhood homeland, now l a i d waste by p o l i t i c a l t u r m o i l and yet f o r that reason \"a l a b o r a t o r y of s t a r t l i n g c o n t r a s t s \" where an experiment of great consequence might be s u c c e s s f u l l y brought o f f , a \"subconscious t h e a t r e or l i b e r a t i o n of men from f a n a t i c a l p u r s u i t s \" (p. 83). Goodrich's notes are i n f a c t that \" g u e r r i l l a t h e a t r e \" : as the c u l t u r a l emissary of a l a r g e r movement, he sets out to undermine both n a t u r a l i s m and the avant-garde, but i s q u i t e w i l l i n g to i r o n i z e h i s own theory of s p a t i a l i t y : one sp r i n g day he stops at Dean Bridge, high above the Water of L e i t h , to ponder the f a t e of those who have l e a p t from there, and i s l o s t i n h i s philosophy of i n t e r f u s e d space when he steps back i n t o the path of a e&r and i s almost k i l l e d . He i s a l s o q u i t e happy to l a y h i s n a r r a t i v e method bare. At the end of the Namless f a n t a s y , there i s an abrupt s h i f t to the f i r s t person, present :-.cohtinuous. I stop w r i t i n g suddenly and c l i p the pages t o g e t h e r — n e a r l y twenty to t h i r t y pages of notes and sketches I have made sin c e J e n n i f e r disappeared s e v e r a l hours ago around a bend i n the B o t a n i c a l Gardens. My notes are c o r r e c t i o n s and r e v i s i o n s of an e a r l y \" d i a r y of Namless\" i n order to b u i l d a new eye of the Scarecrow or stage of theatre of essences occupied by a phenomenon of p e r s o n a l i t y reaching back i n t o the s l a t e of childhood. Upon that s l a t e C l i v e Goodrich i s a given e x i s t e n c e and other buried traumatic existences as w e l l w r e s t l i n g one w i t h the other to express a caveat or unknown f a c t o r , an i n t u i t i v e f i r e music w i t h i n the hub r i s of assured c h a r a c t e r , assured r i t e s of passage i n t o death or namless town (p. 94). Then he begins again: \"My name i s C l i v e Goodrich. Yet a name i s but a cloak and sometimes a strange denuded nameless ' I ' steps f o r t h . \" The beginning again i s pa r t of the l a r g e r theatre.: i t marks a new-109. d e c i s i v e n e s s i n Goodrich which w i l l end i n the e v i c t i o n of Marsden and company. S t r u c t u r a l l y , t h i s d e c i s i o n w i l l end a l s o the n o v e l , but the n a r r a t i v e ' s r e t u r n to a k i n d of beginning, and f u r t h e r , to the notes of an e a r l i e r work, i s the mark of a continuous r e v i s i o n and r e i n s e r t i o n of a part of the o l d i n t o the new. This l o g i c of a margin which eludes the 31 c l e a n sweep i s a r e c o g n i t i o n that one does not i n f a c t begin w i t h nothing, but that what i s next to nothing may be of the highest v a l u e . I t l a y s bare once more the s t r u c t u r a l use of that \"unknown f a c t o r \" or senior form as a p o i n t of departure r a t h e r than a monad or a f i x e d pole i n a dualism. We have already seen H a r r i s adduce West Indian bareness as evidence of the West Indian a r t i s t ' s need to work w i t h the resources at hand, namely man. Now, as Goodrich's t a x i crosses the bleak underworld desert towards Namless, he remarks that \"a curious s u b t l e f l e s h i n g ( i f that was the r i g h t word)\" (p. 82) has appeared upon the r o c k s , w h i l e K n i f e the d r i v e r t e l l s of the . l i b e r a t i o n movement's hopes. I t i s p o s s i b l e to see 32 t h i s as a romanticism, a w i s h f u l humanizing of nature whose c o r o l l a r y i s that p e t r i f a c t i o n or displacement i n t o space of c e r t a i n c h a r a c t e r s . In f a c t the f l e s h i n g does not l a s t , but w h i l e i t i s there i t serves as a reminder of what H a r r i s sees as h i s primary f i c t i o n a l resouce, the marginal human. As Marsden puts i t i n a drunken apostrophe, \"the very desert of human consciousness c r i e s out that t a b u l a r a s a s l a t e i s the theatre of the uhini'tiate\"(p. 31). In the c o n t r a d i c t i o n between a t a b u l a rasa that i s the emblem of an i n i t i a t e avant-garde (with i t s clean sweep of the past) and one that invokes a theatre of the u n i n i t i a t e (with i t s e c l i p s e d past and marginal present) r e s i d e s an acute dilemma f o r the experimental n o v e l i s t . I t i s to H a r r i s ' s e x p l o r a t i o n of t h i s marginal consciousness and i t s f i c t i v e embodiments that we w i l l now t u r n . 110. IV. Experiment and the I n d i v i d u a l A convenient place to begin i s w i t h C l i v e Goodrich's second beginning i n Black Marsden: \"a name i s but a cloak and sometimes a strange denuded nameless ' I ' steps f o r t h \" (p. 94). More than an \" I \" steps out of Goodrich: Marsden i s part of him, too, and out of Marsden step J e n n i f e r Gorgon, K n i f e (there are three of him), and Harp. And yet the sum of these f i g u r e s , when they are ranked below Goodrich, i s not a u n i t but a c i p h e r . The paradox by which \"one\" might be both many and none, i s a mark of the p r e v a i l i n g temper, l i t e r a r y and p h i l o s o p h i c a l , which l a b e l s the c l a s s i c l i b e r a l i n d i v i d u a l an e x t i n c t s p e c ies. I t i s t h i s e x t i n c t i o n which the name \" C l i v e Goodrich\" c l o a k s . The w h i t t l i n g away of the centred l i b e r a l s e l f which began by d i s -carding a creature i n secure possession of a s o u l , was at l a s t to produce a creature possessed only by i t s possessions, notable among these that language of which i t once thought i t s e l f the master. For the b e t t e r part of a century, the d e v o l u t i o n of modernism has r e f l e c t e d , often d e s p a i r i n g l y , an unhappy knowledge that the centre cannot h o l d . Another of i t s l i t e r a r y tags that have passed i n t o common speech i s the hollow man, that c e n t r e l e s s subject which i s the f i r s t lesson of the end of l i b e r a l humanism. As the secure universe of i d e n t i t y has given way to a r e l a t i v i s t u niverse of r e l a t i o n s h i p , the locus of the i n d i v i d u a l — t h a t t e r r i t o r y which once allowed of no d i s p u t e — h a s come to be no more than the crossroads of a l l the t h i n g s he knows, a crossroads l e a d i n g each way to an \" i n t e r p e r s o n a l \" realm where, i n V i c t o r E h r l i c h ' s words, \"the emphasis i s on ' i n t e r ' r a t h e r than 'personal'.\"'' At the same time, and c o n t r i b u t i n g to t h i s d i s s o l u t i o n , the modern period has l e a r n t from Freud to recognize the turbulence that u n d e r l i e s i d e n t i t y , and has come a c c o r d i n g l y to grant d e s i r e a r o l e of such preeminence t h a t the C a r t e s i a n dictum might be modified to read: \" I wish, t h e r e f o r e I am.\" These two concerns, which are i n f a c t one, are brought together i n the t i t l e of an essay by Jacques Lacan, \"The Subversion of the Subject and the D i a l e c t i c of D e s i r e . \" I f d e s i r e seeks a s a t i s f a c t i o n so intense A as to tempt e x t i n c t i o n , i t i s both nothingness and another which support the d e s i r i n g i n d i v i d u a l . The case i s not as simple as t h i s , but to put i t so i s to capture both the l a c k i n the subject and the subject's wish to overcome t h i s l a c k . In t h i s he i s aided by that same language which produced h i s i d e n t i t y : the reader should recognize i n the metaphor of the r e t u r n to the inanimate (which Freud attaches to every l i v i n g body) that margin beyond l i f e that language gives to the human being by v i r t u e of the f a c t that he speaks, and which i s p r e c i s e l y that i n which such a being places i n the p o s i t i o n of a s i g n i f i e r , not only those p a r t s of h i s body that are exchangeable, but t h i s body i t s e l f . 2 The i n d i v i d u a l body, then, becomes not an i r r e d u c i b l e essence but a v i r t u a l i t y of language, the c o n d i t i o n of meaning f o r another, but not a meaning i n . . i t s e l f . T his i n s i g h t i s not n e c e s s a r i l y new (or French), but i t i s a modern one, and w h i l e we owe i t s f o r m u l a t i o n to s t r u c t u r a l i s m — b y which the subject i s i n e f f e c t an e f f e c t , or a s t r u c t u r e of a b s e n c e — we may see an e a r l i e r f i g u r a t i o n i n t h i s theorem of V i r g i n i a Woolf's: Hamlet and a Beethoven quartet i s the t r u t h about t h i s v ast mass we c a l l the world. But there i s no Shakespeare; there i s no Beethoven; c e r t a i n l y and emphatically there i s no God; we are the words; we are the music; we are the t h i n g i t s e l f . - ^ In t h i s sense, there i s no C l i v e Goodrich; there are h i s v a r i o u s aspects, Marsden, J e n n i f e r Gorgon, K n i f e , Harp, but even when these are co l l a p s e d back i n t o him, a l l that remains i s \"a strange denuded nameless 112. ' I ' . \" And now we may i n s e r t the sentence which immediately precedes t h i s announcement, where yet another \" I \" holds up a blank s l a t e . Upon that s l a t e C l i v e Goodrich i s a given e x i s t e n c e and other buried traumatic existences as w e l l w r e s t l i n g one w i t h the other to express a caveat or unknown f a c t o r , an i n t u i t i v e f i r e music w i t h i n the hu b r i s of assured c h a r a c t e r , assured r i t e s of passage i n t o death or .namless town (p. 94). Then . once more: \"My name i s C l i v e Goodrich. Yet a name i s but a cloak and sometimes a strange denuded ' I ' steps f o r t h . \" We must not l o s e s i g h t of t h i s \" I \" (there i s something of a pun on Goodrich's \"scarecrow eye\") f o r i t i s what w i l l d i s t i n g u i s h the H a r r i s i a n i n d i v i d u a l from the Lacanian one, but f o r the moment we may take up that \"hubris of assured c h a r a c t e r . \" When H a r r i s was s t i l l a poet r a t h e r than a n o v e l i s t , that i s , before h i s work could be sai d to in c o r p o r a t e characters p r o p e r l y (or improperly) so c a l l e d , one of h i s e a r l i e s t and acutest c r i t i c s remarked i n h i s poems 4 a t h r u s t ' i n i m i c a l to the i n d i v i d u a l as we understand the term.\" The c r i t i c , L.E. Brathwaite, went on to deplore the f a c t that i n the book of poems under c o n s i d e r a t i o n \"we f i n d no people we can recognize,\" and noted that where an E l i o t attempts to f i x the i n d i v i d u a l i n time and space; H a r r i s i s concerned w i t h a concept of time and space i n which the i n d i v i d u a l has l i t t l e p l a c e ; or at best a r a t h e r e q u i v o c a l i d e n t i t y . 5 The time i s now past, though not long gone, when each of these censures might have t r a n s l a t e d at once as a compliment to the experimental w r i t e r , and i t i s e a s i e r f o r t h i s reason to give Brathwaite's c r i t i c i s m the a t t e n t i o n i t deserves. C o r r e c t l y gauging the temper of the poetry, Brathwaite a l s o sensed, i n advance of H a r r i s ' s n o v e l i s t i c career, the fragmentation to come. What he could not have foreseen was the purpose 113. of t h i s fragmentation, a purpose which H a r r i s l a t e r made c l e a r both i n h i s novels and i n v a r i o u s c r i t i c a l and t h e o r e t i c a l essays. In one of h i s e a r l i e s t essays, H a r r i s declared that \"the i n d i v i d u a l i s not the s t a r t i n g p o i n t nor the goal of the human world\" (RT p. 21), and i n \" T r a d i t i o n and the West Indian Novel,'1'where h i s f i c t i o n a l programme i s set out, he s t a t e s f l a t l y : \"one i s r e j e c t i n g the sovereign i n d i v i d u a l as such\" (TW p. 34). In a s t i l l l a t e r essay, he speaks of \"the p h i l o s o p h i c a l hollowness of man,\" and remarks that w i t h i n every p r i s o n e r of h i s t o r y i s an attachment, i n v o l u n t a r y perhaps but concrete, to the very premises of h i s age. How could i t be otherwise when those premises are a l l he possesses or i s possessed by? (BC pp. 45 and 44) Yet there i s a sense i n which Brathwaite has put h i s f i n g e r u n e r r i n g l y on the nub of the matter, f o r i n the course of a remark on the omnipresence of c o n t r a d i c t i o n i n H a r r i s ' s work, he suggests that t h i s f e a t u r e i s \"an expression of u n c e r t a i n t y from the poet h i m s e l f . \" I t i s as an i l l u s t r a t i o n of t h i s u n c e r t a i n t y that he addresses H a r r i s ' s treatment of the i n d i v i d u a l . Such a d i v i s i o n indeed e x i s t s i n the n o v e l i s t , but i t i s one which he turns to advantage. While on the one hand H a r r i s has u n f a i l i n g l y and i n c r e a s i n g l y produced i n h i s work \" i n d i v i d u a l s \" whose masks s h i f t and crumble, whose i d e n t i t y i s always uns t a b l e , on the- other he speaks w i t h equal r e g u l a r i t y of \"the c r e a t i v e imagination as a centering process\" which may \" i n f u s e a d i v e r s e u n i t y of consciousness i n t o every c l o a k or v e h i c l e of memory; thereby s u s t a i n i n g the h i s t o r y of c r i s i s as a l i v i n g process of i n d i v i d u a t i o n r a t h e r than as an expendable and f o r t u i t o u s creed\" (UC p. 45). The c o n t r a d i c t i o n — c a p t u r e d here i n \"d i v e r s e u n i t y \" — is- replaced a l i t t l e l a t e r i n another such ambivalent phrase•which c a l i s up \"a c l a s s i c a l / g r o t e s q u e animal of which we know so l i t t l e \" (UC p. 47). I t i s as i f both the c l a s s i c a l and the modern i n d i v i d u a l were to be made one f l e s h . W r i t i n g of the o p p o s i t i o n between h i s t o r i c a l l i n e a r i t y and imaginative rupture, H a r r i s observes that \" i t takes a p e c u l i a r k i n d of mind...to per c e i v e both s i d e s of the c o i n i n h i s l i f e t i m e , namely the w a l l of p r e j u d i c e and the i n f i n i t e phenomenal resources f o r divergence and d i s c o n t i n u i t y \" (HFM p. 26), and perhaps t h i s c a p a c i t y f o r s u s t a i n i n g the dual accounts f o r the c o n t r a d i c t i o n . But on the evidence of the nove themselves, j u s t as we saw a preference f o r the discontinuous over the l i n e a r i n n a r r a t i v e , so we s h a l l f i n d the balance i n favour of the grotesque over the c l a s s i c a l i n character. And t h i s may be f o r no other reason than that i d e a l u n i t y i s destined to elude the most s t a l w a r t o r g a n i c i s t . In t h i s sense, the \"discontinuous or dotted l i n e \" which H a r r i s proposes f o r the p a t t e r n of h i s t o r y might e q u a l l y t r a c e the i n d i v i dual were not t h i s \" i d e n t i t y \" one which \" c o n s t a n t l y s l i p s from our grasp\" (AC p. 8). To t h i s end H a r r i s quotes Yeats: \"Man can embody the t r u t h but he cannot know i t , \" and coming upon the resurgence of d e s i r e we have not i c e d i n modern w r i t i n g , t h i s maxim assumes a s p e c i a l s i g n i f i c a n c e . These are, of course, p r o p e r l y p h i l o s o p h i c a l i s s u e s , and H a r r i s ' s experimentation t r e a t s them on i t s own terms. Our concern, t h e r e f o r e , must be w i t h the a e s t h e t i c consequences of p l a c i n g \" t h i s body i t s e l f \" i n the p o s i t i o n of a s i g n i f i e r , and we are shown the f i r s t of these by M i c h e l Foucault. Marking the end of c l a s s i c a l thought, Foucault records the enormous t h r u s t of a freedom, a d e s i r e , or a w i l l p o s i t e d as the metaphysical converse of consciousness. Something l i k e a w i l l or a f o r c e was to a r i s e i n the modern e x p e r i e n c e — c o n s t i t u t i n g i t perhaps, but i n any case i n d i c a t i n g that the C l a s s i c a l age was now over, and w i t h i t the r e i g n of represen-t a t i v e d i s c o u r s e , the dynasty of a r e p r e s e n t a t i o n s i g n i f y i n g i t s e l f and g i v i n g v o i c e i n the sequence of i t s words to the order that l a y dormant w i t h i n things.1 115. In l i t e r a t u r e , the age of r e p r e s e n t a t i o n was i n f a c t to o u t l a s t the '. Enlightenment and indeed to come i n t o i t s own i n an age of empiricism; the d e s t r u c t i o n of character begins i n earnest only w i t h that expressionism whose cano n i c a l example i s the Nighttown episode of Joyce's Ulysses. The r e j e c t i o n of the \" s t a b l e ego\" extends even to a l a r g e l y n a t u r a l i s t i c g Lawrence, but i t i s not u n t i l the nouveau roman that the impulse to c h a r a c t e r i z e works i t s e l f out. \"The c h i e f c h a r a c t e r — o n e l e a r n s — i s dishonest. He i s honest,\" says the bland n a r r a t o r of R o b b e - G r i l l e t ' s 9 Jealousy. More recent experimental f i c t i o n has c a r r i e d t h i s d i s i n t e g r a t i o n much f u r t h e r , and though there have l a t e l y been some moral noises about a r e t u r n to i d e n t i f i a b l e . c h a r a c t e r s , i t w i l l not be easy to put the pieces together again. Of h i s characters i n Palace of the Peacock, H a r r i s has s a i d that he wished to b r i n g them together \" i n a c u r i o u s kind of simultaneous sacred self-exposure and rhythm, ra t h e r than i n v e s t i n p o l a r i z e d i d e n t i t i e s \" (SI p. 44). Elsewhere, he speaks of Donne, Fenwick and Stevenson as \"agents of p e r s o n a l i t y . They are not sovereign p r i n c i p l e s \" (KK p. 52). A c c o r d i n g l y , when he comes to t r e a t the novels of others, he i s c r i t i c a l of the c o n s o l i d a t i n g impulse. In Conrad's Heart of Darkness, he sees Marlow d r i v e n to conceal from Kurtz's intended the t r u t h of Kurtz's \"malaise of i d e n t i t y , against h i s profoundest, most d i s t u r b i n g i n t u i t i o n of an otherness...the p u l l of l e g a c i e s of p u r i t a n s o l i d a r i t y triumphs and he c o n s o l i d a t e s a f r e s h a hollow p a t t e r n of self-made d e i t y \" (FP p. 7). In P a t r i c k White's Voss, he diagnoses a \"pathology of c h a r a c t e r \" (FP p. 8) which the n a r r a t i v e i t s e l f s u c c e s s f u l l y r e s i s t s : Voss's v e r s i o n of himself i s unexpectedly subverted. And of Naipaul's A House f o r Mr. Biswas, he remarks that the \"inner and outer poverty of Naipaul's c h a r a c t e r s — 116. w h i l e achieving at times memorable pathos—never erupts i n t o a r e v o l u t i o n a r y or a l i e n question of s p i r i t , but serves u l t i m a t e l y to c o n s o l i d a t e one's preconception of humanity.\" Thus we have \"a persuasion of s i n g u l a r and p a t h e t i c enlightenment r a t h e r than a t r a g i c c e n t r a l i t y or a c a p a c i t y f o r p l u r a l forms of profound i d e n t i t y \" (TW p. 40). These p l u r a l forms of i d e n t i t y i n h a b i t a l l of Harris''s>novels: none of those that I have c o n s i -dered so f a r i s without i t s doubles, and i n l a t e r works l i k e Black Marsden, these doubles become m u l t i p l e s . But j u s t as characters tend to s p l i t o f f from one another, there i s o f t e n a movement i n which t h i s d i r e c t i o n i s reversed and two separate i d e n t i t i e s overlap. Such a s t a t e c h a r a c t e r i z e s Harris's-seventh novel, The Waiting Room (1967). The Waiting Room i s an account f o r the most part of the imaginings of a b l i n d woman, Susan F o r r e s t a l . Susan's opposite number i n t h i s psycho-drama i s i n f a c t not her \"other,\" though he i s the \"other man,\" w i t h whom she once l i v e d r a t h e r than her present husband. He i s , moreover, a v i s i t o r i n memory alone, c a l l e d up out of a past which he and Susan shared before t h e i r e x p l o s i v e s e p a r a t i o n . So, as the Author's Note e x p l a i n s , \"he i s sheer phenomenon of s e n s i b i l i t y r a t h e r than i d e n t i c a l character i n the conventional sense\" (WR p. 11), and i n t h i s way the w a i t i n g room becomes both Susan's u p s t a i r s r e t r e a t and her very s k u l l which the o l d l o v e r penetrates from time to time. Susan's husband, who does not d i r e c t l y enter the n a r r a t i v e , i s s o l i c i t o u s i n the extreme but unable to touch h i s w i f e i n a v i t a l p a r t ; h i s very p r o t e c t i v e n e s s makes of him a \"watchman\" where the o l d l o v e r had been a \" t h i e f \" and r a v i s h e r . The l o v e r , who i s deaf even as Susan i s b l i n d (the husband i s n e i t h e r ) , i s known simply as \"he,\" a t h i r d person whose former crime t r a n s l a t e s at l a s t i n t o a t h e f t of guarded selfhood which undoes the c a t e g o r i e s t h i e f and watchman. In 117. the end, Susan and her husband are k i l l e d i n an e x p l o s i o n which destroys the w a i t i n g room and l a t e r , i n a \"delayed b l a s t , \" the l o v e r as w e l l . \"He,\" i n the j u n g l e s f a r away, has at l a s t entered the \"cave of Susan.\" The novel i s based on the j o i n t but d i s j o i n t e d d i a r y of the F o r r e s t a l s ( i n t o which \"he\" has made c e r t a i n i n r o a d s ) , a d i a r y which s u r v i v e s the e x p l o s i o n . Although t h i s e x p l o r a t o r y \"logbook\" i s \" h a l f - o b l i t e r a t e d , \" the fragmentation only served \"to enhance the e s s e n t i a l composition of the manuscript that i n v o l v e d a c c i d e n t a l d e l e t i o n s or d e l i b e r a t e erasures, r e a p p r a i s a l s , marginal notes, d i s s o c i a t i o n s of l i k e l y m a t e r i a l (as w e l l as a s s o c i a t i o n s of u n l i k e l y m a t e r i a l ) \" (p. 10), i n s h o r t , a l l those devices w i t h which we are now f a m i l i a r i n \"W.H.\"'s f i c t i o n . D i v i d i n g chapter f o r chapter i n t o two m i r r o r h a l v e s , the novel i s truncated f o l l o w i n g the chapter, \" B l a s t , \" so that Book I I , \"The Vortex,\" l a c k s two chapters which might have completed the correspondence w i t h Book I , \"The V o i d . \" The v o i d we w i l l now recognize as a common f i x t u r e i n H a r r i s ; the v o r t e x i s here a kind of s t i r i n the v o i d , being that point at which the v o i d i s breached, or at any r a t e , reached. In t h e i r p u r s u i t of each other and of e x t i n c t i o n i n t h i s v o i d , Susan and her l o v e r are to some degree helped i n that the one i s u n d i s t r a c t e d by l i g h t and the other undisturbed by sound. To emphasize t h i s f o r t unate d e p r i v a t i o n , H a r r i s has hung as b a c k c l o t h to t h i s drama that p o r t i o n of the myth of Ulysses's f l i g h t from C i r c e which shows the hero bound to the mast as h i s crew row past the s i r e n s , t h e i r ears sealed to the treacherous l u r e of the s i n g i n g . The myth i l l u s t r a t e s once more that paradox of possession i n d i s p o s s e s s i o n which The Eye of the Scarecrow described as \"seeing without succumbing.\" Here, i t i s a v i c t o r y over d e s i r e which i s yet a submission to d e s i r e , an embrace of the d e s t r u c t i o n which nonetheless preserves the i n d i v i d u a l 118. and allows him to hear without succumbing. The novel's f i r s t epigraph, from Keats's l e t t e r of October 1818 to Richard Woodhouse, states the opening premise of t h i s argument: It i s a wretched thing to confess; but i t i s a very truth that not one word I ever u t t e r can be taken for granted as an opinion growing out of my i d e n t i c a l nature—how can i t , when I have no nature? The i n d i v i d u a l has no \" i d e n t i c a l nature\"—has \"no nature\" at a l l — a n d yet i t i s p r e c i s e l y t h i s awareness which supports him i n that ambivalent return which was the subject of the Nightingale and Melancholy odes. By no accident has Harris chosen the least romantic of the Romantic poets to point t h i s theme; i n treating the same myth elsewhere he speaks of i t as i l l u s t r a t i n g \"a new form of ' c l a s s i c a l ' animation rather than 'romantic' escape or s e l f - d e l u s i o n \" (WS p. 53). I t i s t h i s recognition and di s p l a c e -ment of nothingness which gives the i n d i v i d u a l a bare capacity to act while di v e s t i n g h i s s o l i t a r y i d e n t i t y of a l l except those attachments which surround i t s u n r e a l i t y and postpone i t s drive to a n n i h i l a t i o n . In The Waiting Room (which room we have seen i s a kind of enclosing void, an intermediate place) t h i s i s expressed as \"the o b l i t e r a t i o n of the bubble of personality i n the ornament of love\" (p. 26): the i n d i v i d u a l i s allowed to \"know\" e x t i n c t i o n , or that c e n t r a l nothingness which personality occludes, while remaining insulated from i t s f i n a l i t y . Yet the purchase of t h i s i n s u l a t i o n i s possible only a f t e r the \"hubris of assured character\" has been abandoned. We may r e c a l l Zachariah Stevenson of Heartland, r e f l e c t i n g i n the forest on the lesson every conquistador who had been there before him had missed: \"They had apparently f a i l e d i n t h e i r mission to catch the u n r e a l i t y of themselves\" (p. 30). In the same way, Susan and her lover have been creatures of \" i d e a l c o n t r o l \" (p. 42), who b u i l t a \"curious superstructure of love and p r e s t i g e \" (p. 36) 119. about themselves. Only when they begin to demolish t h i s structure and plumb the void i t straddles do they approach the condition described i n the novel's t h i r d epigraph, from E l i o t : \"...a moment of exhaustion, of appeasement, of absolution, and of something very near a n n i h i l a t i o n . \" When t h i s process i s begun, the \"convertible v o i d \" of the waiting room turns from a \"dock\" and \"courtroom\" i n which Susan arraigns the lover who once.assaulted her, into a \"theatre of rehearsal\" that i s also an operating theatre. Here, both the assault and the successive eye operations which f a i l e d to save Susan's sight, are rehearsed simul-taneously. On the edge of consciousness, Susan i s also \"on an acute threshold of the cavern of r e a l i t y \" (p. 45) which i s exactly the u n r e a l i t y of h e r s e l f . No wonder as the seal of l i g h t was torn, the ornamental atmosphere and c u r t a i n rent, that the very t a t t e r s and figments of recollection...preconception...seemed to wave and f l o a t within and above an e s s e n t i a l bareness of conception, g l i m p s e d — f o r the f i r s t i n c r e d i b l e time—but t h i s , too, i n i t s inner conviction and r e a l i t y , was slowly descending into the abstract blaze of s o l i d darkness—immensity of f r a i l d i s t i n c -t i o n . It was t h i s d i s t i n c t i v e n i g h t . . . l i g h t . . . t h e most curious awareness of self-deception, i f self-deception i t was, border-ing as i t did upon the black s a i l of r e a l i t y — w h i c h cast- a dying i l l u m i n a t i o n upon a once f a m i l i a r (now unfamiliar) s e r i e s of landscape carved by the axe of the sea, r o l l i n g marble of ocean, k n i f e - l i n e of the r i v e r s — i o d i n e and grain of earth. Dying wound of i l l u m i n a t i o n and yet the strange thing was that there emerged a f r a i l t y of convertible properties l i k e a healing thread...design...which seemed to endure and outlast every shattered bone or region, stone or age, buried f r o n t i e r or condition (pp. 45-46). Now unconscious, Susan surrenders h e r s e l f as to a \"black\" p i l o t , weathered masthead, phantom of f l e s h within but beyond the sound of f l e s h , the echo of s e l f - r e g a r d , song of the sirens...One embraced and was held i n turn by t h i s \"deaf\" mast to which one was t r u l y bound and secured within the elements of d i s t r a c t i o n , paradoxical structure of l i b e r a t i o n , and within c e r t a i n undefinable radius of which—acute coherence and conversion of the s o u l — l a y the 120. choirs of v i s i o n — s h e e r tenacity (even profane c u r i o s i t y ) of the \"awakened\" eye within the l a t e n t crash and operation of darkness, sheer r e l a t i v e beam, heavy and l i g h t , g ravity as w e l l as i r o n i c weightlessness... Out of t h i s crash of darkness began to emerge one's \" l i g h t \" c r a f t . . . b i l l o w of the senses: l i g h t n i n g spar... canvas of surf unfurled...in the very teeth...grinding fury, thunder of engines... sea (pp. 47-48). The experience of nothingness (\"black s a i l of r e a l i t y , \" \"'black' p i l o t \" ) supports and indeed constitutes Susan inasmuch as she i s a h a l f -knowing, haIf-unknowing survivor. Being of non-being, that i s how t h i s J. as subject comes on the scene, conjugated with the double aporia of a true s u r v i v a l that i s abolished by knowledge of i t s e l f , and by a discourse i n which i t i s death that sustains existence.-^ So Lacan, on the subject's question, \"Who am I?\" one which he gives an e x c l u s i v e l y grammatico-linguistic answer: f i r s t person singular. The modern cogito's s e l f - i n q u i r y has absorbed philosophers from Descartes to Heidegger and Derrida. Harris treats i t i n passing i n a piece of l i t e r a r y c r i t i c i s m which he c h a r a c t e r i s t i c a l l y enters himself. Approaching the San Dominick i n h i s essay \"Benito Cereno,\" he asks: \"Who are the members of i t s crew? Whose value-studded masks do they wear? Who am I? What mask should I wear? \"(BC p. 46). These are pertinent questions for an author who, as author, i s not exempt from that f i s s i o n v i s i t e d on h i s f i c t i o n a l i n d i v i d u a l s , and who has declared that \"character\" i n the novel r e s t s more or le s s on the s e l f -s u f f i c i e n t i n d i v i d u a l — o n elements of persuasion (a refined or l i b e r a l persuasion at best i n the s p i r i t of the philosopher Whitehead) rather than \"dialogue\" or \" d i a l e c t i c \" i n the profound and unpredictable sense of person which Martin Buber, for example evokes (TW p. 29). Harris's invoking of Buber i s revealing, for there i s a d i s t i n c t mark of e x i s t e n t i a l phenomenology about h i s i n d i v i d u a l , and i t i s here that h i s hollow person would part company with Lacan's empty subject, for a l l that the void sustains both. Indeed the phrase \" p h i l o s o p h i c a l hollowness 121. of man,\" which occurs i n the essay \"Benito Cereno,\" i s followed by a t e l l i n g parenthesis: \"(hollow i n e r t i a yet s p a t i a l ground of hope).\" It i s t h i s hope that The Waiting Room sounds, and i t seeks to do so by advancing a claim for \"community\" which makes further recourse to nothing-ness i n order to create the subject's many others. Susan's eye operation i s \" t e c h n i c a l l y s u c c e s s f u l \" i n part because she has been the lover's \" t r i g g e r , \" as i t were operating on him i n her turn: t h e i r s i s a \"common step towards ancient s e l f - p o r t r a i t \" (p. 32). In order for them to discover t h i s otherness, they must discover the nothingness that l i n k s them. Susan l e t her hand f a l l again with b r u t a l resignation upon the blackened f e t i s h of the log-book. I t seemed to her that \" h i s \" anatomy parted i n s t a n t l y and ceased to be the b e l l y of c l o t h she s t i l l remembered l y i n g against her f e e t — p i l l o w or d o l l : i n f a c t nothing stood there now but a handful of skinny s a i l i n g pages h a l f - t o r n from t h e i r covers—broken l i n e s which one surmised had been ruled for r i b and bone. Yet even so Susan did not mourn t h e i r (or his) material departure: i f she were to be held g u i l t y and responsible for incapsulating some portion of her log-book into the void i t seemed she had done the r i g h t and true thing, a f t e r a l l , and that t h i s shattered fragment and image would return and grow ultimately to express a genuine faintness of s p i r i t l i k e the r a r e s t body of atmosphere imaginable to confirm those immaterial and c o n f l i c t i n g rumours of r e l a t i o n s h i p between creatures whose bodily s i m i l a r i t y and u n i f o r m i t y — profession or s t a t u s — s e r v e d to d i v i d e (whereas one would have thought i t would have united) them i n t h e i r i n t e r e s t s (pp. 35-36). The chapter which follows \"The Operation,\" \"Thing,\" attempts to v i s u a l i z e that (no)thing which runs through doctor and patient, who are now \" i n e x t r i c a b l y involved with the 'dead' choirs of v i s i o n they had i n f l i c t e d upon each other\" (p. 52). Accordingly the waiting room i s now once more that f l y i n g v essel which binds and l i b e r a t e s them. As t h e i r \"shared skeleton,\" i t becomes a mast \"of love, half-animal, half-human (saddle of earth, car of sky)—mnemonic cloud—'ground' of f l i g h t . . . compass of origins—convergence upon 'concrete' t r a v a i l — f l e s h 122. —THING...\" (p. 53). In h i s reading of the Ulysses myth, Harris speaks of the community of i n t e r e s t s on the deck of the ship as betokening a mutual support among di s c r e t e elements (captain, crew, mast, ship) through a displacement of responses from one to another. In t h i s way the waiting room becomes a \"waiting room of self-surrender or community\" (p. 36). At the end of \"The Void,\" Susan f e e l s that \"one was drawn by the skin of the vortex into the other's rent\" (p. 54), and i n the same way the novel ends with a r e p e t i t i o n , a kind of anterior r i b taken from i t s own body: *She drew him clo s e r s t i l l within the skin of another incongruous skeleton they shared, f l e s h or wood, swimming i n the glass of t h e i r shop window within and without. Antique display. Waiting room* (pp. 17 and 80). The concert envisaged i n The Waiting Room—Susan and her lover mating and remaking each other, the deaf crew acting for Ulysses, the mast that i s both Ulysses and h i s support, Ulysses hearing where the crew cannot— t r i e s to give consciousness a negative dimension which goes beyond both romantic f a s c i n a t i o n with the death of s e l f and absurdist preoccupation with the anxieties of the e x i s t i n g subject. Such a project must begin with a recognition of the i n d i v i d u a l ' s d e s i r e to appropriate the other, to make the other-in h i s image, for t h i s i s part of the desire that i s to be overcome. Like the representational s e l f , t h i s other i s also a kind of v e r i s i m i l i t u d e , only one projected rather than mimed, a representation of the other as oneself. It i s t h i s order, that of persuasion or c o n t r o l , which comes to be fragmented: hence the \"rent\" i n the other, the broken image. But beyond t h i s surrender of power there i s an admission of weakness which remains to be made, a weakness which must \"confess i t s own broken existence to plumb and v i s u a l i z e i t s true r e l a t i o n s h i p to freedom\" (p. 10). A thesis of strength-despite-weakness w i l l come out of t h i s confession, so that one must not top quickly dismiss i t as pragmatically unsound: p r e c i s e l y the completeness (or the realism) of categories such as \"weak\" and \"strong\" i s i n question, j u s t as the nature of an i n d i v i d u a l ' (or a group's) capacity to survive i s not explicable i n terms of power alone. S t i l l , there i s a way of showing t h i s r e s i l i e n c e , i f only f r a c t i o n -a l l y , and that i s the f i c t i o n i t s e l f . \"Art,\" Susan's lover pronounces, \" i s the phenomenon of freedom....What do I mean by phenomenon? The hole i n the monument, that's what I mean\" (p. 66). P l a i n l y , the author f e e l s t h i s t r u t h keenly (since he i s here tempted into speaking i n h i s own v o i c e ) , knowing what John Mepham has c a l l e d the \"desire to speak with appropriate i n t e n s i t y about things of which our knowledge i s most 12 uncertain.\" We must now ask whether t h i s desire finds expression i n a form which f i t s i t s i n t e n s i t y , whether the music the deaf ear hears i s given apt notation. Since what i s to be conveyed does not cohere sensibly, the form cannot be representational; Harris's f i c t i o n i s f o r t h i s reason i n v a r i a b l y fractured. \"Appearances cannot be grasped i n t h e i r e n t i r e t y , \" the lover continues. \"There's always t h i s 'negative' race with or against something...And one can never keep dead i n step\" (p. 67). Art, that i s to say, becomes t h i s negative way of showing an ungraspable r e a l i t y , one destined always to elude the sin g l e consciousness. The tableau of Ulysses and the sirens i s for t h i s reason described as \"the l i f e of consciousness i n a c i r c u i t of r e l a t i o n s h i p s — a d i a l e c t i c a l meeting ground i n t e r i o r l y v i s u a l i z e d of dance, of music and of images h a l f - s c u l p t u r e , h a l f - p a i n t i n g , \" giving r i s e to\"marginal f i g u r e s or species of f i c t i o n . . . \" (WS p. 53). The c i r c u i t of r e l a t i o n s h i p s , completed by halves and by marginal fi g u r e s , i s best shown j u s t before the end. Susan, who has been t a l k i n g 124. to her husband on the telephone, replaces the receiver and seems to wait for another c a l l . As she l i s t e n s , there i s a crash by which the na r r a t i v e a n t i c i p a t e s the b l a s t that w i l l destroy the antique room and those i n i t . The sea of t r a f f i c i n the street suddenly appeared to r i s e and she f e l t a f a i n t dry wave or shudder s t r i k e the wreck of the room: a blow not unlike the sound of her own f i s t dislodging i t s e l f from i t s shadow pressing into the eye of each f i n g e r - t i p . R o l l i n g \"log\"-book. Stranded telephone within the dust of memory. Toppling s k u l l , ornamental ear and mouthpiece. H a l f - t r a i l i n g , half-knotted s i g n a l and l i n e . Watchman. THIEF. Nothing moved. It was the strangest discordant f l i g h t of consequences she experienced—agitated body (vacant s t r u c t u r e ) , nerve-end, s t r i n g (bodiless s p l i n t e r ) , tautness of s a i l s t i f f as a comb upon whose giant ;brow nothing moved as i f \"nothing\" were \"something\". So obscure t h i s s h i f t or severance was i t seemed l i t t l e more than the p r i c k of an eye-tooth, the pressure of a f i n g e r - n a i l upon the palm of one hand. Nothing s t i l l moved—a f a i n t shadow perhaps against the b a n a l i t y and monument of s o l i p s i s : phantom erection and e j e c t i o n of parts i s s u i n g from the s o l i d tyranny of proportion to swing into new clockwise mouth and head, anti-clockwise defiant trunk and limb (p. 65). Here at l a s t the hole ( i n the \"monument of s o l i p s i s \" ) i s given shape; here i s that f r a c t i o n a l space, which we saw i n The Eye of the Scarecrow, where one i s able to \"be\" another. Out of t h i s vortex i n the void the other's c a l l comes: \"He addressed her from within h i s new s p i r a l \" (p. 66), and i t i s here that the c r y p t i c promise of the Author's Note i s r e a l i z e d : \"a f i c t i o n which appears to grasp nothingness runs close to a freedom of r e a l i t y which i s somethingness\" (p. 10). If the resort to paradox and apostrophe grate on s e n s i b i l i t i e s accustomed to the bald statement of f a c t , t h i s i s a mark not so much of a momentary opaqueness i n Harris's 13 most minimal f i c t i o n as of the intransigence of the models of f a c t i c i t y i t confronts. Tumatumari (1968), Harris's next and longest novel to date, i s an attempt to externalize the lessons of consciousness we have j u s t been considering. The i n t e r i o r world of The Waiting Room now opens onto a landscape r a t h e r . l i k e that i n Heartland (but a l i t t l e further into Guyana) and the cast comprises people whom, by Brathwaite's early c r i t e r i o n , we can recognize and hope to know. We would, however, be i l l - a d v i s e d to prod t h i s or that character, for Harris has not put away his hollowing t o o l s , wishing as before to undermine the \"convention of consciousness— i n s u l a r day or n i g h t — t o v i o l a t e a ghetto of temperament\" (p. 79). In order the better to follow h i s project, and consistent with i t s new topography, we w i l l pass from matters; l a r g e l y p h i l o s o p h i c a l to those psychological. The novel i s i n fa c t the record of a crumbling not so much of :the subject as of the subject's mental economy; the heroine, Prudence, suf f e r s a collapse which makes of the novel a \"THEATRE OF NERVOUS BREAKDOWN\" (p. 123) and a kind of l i b i d i n a l c r i t i q u e of pure reason. Prudence i s thirteen-months-married to the engineer Roi Solman who i s i n charge of a h y d r o e l e c t r i c scheme above the Tumatumari f a l l s . Labour problems with the l o c a l Indians have sent Roi to another part of the country i n search of fresh r e c r u i t s and he leaves Prudence, whose f i r s t c h i l d w i l l die i n infancy, i n the care of t h e i r maid (and h i s mistress) the Amerindian, Rakka. Roi races back when he hears of the death, but i n crossing the r i v e r h i s boat miscarries and he i s swept over the f a l l s and decapitated. When Rakka breaks the news of t h i s fresh tragedy, Prudence s u f f e r s a relapse. Confined to her bedroom, she dreams what i s the opening scene of the novel: coming down to the r i v e r at dawn, she finds the head of her sun king i n the water. The r e s t of the novel i s an evocation of her past, the t h i r t e e n months with Roi and Rakka at Tumatumari, and her Georgetown childhood as one of f i v e children of the celebrated h i s t o r i a n , Henry Tenby. Roi and Tenby have much i n common, chief among t h e i r shared t r a i t s being an apollonian f a i t h to which t h e i r respective professions commit them. That t h i s need not be so, that neither science nor art need be circumscribed by reason, i s part of the novel's th e s i s . Both men therefore s u f f e r a symbolic decapitation, each discovering himself to have been a \"clown of realism,\" the prisoner of a s t r i c t l y r a t i o n a l s e l f . Tumatumari, the name of an actual w a t e r f a l l , means \"sleeping rocks.\" Yet the s i t e i s also for Prudence a \"THEATRE OF AROUSAL\" (p. 123), an arousal, then, of that which sleeps. Through her \"game of the rapids,\" which she also c a l l s \"the game of inner space\" (p. 152), Prudence wakens both i n h e r s e l f and r e t r o s p e c t i v e l y i n Roi and Tenbyj. this.other'sleeper, discovering that turbulence which l i e s beneath the smooth face of the r i v e r . An epigraph makes th i s arousal the more p l a i n : The h a l f world i s the world of the shadow wherein the union of nature and society v i o l a t e s and k i l l s the incestuous image. The incestuous image loves i t s own kind, or that which i s made i n i t s image, being thereby v i s i b l y complete and s u f f i c i e n t i n i t s e l f . This image the h a l f w o r l d — t h a t which sleeps below the surface, that which i s other ( i t or id)—overwhelms. The \"union of nature and s o c i e t y \" has implications we s h a l l come back to; here we must follow the epigraph to i t s conclusion: An enormous mourning camouflage develops around the occasion, an occasion that i s i t s e l f i n deepest correspondence with what i s l o s t and a l i e n and dies to be reborn. Another element has been introduced here, or a correspondence with another the concept not only of what i s buried and submerged but also of what i s a l i e n and removed. Where the f i r s t concerns, as we have seen, the three main characters, the second has i t s f i c t i o n a l embodiment i n rcertain.minor 127. characters of the novel, beginning with Rakka h e r s e l f , and a small band of \" l o s t \" Indians who are wasting away, but extending as well into the Tenbys, a coloured family who have c e r t a i n skeletons i n t h e i r c l o s e t . Roi's flaw i s of a d i f f e r e n t kind. He does not conceal the f a c t that he i s part Indian, but h i s very admission that he i s an \"employer of consciousness ( h a l f - n a t i v e , h a l f - f o r e i g n ) . An i n s i d e r / o u t s i d e r \" (p. 52) commits him to a paternal gambit by which he seeks to r i t u a l l y placate, and thereby c o n t r o l , h i s labourers. By t h i s means they become \"his 'Indians', h i s ' c h i l d r e n ' , \" and Rakka h i s \"Mistress in>the cupboard\" (p. 47). His strategy i s pursued i n the name of \"day-to-day r u l e , \" \"emancipation— enlightenment,\" and with a r e s o l u t i o n that makes of him an \" e l e c t r i c f i e n d . \" Yet he has had h i s warning: f i v e years e a r l i e r , while i n s t a l l i n g an automatic gauge i n a well above the f a l l s , he slipped to a \"head-on (bulb of safety within) collision...'When they pulled me up I f e l t l i k e glass. Shining and white. E l e c t r i c i t y to l a s t a l i f e t i m e ' \" (p. 25). Later the well was abandoned, but, boarded over, i t s concrete s h e l l was to become Prudence's favourite chair and the rock at i t s bottom the alchemical counterpart of that beneath the f a l l s . Here Prudence s i t s to conjure up the past, so that i t i s both her father's \"Chair of History\" and a \"chair of pride\" (which, one might say, goeth before a f a l l s ) . There i s a sense i n which Prudence assumes r e s p o n s i b i l i t y f o r her husband's death, so that he dies \"THROUGH HER (AS IF SHE WOULD SUMMON HIM, PUSH HIM)\" (p. 28), ju s t as Nameless pushed L into the canal i n The Eye of the Scarecrow, turning her love into a d i s i n t e r e s t e d thing. This temper she has learnt from Roi himself, who wishes to implant i n her \"not the incestuous mirror of love but the sceptic withdrawal at the heart of nature\" (p. 27). In her memory he becomes \"no longer a ti s s u e of fear 128. but wires knotted into a c r u c i a l rose which penetrated her\" (p. 54). The type of technocratic pride, Roi appears to know his lesson before he has learnt i t : he seems already informed of (and w i l l i n g to discourse on) the s t o i c truth which the Indians of the story come to represent, and t h i s before h i s f a l l . So that i t i s i n Henry Tenby that the narrative achieves a success which the half-autobiographical Roi (with h i s ready insi d e knowledge) does not allow. In speaking of another coloured hero, t h i s time the r e a l l i f e revolutionary Toussaint L'Ouverture, as depicted i n C.L.R. James's Black Jacobins, Harris has remarked that h i s bold r e a l i z a t i o n by the author avoided \" f a s c i s t ornament or l i b e r a l s elf-deception,\" but that the \"curious almost unwitting irony of the work\" i s that Toussaint \"emerges not because he f i t s i n where James wants him to stand, but because he escapes the author's self-determination i n the end\" (TW p. 44). Quite the same might be said of the composite appollonian f i g u r e , Roi-Tenby: where Roi seems precast, h i s father-in-law takes shape i n the very instant he loses dimension. Tenby's moment of truth comes at the end of h i s l i f e (though he has had glimpses of i t e a r l i e r ) and i t i s only as a ghost brought back by h i s daughter that he speaks with authority. In h i s dissolved person, we in'-.turn get a 14 glimpse of what might be c a l l e d \" h o r r i f i e d consciousness.\" As he died, Tenby's expression was \"so twisted he became a creature cloven i n two, one face beneath emerging from the o l d \" (p. 45). He had, of course, been aware of h i s divided l i f e , and at times of c r i s i s reminded h i s wife of h i s \"bogus h i s t o r i c a l mask,\"but for the most part he had managed a compromise \" u n t i l the day of h i s death when something else, the daemon behind the virtuous mask, sprang into view\" (p. 46). In Tenby, the two \"others\" coalesce; both psychological and s o c i a l 1 2 9 . denials merge. The concealment (when distinguished guests are present) of Hugh Skelton, the black son among four white c h i l d r e n , a concealment which Tenby does not authorize but which he countenances, i s of a piece with h i s purging of a l l emotion from h i s wr i t i n g . Thus the d i v i s i o n between h i s published and h i s unpublished work sets up a d u a l i t y of ego and i d , conscious and unconscious. On the one hand, refinement, s t a t i s t i c s , the mask of a public s t y l e : \"RADIO SKELETON. Committed to formal documen-tary, s k i n f l i n t essays, h i s t o r i c a l a t t r i b u t i o n s which were bland and persuasive, vested i n t e r e s t \" (p. 1 2 9 ) ; on the other, secret d i a r i e s and unpublished plays, whose atmospherics disturb h i s program: \"secret wave-length from the f u t u r e — T h e a t r e of Nervous Breakdown—hum of the grotesque\" (p. 1 2 9 ) . The stage i s set, then, for a return of the repressed, and i t comes as surely as i t does to that other c l a s s i c a l h i s t o r i a n , the Baron von Aschenbach. The year Hugh Skelton Tenby was born, h i s father wrote h i s essay on the \"Population Question.\" As Prudence s i t s i n her \"Chair of the Well,\" quotations from t h i s essay appear at random i n the body of the narr a t i v e : \" 3 , 0 1 0 , 0 0 0 Negroes were transplanted from A f r i c a to the B r i t i s h Colonies from 1680 to 1 8 3 4 . At the time of emancipation but 5 0 0 , 0 0 0 slaves remained to be freed\" (p. 9 8 ) . Among East Indians, \"at no time were ever more than 33 women brought i n to each hundred men\"; the \"Chinese of 1853 never saw a sing l e woman of th e i r race u n t i l 1 8 6 0 , \" and then there were \"about 15 females to every hundred males\"; Amerindians suffered \"a depletion of 2 0 , 0 0 0 souls during the f i r s t hundred years of Dutch occupation\" (pp. 9 7 - 9 8 ) . \"But canes were growing\" (p. 9 9 l ^ Then Tenby's pen f a l l s from h i s hand into the we l l , and a new h i s t o r y , driven by a l l the desire pent and punished i n those words, comes to be written. It i s a magnificent piece of w r i t i n g : the remainder of the novel shows Harris at work with an i n t e n s i t y and daring sustained at t h i s p i t c h so f a r only i n Palace of the Peacock. The Tenby who has hit h e r t o conscripted h i s \"muse\" (\"I must do nothing so hideous as erect a scandal. Merely report an e r e c t i o n \" ) , now finds himself confronted by a \"waif of the s t r e e t s \" he had met i n the grim post-War Europe of 1919. Married to t h i s new \"muse of h i s t o r y , a l i e n f a b r i c — d e g r e e s of fear, fear of the unknown, psyche of a new world\" (p. 103), he fi n d s h i s w r i t i n g become un d i f f e r e n t i a t e d , promiscuous i n the very sense of the word. Linked to the primary process, i t records the many faces of anxiety and neurosis, d e s i r e and fear, shaking o f f that control whose order too e a s i l y translates as domination.\"*\"^ ROOM NUMBER 1924. Brothel, of Masks. I t was long past midnight. Prudence discerned him (her father) far beneath strapped i n h i s space ship. No longer half-man, half-horse but half-man, half-mask. Half-man, half-woman. Business was poor on the mountain of souls. A l l he had been able to squeeze out of the b i t c h who ran the establishment was a cursed j o b — l o o k e d l i k e a c r i p p l e . Underweight. Undernourished. Sometimes there was a shortage of f a b r i c . One and the same. One had to bear with i t . Limbs of straw. Bed of stone. Postwar years. P o s t - r i o t days. The whole land mourned and awaited the return of the Hero—the coming of a god—long since consigned to rot and waste—womb of s i l e n c e . The space ship heaved—casket and hearse—stood on i t s t a i l l i k e a dog at a post—lamp-post—epitaph: half-mask or woman rose into view sprinkled by immensity—a patient yet inexhaustible c r e a t u r e — goddess of urine and s t a r l i g h t — b r u i s e d by her father's f i s t s — black and blue. Conception of Hugh Skelton—Skeleton i n the Cupboard 1924 Born 1938 Prudence shivered. Unholy brother and treaty of s e n s i b i l i t y . Shove him underground. The whole land mourned for the b i r t h of s a c r i f i c e . Wailing women under the s t a r s , the moon and the sun. Sprinkled by immensity. Shove him underground. It was a strange wild outcry—hoarse and f a n t a s t i c within the throat of the waif of the s t r e e t s . Waif of the docks and s t r e e t s . Waterfall of prophecy. Bath. SHIP OF THE WAIF. Within t h i s s p r i n k l e — h e r father's quest of loathing and des i r e , treaty of s e n s i b i l i t y — o n e saw the shoal of h i s t o r y — t h e remoulding of every vessel into the Matriarch of Obsession. Bury him s i x feet underground. He had abused her, bruised her for centuries. Sometimes f i f t y i n a sing l e night. Now i t was as i f she saw him ripening in t o one black man. Many men subsumed i n the Phallus. Which must now therefore serve her, s a t i s f y a l l the appetites i t had created, scenes—scores of m i l l i o n s . I t was her t u r n — the turn of a l l the women he had raped to l o r d i t over him. To p u s h - p u l l - d r i v e . .. (pp. 100-101). When the old taboos have been v i o l a t e d and fear of the other overcome, the s p e l l of sameness i s broken. U n t i l then, (one can only whisper with the breath of the wind)—archangel of the future, sculpture of earth-shaking compassion and immunity to fear upon which dogs of ivory are chained whose masks of s o l i p s i s no longer confine u s — i v o r y tower of poverty, ivory tower of wealth, ivory tower of race, ivory tower of...Their name i s Legion. A long way to go before t h e i r b i t e can be endured: sink into the ground—give teeth to conscience?:-borie to conscience, blood to conscience....\" \"Prick to conscience.\" \"Yes. Pr i c k to conscience. In the meantime....\" \"In the meantime what?\" the waif of the docks and stre e t s asked. \"We must l i v e with FACE LIFT...\" he laughed with a groan and a bark. \"Jack History,\" the waif of the streets c r i e d . \"What an enormous face l i f t . Enormous joke. There's a p r i c k f or you.\" (pp. 104-105). The \"Population Question\" has taken on quite another colour, and to emphasize the matter of r e s p o n s i b i l i t y , the narr a t i v e presents a picture of Hugh Skelton shot i n the stre e t s of Georgetown i n the Budget Riots of 1962: \"Message for Hugh Skelton. This b u l l e t f i r e d by your father's r i c h k i t h and k i n — a l l races of endeavour—white+brown+black\"(p• 120). Here again i s that \"nightmare of h i s t o r y \" we saw Nameless invoke i n The Eye of the Scarecrow, and only now i s that unkept promise, to trace some v i c t i m of p o l i c e f i r i n g , f u l f i l l e d . The purpose of t h i s exercise? \"Dream therapy—shock therapy... Resurrect the past i n order to see through the present\" (p. 126). So, when Prudence begins to learn the rules of t h i s historico-psychotherapy, she sees an eye open i n the w e l l , the mark of that other or \" I T \" which gives the l i e to the ego's representations, being \"a h a i r l i n e or crack within the Obsessional Mask of an Age\" (p. 114). For the i n d i v i d u a l , Harris's p r e s c r i p t i o n i s f i r s t a kind of descent into \"oneself\" which recognizes the hollowness of t h i s s e l f . Seated i n h i s Chair of History, Prudence's father c r i e s out to her: \"Close your eyes. Tight. What do you see?\" \"I see nothing. Just a few strokes...dots...spread out l i k e a map... shapes i n a bottomless pool...\" \"Nothing,\" he agreed....One day you may learn to look back at t h i s dwindling moment (soul's straw) and wonder... whether there was anybody there but an abstraction of y o u r s e l f \" (p. 123). But, eyes open, Tenby demands a further recognition, one which Roi, who i s \" i n pursuit of and pursued by 'contradictions',\" a n t i c i p a t e s : \"a digestion of contrary elements\" which might lead to that \" c l a s s i c a l / grotesque\" s e l f Harris p o s i t s . This motion passes at l a s t into the primal state of the i n d i v i d u a l unconscious, \"the Dark, black amoral dark\" (p. 134) where there i s no negation. This i s , as Harris recognizes, treacherous, even forbidden ground, but p r e c i s e l y because i t i s forbidden i t i s to be v i o l a t e d . Its s o c i a l and natural equivalent i s more troubling: an \"underlying sardonic f l u x \" to things, where the contradictions of h i s t o r y seem dissolved or at l e a s t held i n suspension. Here then i s the \"union of nature and s o c i e t y \" foreshadowed i n the novel's second epigraph, one which f i n d s i t s philosophic expression i n a r e v i v a l of that \" d i s c r e d i t e d manifesto—red-in-tooth-and-claw evolutionary materialism' (p. 141). Not s u r p r i s i n g l y , the Indians of the novel come to embody the v i r t u e of stoicism.\"'\"'7 Stoicism i s an i n d i v i d u a l a f f a i r ; the \" c o l l e c t i v e \" Brathwaite saw i n the poems turns out to be something nearer a c o l l e c t i v e unconscious, which supports rather than undermines the i n d i v i d u a l . But the sense (and even a doctrine) of \"community\" i s strong i n Harris's work, and the q u a l i t i e s of compassion and love, which carry h i s philosophy beyond a s o c i a l Darwinism, are the l e a s t private of responses. We do not, then, f i n d the c l a s s i c a l i n d i v i d u a l restored; what suf f e r s i s that i n d i v i d u a l ' s r e c o g n i z a b i l i t y (which we w i l l remember to have been Brathwaite's c r i t e r i o n ) , f or from the s t a r t Harris has i n s i s t e d on confronting \"the unrecognizable features of the human heart\" (FJO p. 79), those which astonish Tenby at the end of h i s l i f e . The n a t u r a l i z i n g of society and the i n d i v i d u a l (a motion consistent with the displacement of time into space, or h i s t o r y into nature, which we noticed i n the l a s t chapter) i s only ha l f the programme, and though i t 18 sometimes verges on what might be c a l l e d Gnostalgia, i t i s not auto-m a t i c a l l y a reactionary impulse. Nor are the reasons for t h i s exploration of \"neglected areas within ourselves\" (SI p. 41) to be roundly diagnosed as a p r o j e c t i o n into n a r r a t i v e of personal contradictions (Brathwaite's \" d i v i s i o n i n the poet,\" or indeed Roi's \"extremes—extremity of loathing and d e s i r e \" [p. 92]) and the matter l e f t there. \"One must not read too much into the night of things,\" the lover declares i n The Waiting Room, and while a psychoanalytic response to t h i s d e n i a l might be to begin i n v e s t i g a t i n g here and at once, I would suggest that we read H a r r i s ' s engagement with darkness and void (which go by many names, from \"inner space\" to a Jungian \"objective psyche\") as a f i g u r a t i v e attempt to keep open and a l i v e a contradictory other which w i l l not succumb to the homo-genizing advances of the same. The nature of community, as Harris conceives i t , i s p r i m a r i l y hetero-geneous: hence h i s r e i t e r a t i o n of the need to l i v e with contraries (as d i s t i n c t , f o r example, from \"the t o t a l i t a r i a n basis of community—the t a c t i c of fascism which battens on fear of contrasts\" [NP p. 144]). 134. In turn, t h i s i s where i n d i v i d u a l i t y finds a precarious raison d'etre: the very fragmentation of the i n d i v i d u a l ' s wholeness, i n a \"theatre of nervous breakdown,\" for example, becomes a model of a larger s o c i a l process. Her c h i l d and husband dead, Prudence finds h e r s e l f \"searching for a concen-t r a t i o n or l o c a t i o n of loss to serve as the medium out of which a new i l l u m i n a t i o n of f e e l i n g could emerge\" (p. 17). And i t i s j u s t the same with the \" l o s t Indians of the Sun\" i n Tumatumari, or the wasting Amerindian remnant of Guyana, who here as everywhere i n Harris's novels p e r s i s t as what Roi, i n a \"voice from the underground,.\" c a l l s \"the conscience of our age...In t h i s part of the world anyway...our precious scarecrow brood\" (p. 35). The \"necessary v i o l a t i o n \" of cultures then, so f a r from complacently r e i n s t a t i n g natural s e l e c t i o n , requires that the other be part of the heterogeneous community and yet for t h i s reason r e t a i n i t s a l i e n aspect. The \"breakdown\" v i o l a t e s that preservation (or reserv-ation) i n t a c t which marks the persistence of power, whether at the l e v e l of society (where Indians become \"Indians\") or of the i n d i v i d u a l (where love turns out to be protection of the other for oneself).. In each of these cases, the \"character\" of the other i s determined by the representor, who thereby becomes the representative. Hence the deceit of recognizable \"representation,\" of i d e n t i t y i t s e l f , and hence the experimental d i s t o r t i o n of the mimetic mode. The \"fear of the stranger\" within and without, the \"incestuous barricade of f a m i l i e s \" (p. 71), i s a r e j e c t i o n of the contradictory other by a f i x i n g of i t s i d e n t i t y . But what i f that other (not to speak of oneself) were without i d e n t i t y , were so weak or reduced as to be nothing? This i s j u s t how Tenby's new muse appears before him when he returns to the Brothel of Masks, and understandably he has trouble recognizing or placing her: YES SIR GOD FATHER OF LOVE—she had been there a l l along (his l o s t waif of the streets) disguised as nothing, a mere b u t t o n — t h e r e f o r e impregnable: h a i r l i n e or crack i n the obsessional mask of an a g e — f l i c k of transparency which cloaked h i s sight (p. 119). The nothingness of the i n d i v i d u a l has assumed a new dimension, and to match i t , h i s t o r y i s imaged as a \"bottomless pool\" (out of which the waif emerges), receptacle of dregs and r e f u s e , a l l those discarded scraps which, as we saw from h i s patchwork s t y l e i n \"Experiment and Language,\" i t i s Harris's desire to rescue. For the i n d i v i d u a l t h i s s i g n i f i e s both \"the s p l i n t e r i n g of p e r f e c t i o n i s t assumptions... f a l l of Eldorado, f a l l of the c l i f f of f a i t h \" and, a f t e r the f a l l , a source of \"new engines or structures of the psyche\" (p. 153), put together a f t e r a fashion we w i l l examine i n Harris's next novel, Ascent to Omai. Supporting the new h i s t o r y , i s that f a m i l i a r d i v i s i o n i n the Guyana novels between i n e r t i a and v i t a l i t y as figured by coast and i n t e r i o r . In Ascent to Omai (1970), t h i s psychogeography i s l o c a l i z e d . The i n t e r i o r now becomes Omai chasm, an abyss into which the C h r i s t - l i k e hero, V i c t o r , 19 peers from time to time during h i s s o l i t a r y climb up the h i l l of Omai. Invoked i n various c o n t e x t s — t h e chasm in V i c t o r ' s side, the chasm between a p r o s t i t u t e ' s t h i g h s — t h i s deep romantic chasm becomes an unashamed image of the i r r a t i o n a l , a use which i s s p e c i f i e d i n the second of the novel's two epigraphs. Since \"adventure\" and \"science\" have led over many centuries to the denigration of humanity, robot law, unfeeling yoke, there i s no ground of a l t e r n a t i v e s but to recover the \"dangerous\" chasm, the \"forbidden\" ascent and seek a new dimension of f e e l i n g — a new oath of humanity. The quotation marks which set off \"dangerous\" and \"forbidden\" i n t h i s passage should d i s s i p a t e both the notion that t h i s i s an innocent or unwary return to d i s c r e d i t e d emotions and the old fear that that way 136. l i e s a kind of p o l i t i c a l madness we had better shun. Harris i s e n t i r e l y aware of the r i s k he takes, and i t i s along that face where hi s t o r y over-hangs legend and f a c t i c i t y f e e l i n g , that he has chosen to cut hi s f i c t i o n a l d e f i l e . From noon to sunset, s i x hours, V i c t o r climbs i n search of h i s father Adam's mining claim on the h i l l . Struck by a f a l l i n g stone, b i t t e n by 20 a tarantula, he presses on u n t i l he catches the g l i n t of l i g h t o f f f i r s t an aeroplane i n the sky and then the wreckage of one on the ground. Here he discovers the s i t e of h i s pork-knocker father's claim: \"here Adam had f i r s t come and s e t t l e d with a woman upon h i s release from prison\" (pp. 47-48). He crawls into the burnt and now overgrown s h e l l of the crashed plane, h i s head almost touching the ground l i k e one of those limbo dancers he remembers from h i s childhood, \"dancing under a hori z o n t a l pole through what seemed the keyhole of space\" (p. 48). In t h i s f l u i d zone of \" a g i l i t y and r i g i d i t y , v e r t i c a l pole, h o r i z o n t a l couch, wheel and spin, limbo a i r c r a f t , \" he begins to reassemble h i s past and to write, through an imagined judge who went down with the plane, a \"novel h i s t o r y \" of h i s father's past as w e l l . Adam had been a dancer and pork-knocker who, upon the death of h i s wife, became \"stone drunk, crazed by g r i e f , and had returned to h i s o r i g i n a l c r a f t , welding\" (p. 30). Poorly paid, he squandered his l i t t l e money on women he brought home, while the boy V i c t o r would \"hide beneath the p e t t i c o a t of h i s ancient mother and keep h i s eyes glued through i t s misty f a b r i c upon the l i v i n g copulation of the dead\" (pp. 30-31). At ten, V i c t o r won a scholarship to the best day school i n the land, and there proved himself \"a child-prodigy, monster.\" After c l a s s , he would amuse himself by l y i n g i n wait outside the foundry with a mirror i n h i s 137. hand to t r a in the sun on h i s father's face, so that Adam would brush \" f u r i o u s l y , i r r i t a b l y — a t spider or bread.\" One day h i s father did not appear. A s t r i k e had begun, one that was to l a s t s i x months and end only with Adam, driven to desperation, burning down f i r s t the factory and then hi s own house. On hearing the sentence passed—seven years' hard labour — V i c t o r had run away from home and school, leaving only rumours behind him. Now, f o r t y years l a t e r , he journeys to Omai and there imagines a r e t r i a l of the past by the same judge who had sentenced Adam. Sensing that the plane i s to crash, the judge has nevertheless boarded the a i r c r a f t , and i t i s h i s gnomic s c r i b b l e s , t h i r t y thousand feet above ground, which constitute the bulk of the novel. In a c l e v e r l y orchestrated ending, the crash of the plane and the burning of Adam's house merge i n the l a s t f l a r e of day, so that V i c t o r looks up at l a s t to find h i s long-lost father who had set f i r e to the one f i g h t i n g the blaze i n the other. By the end, the hero has come to be \"Victor/Adam,\" a composite f i g u r e whose new authority springs from having reached that c l a s s i c psychoanalytic s t a t i o n , the confronting of the dead father, a r i t u a l we saw enacted i n The Eye of the Scarecrow as w e l l . It i s also a recognition of the death i n oneself of those numerous d i s c r e t e past persons whose apparently seamless contiguity makes up that uniform \"character\" i n whose proper name one masquerades. In Ascent to Omai, the death of these \"old and new persona-l i t i e s \" (TW p. 28), i s the \"game of the stone.\" Looking back on h i s childhood game of tossing pebbles into a canal, V i c t o r inscribes on each of the concentric horizons of h i s l i f e a separate epitaph. This r e a l i z a t -ion that \"he was to die again and again\" (p. 92) i s the \"drama of puberty\" by which the boy V i c t o r frees himself f i r s t from mother (the housecoat retreat) and then from father (the welder's mask) u n t i l he assumes 138. r e s p o n s i b i l i t y f o r h i s own creation. But there are wider implications to the judge's b e l i e f that \"that small boy could be, i n f a c t , the author of himself\" (p. 79). V i c t o r ' s coming to terms with catastrophe and los s i n i t i a t e s as well a philosophy of persistence i n the face of devastation: inoculated by f i r e , insulated from f i r e , he began with the charcoal of memory—epitaphs and s t a g e s — t o adumbrate, from an unconscious/subconscious struggle with fate, a deeper and more far-reaching proccesional note of l i b e r a t i o n (p. 109). The subconscious now touches upon the conscious i n a manner which Harris w i l l endow with both u n i v e r s a l and s o c i a l s i g n i f i c a n c e , through a p h i l o -sophy so intensely held that f or V i c t o r i t \"bordered upon a r e l i g i o u s conviction\" (p. 18). The question i s t h i s : sentence having been passed in the very entrenched nature of things, wherein lay the p o s s i b i l i t y of parole, genuine parole, true parole from the whole f o r l o r n prison-house of adventure, claim of Adam, backside of the moon, OH MY? (p. 51) The answer i s of course not on Omai, but i n Omai chasm. And t h i s chasm i s now conceived as a limbo zone i n both man and nature which allows for a kind of redress i n a world of necessity. The \" s a n c t i f i c a t i o n of space\" (p. 89), which i n the i n d i v i d u a l becomes a \" s a n c t i f i c a t i o n of vacancy\" (p. 34), i s a gesture I traced at some length i n the l a s t chapter. By i t , the chasm i s a repository \"elsewhere\" of what H a r r i s has c a l l e d a \"sacred otherness/darkness\" (BC p. 52), which i s a resource (rather than a source, or origin) i n times of catastrophe. Reduced to u t t e r inconse-quence, the i n d i v i d u a l finds h i s element i n the very n u l l i t y of h i s circumstances, and f a b r i c a t e s a more c r e d i b l e s e l f than any wrought from an o r i g i n a l plenitude. He has, a f t e r a l l , nothing to l o s e . In the p i t t e d landscape of Omai, t h i s i r o n i c discovery of something i n nothing i s expressed by \"glimmers of sun...like e l e c t r i c l i g h t stored i n the ruined body of the bush\" (p. 49). This explains the play (some might say, t r i c k ) of mirrors i n Ascent to Omai: a play by which some of the randomness i n the heap of broken images (glass, t i n , wing-tip) that i s the world, i s given s i g n i f i c a n c e . Coincidence, that i s to say, becomes the novel's many angles of incidence ( i n mirror, aeroplane, welder's a r c l i g h t , surgeon 1 lamp) by which l i g h t i s trained and i d e n t i t y salvaged from r e l a t i o n s h i p . Hence, too, the prominence, i n t h i s and many another Harris novel, of the pork-knocker. For the pork-knocker i s , as I have suggested, that b r i c o l e u r whose a c t i v i t y endows random objects with a conjunctive s i g n i f i -cance beyond (and often despite) t h e i r o r i g i n a l purpose or purposelessness. So Adam, the f i r s t pork-knocker, who upon h i s release from prison must st a r t with nothing, goes to work on the wreckage of the aeroplane. He had salvaged a piece of t i n for a headboard or witness to h i s claim since t h i s had to be erected, according to law, to ensure h i s prospecting r i g h t s . I t was now a l l overgrown with fern V i c t o r saw l i k e tarantula, masked f a b r i c or a i r c r a f t on which had been inscribed—MINING CLAIM TAKEN BY ONE ADAM, MANNA OF SPACE, THIS CENTURY OF GHOSTS, TWENTIETH CENTURY. (It was the habit of porknockers to chri s t e n t h e i r claims with i d i o -s yncratic r e l i s h compounded nevertheless of curious irony and compassion) (p. 48). The salvaging pork-knocker i s an image of Harr i s ' s own symbolic experimentation, an experimentation which snatches meaning from the jaws of the void, even at the pr i c e of a c e r t a i n romancing. The n o v e l i s t i s , of course, a l i v e to t h i s r i s k ; h i s i s no innocent symbolism. Here he allows an Adam imprisoned i n and by things to view a more believable world: A roof, a f t e r a l l , which had been sti t c h e d with planks, convicts' muscle, was nothing but a roof (he reasoned); a stone, a f t e r a l l , which had been quarried and broken, convicts' lungs, nothing but a stone; a tree a f t e r a l l , which had been twisted and bent, convicts' fantasy, nothing but a tree; f l e s h , a f t e r a l l , which have been furred and torn, convicts' cat, nothing but f l e s h . Nerveless i d e n t i t y . 140. It was a l l so l u c i d , so abstract, drained of s u p e r s t i t i o n (cinematic menu, euthanasia of the absurd, consuming appetite of the dead) that he dreamt he had emancipated the \"object\"—overthrown the seal of pain....(p. 41) The implication i s that V i c t o r w i l l discover meaning i n t h i s world, a meaning discoverable i n i t s lapsarian pain. But t h i s u n i v e r s a l s i g n i f i -cance i s only part of the p i c t u r e , for i f i t confronts a consensus of mean-inglessness, i t s s o c i a l equivalent, the salvage of meaning by the \"ruined porknocker,\" must contend with a consensus of weakness—that v i s i o n of absolute d e s p o l i a t i o n which we saw i n the received version of the l o s t Indians of Tumatumari. In fact V i c t o r , whatever h i s un i v e r s a l meaning, i s there to redress what Ha r r i s has elsewhere c a l l e d \" v ictim s t a s i s \" (KK p. 46), that reproduction of the victim's p r o s t r a t i o n which i s i t s e l f 21 a form of v i c t i m i z a t i o n . So, even as he re j e c t s the \"sovereign i n d i -v i d u a l , \" Harris i s w i l l i n g to speak, f o r example, of the \" i n d i v i d u a l A f r i c a n slave,\" i n order to disrupt p r e c i s e l y such a mimesis of slavery. Let us look at the i n d i v i d u a l A f r i c a n slave. I say i n d i v i d u a l d e l i b e r a t e l y though t h i s i s obviously an absurd l a b e l to apply to the persons of slaves i n t h e i r binding h i s t o r i c a l context. But since t h e i r a r r i v a l i n the Americas bred a new and p a i n f u l obscure i s o l a t i o n (which i s d i f f i c u l t to penetrate i n any other terms but a free conceptual imaginat-ion) one may perhaps dream to v i s u a l i z e the s u f f e r i n g and o r i g i n a l grassroots of i n d i v i d u a l i t y . . . H e (the problematic slave) found himself s p i r i t u a l l y alone since he worked side by side with others who spoke d i f f e r e n t d i a l e c t s . The creat i v e human c o n s o l a t i o n — i f one dwells upon i t meaning-f u l l y t o d a y — l i e s i n the search for a kind of inward dialogue and space when one i s deprived of a ready conversational tongue and hackneyed comfortable approach. When therefore one speaks of an i n a r t i c u l a t e body of men, confined on some h i s t o r i c a l plane, as possessing the grass-roots of Western i n d i v i d u a l i t y one i s c r e a t i v e l y r e j e c t i n g , as i f i t were an i l l u s i o n , every given, t o t a l and s e l f -s u f f i c i e n t s i t u a t i o n and dwelling within a capacity for mental and unpredictable pain which the human person endured then or endures- now'in or f o r any time, .or' place., .To develop the point further i t i s clear that one i s r e j e c t i n g the sovereign i n d i v i d u a l as such. For i n spite of h i s emancipation he consolidates every advance by conditioning himself to function s o l e l y within h i s contemporary s i t u a t i o n more or less as the slave appears bound s t i l l upon h i s h i s t o r i c a l and archaic plane. It i s i n t h i s \"closed\" sense that freedom becomes a progressive i l l u s i o n and i t i s within the open capacity of the person—as d i s t i n c t from the persuasive refinements of any s o c i a l o r d e r — w i t h i n the su f f e r i n g and enduring capacity of the obscure person (which capacity one shares with both \" c o l l e c t i v e \" slave and \"separate\" i n d i v i d u a l i n the past and i n the future) that a, scale emerges and continues i n d e f i n i t e l y to emerge which makes i t possible for one (whoever.that one may be, today or tomorrow) to measure and abolish each given s i t u a t i o n (pp. 33-34). I have quoted at length from the important essay, \" T r a d i t i o n and the West Indian Novel,\" because t h i s passage explains i n a remarkable way the recurrence i n Harris's f i c t i o n of the \"obscure person,\" of \"the i r r e l e v a n t disabled of mankind, the i r r e l e v a n t dead, the i r r e l e v a n t beaten, the i r r e l e v a n t b l i n d \" (IN p. 140) . Recognizing that there i s no weakness so c r i p p l i n g as that chosen for the weak, Har r i s i s concerned to go beyond \"given\" weakness. His symbolic experimentation does t h i s by presenting (rather than re-presenting) those whose r e s i d u a l resources (of choice, endurance, courage, compassion) have been defined out of existence, those so marginal as to have become i n v i s i b l e . Hence the \"negative body\" of a drowned s a i l o r i n one of the novel's poems (perhaps the same S a i l o r who gives the boy V i c t o r a lesson at the end); hence again, the \" s a n c t i f i c a t i o n of vacancy\": \" p i t i l e s s divorce from o r i g i n s as well as p i t i f u l v a c a n c y — a l i e n and reconstructive s e l f - d e f i n i t i o n \" (p. 57). In the course of another essay, Harris quotes f i r s t Anthony Burgess and then Georg Lukdcs on the novel hero; then he remarks: From my point of view, weak person and middle-of-the-road hero are of d i s t i n c t i n t e r e s t because i t i s here, I believe, at t h i s l o c a t i o n of uncertainty that a breakthrough from the consolidat-ion of the fashionable absurd (the self-mockery of the contemporary European novel) may well l i e (IN p. 144). 142. I n t e r e s t i n g l y , H a r r i s now extends his c r i t i q u e of consolidated \"character\" from the nineteenth century r e a l i s t novel to the twentieth century absurdist novel. In the face of the i n s t i t u t i o n a l i z e d middle-of-the-road hero, he confesses, \"I must speak of a 'middle-of-the-road' hole within my Iconic landscape.\" He then i l l u s t r a t e s his case: The Ibo of Nigeria are a t e r r i f y i n g example of the engulfment which can suddenly overtake a people within a trauma of help-l e s s n e s s — e x t e r n a l conquest, i n t e r n a l c o l l a p s e . There i s reason to believe that the e a r l i e s t forms of t r a g i c art were born out of a necessity to compensate such losses within the human psyche. With the mutilation and decline of the conquered t r i b e a new shaman or a r t i s t struggles to emerge who finds himself moving along the knife-edge of change. He has been, as i t were, c r o s s - f e r t i l i z e d by v i c t o r and victim...(p. 145). In Ascent to Omai, we see the hole r e a l i z e d , for the judge wishes to present\" the unique density and transparency of h i s v i c t i m ( s p e c t r a l character and dust)\" (p. 85). I t i s even more gr a p h i c a l l y rendered i n the opening scene of the novel, where we f i n d V i ctor pursuing Adam— \"lacuna of the watershed\" (p. 24)—up Omai h i l l . The ruined f i g u r e resumed i t s f l i g h t on the h i l l l i k e someone f a l l i n g up a ladder, looking back a l l the while. It seemed to V i c t o r that the s l a t e of h i s head cracked s t i l l f arther around h i s eyes leaving a blank space a l l of a sudden where his features had been; and t h i s implosive c h a r a c t e r i s t i c began i n turn to eat downwards into h i s shoulders and to his middle l i k e a gigantic c o l l a p s i n g globule, p o r t r a i t of r a i n and chalk. There remained only h i s stalwart legs l i k e trees walking up the h i l l , ragged trousers of leaves. But blue rather than green, blue leaves within a f o r e s t of cloud (pp. 15-16). Here we see foreshadowed that tabula rasa of Black Marsden. The void of a hollow \"character,\" \"blank cheque of compassion\" (p. 85), i s the experimental novel's answer to the photographic i d e n t i t y of t r a d i t i o n a l 22 l i t e r a r y p o r t r a i t u r e . Where the l a t t e r i s posed or composed—or at any rate, c o m p o s i t e — i t s other i s i n perpetual danger of f a l l i n g i n on 143. i t s e l f , inhabiting as i t does that \"borderline t e r r i t o r y \" whose f i c t i o n a l space i s for Harris the reverse of secure r h e t o r i c : Omai i s the other, or \"backside of the moon.\" Technically, the crumbling character i s made of materials not unl i k e those we f i n d i n Adam's poem, \" F e t i s h , \" which the prosecuting counsel i n h i s r e t r i a l describes as \"a kind of rubbish heap of images...compounded of bunk— the blasted bunk of civilizations...Reminds me personally of c e r t a i n p r i m i t i v e borderline areas i n the Tropics. Bunk of shattered sculpture, carcases of the motor car, mast-heads and stranded skins or s a i l s on the r i v e r f r o n t (pp. 71-72). Where he has meant to expose the weakness of the defendant's case, prose-cuting counsel has, a l l unwittingly, stumbled on i t s strength. As defence counsel points out,this d e t r i t u s i s \"a new experimental source of wealth\" (p. 72), f o r i t i s a reminder that the t i d i n e s s of assured i d e n t i t y , i n rh e t o r i c or i n the world, i s purchased at a p r i c e . S a i l o r puts i t another way to V i c t o r : \" s e c u r i t y , i n our age, i s merely the bauble of dispossession, a toy of the manufacturers of unfreedom...\" while Raven, who s i t s on the 23 judge's shoulder and \"traces with the claw of memory,\" continues for him: \"...of slavery i n which we are unwittingly immersed: whereas we should be profoundly c r i t i c a l , c r e a t i v e l y a c t i v e . . . \" (p. 113). The experimental bricolage of character refuses the ornamental solace of i d e n t i t y and i n doing so renders l e s s believable the i d e o l o g i c a l backcloth of t h i s p o r t r a i t . Here, then, i s that \"ruthless c r i t i c i s m of everything that e x i s t s , \" which 24 the young Marx proposed, and curiously the c r i t i c i s m of everything i s made with nothing, or what i s next to nothing. The debris of h i s t o r y and the debris of language are not so p i t i a b l e a f t e r a l l . I cannot here invoke Marx without r e c a l l i n g that Harris's novel includes i n i t s blanket repudiation of security the revolutionary project 144. as w e l l . And now i t might be said that the novel's enshrining of the unconscious as a priv a t e r e t r e a t and \"higher\" court of appeal (for both the boy V i c t o r and the adult Adam) i s a s o c i a l l y regressive act when i t proposes t h i s refuge as a substitute f o r the transformation of s o c i a l r e l a t i o n s . Yet the resurr e c t i o n of a marginal selfhood (that scarecrow 25 eye or I) i s not an altogether a h i s t o r i c a l move. In the f i r s t place, as we saw i n The Waiting Room, the value discovered i n the i n d i v i d u a l i s disclosed i n h i s r e l a t i o n to another, and even, as we saw i n Tumatumari, to another's l o s s . Both these motions depict not sec u r i t y (or what defence counsel c a l l s \"a c e r t a i n i l l u s i o n — s e l f - s u f f i c i e n t i l l u s i o n of character\" [p. 108]) but i n s e c u r i t y , on which broken s l a t e i s scr i b b l e d the barest o u t l i n e of a s e l f . This invention i s what H a r r i s , i n his address, \"The In t e r i o r of the Novel,\" described as \"a 'presence' within an 'absence'\" (IN p. 147). And to t h i s r u l e , the author himself (that now equally defunct category) i s not exempt. Even as a \"character\" i s pieced together of a great v a r i e t y of elements, so, too, the author i s the complex ghost of h i s own landscape of h i s t o r y or work. To put i t another way, h i s poem or novel i s subsistence of memory. In the f i n a l a n alysis the r e a l i t y of h i s existence as agent or clown—as a unity of strange powers-—turns upon f a i t h , f a i t h i n the powers and resources of the human person at many l e v e l s of f e e l i n g , t r a n s l a t i o n , and inquiry to invoke a \"presence\" within an \"absence\" (IN p. 147). The \"landscape of h i s t o r y or work,\" then, i s not something apart from but rather a part of the marginal s e l f . The judge, who refuses \"to impose a f a l s e coherency upon material one had to digest—perhaps a l l one's l i f e , \" describes the task of t h i s marginalism as \"a true groping equation i n art or language to the fundaments of existence through h i s t o r y or the void which was native to h i s t o r y \" (p. 123). Here i s no conjuring away of unpleasant conditions, nor yet a culture of poverty; rather, i t i s a c a p a b i l i t y which begins to discover i t s strength i n l o s s . At the bottom 145. of the sea, V i c t o r asks S a i l o r how the dispossessed welder, Adam, can possibly sign himself \"king of creation.\" VICTOR: But he's masked, S a i l o r , he's gloved and masked i n my sketch. I t ' s l i k e a faceless thing without name or reason. How can he write anything at a l l ? SAILOR: It seems i n c r e d i b l e , I know, you've put him at a considerable disadvantage, but you see the most i n c r e d i b l e of i n c r e d i b l e things has happened to the king of c r e a t i o n — h e ' s dispossessed and he's learnt the arts of dispossession. You must l e t t h i s sink into your head, V i c t o r , i f you want to help him to be f r e e . For therethrough—through his dispossession he i s enabled to enter into the innermost secret locks and prisons and chains of exiled/imprisoned mankind. He knows what slavery i s about—from the i n s i d e , see? He dances through the backdoor, as i t were, anywhere and everywhere: the sea, the watershed/chasm/jungle of Omai....Call i t by any u n i v e r s a l name. This i s h i s innermost theme and function, the celebration of freedom through knowing unfreedom. One has to seek i t d i f f e r e n t l y i n each age. I t always comes from outside/in since whether you see i t or not i t ' s already i n s i d e / o u t — d i s p o s s e s s e d . VICTOR: Charcoal? SAILOR: C a l l i t charcoal i f you wish, V i c t o r . Charcoal signature (p. 110-111). This i s e i t h e r a pretty story ( i n which case dispossession i s dispossession and that i s a l l there i s to i t ) or else the \"advance guard v i s i o n of maturity\" i t proclaims i t s e l f to be ( i n which case the dispossessed have no f i x e d i d e n t i t y whose \"character\" i s determined by the dispossessor). In f a c t , no v i s i o n can wholly escape that ideology which determines a l l readings of the world whether of dispossession or of marginal capacity and community. Very l i k e l y , we see here at once a romance and the repudiation of an assured realism' whose postromantic s e c u r i t y i s i t s e l f a mirage. But i f that i s so, the romance has the v i r t u e of disrupting, even as i t r a r e f i e s , a process which realism completes, even as i t r a t i f i e s , S a i l o r ' s fable i s as much a lesson of d i s t r u s t i n appearances as of f a i t h i n the i n d i v i d u a l ' s powers. In h i s e a r l i e s t novel, Harris spoke of \"the l i m i t e d way a man grasped r e a l i t y \" (PP p. 92), and t h i s confession 146. together with h i s reminder that s e c u r i t y whether of society or of s e l f i s a kind of hubris, should d i s p e l the notion that a new i d o l has replaced the old. What h i s marginalism does intend, i s an assessment of that precarious network whose enabling space i s what one c a l l s \"oneself\" or \"another.\" I t i s also a reminder that t h i s s e l f remains a present locus of a r t i c u l a t i o n , that ideas, words, i n t e l l i g e n c e s , do not i n v a r i a b l y , as 26 the phrase goes, \" i n s c r i b e themselves\"; they are i n s c r i b e d . The i n d i v i -dual does speak, even i f h i s language i s a heap of broken images. At the same time, the \"Jack, joke, poor potsherd, patch, matchwood, immortal diamond\" with which Harris epigraphed The Whole Armour, i s l e s s a creature of s e l f - s u f f i c i e n c y than of an i n s u f f i c i e n c y that achieves a bare or v i r t u a l existence. He i s that protean figure who occurs again and again i n the novels, discovering h i s freedom i n a capacity to survive at the margin, a creature whose turbid past and unstable present so d i s t r e s s l i b e r a l 27 and Marxist orthodoxies a l i k e that he i s e i t h e r dismissed as a picaroon or classed as lumpen because he refuses a l l the customary categories. Not f o r nothing does Harris c a l l Victor/Adam's route \"ANANCY TRAIL\" (p. 23), f o r Anancy i s the A f r i c a n f o l k t a l e type of the t r i c k s t e r who scrapes through the most unpromising of contretemps. The t r i c k s t e r may also be recognized as a psychoanalytic f i g u r e for the eruption of the other i n oneself, and i n i t s unpredictable disordering of the text i t i s the l i t e r a r y manifestation of that anarchic desire I noted at the s t a r t . In speaking of \"Experiment and the I n d i v i d u a l , \" I have intended by \" i n d i v i d u a l \" t h i s marginal persistence, the occurrence of the s e l f i n h i s t o r y and of h i s t o r y i n the s e l f . I t i s because both these things are apprehended only as discourse that the experimental treatment of each becomes possi b l e . In the novels following Ascent to Omai, Harris's work begins to straddle a v a r i e t y of c u l t u r a l t r a d i t i o n s and develop a s t y l e which r e g i s t e r s t h i s m u l t i p l i c i t y . The marginal i n d i v i d u a l , moving at the rim of these heterogeneous f i e l d s , may be seen as the p a r t i c u l a r but s h i f t i n g r e a l i z a t i o n of that s t y l e , a s t y l e which at a more general l e v e l of discourse i s the s t y l e of h i s t o r y . 148. V. Experiment and T r a d i t i o n The paradox of the old i n the new i s one we faced at the outset. It i s now time to show how the new i n Harris engages with the old i n hi s m i l i e u and leaves there i t s mark. And since the mark of experiment may be said not simply to i d e n t i f y t r a d i t i o n but to modify i t as w e l l , we may speak, no l e s s paradoxically, of the weight of experiment and the thrust of t r a d i t i o n even as we measure the impact of the future upon the past. Within the confines of the l i t e r a r y work, t h i s impact constitutes n a r r a t i v e ; outside the work, i t i s a matter of h i s t o r y . When, therefore, I couple experiment with t r a d i t i o n , i t i s not for f a i l i n g to respect the domain of h i s t o r y but simply to avoid a too r i g i d demarcation of i t s l i m i t s , one that might for instance banish l i t e r a r y h i s t o r y i n the i n t e r e s t s of h i s t o r y \"proper.\" Besides, where one may l e g i t i m a t e l y conceive of the opposition \"experiment versus t r a d i t i o n , \" the opposition \"experiment versus h i s t o r y \" i s s t r i c t l y meaningless, unless one has i n mind a very simple version of the past. The outlines of the Caribbean past are well known, or e a s i l y a ccessible, and I do not propose to review them here. European expansion, the A f r i c a n slave trade, Asian indenture, Amerindian marginalization: the r o l e of these forces i n producing today's p l u r a l s o c i e t i e s i n the region has been well documented by two generations of r e v i s i o n i s t h i s t o r i a n s . Further, post-war and post-independence scholars have sought to re-examine the basis of t h e i r p r o f e s s i o n a l assumptions by evolving a historiography native to the region and suited to i t s progressing c u l t u r a l c r e o l i z a t i o n . Harris has himself 2 devoted an important ser i e s of lectures to enunciating the need for a West Indian philosophy of West Indian h i s t o r y , one \" c o r r e l a t i v e to the ar t s of the imagination\" (HFM p. 25). For my own part, and consistent with t h i s f e l t need, I w i l l be concerned (and then b r i e f l y ) with the region's l i t e r a r y h i s t o r y , by way of s i t u a t i n g Harris himself and prepar for a consideration of what I take to be h i s s i g n a l achievement. If West Indian h i s t o r y i s characterized by slavery and indenture, 3 i t s e a rly l i t e r a r y h i s t o r y , l i k e that of many another colony, was one of mimicry. Bound to Europe by t h e i r language, writers took t h e i r l i t e r a r y conventions, and sometimes even t h e i r subjects, unquestioningly from the metropolis. But a revu l s i o n against a l i e n modes was i n e v i t a b l e and was to go beyond a disenchantment with the Old World to the very roots of European c i v i l i z a t i o n i t s e l f . Walt Whitman's cry, quoted by the young Ha r r i s , \"Come, Muse, migrate from Greece and Ionia/Cross out please those immensely overpaid accounts\" (RT p. 21), would f i n d i t s v i t u p e r a t i v e conclusion i n Aime Cesaire's \"Europe/pompous name for 4 excrement.\" The reaction of the English-speaking Caribbean was less blunt, but the great outpouring of West Indian l i t e r a r y work over the past quarter century has shown a decided independence of s p i r i t . Nor i s t h i s s p i r i t any less pronounced i n writers who have chosen e x i l e — often i n the old metropolitan c e n t r e s — h a v i n g found t h e i r own s o c i e t i e s flawed by a larger mimicry, one which deprives them of a l i v e l i h o o d or at le a s t a ready audience.~* Other writers have from time to time sought to return to the land of t h e i r ancestors (the Barbadian, Edward Brathwaite to Ghana, the Trinidadian, V.S. Naipaul to India) but have either veered into a second e x i l e or returned home. S t i l l others, l i k e 150. the St. Lucian poet, Derek Walcott, have remained i n the Caribbean and sought to come to terms with the hybrid t r a d i t i o n s of an Old World grafted onto a New. In h i s polemical essay, \"The Muse of History,\" Walcott invokes the awe of \"Adamic, elemental man\" at the newness of a world without ruins, and berates the nostalgia of those who look to Europe: \"what they are i n awe of i s not t r a d i t i o n , which i s a l e r t , a l i v e , simultaneous, but of h i s t o r y , and the same i s true of the new magnifiers of A f r i c a . \" Yet Walcott's i s no simple r e j e c t i o n of the Old World (and h i s poetry i s p l a i n evidence of t h i s ) , recognizing perhaps the p e r i l s of a New World mysticism,' 7 and a c e r t a i n absurdity i n the idea of the old and the new. It i s here that we must begin to s i t u a t e H a r r i s , f or l i k e Walcott a hybrid, he has repeatedly warned against the f o l l y of shutting out any of the numerous r a c i a l and c u l t u r a l s t r a i n s which have gone into the making of the Caribbean. Be i t never so marginal there i s always a remnant which serves to epitomise the uncounted other, g the always-another-exploited. The Amerindians of Guyana are such a remnant, and Harris's own part-Amerindian o r i g i n s may be one reasOn for h i s reminder, i n the t r i o of poems, \"Troy,\" \"Behring S t r a i t s , \" and \"Amazon,\" of the other route by which Old and New Worlds were bridged. Elsewhere, he has challenged the notion of so-called \"complete\" l i t e r a t u r e s , 9 the product of supposedly homogeneous cultures, and i n a recent a r t i c l e on Conrad's Heart of Darkness, he remarks that \"the l i b e r a l homogeneity of a culture becomes the ready-made cornerstone upon which to construct an order of conquest\" (FH p. 88). Conrad's novel, he argues, throws in t o r e l i e f ( i n ways the author himself may not have suspected) the homogenizing imperatives of Europe, imperatives that underwrote the 151. s t a b l e novel from Conrad i n h e r i t e d . H a r r i s ' s own novels f u n c t i o n i n much the same way as Heart of Darkness, d i s r u p t i n g r a t h e r than perpetuating the i l l u s i o n of completeness and r e c a l l i n g to the reader the p l u r a l i t y of c u l t u r e s which have gone i n t o the making of the r e g i o n . I t i s not t r a d i t i o n as such which i s the object of experimental d i s t o r t i o n ; l i k e Walcott, H a r r i s can speak of i t as \" i n h e r e n t l y a c t i v e at a l l times\" (TW p. 46). Rather, i t i s c l o s e d , s e l f - r e g a r d i n g t r a d i t i o n which wants r i f l i n g . On a v i s i t to Guyana i n 1966, H a r r i s wrote i n the Georgetown j o u r n a l , New World, of the need f o r an e x p l o r a t o r y t r a d i t i o n that w i l l seek to r e l a t e d i s p a r a t e bodies not only i n a p a r t i c u l a r s o c i e t y such as t h i s but throughout a world c i v i l i s a t i o n that i s f a s t being c o n d i t -ioned by r i g i d emplacements and t r a g i c c o n f r o n t a t i o n s (IS p. 19). The asymmetrical r o l e of marginal communities i n a world of closed s o c i e t i e s i s s t i l l so obscure, he confesses, that i n our time i t remains a \" c r i s i s of i n d i v i d u a l s e n s i b i l i t y , \" v i s i b l e i n the \" a l i e n f u n c t i o n of the imaginative a r t i s t . \" What might seem an apology f o r the a l i e n a t e d or s e l f - e x i l e d a r t i s t i s i n f a c t a c a l l f o r s h i f t from u n i f i e d s t r u c t u r e s to heterogeneous ones, a t r a n s i t i o n which c h a r a c t e r i z e s the passage from pure s u b j e c t i v i t y to the s e l f - a s - h i s t o r i c a l - p r o c e s s . I t i s here that experiment-and-the-individual gives way to experiment-and-tradition: l i t e r a r y experiment i s no longer the f r i v o l o u s or s o l i p s i s t i c a c t i v i t y i t i s sometimes taken to be (or indeed may become when reduced to s e l f -parody) but r a t h e r the i n i d i v i d u a l a r t i s t ' s s e i z u r e of (or indeed, by) communal forms as he s t r u g g l e s to give v o i c e to h i s p e c u l i a r experience of the landscape he i n h a b i t s and the h i s t o r y that i n h a b i t s him. The a r t i c u l a t i o n of t h i s i n t e r f a c e suggests that experiment i s not a d e n i a l of t r a d i t i o n but an engagement w i t h i t . \"There are two kinds of r e l a t i o n s h i p to the past,\" w r i t e s H a r r i s , 152. — o n e which derives from the past, and one which i s profound dialogue with the past (one which asks impertinent questions of the past). The nature of t r a d i t i o n i s , i n some degree, a ceaseless question about the nature of e x p l o i t a t i o n , s e l f -e x p l o i t a t i o n , as well as the e x p l o i t a t i o n of others, the e x p l o i t a t i o n of one culture by another (SI p. 45). The v i s i o n of t h i s statement i s of a t r a d i t i o n which i s i t s e l f experimental, or which contains within i t the code of experiment, a \"curious h a l f -b l i n d groping\" towards change. In t h i s l i g h t , t r a d i t i o n i s as much a questioner of experiment as the experimental writer i s an impertinent questioner of t r a d i t i o n . The question, that of the nature of e x p l o i t a t -ion, i s one which a society b u i l t on genocide, slavery and indenture w i l l r e a d i l y understand, but i t i s not a matter of public e x p l o i t a t i o n alone, and t h i s i s why t h e . i n d i v i d u a l a r t i s t i s as well equipped as the h i s t o r i a n to i n t e r p r e t the forms of t r a d i t i o n . I t i s also why Harris makes small d i s t i n c t i o n between s o c i a l and l i t e r a r y forms, a l a t i t u d e which serves him w e l l i n developing h i s pec u l i a r s t y l e of h i s t o r y . In Ascent to Omai (1970), the judge whose \"novel h i s t o r y \" eventually encompasses Victor/Adam's t a l e , describes t r a d i t i o n as a \"sieve,\" the proper converse of that unbroken l i n e a r i t y which stems from \"a desire to conscript time i t s e l f into a materal commodity\" (AO p, 84). Notwith-standing the judge's lament, which extends to our obsession with \"time as comma and period,\" there i s , following t h i s novel, the sense of a break i n Harris's f i c t i o n a l canon. The judge himself has spent a quantity of sighs — n o fewer than seven—over the obtuseness of p h i l i s -t i n e s , and de c l a r e d — a g a i n , more than o n c e — t h a t t h i s w i l l be h i s l a s t novel. Following the p u b l i c a t i o n of Ascent to Omai, Harris turned h i s attention to two c o l l e c t i o n s of Amerindian s t o r i e s , The Sleepers of Roraima: A Carib T r i l o g y (1970), and The Age of the Rainmakers (1971). In hindsight, these c o l l e c t i o n s appear both as the f u l f i l m e n t of that 153. Amerindian promise held out i n so many of Harris's novels, and as a kind of t r a n s i t i o n to what might be c a l l e d , following a convention i n Heidegger scholarship, Harris I I . The break i s not an epistemological one (such as that which i s said to divide the young Marx from the old) or even a s t y l i s t i c one (such as that between Ulysses and Finnegans Wake); what changes^ is p r i n c i p a l l y the s e t t i n g of the l a t e r novels, which are for the most part cast abroad. It i s as i f Harris I, having pressed ever deeper into Guyana, can go ho further than Mt. Roraima (the s e t t i n g of Conan Doyle's The Lost World and the goal of Carpentier's The Lost Steps) and produces at l a s t , a Scottish novel. But Black Marsden i s neither Scottish nor West Indian; i t i s an amalgam of these t r a d i t i o n s worked by a writer whom we have heard deny the v a l i d i t y of \"complete\" literatures-; I t i s only f i t t i n g , then, that we broach the subject of Harris and t r a d i t i o n j u s t when the n o v e l i s t appears to have sold h i s b i r t h r i g h t f or a mess of porridge. In an address c a l l e d \"The Making of T r a d i t i o n , \" Harris t a l k s of the \" d i s t i n c t i o n s of eye and texture which a 'native' writer brings to a 'foreign' lanscape,\" and declares h i s wish \"to h i g h l i g h t the curious residues of a c t i v e t r a d i t i o n one brings with oneself from one landscape to another,\" because, he says, h i s p e c u l i a r background a f f e c t s him as a matter of great urgency. So that when I came to write Black Marsden which i s set i n Edinburgh, Scotland, the sense of concealed layers of t r a d i t i o n affected me; threads of Gaelic, Scottish memories (that r e l a t e d i n part to my own grandfather with h i s Presbyterian and American Indian connections i n B r i t i s h Guiana), Catholic and Protestant legacies, were very important to me within so-called r e a l i s t i c character and a necessity to immerse oneself i n and to unravel hypnotic persuasions became an enormous and subtle cue, a kind of magical r e a l i t y , that bore upon new v i s u a l i s a t i o n s and r e l a t i o n s between Northern C e l t i c and Southern pre-Columbian poles of consciousness, between apparently incompatible bodies and cultures (MT p. 34). 154. By t h i s confession, one comes to see t r a d i t i o n as a structure which i s known only by i t s d i f f e r e n c e from another, a structure that knows i t s e l f only when exotic incursions begin to break i t down. T r a d i t i o n \"embodies mutation of stereotypes and i s therefore susceptible to a making or a remaking\" (MT p. 34); i t i s secure only when at r i s k , of value only when breached. This i s the substance of the f i r s t story of The Sleepers of Roraima, a t a l e i n which a Carib boy, Couvade, repeatedly asks impertinent questions of t r i b a l t r a d i t i o n embodied i n h i s grandfather. I t i s a cautionary t a l e of disobedience and punishment, but curiously, those who break the l a w — Couvade's mother and father, who eat taboo food when they should be f a s t i n g — a r e shown to have imparted a necessary knowledge. The break with t r a d i t i o n , which i s of necessity conservative, appears moreover i n a garb c h e e r f u l l y heterodox: Couvade's vanished parents appear to him i n a dream dressed as curious b i r d s . Perhaps some strange owl or guacharo b i r d since they wore sunglasses—American sunglasses ( i n the r i d i c u l o u s way of dreams) Couvade had seen f a l l from the sky In the wake of a passing aeroplane (SR p. 18). In much the same way, Harris speaks of the sea-change undergone by A f r i c a n customs i n t h e i r passage to the West Indies. Where, for instance, A f r i c a n vodun was strongly conservative, i n Ha i t i a n vodun, \"there i s an absorption of new elements which breaks the t r i b a l monolith of the past and reassembles an i n t e r - t r i b a l or c r o s s - c u l t u r a l community of f a m i l i e s \" (HFM p. 16). Consequently, the recurrence i n Harris's essays of the image of the melting pot must be interpreted guardedly: while a mix of cultures i s indeed intended, the p a r t i c u l a r i t i e s of each are not meant to be subsumed i n a homogeneous product. Harris's use of the i r r a t i o n a l , whether to argue an aesthetic point (as i n the example from H a i t i a n vodun) or indeed i n h i s f i c t i o n (as i n hi s mytlr-making or re-making) has on occasion brought him censure from fellow novelists.\"'''\"' The c r i t i c who sees myths as nothing but tender evasions of h i s t o r y i s l i k e l y to j o i n forces with t h i s opposition, and the present disfavour of mythopoeic w r i t i n g and criticism\"'\"\"'' would seem to c l i n c h the case. In f a c t , Harris's l i t e r a r y shamanism i s rather a s t r a t e g i c move than a d r i f t into some gnostic pleroma. If there are 12 moments when h i s project sounds romantic or chimerical, we may put them down to the e c c e n t r i c i t y of genius; but more importantly, to the experimental writer's need f o r an a l t e r n a t i v e system to the r u l i n g ideology of the day. So construed, h i s \"mysticism\" i s l e s s a (bad) f a i t h than an aberrant reference outside the paradigm of received 13 knowledge, not l e a s t that which informs p o s i t i v i s t historiography. By these means mythic or symbolic f i c t i o n serves an unmasking purpose, functioning i n i t s day i n much the same way as did, say, the experimen-t a l realism of a Zola. The i r r a t i o n a l , then, so far from mystifying becomes i t s e l f a demystifier, but one which recognizes that a l l demysti-f i c a t i o n s work by su b s t i t u t i n g another myth. An example of t h i s unmasking may be found i n the context of Harris's review, on the occasion of i t s being translated into English, of the c l a s s i c , New Chronicle of Good Government: An Indian Account of the Incas and Pre-Incas of Peru, written by F e l i p e Guaman Poma de Ayala. Born at the time of the Spanish Conquest and himself decidedly anti-Inca, the Indian Poma nevertheless sets out, says H a r r i s , \"to i n d i c t the Spaniards by immersing them i n t h e i r own contradictions.\" L i v i n g \"within the gateway of an Inca/Spanish world,\" he i d e a l i z e s the \"'utopian' 156. or timeless pre-Inca universe\" and r e v i l e s the Incas, but so deeply rooted i s h i s sense of dual v i o l a t i o n that i t i s always \"submerged i n h i s n a r r a t i v e \" and must cloak i t s e l f i n \" h i s t o r i c a l outrage, parenthesis of myth\" (FG pp. 120-21). When, therefore, Harris speaks of the need for a philosophy of h i s t o r y to be derived from the f o l k arts of the Caribbean, he recognizes that the sense of v i o l a t i o n , as well as that of compensation, lodged i n these arts i s not to be confused with the p a r t i c u l a r text which r e g i s t e r s i t — w h e t h e r the text be h i s t o r i c a l or mythic. Both myth and h i s t o r y are to be unravelled; neither i s the o r i g i n a l form. The most an enquirer into the past can hope to do i s to capture the lessons embedded i n these vestiges by working out new forms f o r them i n the experimental surface of h i s chosen medium. Harris's Amerindian t a l e s work i n an a l i e n language the legends of a community that suffered the very marginalization that was l a t e r to overtake the larger society i t s e l f : the lesson of h i s parenthetic myth i s no les s 14 pertinent for not being cloaked i n h i s t o r i c a l outrage. It w i l l be the work of another generation to judge the present uses of the i r r a t i o n a l i n a progressively r a t i o n a l ( i f not reasonable) society. In the meantime, West Indian w r i t e r s , conscious of the gap which separates them from the masses, are a l i v e to the f o l l y of paternalism which sta l k s the busy c o l l e c t o r of f o l k l o r e , but equally aware that the t r a d i t i o n a l resources of the people cannot be l i g h t l y dismissed as s u p e r s t i t i o n or mi l l e n n i a l i s m . Walcott on the West Indianization of C h r i s t i a n i t y (\"what was captured from the captor was h i s God\"), or Brathwaite on Rastafarian 15 culture i n Jamaica, or Roy Heath on the f o l k l o r e of Guyana, provide salutary lessons i n i n t e l l e c t u a l humility before a groundswell which they recognize must be recorded and respected before i t can f u r n i s h the materials of a contemporary a r t . Much the same example has been set by L a t i n American n o v e l i s t s , from Asturias and Carpentier to Garcia Marquez, who have compounded t h e i r s p e c i a l l i t e r a r y forms out of equal parts of the myth and the r e a l i t y of t h e i r world. The l i t e r a r y works which r e s u l t from t h i s fusion are symptoms of a n a r r a t i v e urge which informed the o r i g i n a l f o l k l o r e i t s e l f , an urge to j o i n the archaic to the contemporary, to supply what Walter Reed has 16 c a l l e d the \" a u t h o r i t a t i v e story.\" The timely juncture so effected i s a thing apart from the timelessness so commonly associated with myths, although i n the nature of. experiment, the j o i n i s an i r r e g u l a r , even a r b i t r a r y one. Reed i s writing of romantic narrative whose \"language of transformation\" he opposes to the modernist p r a c t i c e of d i s j u n c t i o n , of r a d i c a l beginnings and ends, but there i s no reason why the experi-mental f i c t i o n which takes as i t s text an archaic story cannot e f f e c t such a t r a n s i t i o n . What has changed i s the nature of the t r a n s i t i o n ; modernism ruptures not time but a u n i l i n e a r version of time. The West Indian f a i l u r e to discover t h i s new kind of rapport with the past leaves what Harris has c a l l e d an \"unresolved c o n s t i t u t i o n , \" and the need to resolve that c o n s t i t u t i o n explains h i s long quest for a native aesthetic. It i s also a guiding motive of the Guyana Quartet, which seeks to t e l l the a u t h o r i t a t i v e story of a heterogeneous p e o p l e — a motive shared not only by h i s t o r y and myth but also by that middle item i n Harris's 1970 Guyana le c t u r e : f a b l e . \"Fable\" i s a word well suited to Harris's customary mode, and i f i t suggests the opposite of a world of f a c t s , t h i s i s decidedly the n o v e l i s t ' f i c t i v e i n t e n t i o n . In \"History, Fable and Myth,\" Harris quotes with approval these sentences from Maurice Merleau-Ponty: 158. The act of the a r t i s t or philosopher i s fre e , but not motiveless. Their freedom...consists i n appropriating a de facto s i t u a t i o n by endowing i t with a f i g u r a t i v e meaning beyond i t s r e a l one (HFM p. 8). Such an appropriation i s nowhere more pointedly shown than i n Harris's use of the myth most commonly associated with the Guianas: the legend of E l Dorado. And here i t may be u s e f u l to compare the treatment of the same myth by another—but quite d i f f e r e n t — W e s t Indian n o v e l i s t , V.S. Naipaul. Naipaul's h i s t o r y , The Loss of E l Dorado, bears i n i t s t i t l e the imprint of i t s author's temper. The f i n d i n g of t h i s h i s t o r y i s that there was no h i s t o r y ; a f t e r the \" l o s s , \" there remained only \" h i s t o r y -lessness.\" The Loss of E l Dorado.begins with the end of the quest and i s the long, c y n i c a l p o s t s c r i p t to Walter Raleigh's Discovery of the Large, Rich and B e a u t i f u l Empire of Guiana. As a chronicle, i t s extra-ordinary force owes something to that blend of narrative and h i s t o r y which Naipaul has mastered, and not a l i t t l e to h i s i r o n i c g i f t s . I t i s the record of a simple world corrupted by fantasies of i t s own making, fantasies which i n one way or another stem from the o r i g i n a l New World myth of plenitude. I t t e l l s of \"amateurs In adventure,\" f a n t a s t i c a l schemes, revolutions of \"high p r i n c i p l e s , \" the constant b l u r r i n g of make-believe and r e a l i t y . The Spanish with t h e i r t i t l e s and paperwork are not the only pretenders; there are those who i n s i s t on seeing the noble Indian where there i s only a decayed moiety sunk i n \" a l c o h o l i c ennui\"; there are the underground antics of Negro slaves, whose elaborate and costumed midnight revels (\"that Negro carte r , an e s p e c i a l l y stupid Negro, was a king at night, with twelve c o u r t i e r s and a uniform of h i s own\") end when s o l d i e r s come and search and make the f l a g s and uniforms \"useless.\" The torture of a young g i r l becomes, to the v i c t i m h e r s e l f a f t e r numerous courtroom de s c r i p t i o n s , \"an act of r i t u a l , \" and the j a i l \"a place of myth.\" It i s as i f \"the Spanish waste\" l e f t i t s necessary brand on a society condemned to s i m p l i c i t y , casual violence and f u t i l i t y . Nor i s the fantasy confined to l i f e : i t i n f l i t r a t e s l e t t e r s , eyewitness accounts, journals by various hands. Defeated, Raleigh \"with poetic e l i s i o n , begins to l i e . \" A captain's log, bes ged by wonders, i s \"always s t r a i n i n g a f t e r e f f e c t \" ; r e v o l u t i o n a r i e s , thwarted, become t h e a t r i c a l , using \"borrowed words\"; t h e i r p a t r i c i a n leaders become \"operatic,\" using \"words that cost nothing.\" Acting, pretence, humbug, crowd t h i s h i s t o r y ; and always that arch contaminant, fantasy. The governing assumption of Naipaul's work i s that i f men would see c l e a r l y and report honestly (to others, but e s p e c i a l l y to themselves) they might be saved much hardship. Guiding t h i s assumption i s a conviction that beneath the fantasy world i s a secure and accessible r e a l i t y , an o r i g i n a l substance which may be apprehended i n i t s e l f and conveyed i n an objective, u n t h e a t r i c a l discourse. The spare c l a s s i c a l s t y l e which Naipaul has c u l t i v a t e d speaks h i s desire to convey j u s t such a r e a l i t y i n a transparent language. But however f o r c e f u l h i s book, Naipaul f a l l s short of t h i s i n t e n t i o n . A l i t t l e inspection w i l l reveal the o b j e c t i v i t y , the taking no sides, the merely reporting, to have been a posture. I t i s a Briton's account. The Spaniards may have been greedy, i n e f f e c t i v e ; here they are buffoons. \"The Spanish waste,\" \"the French absurdity,\" are props for the staging of a B r i t i s h entry as dramatic as any hero might wish f o r : \"one ship a f t e r another: eighteen i n a l l to the Spanish squadron's f i v e . Their movements were economical and p r e c i s e . \" Time and again the i m p o s s i b i l i t y of an u n t h e a t r i c a l discourse i s shown by Naipaul's adroit narrative manipulation i n a work that might e a s i l y 160. pass for a novel. Nor i s the author's f a i t h i n a p r i s t i n e text of h i s t o r y better founded than Raleigh's dream of a c r y s t a l mountain. The i r o n i s t ' s t r u s t i n a palpable and immediate knowledge of r e a l i t y , shorn of ideas and p o l i t i c s , a t r u s t which expresses i t s e l f i n a sympathy for men of action (governors on half pay, busy s o l d i e r s ) and an impatience with men of words (pretenders and pamphleteers, either comic or unwittingly baneful), i s at l a s t a fond one. We must now ask why. The a l l u r e of unmediated knowledge i s potent, but i t i s one contem-porary philosophers have taught us to r e s i s t . I t i s now commonly agreed that the study of any object must include r e f l e x i v e l y the s t r a t e g i e s of that study, since these i n v a r i a b l y modify the object i t s e l f as we constitute i t . This i s only to say that i f observation i s always a matter of s e l e c t i o n , d e s c r i p t i o n i s even more apt to impose upon i t s chosen theme. In Naipaul's h i s t o r y , o b j e c t i v i t y quickly becomes a m i r a g e — e s p e c i a l l y i n so layered a n a r r a t i v e — a s the author disposes h i s materials i n the task of c o n s t i -tuting h i s desired object, the r e a l past of Trinidad. Myths of h i s own manufacture (which might amount to no more than h i s choice of two s t o r i e s out of many and h i s ordering of t h e i r subordinate d e t a i l s ) intervene even as he deflates the greater myth, and they do so not for any want of v i g i l a n c e on the h i s t o r i a n ' s part, but because the \" r e a l \" i s appre-hended only as already enmeshed i n discourse. The concrete past he seeks i s not out there awaiting copy; i t i s the object not of h i s reproduction but of h i s production anew. It i s best to allow that pure mimesis, or objective d e s c r i p t i o n of s o c i a l phenomena must remain an i l l u s i o n , and t h i s allowance made, we may p r o f i t a b l y turn to d i s t i n g u i s h i n g the v a r i e t i e s of mediated descrip-t i o n . Such kinds of discourse might range from h i s t o r i e s of a chronological 161. or else l o g i c a l nature to treatments of myth and fable which prefer an e x t r a - l o g i c a l advance, modes of which Naipaul and Harris are a n t i t h e t i c a l exemplars. The i r o n i c E l Dorado i s not r e a l h i s t o r y cleansed of myth, but a. version of that h i s t o r y , one no nearer the concrete than i s meta-phor i c discourse. Nor, by the same token, should a metaphoric E l Dorado, such as Harris's Palace of the Peacock, be deemed more authentic; over-blown notions of metaphor may well encourage p i e t i s t i c readings of that novel. If metaphor and symbol are thought to convey one beyond language Into a zone of pure meaning, then the opposite f o l l y to Naipaul's \" r e a l h i s t o r y \" i s reached, namely \"pure myth.\" But i f i t i s recognized that discourse i s always with us, then the proper object of the l i t e r a r y -h i s t o r i c a l quest i s not for an o r i g i n a l state, such as that unviolated world which Naipaul c u r i o u s l y makes of pre-Columbian America, but an appropriate language, a native mode f i t t e d to the West Indian experience past and present. It i s t h i s quest which runs through Palace of the Peacock, so that not only does the m u l t i - r a c i a l crew's journey upriver lead them to the discovery of a nothingness which binds each man to the next, but the mythic event they repeat becomes a v e h i c l e for the creation of a new kind of language. Rather than imposing what Harris has c a l l e d a \" f a l s e coherency on material one had to digest—perhaps a l l one's l i f e \" (AO p. 123), t h i s language responds to the hollow nature of the expedition. The d i f f e r e n c e between the nothingness Harris finds and the n u l l i t y Naipaul sees may have something to do with the continental s e n s i b i l i t y of the Guyanese and the i n s u l a r s e n s i b i l i t y of the Trinidadian, but the use which each makes of hi's diagnosis i s revealing. Where Naipaul sees a picaroon mentality and an undeveloped sense of community giving the l i e to the New World myth, Harris sees what he has c a l l e d \"the open myth of 162. E l Dorado\" (TW p. 37), but also \"the s p l i n t e r i n g of p e r f e c t i o n i s t assumptions, f a l l of E l Dorado\" (T p. 153), as giving hope as well as reason for a community, one expressed i n the novel by c o l l e c t i v e a t t r i b u t i o n s (\"their eye,\" or \" t h e i r heart\") at moments when the crew are i n great p e r i l . Such d e t a i l s , together with the experimental surface of the whole novel make for an innovative use of t r a d i t i o n i n which both the o r i g i n a l myth and the ethnic r e a l i t y of Guyana are well served. In \"T r a d i t i o n and the West Indian Novel,\" Harris speaks of the problems a writer confronts i n a chapter of h i s t o r y where the sordid i s shot through with the sublime. In fa c t i t would have been very d i f f i c u l t a century ago to present these e x p l o i t s as other than a very material and degrading hunger for wealth spiced by a kind of s e l f -righteous s p i r i t u a l i t y . I t i s d i f f i c u l t enough today within clouds of prejudice and n i h i l i s m ; nevertheless the substance of t h i s adventure, involving men of a l l races, past and present conditions, has begun to acquire a r e s i d u a l pattern of i l l u m i n a t i n g correspondences. E l Dorado, C i t y of Gold, C i t y of God, grotesque, unique coincidence, another window upon the Universe, another drunken boat, another ocean, another r i v e r ; i n terms of the novel the d i s t r i b u t i o n of a f r a i l moment of i l l u m i n -ating adjustments within a long succession and grotesque seri e s of adventures, past and present, capable now of discovering themselves and continuing to discover them-selves so that i n one sense one r e l i v e s and reverses the 'given' conditions of the past, freeing oneself from catastrophic i d o l a t r y and blindness to one's own h i s t o r i c a l and ph i l o s o p h i c a l conceptions and miscon-ceptions which may bind one within a statuesque present or a f a l s e future (TW pp. 35-36). Harris's emphasis here i s i n t e r p r e t i v e rather than d e s c r i p t i v e , concerned with present use rather than past misuse. But there i s more. If the i r o n i c and the metaphoric E l Dorado have an equivalent status as discourse, the one i n the i n d i c a t i v e and the other i n the subjunctive, t h i s does not mean the issue of relevance i s shelved. Eventually we must ask whether c l a s s i c a l p u r i t y and i r o n i c distance are l i t e r a r y q u a l i t i e s suited to the West Indian experience, whether the questions of pluralism and marginality 163. Harris r a i s e s can be addressed by a discourse founded upon these a l i e n t r a d i t i o n s alone. It i s a question I w i l l ask again i n a l i t t l e while. Black Marsden was Harris's f i r s t novel placed at the i n t e r s e c t i o n of t r a d i t i o n s , northern and southern. Harris's next novel, Companions of the Day and Night (1975) annexes yet another culture to the C e l t i c -Carribbean f r i n g e . I t s story i s set for the most part i n Mexico, and draws upon both ancient and modern t r a d i t i o n s of that land as they bear upon the s e n s i b i l i t y of the ce n t r a l character. He i s that same Idiot Nameless who narrates The Eye of the Scarecrow and i s C l i v e Goodrich's other i n Black Marsden. Both Marsden and Goodrich also enter t h i s f i c t i o n , as bookends, the one having come upon the Fool's diary and papers along with h i s paintings and sculptures, and sent them to the other to shape into a novel. Nameless has long prepared for h i s journey to Mexico, having studied i t s pre- and post-Columbian past, though h i s researches concern what he c a l l s p o s t - C h r i s t i a n s o c i e t i e s . The immediate subject of hi s inquiry i s the fate of a C h r i s t i a n nunnery disbanded, along with a l l such r e l i g i o u s orders, upon the Mexican revolution. The s i s t e r s of t h i s order had f l e d , a l l but one, to various c i t i e s i n Europe and the United States, where Name-less has traced them i n an e f f o r t to learn both of the fate and the lesson of the one who remained. Si s t e r Beatrice had gone underground and while i n hiding i n s t i t u t e d a play, \"Christ and the F i r i n g Squad,\" i n which she, dressed as a man, took the leading part. She was exposed and raped, and while her martyrdom would be completed by the i d o l a t r y of such men as the guide whom Nameless h i r e s , i t i s \"her t r i a l of values, her scandal\" and \"the alarming r o l e played by respectable i d o l s \" (p. 45) which i n t e r e s t the I d i o t . In Mexico C i t y , a f i r e - e a t e r introduces him to Si s t e r Beatrice's 164. grand-daughter, the c h i l d of the c h i l d of a rape, who works as an a r t i s t ' s model. Nameless spends a night with her i n h i s Gravity Hotel room, but when he awakes she i s gone. He sets out to follow her along a t r a i l of towns which leads him at l a s t to Teotihuacan. There one night he spies her, but i s detained by a chance argument and loses her again. Not long a f t e r , he succumbs to the \" f a l l i n g \" sickness that has plagued him a l l h i s l i f e . His body i s found at the base of the pyramid of the sun. The companions of the day and night are d i v i s i o n s of a pre-Columbian calendar whose nine i n t e r v a l s the novel r e f l e c t s . Two \"dateless days\" at the end of the cycle carry the narrative back a f t e r Nameless's f a l l . He i s i n New York, on h i s way to Mexico, to interview two other s i s t e r s from the disbanded nunnery, s i s t e r s who l i v e with—and are played b y — Marsden's wife. In taking leave of Mrs. Marsden, Nameless asks i f he might be with her \" f o r a day, and for a night.\" Stunned that the man she regarded as the C h r i s t of the l a t e twentieth century should make so naked a proposal, Marsden's wife shuts the door i n h i s face. The novel's epigraph, an extract from a Puerto Rican folksong, runs: San Josey Maria a Belen llegaron Pidieron posada y se l a negaron which might be rendered Joseph and Mary to Bethlehem hied Asked for room and were denied. Rejection and s a c r i f i c e are the burden of t h i s , Harris's most p o l i t i c a l novel, and i t i s c h a r a c t e r i s t i c that he should emphasize the i n d i v i d u a l ' s r o l e by countering s a c r i f i c e with s e l f - s a c r i f i c e . A passage from an essay written some f i f t e e n years before Companions of the Day and Night may help construe h i s present meaning. Harris has j u s t f i n i s h e d quoting Yeats's \"Man has created death.\" To t h i s he r e j o i n s : \" l i k e a 165. private c o r o l l a r y — b u t above a l l man has created the image of s a c r i f i c e . \" Thenhe continues: S a c r i f i c e f or whom and for what? That i s the question. It i s the r i g i d i t y that appals, one that masks every concept of s a c r i f i c e , and may spring from the death-dealing sanction of t r a d i t i o n , yes, but which defeats the very object and mystery of a l l capacity i n the end, i n that i t makes of the spontaneity of l i v i n g s a c r i f i c e something already 'given' (rather than something belonging to unpredictable experience), something which loses i t s 'negative' f i l m or state of p o s s i b i l i t y (B pp. 24-25). T r a d i t i o n and the i n d i v i d u a l are here p l a i n l y at odds ( i n a manner I have followed by separating the two i n t h i s and the previous chapter); Harris sees the p o s i t i v e (or p o s i t i v i s t ) mask of t r a d i t i o n as one which takes the negative edge o f f the i n d i v i d u a l and h i s acts of freedom. The i n d i v i d u a l ' s willingness to die, to confront death f r e e l y , i s already undervalued by a t r a d i t i o n which, i n the contemporary world, has enshrined the meaningless-ness of death, not excluding s e l f - s a c r i f i c e . So i t i s not death which k i l l s , but \"the death-dealing sanction of t r a d i t i o n . \" And Harris c i t e s the Jamaican, Andrew Salkey's novel,A Quality of Violence, with i t s meaningless death of a c u l t f i g u r e , remarking: \"A f a r cry from Saul's Stephen for whom the heavens shower grace\" (p. 25). The q u a l i t y of s a c r i f i c e Nameless and Si s t e r Beatrice seek to define i n t h e i r own l i v e s i s one divested equally of heroism and a tainted love. \"Each man k i l l s the thing he loves,\" was Black Marsden's mocking reminder of the seed of s e l f - i n t e r e s t sown i n love, and i t i s j u s t so with the purest i d o l a t r y . S i s t e r Beatrice's s a c r i l e g e — o n e inverted by her grand-daughter, who as both whore and model poses for a statue of the V i r g i n — a n d Nameless's advances to MarsderiFs wife, partake of an i d e n t i c a l iconoclasm. Their unhallowing or hollowing of t r a d i t i o n also casts some l i g h t backward on another c r y p t i c remark of Harris's: one has to v i s u a l i s e Che Guevara,, for example,, as the new tenant of memory within the hollow monument of C o r t e s — t h e new tenant of re v o l u t i o n subsisting upon a devolution or breakdown of h i s t o r i c a l premises which has been the fate of L a t i n America, i n a sense, since the Conquest of Mexico (NP pp. 146-47). The \"hollow monument\" i s a recurring image i n Har r i s : here i t r e c a l l s bo the f r i a b l e s h e l l of the p a s t — t h a t \"already 'given'\" against which we heard him r a i l — r a n d a notion of interchangeable subjects whose s a c r i f i c e whether honoured or anonymous i s of equal value. Another, and l i n k e d image of t h i s equivalence i n debt . i s the borrowed cloak or coat, which appeared i n The Secret Ladder and which recurs i n Companions now. I l l and f a i n t , Nameless has stopped by a coffee wagon i n a T e o t i - -huacan square at midnight. He has been following the a r t i s t ' s model but i s now detained by a wayside discussion i n which he does not fare w e l l . Nevertheless, n o t i c i n g h i s state, one of the workers gathered there throws him a coat. \"Whose coat...death do I wear?\" he wonders, and i s led i n t o a t r a i n of unanswerable questions: Cloaked on a l l sides by the fa s t of the sun, b u l l e t - r i d d e n workman, Unknown Warrior and Workman King—two s i l e n t tongues i n h i s head forever \"No,Yes\"—one loud command i n h i s heart FIRE...ultimate buried fate...ultimate buried freedom... A l l t h i s encompassed the Fool and r i d d l e d him u n t i l a l l of a sudden he came to himself and remembered what he was here f o r . The woman. He had followed her across the c i t y from Emperor Square through emperor death into t h i s entanglement i n sovereign hero, brute death i n the overcoat of a dead workman whose name had long been forgotten at the heart of an in s u r r e c t i o n . He had been shot when things got 'out of hand.' And the Idiot was imbued afresh by the terror of banal l i p s , banal dialogue with earth as he sank into unwritten reserves, codes, bodies, window dressing, o v e r a l l s , b u l l e t s , f a c t o r i e s . . . ( p p . 66-67). In pondering h i s i n f i n i t e debt to unknowable i n d i v i d u a l s , the Idiot has not i n fac t been d i s t r a c t e d from h i s quest. Each step around the globe for the Fool, subsisted upon unwritten reserves planted i n the death of obscure men and women who were antecedent to the gods. As though the gods were born of antecedent s i l e n c e s , l o s t buried tongues that set up unfathomable n e c e s s i t i e s of unexpressed f e e l i n g upon which the Idiot subsisted—which drew him through them Into unsuspected spaces that c r i e d f o r a language, the language of creation, the language of the deaf, dumb, b l i n d f a l l e n who lay at the bottom of the world (pp. 67-68). What Nameless struggles to shape i s t h i s language; h i s paintings and sculptures, h i s notes and d i a r i e s are an attempt to give voice to the already v o i c e l e s s , to make speak those intangible l i n k s which bind him to them. The obscurity of h i s work catches something of the sil e n c e of the obscure; i t has abandoned the attempt to represent them. \"We need to see from within ,\" the Fool says shamefacedly to the workman who has dismissed him, \"the r o l e s played by others i n our name, i n the name of the nameless forgotten dead, the nameless forgotten l i v i n g \" (p. 65). The Fool's need i s to discover \"an equation between re v o l u t i o n and r e l i g i o n , to face a f i r i n g squad.\" This had been S i s t e r Beatrice's mission before him, and indeed remains that of today's r a d i c a l clergy and l i b e r a t i o n t h e ologists throughout L a t i n America. In Companions of the,Day and Night the equation reads out as s e l f - s a c r i f i c e . \" P o l i t i c s , \" says the Fool, \" i s the a r t of s a c r i f i c e , \" and i f he i n s i s t s on the i n d i v i d u a l ' s example, i t i s not for being unaware of tyranny's i n s a t i a b l e appetite f or victims but because t h i s ultimate readiness i s a discovery of strength i n weakness. There i s , moreover, a s t r a t e g i c value to Nameless's task of giving voice to the v o i c e l e s s , for what Harris elsewhere c a l l s \"an addiction to absolute power p o l i t i c s \" (CP p. 149), might well serve to complete the process of\" marginalization i t claims simply to describe. To view power as a zero-sum game i s \"to embalm the fac t of e x p l o i t a t i o n \" (HFM p. 28), to accept u t t e r d e s p o l i a t i o n . On the 168. other hand, to accept, as Nameless does, \"that to be born was to be broken i n the dream play of h i s t o r y , \" i s to learn to bargain from a p o s i t i o n of weakness.\"'\"'7 It i s also to learn to \"see through the r i t u a l proprietors of the globe\" (NP p. 148) and t h e i r h i s t o r i e s of \" t o t a l breakdown or t o t a l catastrophe\" (MP p. 30). I t might be said that Harris's v a l u a t i o n of the i n d i v i d u a l leads him to underestimate the power and the p o l i t i c s of the group, and indeed there i s something wishful about the \"element of conscience\" he expects to f i n d i n the powerful. Nevertheless, as a measure of commitment— which w i l l always have an i n d i v i d u a l component—and r i s k , such as that of the revolutionary who \" l i v e s today i n the shadow of the b u l l e t \" (p. 77), the Fool's argument cannot be f a u l t e d . The p i v o t a l opposition i n the novel i s between the Chri s t i a n ' s s e l f - s a c r i f i c e and i n s t i t u t i o n a l i z e d s a c r i f i c e such as the c r u e l r i t e s once performed on the Aztec pyramid of the sun for the renewal of a c a l e n d r i c a l contract. The f e a r l e s s r i s k of the one compared with a f e a r f u l r i g i d i t y i n the other i s also a present reminder of experiment's answer to t r a d i t i o n . A f a i t h — a n d i t i s t h a t — i n the s t o i c endurance of the d i s i n h e r i t e d requires a long view of p o l i t i c s , longer perhaps than the patience of many. The experimental \"remaking/unravelling of t r a d i t i o n \" wants also what H a r r i s , i n speaking of Companions of the Day and Night, c a l l s \"double v i s i o n \" (MT p. 39). And i n the Fool's \"glimpsed proportions through nature and h i s t o r y \" (p. 13), i t i s possible to see a coming together of the mythic and i r o n i c modes. Goodrich's \"Introduction,\" which t e l l s of the Idiot Nameless C o l l e c t i o n as having evoked i n him a \"magic of r e a l i t y , \" and Black Marsden',;s concluding l e t t e r , which speaks of Nameless as having been \"an i r o n i s t i n the deepest sense, perhaps\" (p. 81), both suggest such a union. One purpose of t h i s a l l i a n c e might 169. be to s h o r t - c i r c u i t the ideology of t o t a l loss and i t s mimetic discourse, a charge the novel conducts with much energy. Hence the numerous plays on s o l i d i t y and f r a c t u r e , on black holes and b u l l e t holes and g r a v i t y beyond measure, on the Id i o t ' s own \" f a l l i n g \" sickness, on the absent V i r g i n — t a c t i c s that w i l l be resumed i n a further ser i e s of canvases by another painter, da S i l v a , whose work frames two of Harris's most recent novels. Da S i l v a da S i l v a ' s Cultivated Wilderness (1977) and i t s sequel, The Tree of the Sun (1978), are separated from each other by a n o v e l l a , Genesis of the Clowns: A Comedy of Light (1977), which was issued bound up with the former. Unlike the da S i l v a novels, which are set i n London, Genesis of the Clowns looks back to Guyana. Yet i t represents, as I showed i n \"Experiment and Language,\" an advance upon the manner of the early novels, displaying a greater freedom from r h e t o r i c a l conventions of sentence and symbol and a temper leavened with a new piebald humour. In fa c t the comic s p i r i t and the harlequin s t y l e , with i t s curious and i n v a r i a b l y far-fetched juxtapositions, are two sides of the one coin. A short novel, Genesis of the Clowns nonetheless encapsulates many of Harris's c h a r a c t e r i s t i c q u a l i t i e s and obsessions: \"a l u s t f o r responsi-b i l i t y i n myself and a void of r e s p o n s i b i l i t y i n nature\" (p. 124); a conviction that \"each present i l l u m i n a t i o n s h i f t s the debris of the past a l i t t l e \" (p. 82); and consequently, the sense of a \"need to preserve diametrical opposites i n each unfinished day and age as a capacity to unravel self-deceptions\" (p. 128), whether personal or s o c i a l . As a r e s u l t , the contradictory, punning surface of the novels takes on the look of what protagonist Frank Wellington himself c a l l s \"a Walt Disney/Confucian c o l l a b o r a t i o n \" (p. 135), and h i s enemies ( i n an unintended compliment) c a l l \"a marriage between EBONY AND MARX FATHER AND BROTHERS\" (p. 144). 170. Something of t h i s f a n t a s t i c a l humour and an even greater measure of c r o s s - c u l t u r a l bricolage marks the canvases of da S i l v a . A painter who i s neither Portuguese, nor B r a z i l i a n , nor Arawak Indian, nor European, nor A f r i c a n , but a l i t t l e of each, he i s married to a Peruvian and l i v e s i n London. In Da S i l v a da S i l v a ' s Cultivated Wilderness, the immense \"Anglor-Brazilian mural\" on which the a r t i s t i s at work becomes the f a b r i c of the novel and involves him c l o s e l y with the l i v e s of h i s models, the landscape of h i s c i t y and the past of h i s native South America. His \"Inca\" wife, Jen; the navigator Magellan; the leader of a Guyanese slave r e v o l t , Cuffey; a Peruvian madonna, Manya; a B r i t i s h e a r l : through h i s subjects da S i l v a draws upon a great v a r i e t y of t r a d i t i o n s , blending them with an insp i r e d experimentation. Using montages of place and time, he creates panels of extraordinary density and a l l u s i v e n e s s : Cromwell's helmet above a Caribbean c r i c k e t e r who plays on a f i e l d where the Round-heads held secret t a l k s ; a dry-cleaning machine on the astronauts' t e l e v i s e d moonscape for the s o i l e d coat of a model madonna. I t i s a celebration of a l l that i s out of place i n a time that i s out of j o i n t . The product of t h i s \"Ars combinatoria\" i s a novel teeming with things, a prodigal canvas of sensuous planes and surfaces which marks a new e x t e r i o r i t y i n Harris's work. As da S i l v a paints h i s way downstairs and out along the s t r e e t , h i s brush i n the sky, a richness of colour and image gathers about hi s advance as i f to s o l i d i f y i t s s p a t i a l i t y . It i s a s o l i d i t y which w i l l be undermined i n the sequel, but for the present i t s sensuousness evokes the theme of c r e a t i v i t y which the author has chosen to address, and which finds i t s narrative climax i n Jen's announcement a f t e r eight years of marriage, that she i s pregnant. Once more we f i n d space triumphant: \"the womb of space\" (p. 46), \"the canvas of space\" 171. (p. 54), \"the muse of space\" (p. 64): the progression i s inescapable. If space i s the \" i n f i n i t e c r e d i t o r , \" the p r o d i g a l i t y of nature i s to be matched by a spontaneity i n the a r t i s t , one that i s quite removed from the studiedness of t r a d i t i o n (or of pornography, as the boy da S i l v a learned). It i s where t r a d i t i o n s and cultures clash, where a homogeneous t r a d i t i o n ' s composure i s shaken, that spontaneity can unite with p r o d i -g a l i t y , intruding on the pure. P u r i s t n e o l i t h i c revolution. P u r i s t wheel. S a i l . Winged horse. P u r i s t i n d u s t r i a l r e volution. Hydroelectric i v o r i e s or stables. P u r i s t wing. Plane. The spanner of Hercules. The f l i g h t of Quetzalcoatl. The descent of Icarus. There was a.subtle i n t r u s i o n of epic, a subtle mythical code of i m p l i c i t heroism or pathos or t e r r o r , d i f f u s i o n s of influence or s t y l e East to West, West to East, North to South, South to North, that took root i n h i s brush as he painted techniques and frames, g l i t t e r i n g saddles of Chinese dragons from Hong Kong, gunpowder, n e o l i t h i c wheat, pre-Columbian maize, aeroplane saddles, into d i s t i l l a t i o n s of barbarism and modern power p o l i t i c s masquerading as p u r i s t masks of technology across the imprisoned centuries from which the magi-prodigals set out again and again, the star-gazing prodigals, within each tent of ancient or modern commonwealth (p. 73). Out of t h i s fecund chaos emerges that chain of connections we c a l l h i s t o r y . Yet, da S i l v a contends, i t i s for the a r t i s t to challenge the i n e v i t a b i l i t y of those l i n k s by r e c a l l i n g h i s audience to other corres-pondences, by d i s c l o s i n g those r e l a t i o n s which conventional h i s t o r y might have overlooked. His charge i s not to refute h i s t o r y but to correct a uniformity i n i t . Da S i l v a takes t h i s charge s e r i o u s l y : \"I s u f f e r my r e c u r r i n g twentieth-century dream of a crash that i s n ' t a crash, a c r i s i s that i s i n t e g r a l to change as the body of the future learns to shed a coat i t wears, a p a i n f u l coat that i t has worn so long i t i s v i r t u a l l y cemented into i t s skin u n t i l they seem one and the same i n v e s t i t u r e of space. \"I l i e face down by a sea, by a lake, face up, face sideways. \"And truth takes i t s pick of the unravelling of s e l f - p o r t r a i t s of f a t e . \"Truth flashes through the Magellan mask,the Cuffey mask, that I wear; a naked spark of truth that l i n g e r s , a glimpsed compassion, an o r i g i n a l unity that runs with conformable i n s t i t u t i o n s but i s other than uniform s t y l e , uniform paint, uniform c o n v i c t i o n \" (p. 50). The multitude of b i r t h s and deaths i n t h i s novel, the pattern of death cheated or l i f e cheated, of i n t e r l o c k i n g l i v e s and l i v e s repeated, spins yet again that web of debt which troubled Nameless i n his borrowed coat. Here once more, on the l a s t encounter between da S i l v a and h i s s c a t t e r b r a i n model, madonna, the motif surfaces. In the heart of summer Manya appears i n a heavy black coat, \"a walking cloak or avant-garde spectacle of winter\" (p. 33); she leaves i n a rage having flung the coat across da S i l v a ' s easel. The experimental a r t i s t ' s need to make i n v i s i b l connections v i s i b l e now begins to assert i t s e l f against the sensuous surface of things. In learning to grapple with the obstinate shapes of s u r v i v a l , with the colour of freedom—a colour obscured by \"the long night of h i s t o r y through which the monolith of space flew\" (p. 1 3 ) — da S i l v a must develop a technique by which the uniformity of h i s t o r y and t r a d i t i o n may be f i s s u r e d . The Tree of the Sun begins with t h i s project. Let us watch the f i r s t cracks appear i n the monolith. Da S i l v a i s painting the assassinat ion of Montezuma when h i s attention i s caught by \"the tree of the sun\" outside. Then he resumes work: Da S i l v a turned from the view outside the studio to h i s own gigantic painting, a huge le a f of a canvas that covered one wall of the room, and sought now to trace with a n a i l or a finger an almost imperceptible l i n e of blood that ran along Montezuma's pagan temple, a f a i n t bruise from the glancing blow he had received from the hand of enemy or f r i e n d . 173. The autumn and winter and c r u e l spring of the modern world seemed to c l u s t e r there i n that l i n e , shadow of indeterminacy, stone or arrow, sp l i n t e r e d lacework, remembered dying and l i v i n g cavalry seasons i n the head of sun-king and snow-king (p. 2). The conquistadorial blow which k i l l s Montezuma leaves a subtle bruise: here i t i s the merest h a i r l i n e , but a l i n e of consequence p r e c i s e l y because of i t s iiidetermitiaey'v The,/ images; clustered, about i t preserve t h i s uncertainty: they magnify' arid\" prolong the. i n i t i a l shock of \"enemy^or friend,1'' by linking\" together- u n l i k e l y and even contradictory elements through, paradox and, simple j u x t a p o s i t i o n . Accordingly, t h e i r diverse .materiala and improbable correspondences prepare a ground of. extreme-instability;. so^that the blow which, dispatches- Montezuma at the same time/opens a f i s s u r e \"In the \" f a c t \" of h i s t o t a l reduction or absolute defeat. The crack troops of t h i s assault on the monolith are the a r t i s t ' s images, but they do not pretend to constitute an iconography of the concrete. Far from seeking to be a t h i n g - i n - i t s e l f , the image i s simply an \"opening\" device. I t c h e e r f u l l y takes up i t s burden of discourse, but with t h i s reservation that i t e x i s t by v i r t u e of the space surrounding i t , and (since t h i s space i s o r d i n a r i l y f i l l e d ) i n r e l a t i o n to i t s fellows. This r e l a t i o n i s both a source of strength and a danger, for a disturbance i n any one region w i l l communicate with a l l the others; a l o c a l f r a i l t y can bring the whole tumbling down. Consequently, da S i l v a ' s mural, so f a r from concealing the w a l l , assiduously traces i t s chinks and crannies: one of i t s recurring images i s the eye of the needle, an a l l u s i o n , we r e c a l l , to the smallest gate i n the wall of the Holy C i t y . In remodelling t h e i r apartment to make room for a studio, da S i l v a and Jen have come across a novel and some l e t t e r s which an e a r l i e r husband and wife of a past generation had written i n concealment from 174. each other and secreted i n a w a l l . Now da S i l v a begins to reconstruct the love of t h i s c h i l d l e s s couple, Francis and J u l i a , with such sympathy that they soon come to dominate his work, and eventually, the novel. Not only do Francis and J u l i a begin to communicate with each other In a way they had been rel u c t a n t to i n l i f e , the characters from Francis's novel also enter the p l o t of the larger work and move on the same plane as da S i l v a and Jen. Such a t h i r d - l e v e l character i s Harlequin. A modern ver s i o n of Montezuma, he i s an i n s u b s t a n t i a l creature, yet f a i l e d warrior that he i s he i s u t t e r l y r e a l i n the antagonists with whom he fought ( s t i l l f i g h t s ) , the uncanny way he puts flesh-and-blood on the most un-promising skeletons, guns, b o t t l e s , houses, shattered monuments, f a l l e n trees, broken f i r e s , drought-ridden waters. They are a l l h i s antagonists drawn up into sublimity of feud from a pool of unconsciousness from immemorial miscarriages and myths (p. 44). The crush of images here p i l e d one upon the other without so much as a connective, compounds a mass that i s both f r a g i l e and combustible (\"guns, b o t t l e s \" ) . Yet each element represents both the shrapnel of e a r l i e r and the s t u f f of l a t e r explosions: guns and b o t t l e s do play a modest part i n the text, past and to come. In t h i s way, the apparent density of the w r i t i n g e x i s t s paradoxically to draw attention to i t s own b r i t t l e n e s s , and by the same token to a hollowness i n the f a b r i c of conventional h i s t o r y .`" ]
[ null, "https://open.library.ubc.ca/img/featured/icon-ubctheses.svg", null ]
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https://www.scilit.net/article/2babc9355025bfbe8d53b09dcec0ba3a
[ "### On the Use of Self-oscillations Excited by the Deformation of Polymer Films in the Actuators of Nanomechanical Devices\n\nPublished: 15 September 2021\n\nAbstract: There are a number of tasks that require the creation of executive micro - or nanomechanical devices that allow you to convert one type of mechanical movement (for example, displacement) into another (for example, into oscillatory). Such devices that convert the energy of the input signal (electrical, optical, mechanical, etc.) into an output signal (for example, in controlled motion) are called actuators. Work on the creation of actors is underway in the UK, USA, Japan and a number of other countries. There are prototypes of actuators, but the problem of their autonomy has not yet been solved. In order for the actuator to become a real device suitable for practical use, it is necessary to solve a number of fundamental issues (to develop microminiature energy sources for their drive; to determine the methods and modes of activation of actuators that generate vibrations). Existing experimental and theoretical research in the field of self-oscillation of polymers allows us to hope for a solution to these problems in a simpler way. The studies performed below show that in accordance with the proposed rules for the selection of polymers for actuator drive polymethyl styrene and polycarbonate can be used as polymer systems in which self-oscillations will be excited in the frequency range of 200–250 Hz. The stretching rates at which the self-oscillations of the above polymers begin to be excited have been determined. The heat generated in this case can be used to maintain self-oscillations for a long time. The proposed approach can be considered as an alternative to mechanochemical actuators using methanol as a fuel. The ways of increasing their operating time and thermal effects when self-oscillations are excited in the frequency range of 200–250 Hz are considered. The glass transition temperatures Tg are calculated using the equation $T_{g} = \\frac{{\\left( {\\sum\\limits_{i} {\\Delta V_{i} } } \\right)_{p} }}{{\\sum\\limits_{i} {a_{i} \\Delta V_{i} + \\sum\\limits_{j} {b_{j} } } }},$ where $\\left( {\\sum\\limits_{i} {\\Delta V_{i} } } \\right)_{p}$ is the van der Waals volume of the repeating unit of the polymer; ai is a set of atomic constants characterizing the energy of a weak dispersive interaction as the average contribution of each atom to this interaction; bj is a set of constants characterizing the energy of a strong specific intermolecular interaction, such as dipole-dipole interactions and hydrogen bonds.\nKeywords: Self-oscillations of polymers / Isolation of the high-frequency component / Glass transition temperature / Polycarbonate / Polyethylene terephthalate / Polymethyl styrene\n\n#### Scifeed alert for new publications\n\nNever miss any articles matching your research from any publisher" ]
[ null ]
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https://jetpack.com/support/beautiful-math-with-latex/?site=tongfamily.com
[ "Support Home > Writing > Beautiful Math with LaTeX\n\n# Beautiful Math with LaTeX\n\nLaTeX is a powerful markup language for writing complex mathematical equations, formulas, and more. Jetpack combines the power of LaTeX and the simplicity of WordPress to give you the ultimate in math blogging platforms.\n\nTo enable this feature, visit Jetpack → Settings → Writing in your site’s WP Admin. Scroll down to the Composing section and toggle on the Use the LaTeX markup language to write mathematical equations and formulas option.\n\n### Using LaTeX\n\nTo include LaTeX (", null, "$\\LaTeX$) code in your post, use the following:\n\n$latex your-latex-code-here$\n\nSo, for example,\n\n$latex i\\hbar\\frac{\\partial}{\\partial t}\\left|\\Psi(t)\\right>=H\\left|\\Psi(t)\\right>$\n\nproduces", null, "$i\\hbar\\frac{\\partial}{\\partial t}\\left|\\Psi(t)\\right>=H\\left|\\Psi(t)\\right>$\n\n### LaTeX Error\n\nIf your LaTeX code is broken, instead of the equation, you’ll see an ugly yellow and red error message.\n\nWe can’t provide support for LaTeX syntax, but there are plenty of useful guides elsewhere online. Or a quick post in our forums might find you a solution. One thing to keep in mind is that WordPress puts all of your LaTeX code inside a LaTeX math environment. If you try to use LaTeX that doesn’t work inside the math environment (such as \\begin{align} ... \\end{align}), you will get an error:", null, "$\\LaTeX&s=X$\n\n### LaTeX Size\n\nYou can change the size of the LaTeX by specifying an s parameter after the \\LaTeX code.\n\n$latex \\LaTeX&s=X$\n\nWhere X goes from -4 to 4 (0 is the default). These sizes correspond to", null, "$\\LaTeX$‘s font size commands:\n\ns= font size Example\n-4 \\tiny", null, "$\\LaTeX$\n-3 \\scriptsize", null, "$\\LaTeX$\n-2 \\footnotesize", null, "$\\LaTeX$\n-1 \\small", null, "$\\LaTeX$\n0 \\normalsize (12pt)", null, "$\\LaTeX$\n1 \\large", null, "$\\LaTeX$\n2 \\Large", null, "$\\LaTeX$\n3 \\LARGE", null, "$\\LaTeX$\n4 \\huge", null, "$\\LaTeX$\n\n### LaTeX Colors\n\nWordPress tries to guess the background and foreground colors of your site and generates the LaTeX image accordingly. But, you can change the colors. You can specify bg and fg parameters after the LaTeX code to change the background and foreground colors, respectively. The colors must be in hexadecimal RGB format: ffffff for white, 0000ff for bright blue, etc.\n\n$latex \\LaTeX&bg=ffcccc&fg=cc00ff&s=4$", null, "$\\LaTeX$\n\n### LaTeX Packages\n\nWordPress.com uses standard LaTeX with the following packages:\n\n• amsmath\n• amsfonts\n• amssymb\n\nFor more information about LaTeX, you can visit LaTeX documentation site and TeX Resources by American Mathematical Society.\n\n### Privacy Information\n\nThis feature is deactivated by default. You can toggle it on Jetpack → Settings → Writing page.\n\nData Used\nSite Owners / UsersNone. Site VisitorsNone.\nActivity Tracked\nSite Owners / UsersNone. Site VisitorsNone." ]
[ null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null ]
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https://jp.certara.com/knowledge-base/bioanalytical-calibration-curves/
[ "ホーム / コンテンツ / Knowledge Base / Bioanalytical Calibration Curves\n\n## Bioanalytical Calibration Curves\n\nAt the request of a reader, I have decided to extend my series on bioanalysis to include another topic: calibration curves. The calibration curve is they keystone of bioanalysis. It is what links the instrument response to a specific concentration of drug. It is like the magic decoder ring that helps you decipher the hidden messages. If the ring isn’t right, then the resulting message is not interpretable (or at the least, very difficult to interpret). So, if calibration curves are so important, we should understand how they are built, and what techniques and challenges are involved.\n\nAll calibration curves are created in the same fashion. A set of samples are prepared with known amounts (and therefore concentrations) of the drug of interest. For example, you may have 12 samples between 0.1 and 1000 ng/mL. Each of these samples is processed through the bioanalytical method and the instrument response is recorded. These pairs (concentration, response) are then plotted and the relationship is evaluated. The resulting plot may look something like the hypothetical plot shown below:\n\nThe concentrations are on the X-axis and the instrument response is on the Y-axis. The diamonds represent the observed data from the calibration runs. The red line represents a linear regression of those data points using the model y = mx + b, and the results of that regression are at the top of the plot. Finally blue line represents how the concentration is determined for a sample with unknown concentration: The instrument response is converted to a concentration using the calibration curve.\n\nThis looks easy and straightforward, so what is the challenge? The following image shows real data along with different regression models for that data (thanks to Helmut Schütz):\n\nEach panel represents a different regression of the same data. From top to bottom and left to right, we have a linear model, a log-linear model, an exponential model, a quadratic model, a log-log model, and a 4-parameter logistic model. Which model is best? Which one should we use for determining the concentration of drug in an unknown sample?\n\nLet’s consider each of these visually … the green lines represent the model fit, and the yellow lines represent the confidence interval around the model fit. The linear (top left) and log-log (bottom middle) models do not approximate the data very well at all. But the remaining 4 models all have reasonable fits to the data. Which one is correct? Perhaps a better question is which model will provide the best estimates of concentrations from unknown samples?\n\nWithout delving too deeply into the statistics, you can compare each model fit with the Akaike Information Criterion (AIC, link to wikipedia). The lower the AIC value, the “better” the model fits the observed data. In this specific example that Helmut presented, the 4-parameter logistic model has the lowest AIC and provides the best fit to the data. Using that model will provide the most accurate estimate of concentration based on the instrument response.\n\nWhy is all of this important? I think most pharmacokineticists don’t realize that there is uncertainty in the reported concentrations provided by bioanalytical laboratories. This is partly because bioanalysis is perceived as an “exact” science because it is measuring something quantifiable. A second reason is that pharmacokineticists often don’t realize that the reported concentrations are only estimates, based on a regression model. It may be worthwhile to review the calibration curve and the model fit generated by the bioanalytical laboratory to make sure you are comfortable with the model fit and the method used to estimate concentrations from the instrument response.", null, "" ]
[ null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20170px%200'%3E%3C/svg%3E", null ]
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https://zbmath.org/?q=an:0878.12002
[ "## Differential Galois theory of infinite dimension.(English)Zbl 0878.12002\n\nKolchin introduced the notion of strongly normal extensions of differential fields and developed an elegant theory of finite-dimensional differential Galois extensions which extended the Picard-Vessiot theory. However, strongly normal extensions do not generalize Galois extensions of abstract fields (when considered as fields with trivial derivation).\nIn this paper, the author introduces several functors from the category of algebras over a commutative ring $$R$$ to the category of groups. For example the Lie-Ritt functor $$\\Gamma_{nR}$$, which associates to each commutative $$R$$-algebra $$A$$ a group $$\\Gamma_n(A)$$ of all infinitesimal coordinate transformations of $$n$$-variables defined over $$A$$, the functor $${\\mathcal F}$$, which associates with each algebra $$A$$ over an abstract field $$L$$ the set of all differential homomorphisms from $${\\mathcal L}$$, the subfield of the formal Laurant series over $$L$$ (namely contained in $$L[[t]] [t^{-1}]$$ generated by $$L^*$$ and this is shown to be independent of the choice of the transcendental basis of $$L$$ over $$K$$ (as abstract fields)). There is another functor $$\\text{Inf-diff bir}_K(L)$$, which is a group functor from the category of $$L$$-algebras to the category of groups, which is in fact a Lie-Ritt functor. The main result (Theorem 5.15) shows that when $$L$$ is a strongly normal extension of $$K$$ with Galois group $$G$$, then $$\\text{Inf-diff bir}_K(L)$$ is the formal group associated with the algebraic group scheme $$G$$ and that this group ignores algebraic extensions and extensions generated by constants.\n\n### MSC:\n\n 12H05 Differential algebra 14L30 Group actions on varieties or schemes (quotients)\nFull Text:\n\n### References:\n\n Kinokuniya, Tokyo pp 771– (1987) Lecture Notes in Math., vol. 151 (1970) Lie algebras and Lie groups (1965) DOI: 10.2307/1969379 · Zbl 0037.18501 Differential Galois theory (1983) · Zbl 0539.12013 DOI: 10.2307/2374080 · Zbl 0552.14010 Nagoya Math. J 133 pp 1– (1994) · Zbl 0802.12006 Differential algebra and algebraic groups (1973) DOI: 10.1090/S0002-9904-1978-14437-1 · Zbl 0382.14016 Annales sci. de l’École normale Sup 15 pp 243– (1898) · JFM 29.0349.06 Annales sci. de l’Ecole normale Sup 63 pp 1– (1946) · Zbl 0061.16703 Annales sci. de l’École normale Sup 21 pp 9– (1904) · JFM 35.0351.03 Nagoya Math. J 144 pp 1– (1996) · Zbl 0885.12004 Algebra, Addison-Wesley, Reading, Massachusetts (1971)\nThis reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching." ]
[ null ]
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https://unofficed.com/courses/volatility-spreads/lessons/ratio-spreads/
[ "When we are discussing Volatility spreads, it is not necessary for traders to have no view in the market. In Ratio Spreads, the trader benefits if there is a movement towards one direction. We have already discussed one such variation of Ratio Spreads namely Ratio Straddle!\n\nHere, The term “Ratio” comes because the options trader is constructing the strategy with buying/selling unequal ratios of put options and call options, mostly to keep the net strategy delta neutral.\n\n• A ratio spread where more options are purchased than sold is sometimes referred to as back spread.\n• A ratio spread where more options are sold than purchased is sometimes referred to as front spread.\n\nUnder the assumption of Black Scholes Model, if we construct delta neutral ratio spreads, even when the options are purchased more than sold, will always result in a net credit.\n\nGenerally, the Ratio Spreads have all PEs or all CEs. If it has all PEs, it is referred to as Put Ratio Spread and if it has all CEs, it is referred to as Call Ratio Spread.\n\nLesson Content\n0% Complete 0/2 Steps\n×Close" ]
[ null ]
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https://www.vedantu.com/question-answer/internal-angle-of-a-regular-17sided-po-class-10-maths-cbse-60a6d98bfe5fac7451160dd5
[ "Courses\nCourses for Kids\nFree study material\nOffline Centres\nMore", null, "Last updated date: 02nd Dec 2023\nTotal views: 280.8k\nViews today: 4.80k\n\n# What is the internal angle of a regular 17-sided polygon?", null, "Verified\n280.8k+ views\nHint: To find the internal angle of a regular 17-sided polygon, we will use the formula for the sum of interior angles of a polygon which is given by $S=180\\left( n-2 \\right)\\text{ degrees}$ . We will substitute $n=17$ in this formula and find the sum. The measure of one interior angle can be obtained by dividing this sum of the interior angles by the number of sides of the polygon.\n\nComplete step by step solution:\nWe have to find the internal angle of a regular 17-sided polygon. We know that an interior angle of a polygon is an angle formed inside the two adjacent sides of a polygon. Or we can say that they are the angle measures at the interior part of a polygon.\nWe know that the sum of interior angles of a polygon is given by the formula\n$S=180\\left( n-2 \\right)\\text{ degrees}$\nwhere, n is the number of sides of the polygon.\nWe are given a 17 sided polygon. Therefore, $n=17$ . Let us substitute this value in the formula for the sum of the interior angles.\n$\\Rightarrow S=180\\left( 17-2 \\right)$\nWe have subtract 2 from 17.\n$\\Rightarrow S=180\\times 15$\nWe have to multiply 180 and 15.\n$\\Rightarrow S=2700{}^\\circ$\nTherefore, the sum of all the angles in a 17 sided polygon is $2700{}^\\circ$ .\nTherefore, the measure of 1 interior angle can be obtained by dividing the sum of all the interior angles by the number of sides.\n$\\Rightarrow$ Measure of one interior angle $=\\dfrac{S}{n}$\nLet us substitute the values in the above formula.\n$\\Rightarrow$ Measure of one interior angle $=\\dfrac{2700{}^\\circ }{17}$\n$\\Rightarrow$ Measure of one interior angle $=158.823{}^\\circ$\nThe figure for a regular 17 sided-polygon called a heptadecagon is shown below.", null, "Therefore, the internal angle of a regular 17-sided polygon is $158.823{}^\\circ$ .\n\nNote: Students must note the formula for the sum of the interior angles of a polygon remains the same for a regular and an irregular polygon but the individual angles vary in the latter. The sum of interior angles of a polygon is always a constant value. A polygon that does not have all sides equal and all angles equal. Is called irregular polygon in which a regular polygon will have all equal sides and equal angles. Students must never forget to put the symbol of degree after finding the measure of the angles." ]
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https://file.scirp.org/Html/10-1240533_58780.htm
[ " On the Estimation of a Univariate Gaussian Distribution: A Comparative Approach\n\nOpen Journal of Statistics\nVol.05 No.05(2015), Article ID:58780,9 pages\n10.4236/ojs.2015.55046\n\nOn the Estimation of a Univariate Gaussian Distribution: A Comparative Approach\n\nCliff R. Kikawa*, Michael Y. Shatalov, Petrus H. Kloppers, Andrew C. Mkolesia\n\nDepartment of Mathematics and Statistics, Tshwane University of Technology, Pretoria, South Africa\n\nCopyright © 2015 by authors and Scientific Research Publishing Inc.", null, "", null, "", null, "Received 19 June 2015; accepted 10 August 2015; published 13 August 2015\n\nABSTRACT\n\nEstimation of the unknown mean, μ and variance, σ2 of a univariate Gaussian distribution", null, "given a single study variable x is considered. We propose an approach that does not require initialization of the sufficient unknown distribution parameters. The approach is motivated by linearizing the Gaussian distribution through differential techniques, and estimating, μ and σ2 as regression coefficients using the ordinary least squares method. Two simulated datasets on hereditary traits and morphometric analysis of housefly strains are used to evaluate the proposed method (PM), the maximum likelihood estimation (MLE), and the method of moments (MM). The methods are evaluated by re-estimating the required Gaussian parameters on both large and small samples. The root mean squared error (RMSE), mean error (ME), and the standard deviation (SD) are used to assess the accuracy of the PM and MLE; confidence intervals (CIs) are also constructed for the ME estimate. The PM compares well with both the MLE and MM approaches as they all produce estimates whose errors have good asymptotic properties, also small CIs are observed for the ME using the PM and MLE. The PM can be used symbiotically with the MLE to provide initial approximations at the expectation maximization step.\n\nKeywords:\n\nMean Squared Error, Method of Moments, Maximum Likelihood Estimation, Regression Coefficients", null, "1. Introduction\n\nThe Gaussian distribution is a continuous function characterized by the mean µ and variance σ2. It is regarded as the mostly applied distribution in all of the science disciplines since it can be used to approximate several other distributions. We consider a single observation x obtained from a univariate Gaussian distribution with both the mean µ and variance, σ2, unknown, that is", null, ",", null, ". In this paper the problems of estimating the sufficient parameters of a normal distribution using the iterative methods are discussed. We then propose an algorithm that mitigates the problems associated with the iterative techniques. A thorough discussion of the iterative techniques and their related algorithms can be obtained from - . The mean µ and the variance σ2 are referred to as sufficient parameters in most of the statistics literature and this is due to the fact that they contain all information about the probability distribution function, see Equation (1).", null, "(1)\n\nAn important problem in statistics is to obtain information about the mean, µ, and the variance, σ2 of a given population. The estimation of these parameters is central in areas such as machine learning, pattern recognition, neural networks, signal processing, computer vision and in feature extraction, see - .\n\nThe rationale and motivation for the proposed approach are presented in Section 2. The methodological steps and the datasets simulated to validate the proposed approach are discussed in Section 3. Explicit estimation steps using the ordinary least squares method are presented in Section 4. Statistical analysis results on simulations are presented in Section 5. The error distribution analyses are presented in Section 6. Accuracy results for the proposed method (PM) and maximum likelihood estimation (MLE) methods are presented in Section 7. In Sections 8 and 9 we provide a thorough discussion of the results and some concluding remarks on the study findings.\n\n2. Rational and Motivation\n\nNumerical methods for estimating parameters of a Gaussian distribution function are well known like the bisection method, Newton-Raphson, secant, false position, Gauss-Seidel, see - . Other methods for obtaining analytical solutions are, the maximum likelihood estimation (MLE), maximum distance estimation, maximum spacing estimation and moment-generating function method, see - . However, these approaches are largely dependent on guess initial values. The guess initial values may not guarantee convergence, could take a longer time or even fail to converge in case they are far from the optimal solution, hence requiring high expertise for their application, see . The MLE is regarded as the standard approach to most of the nonlinear estimation problems as it always converges to the required minimum given “good” initial guess approximations, however, it requires the maximization of the log-likelihood method . Application of the MLE procedure may present a challenge if necessary software is not available; it requires the applicant to have a mathematical background as it is necessary for the user to transform the likelihood function into its natural logarithm, referred to as the log-likelihood in most of the statistical literature. Since the maximum of the function is usually required, it is constrained that the derivative of the parent function is obtained a priori, and solving for the parameters being maximized. However, this can only be achieved by maximizing the log-likelihood function and not the parent function. Another difficulty is encountered at the initialization step, according to : “One question that plagues all hill-climbing procedures is the choice of the starting point. Unfortunately, there is no simple, universally good solution to this problem.” as cited by . We present a method for computing acceptable parameter values for the mean and variance that could be applied as initial guess values when the proposed approach is used symbiotically with the MLE.\n\n3. Methodology\n\nWe transform the Gaussian density function (1) into a new function that is linear with respect to some of the unknown parameters or their combinations in an appropriate form. For linearization, we consider the derivatives for the parent function (1). The unknown regression parameters are then estimated using the ordinary least squares (OLS) methods. The employed frame-work was first proposed by and has been used in the estimation of exponential functions; see . We propose a version of this frame-work and use it to estimate the Gaussian distribution parameters. The PM is compared with both the MLE and MM the traditional estimation procedures on three simulations of normal datasets of known mean and standard deviation. The first two datasets are concerned with the study of hereditary physical characteristics see in which both the father and daughter’s heights were studied. The third dataset was concerned with the morphometric analysis of DDT-resistant and non?resistant housefly strains, in which the housefly wing lengths are analyzed, see . We estimate the known mean, µ, and standard deviation, σ, of the respective datasets using the three methods, that is the PM, MLE and MM.\n\nIn the course of estimation of the parameters using the PM, we anticipate that, there is a shift of the estimated parameters from their “true” values. The amount of this shift is what is commonly referred to as accuracy, and is computed as the difference between the known values and the estimates from the underlying process . The distribution of the errors from the evaluated approaches is an important aspect that gives a clue on which assessment methods are to be employed, that is standard, visual or otherwise non parametric measures.\n\nTransformation and Re-Characterization\n\nIt is always a requirement to estimate the parameters of a Gaussian distribution in most of the data modelling aspects involving normally distributed observations. In this section the method we present has not been considered before in the statistical literature that has been reviewed. The approach is to transform the original Gaussian function (1), and this is done by taking its first derivative and subsequently introducing new parameters either as linear or their combination.", null, "(2)", null, "(3)", null, "(4)", null, "(5)\n\nRe-arranging Equation (5)", null, "(6)\n\nWe observe from Equation (6) that the original function (1) is contained in both the first and second terms. Hence, we write Equation (6) as", null, "(7)", null, "(8)\n\nwhere", null, ".\n\nIntroducing new parameters in Equation (8) to formulate a model linear in the new parameters, we obtain a simple linear model of the form", null, "(9)\n\nwhere", null, "and", null, ".\n\nThere are well-recognised approaches for obtaining the parameter,", null, "and such as, least-squares, Baye- sian techniques and maximumlikelihood methods - . In this estimation problem we consider the least squares method since Equation (9) represents a simple linear least square model and it satisfies atleast one or two of the following assumptions:\n\n1) Each of the independent variables (in this case) in the model is multiplied by an unidentified para- meter.\n\n2) The model contians at most one unidentified parameter that does not have an independent variable.\n\n3) All the discrete terms are summed to yield the ultimate model value .\n\n4. Estimation Criteria\n\nParameter estimation is an important aspect in most of the statistical modelling frame-works. The major goal of estimation is to obtain the numerical values of the regression coefficients associated with individual or a com- bination of the regressors . For the proposed approach the estimation is as follows,\n\nIf a dataset say, for is available, then let\n\n(10)\n\nbe an estimation of at the point with the error of this estimation as\n\n. (11)\n\nWe estimate the error, since it is known that an important part of estimation is the assessment of how much the computed value will vary due to noise in the dataset. When information concerning the deviations is not available, then there is no basis on which comparison of the estimated value to the “true” or target value can be done .\n\nThe sum of squares of the errors over all the data points is\n\n(12)\n\n(13)\n\n(14)\n\nIn Equation (14), variables and are known; can be computed uisng numerical methods, Davis (2001), in this case we apply the Newton’s difference quotient method \n\n(15)\n\nSo that,\n\n(16)\n\nas the goal function for the ordinary least sqaures estimation of the parameters and. Available statistical software packages can be used to obtain estimates and. It is now possible to relate the model (1) para- meters with the estimated parameters of Equation (16) as\n\n(17)\n\nThe estimates of Gaussian distribution parameters are then estimated as\n\n(18)\n\n5. Method Evaluation\n\nIn oder to evaluate the performance of the proposed method (PM), we perform simulations of the father and daughters heights using Mathematica software and compute their respective means and standard deviations, and as the required or true parameters. Another dataset on housefly wing lengths is also simulated and it’s mean and standard deviation computed, that is,.\n\nWe now require to estimate the known means and standard deviations of the considered datasets using the PM, MLE and MM. The analysis is done on two samples, and. This is to ascertain the perfor- mance of the PM on both small and large samples, see Tables 1-3.\n\nTable 1. Height of the father, required parameters, , Pearson and Lee (1906).\n\nTable 2. Height of the daughter, required parameters, , Pearson and Lee (1906).\n\nTable 3. Housefly wing lengths, required parameters, , Sokal and Hunter (1955).\n\n6. Error Distribution Analysis\n\nWe are frequently faced with a situation of processing volumes of data whose generative process we are uncertain about, yet it is always necessary to understand the sampling theory and statistcial inference before carrying out any parameter estimation in statistical modelling problems . In this paper we consider perform- ing exploratory analysis on the error distribution as generated by each of the three evaluated approaches on esti- mating the “true” or required parameters and.\n\n6.1. Visualization of Normality\n\nWe aim at establishing the distribution of the errors from the PM in comparison to those from the standard method, that’s MLE. We would wish to use the easier standard statistical techniques like, the Pearson Chi- Square, the Jacque-berra, and the Kolmogorov-Smirnov methods to test for normality in the errors, but such tests are usually more receptive in case of large datasets. In that case visual methods have been preferred, see Figures 1-6, and these have several advantages .\n\n6.1.1. Histogram Plots\n\nError distribution can with little effort be observed by a histogram of the sampled errors, where the error counts are plotted. Such a histogram presents an overview of the normality of the error distribution, see Figures 1-6. For comparison with normality, normal distribution curves are superimposed on the histograms. The figures illu- strate the distribution of errors, , in inches for father’s height and housefly wing length. All plots from the PM and MLE almost a “perfect” match as there is no heavy tailing. This could be attributed to absence of outliers in the datasets and also errors originating from normally distributed datasets.\n\nBetter diagnostic methods for checking deviations from a normal distribution are the so called quantile-quan- tile (Q-Q) plots, see . Quantiles of empirical distribution functions are plotted against the hypothetical quantiles of the Gaussian distribution. For one to conclude that indeed the actual underlying distribution is Gaussian, the Q-Q plot should be able to yield a straight line. Observing Figure 3 and Figure 4 which are based on large samples, that is, , there is no noticeable deviation from the straight line, which indicates that the error distribution is Gaussian as expected. However, in Figure 5 and Figure 6, we notice a significant deviation from the assumption of normality, this could be that these errors are generated from a small sample, n = 100. This could call for further investigation on the performance of the PM on small samples, but the question would be why is it that the standard MLE approach as well produces a poor plot?\n\nFigure 1. Error distribution for the MLE on father’s height, expected counts μ = 0.15; σ = 0.09.\n\nFigure 2. Error distribution for the PM on father’s height; expected counts μ = 0.11; σ = 0.09.\n\nFigure 3. Normal Q-Q plot for the error (∆h) distribution from MLE on the father’s height, n = 1000.\n\nFigure 4. Normal Q-Q plot for the error (∆h) distribution from PM on the father’s height, n = 1000.\n\nFigure 5. Normal Q-Q plot for the error (∆h) distribution from MLE on the housefly wing lengths, n = 100.\n\nFigure 6. Normal Q-Q plot for the error (∆h) distribution from PM on the housefly wing lengths, n = 100.\n\n7. Accuracy Assessment\n\nWhen normal distribution for the parent dataset, and no outliers are exhibited as shown in Section 6, then the accuracy measures in Table 4 can be adopted. The accuracy measures in the normal distribution fram-work are defines as follows\n\nIn Table 4, ∆hi denotes the difference between the observed and estimated value. Where i is the sampled data point, and n is the sample size. Assuming that the generated errors follow a normal distribution as established in Section 6, see Figures 1-6. Then from the theory of errors, it is well known that 68.3% of data will fall within the interval, where μ is the systematic mean error and σ is the standard deviation, . When we require to measure accuracy based on the 95% confidence level, then the interval will be. In this work we have employed and compared the methods described in Table 4 since the underlying errors from all the estimation methods assumed a normal distribution. Both the histogram and Q-Q plots have justified the assumption of normally.\n\nAccuracy Results\n\nResults generated by the standard measures of Table 4, are presented. We note that application of the standard measures impies that the generated errors follow a normal distribution as established in Section 6. Tables 5-8 show results for PM and MLE.\n\nTables 5-8 show the accuracy measures considered to evaluate the performance of the PM and the MLE, on two datasets of different sizes, that is and, for the father’s height and housefly wing lengths The PM produces smaller standard deviations as compared to the MLE on the small sample, for the large samples, the methods produce the same standard deviation, which could be interpreted as equal performance of the methods on large samples, though this cannot be generalised subject to further research.\n\n8. Results and Discussion\n\nThe PM has been compared with some of the current methods in use that is, MM and MLE. These were preferred\n\nTable 4. Measurement of accuracy for statistical methods presenting normally distributed errors.\n\nTable 5. Measure of accuracy for the MLM approach; father’s height, n = 1000.\n\nTable 6. Measure of accuracy for the PM approach; father’s height n = 1000.\n\nTable 7. Measure of accuracy for the MLM approach; housefly wing lengths n = 100.\n\nTable 8. Measure of accuracy for the PM approach on the housefly wing lengths (n = 100).\n\ndue to their computation lure and availability inmost of the statistical Software packages. Secondly the MLE method is more preferred and widely applied due to its good asymptotic properties. Three standard datasets from and have been used. However, on further tests only two datasets were considered, that is the height of the father and housefly wing lengths; this was to decrease on the intensity of the work to be presented.\n\nSection 5, contains the computation results for PM, MM and MLE. Tables 1-3 illustrate and show the parameter estimates obtained from the methods. It is observed that all the approaches give comparable results with the “true” or required values of the parameters given in the captions of the respective tables.\n\nIn order to use standard techniques that are employed for accuracy measurements, the errors have been tested for normality, see Section 6. Statistical visualization techniques were preferred to other statistical tests which are said to be sensitive in the presence of outliers and large datasets . Figure 1 and Figure 2 illustrate the histograms of the errors and clearly show a normal distribution since more of the information contained in the errors lies under the normal curve that is superimposed. The Q-Q plots in Figures 3-6 have also been used as a measure of testing for normality of the generated errors. It is observed that there are almost straight lines produced in all the cases. This implies that the actual distribution of the generated errors is indeed normally distributed.\n\n9. Conclusion\n\nThis research laid out an easy approach to computing the parameters of a univariate normal distribution which is an important distribution in applied statistics and in most of the science disciplines. It serves as a platform or bench mark for studying more complex distributions, like the mixture of two or more Gaussians, mixture of exponentials and other continuous distributions which are very useful in pattern recognition, machine learning and unsupervised learning. The simplicity of the approach is time saving in computation and guarantees convergence to the required values, this is not usually the case in the conventional analytical and numerical methods as these may fail or take a long time to converge depending on the quality of initial approximations.\n\nAcknowledgements\n\nThe authors wish to thank the Directorate of Research and Innovation of Tshwane University of Technology for funding the research under the Postdoctoral research fund 2014/2015. The anonymous reviewer and editors whose criticisms led to an improved version of the manuscript.\n\nCite this paper\n\nCliff R.Kikawa,Michael Y.Shatalov,Petrus H.Kloppers,Andrew C.Mkolesia, (2015) On the Estimation of a Univariate Gaussian Distribution: A Comparative Approach. Open Journal of Statistics,05,445-454. doi: 10.4236/ojs.2015.55046\n\nReferences\n\n1. 1. Anita, H.M. (2002) Numerical Methods for Scientist and Engineers. Birkhauser-Verlag, Switzerland.\n\n2. 2. Baushev, A.N. and Morozova, E.Y. (2007) A Multidimensional Bisection Method for Minimizing Function over Simplex. Lectures Notes in Engineering and Computer Science, 2, 801-803.\n\n3. 3. Darvishi, M.T. and Barati, A. (2007) A Third-Order Newton-Type Method to Solve Systems of Nonlinear Equations. Applied Mathematics and Computation, 87, 630-635.\n\n4. 4. Jamil, N. (2013) A Comparison of Iterative Methods for the Solution of Non-Linear Systems of Equations. International Journal of Emerging Science, 3, 119-130.\n\n5. 5. Murray, W. and Overton, M.L. (1979) Steplength Algorithm for Minimizing a Class of Nondifferentiable Functions. Computing, 23, 309-331.\nhttp://dx.doi.org/10.1007/BF02254861\n\n6. 6. Hornberger, G. and Wiberd, P. (2005) User’s Guide for: Numerical Methods in the Hydrological Sciences, in Numerical Methods in the Hydrological Sciences.\nhttp://dx.doi.org/10.1002/9781118709528\n\n7. 7. Bishop, C.M. (1991) A Fast Procedure for Retraining the Multilayer Perceptron. International Journal of Neural Systems, 2, 229-236.\nhttp://dx.doi.org/10.1142/S0129065791000212\n\n8. 8. Bishop, C.M. (1992) Exact Calculation of the Hessian Matrix for the Multilayer Perceptron. Neural Computation, 4, 494-501.\nhttp://dx.doi.org/10.1162/neco.1992.4.4.494\n\n9. 9. Bishop, C.M. and Nabney, I.T. (2008) Pattern Recognition and Machine Learning: A Matlab Companion. Springer, In preparation.\n\n10. 10. Mackay, D.J.C. (1988) Introduction to Gaussian Processes. In: Bishop, C.M., Ed., Neural Networks and Machine Learning, Springer.\n\n11. 11. Mackay, D.J.C. (2003) Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge.\n\n12. 12. Richard, J., Douglas, F. and Burden, L. (2005) Numerical Analysis. 9th Edition, Cengage Learning, Boston.\n\n13. 13. Robert, W.H. (1975) Numerical Analysis. Quantum Publishers, New York.\n\n14. 14. Bhatti, S. (2008) Analysis of the S. pombe Sister Chromatid Cohesin Subunit in Response to DNA Damage Agents During Mitosis. PhD Thesis, University of Glasgow.\nhttp://theses.gla.ac.uk/292/\n\n15. 15. Wood, G. (1989) The Bisection Method in Higher Dimensions. Mathematical Programming, 55, 319-337.\n\n16. 16. Myung, I.J., Forster, M. and Browne, M.W. (2000) Special Issue on Model Selection. Journal of Mathematical Psychology, 44, 1-2.\n\n17. 17. Myung, I.J. (2003b) Tutorial on Maximum Likelihood Estimation. Journal of Mathematical Psychology, 47, 90-100.\nhttp://dx.doi.org/10.1016/S0022-2496(02)00028-7\n\n18. 18. Berndt, E.K., Hall, B.H. and Hall, R.E. (1974) Estimation and Inference in Nonlinear Structural Models. Annals of Economic and Social Measurement, 3, 653-665.\n\n19. 19. Kloppers, P.H., Kikawa, C.R. and Shatalov, M.Y. (2012) A New Method for Least Squares Identification of Parameters of the Transcendental Equations. International Journal of the Physical Sciences, 7, 5218-5223.\nhttp://dx.doi.org/10.5897/IJPS12.506\n\n20. 20. Krishnamoorthy, K. (2006) Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC, London.\nhttp://dx.doi.org/10.1201/9781420011371\n\n21. 21. Duda, R.O., Hart, P.E. and Stork, D.G. (1995) Pattern Classification and Scene analysis. John Wiley and Sons, New York.\n\n22. 22. Fayyad, U., Reina, C. and Bradley, P.S. (1998) Initialization of Iterative Refinement Clustering Algorithms. Proceedings of the 4th International Conference on Knowledge Discovery and Data Mining (KDD98), New York, 27-31 August 1998, 194-198.\n\n23. 23. Kikawa, C.R., Shatalov, M.Y. and Kloppers, P.H. (2015) A Method for Computing Initial Approximations for a 3-Parameter Exponential Function. Physical Science International Journal, 6, 203-208.\nhttp://dx.doi.org/10.9734/PSIJ/2015/16503\n\n24. 24. Pearson, K. and Lee, A. (1903) On the Laws of Inheritance in Man: Inheritance of Physical Characters. Biometrika, 2, 357-462.\nhttp://dx.doi.org/10.1093/biomet/2.4.357\n\n25. 25. Sokal, R.R. and Hunter, P.E. (1955) A Morphometric Analysis of DDT-Resistant and Non-Resistant Housefly Strains. Annals of the Entomological Society of America, 48, 499-507.\nhttp://dx.doi.org/10.1093/aesa/48.6.499\n\n26. 26. Hohle, J. (2009) Accuracy Assessment of Digital Elevation Models by Means of Robust Statistical Methods. Japan Society of Photogrammetry and Remote Sensing, 64, 398-406.\nhttp://dx.doi.org/10.1016/j.isprsjprs.2009.02.003\n\n27. 27. Searl, R.S. (1971) Linear Models: John Wiley and Sons, Hoboken.\n\n28. 28. Kay, M.S. (1993) Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Upper Saddle River.\n\n29. 29. Muller, K.E. and Stewart, P.W. (2006) Linear Models Theory: Univariate, Multivariate, and Mixed Models. John Wiley and Sons, Hoboken.\nhttp://dx.doi.org/10.1002/0470052147\n\n30. 30. NIST/SEMATECH (2012) e-Handbook of Statistical Methods.\nhttp://www.itl.nist.gov/div898/handbook/\n\n31. 31. Burden, R.L. and Douglas, J.F. (2000) Numerical Analysis. 7th Edition, Brooks/Cole, Pacific Grove.\n\n32. 32. D’Agostino, R.B., Belanger, A., Ralph, B. and D’Agostino Jr., R.B. (1990) A Suggestion for Using Powerful and Informative Tests of Normality. The American Statistician, 44, 316-321.\n\nNOTES\n\n*Corresponding author." ]
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https://betterlesson.com/lesson/531231/transformations-how-to-guide
[ "# Transformations \"How To\" Guide\n\n9 teachers like this lesson\nPrint Lesson\n\n## Objective\n\nSWBAT explain how to perform horizontal and vertical transformations of functions.\n\n#### Big Idea\n\nStudents will be producing a \"how to\" guide for horizontal and vertical transformations of functions.\n\n## Open\n\n7 minutes\n\nWrite the following functions on the board and ask students to describe the transformation that each function represents:\n\n1) f(x) = (x-5)^2\n\n2) g(x) = (x+5)^2\n\n3) h(x) = x^2 + 5\n\n4) j(x) = x^2 - 5\n\nHave students work on this problem individually first and then share their work with a partner.  In this case have students refrain from sharing their ideas out with the class.  This is the work of the day's lesson.\n\n## Constructing \"How To\" Guide\n\n28 minutes\n\nHave students work with a partner of similar ability level on this project.  Now that students have investigated transformations, it is their turn to show off what they know.  Their goal is to build a \"how to\" guide for transformations of functions going both horizontally and vertically.  (NOTE: in order to solidify the concept underlying these transformations they were done separately from stretching and reflecting).\n\nLeave this project very open ended so that students will make choices that can make their work more appealing and usable (MP1).  I tell students that their goal is to make a guide that could be used by a student who has not seen transformations of functions.  Their guide should make the concept understandable and use multiple representations to illustrate the process of moving a function around the coordinate plane (MP3).\n\nEnsure that students have the use of a calculator when constructing their project.  This will help them to experiment with different transformations and ensure that their algebraic equations are constructed correctly (MP2) (MP7).\n\n## Closure\n\n5 minutes\n\nEnsure that students are working on this exit ticket independently.  In this ticket out (transformations_how_to_close.doc) students will be using their knowledge of transformations to write the equation for each function.  Based on the ability of your class you may want to tell them that the parent function is the absolute value function.  However, based on the work completed in the lessons leading up to this one students should recognize this function.\n\nAs an extension, if time permits, students can also write how they determined the equation for one or all of their functions.  This can be written at the bottom of the page and will give you some insight into how the students are thinking about these transformations." ]
[ null ]
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https://rdrr.io/cran/optpart/man/tabdev.html
[ "# tabdev: Classification Validity Assessment by Table Deviance In optpart: Optimal Partitioning of Similarity Relations\n\n## Description\n\nTable deviance is a method to assess the quality of classifications by calculating the clarity of the classification with respect to the original data, as opposed to a dissimilarity or distance matrix representation\n\n## Usage\n\n ```1 2 3 4 5 6``` ``` ## Default S3 method: tabdev(x,clustering,nitr=999,...) ## S3 method for class 'stride' tabdev(x,taxa,...) ## S3 method for class 'tabdev' summary(object,p=0.05,...) ```\n\n## Arguments\n\n `x` a matrix or data.frame of multivariate observations, with objects as rows, and attributes as columns `clustering` a vector of integer cluster assignments, or an object of class ‘clustering’ or ‘partana’ `nitr` number of iterations to perform in calculating the probability of obtaining as effective a classification as observed `taxa` a data.frame with samples as rows and species as columns `object` and object of class ‘tabdev’ `p` the maximum probability threshold to list species in the summary table `...` ancillary arguments to maintain compatibility with generic summary function\n\n## Details\n\nTabdev calculates the concentration of values within clusters. For each column, tabdev calculates the sum of values within classes and the sum within classes divided by the sum of that column to get fractional sums by class. These values are used to calculate the deviance of each row. Attributes that are widely dispersed among classes exhibit high deviance; attributes that are concentrated within a single class contribute zero deviance. An effective classification should exhibit low deviance.\n\nTabdev then permutes the values within columns and calculates the probability of observing as low a deviance as observed as \\$\\$ (m+1)/(niter + 1)\\$\\$ where \\$m\\$ is the number of cases with as low or lower deviance as observed.\n\n## Value\n\na list with components:\n\n `spcdev` a data.frame with species, deviance, and probability as columns `totdev` the total deviance of the entire table\n\n## Author(s)\n\nDavid W. Roberts droberts@montana.edu http://ecology.msu.montana.edu/labdsv/R\n\n## Examples\n\n ```1 2 3 4``` ```data(shoshveg) dis.bc <- dsvdis(shoshveg,'bray/curtis') opt.5 <- optpart(5,dis.bc) tabdev(shoshveg,opt.5) ```\n\noptpart documentation built on March 26, 2020, 6:18 p.m." ]
[ null ]
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https://optovr.com/excel-math-worksheets-grade-addition-double-digit-color-number-expressions-equations-area-perimeter-workbooks-free-line/
[ "# Excel Math Worksheets Grade Addition Double Digit Color Number Expressions Equations Area Perimeter Workbooks Free Line", null, "Excel Math Worksheets Grade Addition Double Digit Color Number Expressions Equations Area Perimeter Workbooks Free Line.\n\nUse the double number line to reason about rates and solve real-world problems develop strategies to use the unit rate to solve problems compare unit rates between two simultaneous situations standards alignment common core - math.rp.a. understand the concept of a unit rate ab associated with a ratio ab with b, and use rate.\n\nSingle digit subtraction fluency worksheets exercise numeracy arithmetic teacher math problems solved mathematical formula work free equation double number line. Recognize equivalent fractions number lines double line worksheets. Math resources fun teaching double number line worksheets. Math games grade kids double number line worksheets. Grade math linear equations double digit worksheets high school dependent early negative rational number integer common core answers line. Maths number puzzles kids printable worksheet double line worksheets. Number bonds free math worksheets double line." ]
[ null, "https://optovr.com/images/excel-math-worksheets-grade-addition-double-digit-color-number-expressions-equations-area-perimeter-workbooks-free-line.jpg", null ]
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https://academia.stackexchange.com/questions/42884/how-to-build-bridges-between-mathematicians-computer-scientists-and-biologists
[ "# How to build bridges between mathematicians, computer scientists and biologists?\n\nI am part of a recently founded laboratory in computational biology and we are trying to get all the parts (biologists, computer scientists, mathematicians, and so on) to speak the same language, or at least one we can all understand. To do so, we want to figure out some strategies beside seminars and weekly lectures.\n\nI am not the only one who went through this challenge, see: . For example, How to explain core biological concepts like evolution and selection to a mathematician? How to explain a mathematical formalization to a biologist (beyond the very basic models the majority of biologists know, such as predator-prey and logarithmic growth)?\n\nThere must be strategies; for instance, books that are in an effective middle (mathematically rigorous, but stepped enough that a biologist can understand it). This is a long term project and we need to devise strategies to progressively \"retrain\" ourselves. (Bibliography suggestions are welcome.)\n\n• It is easy to explain evolution and selection to a mathematician. The hard part is to show them that the World is messy, complicated and each assumption is a very, very coarse approximation of the observed data (NOT \"reality\"!). In other words, that the land of biologists is very far from the Platonic Cave. – Piotr Migdal Apr 3 '15 at 22:06\n• In my experience there is sometimes an insurmountable cultural gap between biologists and mathematicians. In this case the only solution is to have someone in between who you can both talk to. Basically, if the biologist has never tried to formulate their problem mathematically because they don't see the point, then talking to a mathematician is not likely to work. Also, both sides need to be happy to accept each other's motivation. It's no good if the biologist feels they \"own\" the real problem. – dorothy Apr 4 '15 at 8:39\n\nDisclosure: I'm a mathematical biologist that came into it from the biology side.\n\nI don't think it is necessary to retrain the biologists so they understand maths and retrain the mathematicians so they understand biologists, although these things should occur naturally to some degree with interdisciplinary work. Rather, I think it is important to understand the motivations of each 'type' and to tailor the language to the audience.\n\nTo grossly generalise, biologists are more interested in quantitative methods as a tool to answer interesting biological questions and mathematicians are more interested in the method/analysis used to answer that question.\n\nSo when mathematicians talk to biologists, they need to place less emphasis on the technical details of a model/analysis and focus on the general features. For example, if you are building a model to answer an evolutionary or ecological question, a biologist is more interested in the biological assumptions the model is making and whether or not the model is a reasonable abstraction of the biological system. In turn, the mathematician may need to explain why certain details of the system can't or shouldn't be included in the model (e.g. because they would complicate the analysis for little gain in intuitive understanding).\n\nWhen biologists talk to mathematicians they need to frame their questions in a way that is conducive to a quantitative framework. If a mathematician is trying to build a model, they don't need or want to know every minute detail of a system. It's overkill and will just lead to confusion. What are the most relevant points? For example, if a biologist is interested in how the density of cows affects the density of grass in a paddock, then it isn't helpful for the biologist to give the mathematician a lesson on all the intricacies of grass growing and grass eating. It would be better if the biologist comes with a defined question, such as 'how does increasing the number of cows in a paddock affect grass regeneration?' and points out that the main elements in the system are 1. how grass grows (as some function of grass density) and 2. how grass is eaten (as some function of cow density).\n\nIf you want a book about mathematical biology that is written for biologists then I'd recommend \"A Biologist's Guide to Mathematical Modeling in Ecology and Evolution\" by Sarah P. Otto & Troy Day\n\nThese kinds of interdisciplinary collaborations are becoming increasingly common. I am sure there are books covering at least 2 if not more disciplines but I think communication that is specific to the collaborative needs would be more effective. I would try to figure out what each of the party really needs to know about the other discipline. Try to find this out by simply asking over meetings, mails etc.\n\nFor the long run, depending on who is the \"host\" for a particular meeting or discussion, they take charge and deliver a talk about basics accompanied by slides, pointers etc.\n\nFor example, say the Mathematician is the host for a meeting about porting a program to a Beowulf cluster that does formal analysis of a particular gene expression over time (hypothetical scenario). In such a scenario, the mathematician would introduce the nitty-gritty about the formal analysis methods, things that needs to be considered and things that could be safely ignored and such.\n\nIf the computer scientist is the host in the same scenario, they will speak about the parameters needed for the program execution, why scaling up is important and issues such is numerical precision and software bugs that needs to be taken care of. Accompany the discussion with slides and provide pointers to basic concepts.\n\nOver sufficient time, and enough communication, each party will become familiar with other party's jargons. Things may start slow but a cumulative effect will help accelerate the process as time passes.\n\nHave people well-versed in more than one area. They are very useful for bridging between the two camps. After a while, the people who are not as well versed in more than one area will at least gain a better understanding of what the others need to be useful, and of what is practical, what is possible but impractical, and what is impossible.\n\nYou all know how to teach and learn the formal parts of any discipline. I'd suggest teaching each other the assumptions, and the things that don't work quite as well as they do in theory, and the jokes.\n\nAlthough most feelings of \"huh, that's funny\" about the next discipline's work are going to be embarassing undergraduate misconceptions, always share them. Some of them are the sign of a mismatch in disciplinary assumptions and you want those to be discussed as soon as possible.\n\nSince you ask for potentially appropriate books, you may find Mathematical Biology: An Introduction with Maple and Matlab by Shonkwiler and Herod helpful for bridging the gap. What struck me about this book is that it takes the time to explain the biology to mathematicians, which I appreciated coming from the mathematics side. (Whether it is as successful at explaining the mathematics to biologists is more difficult for me to judge.) The final three chapters introduce genetics, genomics and phylogenetics, including a brief introduction to algebraic statistics.\n\nI should emphasize that the book is just an introduction, so do not expect to find an in-depth examination of any of the topics. However, it could be a useful stepping stone.\n\nAs for helping biologists to understand mathematics, I think a key step is to provide motivation: Why is the mathematics useful and what can it do to aid analysis, solve biology problems, or even deepen understanding of biology itself? In particular, what worthwhile things can be achieved with mathematics that would be difficult or impossible without it? What's the payoff? A following or concurrent step is to make connections with prior knowledge. For instance, what mathematics/statistics do biologists already know and use? How do new proposed methods/algorithms/formalisms build on and improve on previous ones?\n\nAs an example of the latter, in Gilbert Strang's classic Introduction to Applied Mathematics, he masterfully introduces the Kalman filter step-by-step by starting with least squares and linear regression, then going on to weighted least squares (what can you do when you trust some observations or measurements more than others), then introducing recursive least squares (when your measurements arrive one at a time and you want adjust your model without a full recalculation each time) and finally bringing in the Kalman filter to deal with the situation when your model is non-stationary (see sections 1.4 and 2.5 of his book for details). While this example is not specific to biology (although the Kalman filter is used in systems biology), it shows the step-by-step process, starting with a familiar topic." ]
[ null ]
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https://web2.0calc.com/questions/differentiation-graph
[ "+0\n\n# Differentiation graph\n\n+1\n297\n24", null, "Find the values of t for which the height of the water is decreasing.\n\nI tried typing in the graph on desmos expecting a cubic graph but it just gave me a straight line\n\nDec 17, 2018\n\n#1\n0\n\nThat is where the graph caught you off guard! The graph is actually not a straight line. Zoom out, and you will see that the graph curves like an \"N\" at around y = 58!\n\n- PM\n\nDec 17, 2018\n#4\n0\n\nunfortunately the reason why i typed it in to desmos is i thought there would be roots to help me solve it but the range is a bit far for me haha\n\nYEEEEEET  Dec 17, 2018\nedited by YEEEEEET  Dec 17, 2018\n#5\n0\n\nSo there you have it... the height of the water decreases around \\(t = 2.25\\).\n\nHope this helps,\n\n- PM\n\nPartialMathematician  Dec 17, 2018\nedited by PartialMathematician  Dec 17, 2018\n#3\n+4\n\nTake the derivative\n\nh ' =   12t^2 - 59t + 72\n\nSet this to 0    and set to 0\n\n12t^2 - 59t + 72 =  0\n\n(4t -9) (3t - 8) = 0\n\nSetting both factors to 0 and solving for x gives\n\nt = 9/4          t  = 8/3\n\nTake the second derivative\n\n24t - 59\n\nPlugging   9/4 into this gives   - 4....so....we have a max at  t = 9/4 sec = 2,25 sec\n\nPlugging  8/3 into this  gives  5....so....we have a min at t = 8/3 sec = 2.66 sec\n\nSo...the water height is decreasing from  2.25 sec to 2.66 sec\n\nHeres the graph : https://www.desmos.com/calculator/ne2dnm3tks\n\nYEEEEEET.......This does look like a straight line if you don't \"zoom in\"....very subtle....!!!!", null, "", null, "", null, "Dec 17, 2018\n#6\n+1\n\nahhh ok thank you very much\n\nYEEEEEET  Dec 17, 2018\n#7\n-1\n\nYou are welcome! (I didn't exactly do much)\n\nPartialMathematician  Dec 17, 2018\nedited by PartialMathematician  Dec 17, 2018" ]
[ null, "https://web2.0calc.com/api/ssl-img-proxy", null, "https://web2.0calc.com/img/emoticons/smiley-cool.gif", null, "https://web2.0calc.com/img/emoticons/smiley-cool.gif", null, "https://web2.0calc.com/img/emoticons/smiley-cool.gif", null ]
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https://ie.vwr.com/cms/acceleration-conversion
[ "# Acceleration Conversion\n\nConvert units of Acceleration instantly. Choose from 19 different units including decimeter/square second, meter/square second, kilometer/square second, hectometer/square second, dekameter/square second ...\n\n From: To: decimeter/square second [dm/s^2]meter/square second [m/s^2]kilometer/square second [km/s^2]hectometer/square second [hm/s^2]dekameter/square second [dam/s^2]centimeter/square second [cm/s^2]millimeter/square second [mm/s^2]micrometer/square second [µm/s^2]nanometer/square second [nm/s^2]picometer/square second [pm/s^2]femtometer/square second [fm/s^2]attometer/square second [am/s^2]gal [Gal]galileo [Gal]mile/square second [mi/s^2]yard/square second [yd/s^2]foot/square second [ft/s^2]inch/square second [in/s^2]Acceleration of gravity [g] decimeter/square second [dm/s^2]meter/square second [m/s^2]kilometer/square second [km/s^2]hectometer/square second [hm/s^2]dekameter/square second [dam/s^2]centimeter/square second [cm/s^2]millimeter/square second [mm/s^2]micrometer/square second [µm/s^2]nanometer/square second [nm/s^2]picometer/square second [pm/s^2]femtometer/square second [fm/s^2]attometer/square second [am/s^2]gal [Gal]galileo [Gal]mile/square second [mi/s^2]yard/square second [yd/s^2]foot/square second [ft/s^2]inch/square second [in/s^2]Acceleration of gravity [g] Result:\n\n## How to use converter:\n\n1. Select the unit to convert from in the input units list. The line containing the selected unit will become highlighted.\n2. Select the unit to convert to in the output units list. The line containing the selected unit will become highlighted.\n3. Enter the value to convert from into the input box on the left. The conversion result will immediately appear in the output box.\n\nAcceleration Conversion - factors provided by unitconversion.org" ]
[ null ]
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https://socratic.org/questions/how-do-you-define-a-variable-and-write-an-expression-for-each-phrase-a-number-de
[ "# How do you define a variable and write an expression for each phrase: a number decreased by three-fourths of the number?\n\nApr 16, 2016\n\n$n - \\frac{3 n}{4}$ (which can be simplified to $\\frac{n}{4}$)\n\n#### Explanation:\n\nA variable is just anything in the question that we don't know, and in most questions we try to find out its value.\n\nFor this question, the variable is the 'number', which we'll call $n$.\n\nNow we can convert the word question into an equation bit by bit:\n\nA number decreased by three-fourths of the number =\n$n - \\left(n \\cdot \\frac{3}{4}\\right)$\n=$n - \\frac{3 n}{4}$ , and this is the expression for the question.\n\nHowever, we can simplify this:\n$= \\frac{4 n}{4} - \\frac{3 n}{4}$\n$= \\frac{n}{4}$" ]
[ null ]
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http://riverhawktutors.com/subjects/index.php?client_Subject=matlab&action=practice_Test
[ "Subjects > MATLAB >Practice Test\n\n### MATLAB\n\n 0 How can MATLAB be used in the following fields: Robotics Linear Algebra Calculus Electrical circuits Mechanical engineering Show answer MATLAB is used to generate numerical solutions in each of the above-listed fields and many more fields. 1 How does one start writing a MATLAB script? Show answer Control + N or File > New 2 What is a .mat file? Show answer A .mat file is a file that contains variables saved from the workspace. This can be useful when evaluating various scenarios. 3 How can you plot multiple plots on the same window as shown below", null, "A plot showing cumulative solar energy collected by a solar thermal collector Show answer Use subplot(m,n,p) function. Review the code that generated the plot shown earlier here. 4 How can you solve a set of ordinary differential equations (ode)? Show answer Use MATLAB solvers such as ode45, ode23, e.t.c. Contact River Hawk Tutors for specific advice 5 You are a new intern at a children's hospital. One day your boss asks that you make a MATLAB animation using 2-years-worth of data. The animation should show data being plotted and nothing else. Show answer Contact River Hawk Tutors for a detailed solution Think about using a 'for loop' and saving each plot as a frame of a video. Once we talk about videos, be aware of the video frames per second (fps), codecs, and color. 6 It so happens that during your research on solar PV cells, you come across a collection graphs that will be useful in your research data analysis (such as shown below). How can you use MATLAB to read this collection of graphs? You do not have time to read each one of the graphs manually. Eventually, for each graph, you want to have a 2D array of x and y points.", null, "Image showing the original and extracted spectral response of an experimental solar PV cell Show answer Find the code here A simplified flow chart of the proposed solution is shown below", null, "7 How can you change a transfer function to its digital form? Show answer Contact River Hawk Tutors for a detailed solution\nScroll to Top" ]
[ null, "http://riverhawktutors.com/subjects/matlab/Problem_3_HW3_Solar_Fundamentals_01.png", null, "http://riverhawktutors.com/subjects/matlab/dataExtractor_03.png", null, "http://riverhawktutors.com/subjects/matlab/dataExtractor_04.png", null ]
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https://dataaspirant.com/central-limit-theorem/
[ "# Ultimate Guide For Central Limit Theorem", null, "If maths is the magician, then the central limit theorem is like a magic trick that happens when you add up lots of little things!\n\nDidn’t understand? Well, let’s dive deep into this 😉\n\nAnyone studying statistics eventually comes across the concept of the Central Limit Theorem. While some find it difficult to understand, it is a fundamental statistical concept that can be broken down into simpler terms.\n\nULTIMATE GUIDE FOR CENTRAL LIMIT THEOREM\n\nThis guide will explain the Central Limit Theorem and how it works, making it perfect for beginners who may be struggling with the concept.\n\n## What is Central Limit Theorem?\n\nLet's say you have a bunch of friends, and you want to see how tall they are. You could measure each friend's height, and then find the average height of all your friends.\n\nBut what if you don't have time to measure every single friend?", null, "Here's where the central limit theorem comes in. It says that if you add up a bunch of random things, like the heights of your friends, the total will look like a bell-shaped curve. This curve is called a normal distribution.\n\nSo, let's say you only measure the height of a few of your friends, maybe 5 or 10 of them. Even though you haven't measured all of your friends, if you add up all their heights and plot them on a graph, you'll see that the curve looks like a bell shape.\n\nThe cool thing is that the central limit theorem works for many things, not just height. It works for things like test scores, the number of people who visit a website, or the weight of apples in a basket.\n\nSo, to sum it up, the central limit theorem is a magic trick that says if you add up lots of little things, like the heights of your friends, the total will look like a bell-shaped curve.\n\n## Using Central Limit Theorem in Statistics and Data Science", null, "The central limit theorem (CLT) is a fundamental concept in statistics and data science that helps solve various problems. Some of the key problems that the CLT solves are:\n\n1. Estimating Population Parameters: The CLT helps us estimate population parameters, like the mean and standard deviation, by using a sample of the data. This is important because it allows us to make inferences about the entire population based on a smaller sample.\n2. Hypothesis Testing: The CLT is used to test hypotheses about population parameters, such as whether two means are statistically different or not.\n3. Confidence Intervals: The CLT helps us create confidence intervals, which are ranges of values that we are confident contain the true population parameter.\n4. Model Fitting: The CLT is also used in model fitting, where it helps us estimate the parameters of a statistical model by using data.\n\n## Limitations of the Central Limit Theorem", null, "The CLT has some limitations. These include\n\n1. Sample Size: The CLT assumes that the sample size is large enough for the normal distribution to emerging. The CLT may not be applicable if the sample size is too small.\n2. Independence: The CLT assumes that the samples are independent of each other. If the samples are not independent, the CLT may not be applicable.\n3. Outliers: The CLT is sensitive to outliers, which can skew the distribution and affect the accuracy of the results.\n4. Non-Normal Distributions: The CLT only applies to populations with a normal distribution. The CLT may not be applicable if the population is not normally distributed.\n\n## Central Limit Theorem Assumptions\n\nThe central limit theorem has below four key assumptions. These assumptions are largely talk about samples, sample sizes, and the population of data.", null, "1. Sampling is successive: Some sample units are common with sample units selected on previous occasions.\n2. Sampling is random: The sample selection must be random so that they have the same statistical possibility of being selected.\n3. Independent Samples: The selections or results from one sample should not affect future samples or other sample results.\n4. Samples should be limited: If sampling is done without replacement, the sample should be no more than 10% of the population. In general, larger population sizes warrant the use of larger sample sizes.\n\n## What are the 3 main rules of Central Limit Theorem\n\nThe 3 main rules of central limt theorem are Independence, Sample Size, Population distribution.  Let's understand these in detail.\n\n### Independence\n\nThe observations in the sample should be independent of each other. Independence ensures that the sample is representative of the population and that the observations in the sample are not affected by each other.\n\nFor example, if we are sampling the heights of students in a classroom, we would want to ensure that each student's height is independent of the height of other students.\n\nIf two students are related, their heights may be correlated, and the sample may not represent the population.\n\n### Sample Size\n\nThe sample size should be sufficiently large. This ensures that the sample mean is a good estimate of the population's mean. If the sample size is too small, the sample mean may not be representative of the population mean.\n\nThe exact sample size required depends on the underlying distribution of the population. If the population distribution is normal, a sample size of at least 30 is generally sufficient.\n\nHowever, if the population distribution is highly skewed or has heavy tails, a larger sample size may be required to ensure that the CLT applies.\n\n### Population Distribution\n\nThe population distribution should be finite or well-defined. This means that the population should have a mean and a finite variance. If the population distribution is undefined or infinite, the CLT may not apply.\n\nFor example, if we are sampling the number of cars passing through a toll booth daily, we would assume that the population has a finite mean and a finite variance.\n\nIf we are sampling the number of bacteria in a petri dish, we would assume that the population has a finite mean and a finite variance.\n\n## Why n ≥ 30 Samples In CLT\n\nA sample size of 30 is often used as a rule of thumb in statistical practice for applying the Central Limit Theorem (CLT). However, it's important to note that the actual required sample size can vary based on the population distribution and the desired level of precision.\n\nIn general, a larger sample size will provide a more accurate estimate of the population mean. Still, there are several reasons why a sample size of at least 30 is often considered a good starting point\n\n### Normality Assumption\n\nOne reason for the sample size of 30 or more is that it helps to fulfill the normality assumption, which is one of the requirements for the CLT to apply.\n\nWhen the sample size is less than 30, the distribution of the sample mean may not be normal, and therefore the CLT may not hold.\n\nHowever, when the sample size is greater than or equal to 30, the distribution of the sample mean tends to be approximately normal, regardless of the shape of the population distribution.\n\n### Large Enough to Capture Variation\n\nAnother reason for a sample size of at least 30 is that it is generally large enough to capture the variation in the population.\n\nA sample size of less than 30 may not provide enough information about the population, and the estimate of the population mean may be too variable to be useful.\n\nA larger sample size can help to reduce this variability and provide a more accurate estimate of the population mean.\n\n### Sufficient Precision\n\nA sample size of 30 or more can also provide sufficient precision in estimating the population mean.\n\nWith a larger sample size, the standard error of the sample means decreases, which means that the sample mean is more likely to be close to the population mean.\n\nThis increased precision can be useful in making more accurate inferences about the population.\n\n## Understanding the Maths behind Central Limit Theorem", null, "The CLT theorem tells us that when we take a large enough sample size (n) from any population, the sample means will approximate a normal distribution, regardless of the distribution of the population.\n\nThis is true as long as the sample is random, independent, and identically distributed (iid).\n\nThe CLT can be expressed mathematically as follows:\n\nLet X1, X2, ..., Xn be a random sample of size n from any population with mean μ and standard deviation σ.\n\nThen, as n approaches infinity, the sampling distribution of the sample meanapproaches a normal distribution with mean μ and standard deviation σ/√n.\n\nIn other words, the mean of the sampling distribution of the sample mean is equal to the population mean, and the standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size.\n\nFor example, let's say we want to estimate the average height of all students in a school. We take a random sample of 100 students and measure their heights. The mean height of our sample is 5 feet 8 inches, with a standard deviation of 3 inches.\n\nAccording to the CLT, as we increase the sample size, the distribution of the sample means will approach a normal distribution.\n\nLet's take another random sample of 1,000 students and measure their heights.\n\nThe mean height of this new sample will be normally distributed with a mean equal to the population mean (the true average height of all students in the school) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (in this case, 3 inches/√1000 ≈ 0.09 inches).\n\nThe CLT is a powerful mathematical concept that is used in many areas of statistics and data science to make inferences about populations based on sample data.\n\nRemembering the CLT's assumptions and limitations to ensure accurate and reliable results is important.\n\n## Real-world applications\n\nThe Central Limit Theorem has many real-world applications, particularly in the field of statistical analysis.\n\nFor example, it can be used to conclude a population by making inferences from a sample group.\n\nThis is important for drawing accurate conclusions about public opinion or customer preference based on survey data.\n\nIn addition, CLT is also used in quality control to make decisions about whether or not to accept batches of manufactured products by analyzing samples taken from the batch.\n\nTherefore, understanding the Central Limit Theorem can be invaluable in many different industries and fields where statistical analysis is used.\n\n## Limitations and Alternatives to the Central Limit Theorem (CLT)\n\nWhile the Central Limit Theorem is a powerful tool for statistical analysis, its application has certain limitations.\n\nFor example, it assumes that the sample size is large enough and that the observations in the sample are independent of each other.\n\nIn addition, there may be situations where the population being studied does not follow a normal distribution or has extreme outliers, which could impact the validity of using CLT.\n\nAlternatives to CLT include bootstrapping and permutation tests, which can also provide accurate results when studying a population.\n\nIt’s important to understand the limitations and alternatives to CLT when conducting statistical analysis to ensure accurate conclusions are drawn from data.\n\n## CLT Python Implementation\n\nLet's say we have a population of numbers with a uniform distribution between 0 and 1, and we want to see how the sample mean changes as we increase the sample size.", null, "We can use the CLT to predict that the sample mean will approach a normal distribution as the sample size increases.\n\nNot let's write script to create the graphs.", null, "In this code, we first generate a population of 10,000 numbers with a uniform distribution between 0 and 1 using the NumPy random. uniform function.\n\nWe then define a function called calculate_sample_means that takes a sample size and the number of samples to draw and returns a list of sample means.\n\nThis function randomly selects a sample of the specified size from the population without replacement using the NumPy random. choice function calculates the mean of the sample using the NumPy mean function and appends the sample mean to a list.\n\nWe then loop over different sample sizes (5, 10, 50, and 100) and calculate the sample means for each sample size using the calculate_sample_means function. We store the sample means in a dictionary called sample_means.\n\nFinally, we plot histograms of the sample means for each sample size using the Matplotlib hist function. We use the tight_layout function to adjust the spacing between the subplots and the show function to display the plot.\n\nWhen we run this code, we should see a plot with four subplots, each showing the histogram of the sample means for a different sample size.\n\nWe should see that as the sample size increases, the distribution of the sample means becomes more normal, which confirms the prediction of the CLT.\n\n# Conclusion\n\nIn conclusion, the Central Limit Theorem is a fundamental concept in statistics and data science that helps solve a variety of problems such as estimating population parameters, hypothesis testing, confidence intervals, and model fitting.\n\nHowever, the CLT has some limitations, including sample size, independence, outliers, and non-normal distributions. The CLT assumptions include sampling, random selection, independent samples, and limited samples.\n\nThe three main rules of the CLT are independence, sample size, and population distribution, and a sample size of 30 is often used as a rule of thumb.\n\nDespite its limitations, the CLT is a powerful tool in statistical analysis that allows us to make inferences about populations based on smaller sample sizes.\n\n#### Recommended Courses\n\nRecommended", null, "#### Basic Statistics Course\n\nRating: 4/5", null, "#### Inferential Stats Course\n\nRating: 4/5", null, "Rating: 5/5" ]
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https://studylib.net/doc/25314461/powerhw
[ "Uploaded by LeoGrandThio\n\n# PowerHW\n\nadvertisement", null, "Name____________________________ Date______________ Period__________\n\n## Power worksheet\n\nShow all work. Write equation, substitute values, then solve.\n\n1. A motor does 2,000 joules of work in 20 seconds. What is the power of the motor?\n\n2. A machine does 2,500 joules of work in 30 seconds. What is the power of this machine?\n\n3. A hair dryer uses 22,000 joules of energy in 60 seconds. What is the power of this hair dryer?\n\n4. A toaster oven uses 27,500 joules of energy in 45 seconds to toast a piece of bread.\n\nWhat is the power of the oven?\n\n5. A horse moves a sleigh 2.00 kilometer by applying a horizontal 2,000-newton force on its harness for 45 minutes. What is the power of the horse? (Hint: Convert time to seconds.)\n\n6. A wagon is pulled at a speed of 2.40 meters/sec by a horse exerting an 1,800newton horizontal force. What is the power of this horse?\n\n7. Suppose a force of 200 newtons is used to push an object a distance of 5 meters in\n\n15 seconds. Find the work done and the power for this situation.\n\n8. Emily\n\n’s vacuum cleaner has a power rating of 200 watts. If the vacuum cleaner does\n\n260,000 joules of work, how long did Emily spend vacuuming?\n\n9. Nicholas spends 20 minutes ironing shirts with his 2,800-watt iron. How many joules of energy were used by the iron? (Hint: convert time to seconds).\n\n10. It take a clothes dryer 25 minutes to dry a load of towels. If the dryer uses\n\n6,750,000 joules of energy to dry the towels, what is the power rating of the machine?\n\n11. A 2000-watt microwave oven takes 90 seconds to heat a bowl of soup. How many joules of energy does it use?\n\n12. A force of 200 newtons is used to move an object a distance of 15 meters with a power of 25 watts. Find the work done and the time it takes to do the work.\n\n13. If a small machine does 2,500 joules of work on an object to move it a distance of\n\n200 meters in 10 seconds, what is the force needed to do the work? What is the power of the machine doing the work?\n\n14. A machine uses a force of 100 newtons to do 20,000 joules of work in 20 seconds.\n\nFind the distance the object moved and the power of the machine. (Hint: A joule is the same as a Newton-meter.)\n\n15. A machine that uses 100 watts of power moves an object a distance of 15 meters in 25 seconds. Find the force needed and the work done by this machine." ]
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https://en.cppreference.com/w/cpp/utility/functional/greater_void
[ "# std::greater<void>\n\n< cpp‎ | utility‎ | functional\n\nC++\n Language Standard Library Headers Freestanding and hosted implementations Named requirements Language support library Concepts library (C++20) Diagnostics library Utilities library Strings library Containers library Iterators library Ranges library (C++20) Algorithms library Numerics library Localizations library Input/output library Filesystem library (C++17) Regular expressions library (C++11) Atomic operations library (C++11) Thread support library (C++11) Technical Specifications\n\nUtilities library\n Language support Type support (basic types, RTTI, type traits) Library feature-test macros (C++20) Dynamic memory management Program utilities Error handling Coroutine support (C++20) Variadic functions launder(C++17) initializer_list(C++11) source_location(C++20) Three-way comparison (C++20) three_way_comparablethree_way_comparable_with(C++20)(C++20) strong_ordering(C++20) weak_ordering(C++20) partial_ordering(C++20) common_comparison_category(C++20) compare_three_way_result(C++20) compare_three_way(C++20) strong_order(C++20) weak_order(C++20) partial_order(C++20) compare_weak_order_fallback(C++20) is_eqis_neqis_ltis_lteqis_gtis_gteq(C++20)(C++20)(C++20)(C++20)(C++20)(C++20)\nGeneral utilities\nDate and time\nFunction objects\nFormatting library (C++20)\n(C++11)\nRelational operators (deprecated in C++20)\nInteger comparison functions\n(C++20)\nSwap and type operations\n swap ranges::swap(C++20) exchange(C++14) declval(C++11)\n forward(C++11) move(C++11) move_if_noexcept(C++11) as_const(C++17)\nCommon vocabulary types\n pair tuple(C++11) apply(C++17) make_from_tuple(C++17)\n optional(C++17) any(C++17) variant(C++17)\nElementary string conversions\n(C++17)\n(C++17)\n\nFunction objects\n Partial function application bind_front(C++20) bind(C++11) is_bind_expression(C++11) is_placeholder(C++11) _1, _2, _3, ...(C++11)\n Function invocation invoke(C++17) Identity function object identity(C++20)\n Reference wrappers reference_wrapper(C++11) refcref(C++11)(C++11) unwrap_referenceunwrap_ref_decay(C++20)(C++20)\nOperator wrappers\n Negators not_fn(C++17) Searchers default_searcher(C++17) boyer_moore_searcher(C++17)\n Constrained comparators ranges::equal_to(C++20) ranges::not_equal_to(C++20) ranges::greater(C++20) ranges::less(C++20) ranges::greater_equal(C++20) ranges::less_equal(C++20)\n unary_function(until C++17) binary_function(until C++17) ptr_fun(until C++17) pointer_to_unary_function(until C++17) pointer_to_binary_function(until C++17) mem_fun(until C++17) mem_fun_tmem_fun1_tconst_mem_fun_tconst_mem_fun1_t(until C++17)(until C++17)(until C++17)(until C++17) not1(until C++20) not2(until C++20)\n binder1stbinder2nd(until C++17)(until C++17) bind1stbind2nd(until C++17)(until C++17) mem_fun_ref(until C++17) mem_fun_ref_tmem_fun1_ref_tconst_mem_fun_ref_tconst_mem_fun1_ref_t(until C++17)(until C++17)(until C++17)(until C++17) unary_negate(until C++20) binary_negate(until C++20)\n\n Defined in header template<> class greater; (since C++14)\n\nis a specialization of std::greater with parameter and return type deduced.\n\n## Contents\n\n### Member types\n\n Member type Definition is_transparent /* unspecified */\n\n### Member functions\n\n operator() tests if the lhs compares greater than rhs (public member function)\n\n## std::greater<>::operator()\n\n template< class T, class U> constexpr auto operator()( T&& lhs, U&& rhs ) const   -> decltype(std::forward(lhs) > std::forward(rhs));\n\nReturns the result of lhs > rhs.\n\n### Parameters\n\n lhs, rhs - values to compare\n\n### Return value\n\nThe result of lhs > rhs." ]
[ null ]
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https://math.eretrandre.org/tetrationforum/showthread.php?tid=956&pid=7684#pid7684
[ "• 0 Vote(s) - 0 Average\n• 1\n• 2\n• 3\n• 4\n• 5\n tommy equation", null, "tommy1729", null, "Ultimate Fellow", null, "", null, "", null, "", null, "", null, "Posts: 1,493 Threads: 356 Joined: Feb 2009 02/16/2015, 02:59 AM g is an entire function. \" tommy equation \" g(f(a x^b)) = f(c x^d) a,b,c,d integers >0. prototype solution Taylor(ln(x),x) ... maybe more later. with thanks to Kouznetsov. regards tommy1729", null, "tommy1729", null, "Ultimate Fellow", null, "", null, "", null, "", null, "", null, "Posts: 1,493 Threads: 356 Joined: Feb 2009 03/16/2015, 11:30 PM Ok I tried some things with the tommy equation. First a usefull link with thanks to my friend mick : http://math.stackexchange.com/questions/...lor-series So this explains what type of series expansions I am talking about ; the Tommy-Kouznetsov expansion of some order. So back to the tommy equation and considering parabolic fixpoints. Without going into detail we can recenter the parabolic fixpoint at 0. THE CORRECT SERIES EXPANSIONS FOR PARABOLIC FIXPOINTS ARE NOT KNOWN ?? Anyway Kouznetsov conjectured that for large x , Tommy-Kouznetsov expansions of order 1 are asymptotically correct. However I commented that by taylor's theorem and/or fake function theory ( and A few others ) this is also true for the simpler Taylor series. So I considered these expansions as EXACT solutions for real x > 0. That lead to the tommy equation ( as explained/introduced in post 1 ) , with g now having a parabolic fixpoint at 0. However after playing around I seemed to be getting into trouble. There were no Tommy-Kouznetsov expansions that solved the equation in most cases. In a kind of pseudocode this is what I wrote ( in simple Notepad ). ( if unclear let me know ) *** fix at 0 ( fix a = f(a) => f* (0) = 0 ) larger then x asymp x x + x^2 = p(x) p(f(x)) = f(ex) f(x) + f(x)^2 = f(ex) (b + c ln(x)) x +o(xx) + ((b + c ln(x)) x + o(xx))^2 = (eb + ec + ec ln(x)) x + o(xx) => b = eb + ec c = ec => error restart (b + c ln(x) + d ln(x)^2) x = (b + c + c ln(x) + d (ln^2 + 2 ln + 1) ) ex => = (eb + ec + ed + (ec + 2ed) ln + ed ln^2 ) x ed = d => error etc Same problem higher order Same problem p(f(A x^B)) = f(C x^D) for nontrivial cases of A,B,C,D. *** Notice o(xx) means o(x^2) and this goes to 0 very fast for small x , faster then the other terms hence they are ignored. Then it should be clear to you that no solution exists in general. SO I REPEAT : THE CORRECT SERIES EXPANSIONS FOR PARABOLIC FIXPOINTS ARE NOT KNOWN ?? Or am I wrong here ? Maybe we need a new equation to replace the tommy equation. I call it the tommy-abc equation for now. And if it works I call it the shadow equation. Here it is : p( f(x) ) = f(ax) + b f(cx) Hopefully this works better. I think the tommy-abc equation or shadow equation is new. regards tommy1729 \" Truth is whatever does not go away when we stop believing in it \" tommy1729", null, "tommy1729", null, "Ultimate Fellow", null, "", null, "", null, "", null, "", null, "Posts: 1,493 Threads: 356 Joined: Feb 2009 03/17/2015, 11:45 PM The problem might be p( f(x) ) = f(ax) + b f(cx) is nice but does it mean p^[z] ( f(x) ) = f(a^z x) + b^z f(c^z x) or does p^[z] ( f(x) ) = f(a^z x) + b f(c^z x) or something else ? I noted that since p(0) = 0 : Let f(A) = 0 p(f(A)) = f(aA) + b f(cA) = 0 Not sure what to make of that ... regards tommy1729", null, "sheldonison", null, "Long Time Fellow", null, "", null, "", null, "", null, "Posts: 683 Threads: 24 Joined: Oct 2008 03/18/2015, 08:52 AM (03/16/2015, 11:30 PM)tommy1729 Wrote: ...considering parabolic fixpoints. Without going into detail we can recenter the parabolic fixpoint at 0. THE CORRECT SERIES EXPANSIONS FOR PARABOLIC FIXPOINTS ARE NOT KNOWN Is this related to Jean Ecalle's formal solution for the Abel function for the parabolic case? See for example: Jean Ecalle's solution - Sheldon « Next Oldest | Next Newest »\n\n Possibly Related Threads... Thread Author Replies Views Last Post tommy beta method tommy1729 0 145 12/09/2021, 11:48 PM Last Post: tommy1729 Tommy's Gaussian method. tommy1729 24 5,071 11/11/2021, 12:58 AM Last Post: JmsNxn tommy's singularity theorem and connection to kneser and gaussian method tommy1729 2 625 09/20/2021, 04:29 AM Last Post: JmsNxn \" tommy quaternion \" tommy1729 14 5,778 09/16/2021, 11:34 PM Last Post: tommy1729 [MSE] Help on a special kind of functional equation. MphLee 4 1,158 06/14/2021, 09:52 PM Last Post: JmsNxn", null, "Logical tetration equation Xorter 0 3,028 02/01/2018, 10:29 PM Last Post: Xorter tommy's simple solution ln^[n](2sinh^[n+x](z)) tommy1729 1 5,178 01/17/2017, 07:21 AM Last Post: sheldonison Tommy's matrix method for superlogarithm. tommy1729 0 3,442 05/07/2016, 12:28 PM Last Post: tommy1729 Dangerous limits ... Tommy's limit paradox tommy1729 0 3,552 11/27/2015, 12:36 AM Last Post: tommy1729 Tommy's Gamma trick ? tommy1729 7 12,566 11/07/2015, 01:02 PM Last Post: tommy1729\n\nUsers browsing this thread: 1 Guest(s)", null, "" ]
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https://courses.lumenlearning.com/introchem/chapter/free-energy-and-cell-potential/
[ "## Free Energy and Cell Potential\n\n#### Learning Objective\n\n• Calculate the change in Gibbs free energy of an electrochemical cell, and discuss its implications for whether a redox reaction will be spontaneous\n\n#### Key Points\n\n• In a galvanic cell, the Gibbs free energy is related to the potential by: ΔG°cell = −nFE°cell.\n• If E°cell > 0, then the process is spontaneous (galvanic cell).\n• If E°cell < 0, then the process is nonspontaneous (electrolytic cell).\n\n#### Terms\n\n• electrode potentialThe potential difference of a half-reaction that occurs across a reversible cell made up of any electrode and a standard hydrogen electrode.\n• galvanic cellElectrochemical cell that derives electrical energy from spontaneous redox reaction taking place within the cell.\n• oxidizing agentAny substance that oxidizes, or receives electrons from, another; in so doing, it becomes reduced.\n• Gibbs free energyThe difference between the enthalpy of a system and the product of its entropy and absolute temperature; a measure of the useful work obtainable from a thermodynamic system at constant temperature and pressure.\n\nThe basis for an electrochemical cell, such as the galvanic cell, is always a redox reaction that can be broken down into two half-reactions: oxidation occurs at the anode, where there is a loss of electrons, and reduction occurs at the cathode, where there is a gain of electrons. Electricity is generated due to the electric potential difference between two electrodes. This is related to how easily the oxidized species gives up electrons and how badly the reduced species wants to gain them.", null, "Electrochemical cellA demonstration electrochemical cell setup resembling the Daniell cell. The two half-cells are linked by a salt bridge carrying ions between them. Electrons flow in the external circuit.\n\nIn electrochemistry, the standard electrode potential, abbreviated E°, is the measure of the individual potential of a reversible electrode at standard state, which is with solutes at an effective concentration of 1 M, and gases at a pressure of 1 atm. The values are most often tabulated at 25 °C (298 K).\n\n## Is It Oxidized or Reduced?\n\nSince the standard electrode potentials are given in their ability to be reduced, the bigger the standard reduction potentials, the easier they are to be reduced; in other words, they are simply better oxidizing agents. For example, F2 has a potential of 2.87 V and Li+ has a potential of -3.05 V. F2 reduces easily and is therefore a good oxidizing agent. In contrast, Li(s) would rather undergo oxidation, so it is a good reducing agent.\n\nIn the example of Zn2+, whose standard reduction potential is -0.76 V, it can be oxidized by any other electrode whose standard reduction potential is greater than -0.76 V and can be reduced by any electrode with standard reduction potential less than -0.76 V.\n\n## The Sign of the change in Gibbs Free Energy\n\nIn a galvanic cell, where a spontaneous redox reaction drives the cell to produce an electric potential, the change in Gibbs free energy must be negative. This is the opposite of the cell potential, which is positive when electrons flow spontaneously through the electrochemical cell. The relationship between $\\Delta G^o$ and $E^o$ is given by the following equation:\n\n$\\Delta G^o = -nFE^o$\n\nHere, n is the number of moles of electrons and F is the Faraday constant (96,485$\\frac {Coulombs}{mole}$). As such, the following rules apply:\n\n• If E°cell > 0, then the process is spontaneous (galvanic cell)\n• If E°cell < 0, then the process is non-spontaneous (the voltage must be supplied, as in an electrolytic cell)\n\n## Example\n\nCalculate the change in Gibbs free energy of an electrochemical cell where the following redox reaction is taking place:\n\n$Pb^{2+} + Ni \\rightarrow Ni^{2+} + Pb \\ \\ \\ \\ \\ \\ \\ \\ E^o = 0.12\\ V$\n\nTo solve, we need to use the equation:\n\n$\\Delta G^o = -nFE^o$\n\nThe number of moles of electrons transferred is 2, while the cell potential is equal to 0.12 V. One volt is $1\\frac {Joule}{Coulomb}$.\n\n$\\Delta G^o = -2 \\ moles\\ e^- \\times 96485\\frac {Coulombs}{mole} \\times 0.12 \\frac {Joules}{Coulomb}$\n\n$\\Delta G^o = -23,156 \\ J\\ = -2.3 \\ kJ$\n\nBecause the change in Gibbs free energy is negative, the redox process is spontaneous." ]
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https://www.excelhow.net/how-to-check-if-cell-contains-all-values-from-range.html
[ "# How to Check If Cell Contains All Values from Range\n\nThis post explains that how to check if a cell contains all of several values from a range in excel. How to check if cell contains all of many values in a list in excel 2013. How to check if all of values in a list can be found in a cell, if TRUE, then return TRUE, otherwise, returns FALSE.\n\n## Check if Cell Contains all values from range\n\nIf you want to check if a cell contains all values in a list, you can use a combination of the SEARCH function, the SUMPRODUCT function, the ISNUMBER function and COUNTA function. And you need to create a new formula to count all matches at once, then compare to the total number of all values in list, if equal, we can know that that cell contains all values of list.\n\nFor example, assuming that you have a list of text strings in the range B1:B3, and you want to check if the Cell B1 contains all of values in another range E1:E3, you can write down the following formula:\n\n`=SUMPRODUCT( -- ISNUMBER(SEARCH(\\$E\\$1:\\$E\\$3,B1)))=COUNTA(\\$E\\$1:\\$E\\$3)`\n\nLet’s see how this formula works:\n\n=SEARCH(\\$E\\$1:\\$E\\$3,B1)\n\nThe SEACH function returns position of the first character of find_text in a text string. And this formula will search each value from the range E1:E3 inside within_text in Cell B1, then returns position of each text string in Cell B1, so it will return an array result like this:\n\n`{1;7;12}`\n\nThe returned result goes into the ISNUMBER function as its argument.\n\n=ISNUMBER(SEARCH(\\$E\\$1:\\$E\\$3,B1))\n\nThe ISNUMBER function will check if a cell contains a numeric value, and this formula will check each items of array result returned by the SEACH function, if the item is a numeric value, then return TRUE, otherwise, returns FALSE. So it will return another array result like this:\n\n`{TRUE;TRUE;TRUE}`\n\n=– ISNUMBER(SEARCH(E1:E3,B1))\n\nThe double-dash is known as a double unary operator, it can convert the TRUE values to 1 and FALSE values to 0. So this formula returns an array of numbers like this:\n\n`{1,1,1}`\n\n=SUMPRODUCT( — ISNUMBER(SEARCH(\\$E\\$1:\\$E\\$3,B1)))", null, "The SUMPRODUCT returns a total sum of the array result returned by the ISNUMBER function with double-dash operator. So it returns 3.\n\n= COUNTA(\\$E\\$1:\\$E\\$3)", null, "This formula returns the number of cells that are not empty in range E1:E3. It returns 3.\n\n=SUMPRODUCT( — ISNUMBER(SEARCH(\\$E\\$1:\\$E\\$3,B1)))=COUNTA(\\$E\\$1:\\$E\\$3)", null, "If the result returned by the SUMPRODUCT is equal to the number of items in the range E1:E3, then we can know that all values in range E1:E3 can be found in Cell B1. The number of items of range E1:E3 can be got from the COUNTA function. So it returns TRUE.\n\n### Related Formulas\n\n• Check if Cell contains one of many values from range\nAssuming that you have a list of text strings in the range B1:B3 and you want to check each text string if it contains one of several values in a range E1:E3. If it contains any of text string in range E1:E3, then it should be return TRUE value, otherwise, it should return FALSE…\n\n### Related Functions\n\n• Excel SEARCH function\nThe Excel SEARCH function returns the number of the starting location of a substring in a text string.The syntax of the SEARCH function is as below:= SEARCH  (find_text, within_text,[start_num])…\n• Excel SUMPRODUCT function\nThe Excel SUMPRODUCT function multiplies corresponding components in the given one or more arrays or ranges, and returns the sum of those products.The syntax of the SUMPRODUCT function is as below:= SUMPRODUCT (array1,[array2],…)…\n• Excel ISNUMBER function\nThe Excel ISNUMBER function returns TRUE if the value in a cell is a numeric value, otherwise it will return FALSE.The syntax of the ISNUMBER function is as below:= ISNUMBER (value)…\n• Excel COUNTA function\nThe Excel COUNTA function counts the number of cells that are not empty in a range. The syntax of the COUNTA function is as below:= COUNTA(value1, [value2],…)…\n\n### You might also like:\n\nSidebar", null, "" ]
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http://nz.openfisca.org/variables/is_in_de_facto_relationship
[ "### Is in a de facto relationship?\n\nBoolean MONTH Person Formula Included used 1 time\n\nValue type Boolean . Default value false Entity person\n\n### How is this calculated?\n\nTo calculate this variable, the following input is used\n\n### Where is this used?\n\nThis variable is referred to by these other variables in their own calculations\n\n### Formulas\n\nThis is the formula used to calculate the value of is_in_de_facto_relationship\n\n### 0001-01-01\n\nThis formula is used for scenarios from the date 0001-01-01 onwards. More info on formulas\n\n``````def formula(persons, period, parameters):\nreturn persons('property_relationships__is_in_de_facto_relationship', period)``````" ]
[ null ]
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https://www.programminghomeworkhelp.com/program-to-implement-matrices-and-plotting-in-python/
[ "# Create a Program to Implement Matrices and Plotting in Python Assignment Solution.\n\n## Instructions\n\nObjective\nWrite a program to implement matrices and plotting in python language.\n\n## Requirements and Specifications", null, "", null, "", null, "", null, "", null, "Source Code\n\n# Assignment 5: Matrix as a Linear Transformation ## DTSC 680: Applied Machine Learning ## Name: The purpose of this assignment is for you to gain experience working with matrices and vectors, as well as to understand the idea that a matrix can be viewed as a ___linear transformation___. This requires us to think of a matrix $\\mathbf{A}$ as an object that \"acts\" (or \"operates\") on a vector $\\mathbf{x}$ by multiplication to produce a new vector called $\\mathbf{Ax}$. The original vector is $\\mathbf{x}$, and the transformed vector is $\\mathbf{Ax}$. In this assignment you will transform an ensemble of vectors using several different matrices (i.e. several different transformations) and observe the results. Before you continue, take a look at this video from 3Blue1Brown: [Linear transformations and matrices](https://youtu.be/kYB8IZa5AuE) In Assignment 4, you computed matrix-vector multiplications by hand for just a single vector - that is, you computed $\\mathbf{b}$ as $\\mathbf{Ax} = \\mathbf{b}$ manually. For instance, you might have computed the following by hand: $$\\begin{bmatrix} 4 & -3 & 1 & 3 \\\\ 2 & 0 & 5 & 1 \\end{bmatrix} \\times \\left[ \\begin{array}{c} 1 \\\\ 1 \\\\ 1 \\\\ 1 \\end{array} \\right] = \\left[ \\begin{array}{c} 5 \\\\ 8 \\end{array} \\right]$$ $$\\begin{bmatrix} 4 & -3 & 1 & 3 \\\\ 2 & 0 & 5 & 1 \\end{bmatrix} \\times \\left[ \\begin{array}{c} 1 \\\\ 4 \\\\ -1 \\\\ 3 \\end{array} \\right] = \\left[ \\begin{array}{c} 0 \\\\ 0 \\end{array} \\right]$$ These equations say that multiplication by the matrix $\\mathbf{A}$ transforms the vector $\\left[ \\begin{array}{c} 1 & 1 & 1 & 1 \\end{array} \\right]^T$ into $\\left[ \\begin{array}{c} 5 & 8 \\end{array} \\right]^T$ and transforms the vector $\\left[ \\begin{array}{c} 1 & 4 & -1 & 3 \\end{array} \\right]^T$ into $\\left[ \\begin{array}{c} 0 & 0 \\end{array} \\right]^T$. (Note: The superscript T denotes the transpose, which essentially means \"the rows become columns, and the columns become rows\".) Suppose that we wanted to perform this transformation not for just one vector (i.e. one single data point), but for many vectors (i.e. many data points) at the same time. We could accomplish this by thinking of our vector now as a matrix of vectors, and we will apply the linear transformation to each of these vectors in the matrix. (So, now we will be performing matrix multiplication.) For example, to apply the linear transformation to the above two vectors at the same time, we would write: $$\\begin{bmatrix} 4 & -3 & 1 & 3 \\\\ 2 & 0 & 5 & 1 \\end{bmatrix} \\times \\left[ \\begin{array}{c} 1 & 1\\\\ 1 & 4 \\\\ 1 & -1 \\\\ 1 & 3 \\end{array} \\right] = \\left[ \\begin{array}{c} 5 & 0 \\\\ 8 & 0 \\end{array} \\right]$$ So, what will we be doing in this assignment? You will plot a simple dataset of points, where each point can be thought of as an individual vector in 2D Cartesian space. You will then perform several different geometric linear transformations in real 2D space on this data (i.e. \"do some matrix multiplication with a supplied matrix\"). You will then plot the original data and the transformed data, and observe the transformation. At the end, you will be asked to correctly label each of the different linear transformation matrices with its name based on the transformation results. The data you will read in has the typical format for 2D spatial data (typicaly for our class, that is) - there are three columns for the x, y, and z coordinates. For example, the data you import will have the following form (Atually, this is not true! Your data will be in 2 dimensions, but I will show you 3 here.): $$\\begin{bmatrix} x_1 & y_1 & z_1 \\\\ x_2 & y_2 & z_2 \\\\ x_3 & y_3 & z_3 \\\\ \\vdots & \\vdots & \\vdots \\\\ x_n & y_n & z_n \\end{bmatrix}$$ We can view each data point as a vector. So, the first vector would be $$\\mathbf{v} = \\left[ \\begin{array}{c} x_1 \\\\ y_1 \\\\ z_1 \\end{array} \\right]$$ Do you see how we need a column vector for the matrix multiplication to work properly, but each vector appears as a row vector in the matrix? Well, in order for the matrix multiplcation to work properly, the dimensions of our matrices must agree. Accordingly, we must employ the [transpose](https://www.youtube.com/watch?v=TZrKrNVhbjI) when multiplying our matrix of vectors by our transformation matrix. What I am referring to is that, for matrix multiplication to work, the number of columns in the first matrix must be equal to the number of rows in the second matrix - this is spelled out in one of the lecture videos you watched for Assignment 4. A couple last notes: Use NumPy arrays to represent your matrices, so that matrix multiplication can be performed using the [dot()](https://numpy.org/doc/stable/reference/generated/numpy.dot.html) method. Also, you can get the transpose of a Numpy array by using its [T](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.T.html) attribute. # Preliminaries Let's import some common packages: import matplotlib.pyplot as plt import matplotlib as mpl from matplotlib import cm import numpy as np import pandas as pd %matplotlib inline mpl.rc('axes', labelsize=14) mpl.rc('xtick', labelsize=12) mpl.rc('ytick', labelsize=12) import os # Where to save the figures PROJECT_ROOT_DIR = \".\" FOLDER = \"figures\" IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, FOLDER) os.makedirs(IMAGES_PATH, exist_ok=True) def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300): path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension) print(\"Saving figure\", fig_id) if tight_layout: plt.tight_layout() plt.savefig(path, format=fig_extension, dpi=resolution) # Write Plotting Function You must define a function called plotTransformedData(original_df, trans_df, colors, size, limits) that accepts two Pandas DataFrames (composed of 2 spatial coordinates each) called original_df and trans_df. The former is the original data that you will read in, and the latter is that data after you applied a linear transformation to it. You will plot both, side-by-side, to compare the before and after effects of the transformation. The function must use [scatter()](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html) to plot the data. Additionally, the plotTransformedData function accepts three other parameters: colors, size, and limits. The colors parameter is passed to the scatter function through its c parameter. The colors parameter must be a $(n,3)$ NumPy array, where $n$ is the number of data points and each of the three columns corresponds to an RGB value in the range [0,1]. The size parameter is passed to the scatter function through its s parameter. The size parameter controls the size of the marker used to represent the data point, and must be a Numpy array of size $(n,)$. (This is not a mistake: the size should really be $(n,)$. You can use np.linspace() to create the array). Lastly, the limits parameter is a list that looks like this: limits = [xmin, xmax, ymin, ymax], where the values are the limits for the x and y axes. You must specify these limits values so that they are equal to mine (I used -2.25 and +2.25 for both x and y as my limits, do not hard-code these values in the function definition though!). You must place the definition of the plotTransformedData(original_df, trans_df, colors, size, limits) function in the following cell. Be sure to include titles for each of the subplots (i.e. \"Original Data\" and \"Transformed Data\"). Note: An example figure is shown below for the Identity Matrix transformation, and you should emulate this figure as closely as possible when creating your function. def plotTransformedData(original_df, trans_df, colors, size, limits): # Create figure fig, axes = plt.subplots(nrows = 1, ncols = 2) # Plot first dataset original_df.plot.scatter(x = original_df.columns, y = original_df.columns, c = colors, s = size, ax = axes) trans_df.plot.scatter(x = original_df.columns, y = original_df.columns, c = colors, s = size, ax = axes) # Set figure size axes.set_xlim(limits[:2]) axes.set_ylim(limits[2:]) axes.set_title('Original') axes.set_xlim(limits[:2]) axes.set_ylim(limits[2:]) axes.set_title('Transformed') plt.show() # Import Data Import data from the file called 2D_data.csv. Name the returned DataFrame data. data = pd.read_csv('2D_data.csv') data.head() # Plot Initial Data Begin by specifying the colors, sizes, and limits parameters for the plotTransformedData function. You will not call the plotTransformedData(original_df, trans_df, colors, size, limits) function in this section, but rather you'll invoke it below in the section called _Perform Linear Transformations and Plot Results_. However, you will plot the data DataFrame here, merely to inspect it, using the marker colors, marker sizes, and axis limits specified by the colors, sizes, and limits parameters. So, plot data here. You should emulate the marker colors and sizes shown below as best as you can. The marker sizes range from small to large, and the marker colors vary from black to red. # size of data n = len(data) # define colors colors = np.zeros((n,3)) colors[:,0] = np.linspace(0, 1, n) limits = [-2.25, 2.25, -2.25, 2.25] sizes = np.linspace(10, 50, n) plt.figure(figsize=(10,10)) data.plot.scatter(x='x', y='y', c =colors, s = sizes) plt.xlim(limits[:2]) plt.ylim(limits[2:]) plt.title('2D Data') # Define Data Matrix and Transformation Matrices Create a NumPy array called X from the data DataFrame above. Further, you must define the following transformation matrices. You must declare these matrices to be NumPy arrays, and name them A1, A2, ..., AN, as shown. # -------------------- Define X NumpPy Array -------------------- # # Data Matrix X = data.values n = len(X) colors = np.zeros((n,3)) colors[:,0] = np.linspace(0, 1, n) limits = [-2.25, 2.25, -2.25, 2.25] sizes = np.linspace(10, 50, n) # -------------------- Define 13 NumPy Arrays -------------------- # k = 0.5 m = 0.5 r = 0.5 c = 2.0 phi = np.pi/4 A1 = np.array([[-1, 0], [0, -1]]) A2 = np.array([[k, 0], [0, 1]]) A3 = np.array([[np.cos(phi), -np.sin(phi)], [np.sin(phi), np.cos(phi)]]) A4 = np.array([[-1, 0], [0, 1]]) A5 = np.array([[1, 0], [0, c]]) A6 = np.array([[1, 0], [r, 1]]) A7 = np.array([[1, m], [0, 1]]) A8 = np.array([[0, -1], [-1, 0]]) A9 = np.array([[1, 0], [0, 0]]) A10 = np.array([[0, 0], [0, 1]]) A11 = np.array([[1, 0], [0, -1]]) A12 = np.array([[0, 1], [1, 0]]) A13 = np.array([[1, 0], [0, 1]]) # Perform Linear Transformations and Plot Results In this section, you will perform the following: $$\\mathbf{X}_{trans} = \\mathbf{A} \\mathbf{X}^T$$ where $\\mathbf{X}$ is the data you read in from the file, $\\mathbf{A}$ is any one of the thirteen transformation matrices, and $\\mathbf{X}_{trans}$ is the transformed data. You should express the matrix multiplication in one line of code! ### Identity Matrix Any matrix $\\mathbf{A}$ multiplied by the ___Identity Matrix___ $\\mathbf{I}$ is equal to itself! That is, $\\mathbf{AI} = \\mathbf{A}$. The 2D identity matrix is given below. # Perform Matrix Multiplication Xtrans = np.dot(A13, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) For the rest of the following linear transformations, you can Google the definitions to learn more. ### Rotation Matrix # Perform Matrix Multiplication Xtrans = np.matmul(A3, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) ### Reflection Matrices # Perform Matrix Multiplication Xtrans = np.matmul(A1, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) # Perform Matrix Multiplication Xtrans = np.matmul(A4, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) # Perform Matrix Multiplication Xtrans = np.matmul(A8, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) # Perform Matrix Multiplication Xtrans = np.matmul(A11, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) # Perform Matrix Multiplication Xtrans = np.matmul(A12, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) ### Contraction and Expansion Matrices # Perform Matrix Multiplication Xtrans = np.matmul(A2, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) # Perform Matrix Multiplication Xtrans = np.matmul(A5, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) ### Shearing Matrices # Perform Matrix Multiplication Xtrans = np.matmul(A6, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) # Perform Matrix Multiplication Xtrans = np.matmul(A7, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) ### Projection Matrices # Perform Matrix Multiplication Xtrans = np.matmul(A9, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) # Perform Matrix Multiplication Xtrans = np.matmul(A10, X.T).T # Plot Transformation # Construct DataFrames again Xdf = pd.DataFrame(data = X, columns = ['x', 'y']) Xtransdf = pd.DataFrame(data = Xtrans, columns = ['x', 'y']) plotTransformedData(Xdf, Xtransdf, colors, sizes, limits) # Connect the Dots In this section, you must correctly label linear transformations their names. The pool of transformations is given below: - Identity Matrix - Rotation Matrix - Reflection through the x Axis Matrix - Reflection through the y Axis Matrix - Reflection through the Line y = x Matrix - Reflection through the Line y = -x Matrix - Reflection through the Origin Matrix - Horizontal Contraction/Expansion Matrix - Vertical Contraction/Expansion Matrix - Hortizontal Shear Matrix - Vertical Shear Matrix - Projection onto x Axis Matrix - Projection onto y Axis Matrix You must correctly label the following linear transformations with the above names. 1. A1: Reflection through the Origin Matrix 2. A2: Horizontal Contraction/Expansion Matrix 3. A3: Rotation Matrix 4. A4: Reflection through the y Axis Matrix 5. A5: Vertical Contraction/Expansion Matrix 6. A6: Vertical Shear Matrix 7. A7: Hortizontal Shear Matrix 8. A8: Reflection through the Line y = -x Matrix 9. A9: Projection onto x Axis Matrix 10. A10: Projection onto y Axis Matrix 11. A11: Reflection through the x Axis Matrix 12. A12: Reflection through the Line y = x Matrix 13. A13: Identity Matrix" ]
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https://mycareerwise.com/content/closer-property-of-regular-language/content/exam/nta-net/computer-science
[ "## Closer property of Regular Language\n\n1.  Regular Language closed under union.\n\nIf  L1 = Regular Language and L2 = Regular Language then L1 U L2 = Regular Language.\n\nExample:\n\nL1 = ${\\mathrm{a}}^{\\mathrm{n}}$ , L2 = ${\\mathrm{a}}^{2\\mathrm{n}}$  and L3 = ${\\mathrm{a}}^{3\\mathrm{n}+5}$  then\n\nL= L1 U  L2 U L3 =    it is also regular language\n\n2.  Regular Language closed under intersection.\n\nIf L1= Regular Language and L2 = Regular Language then L1∩ L2 = Regular Language.\n\nExample:\n\nL1 = Mod 2  and L2 = Mod 4 then\n\nL = L1 ∩ L2 = Mod 2 ∩ Mod 4 = Mod 4 = Regular Language\n\n3.  Regular Language closed under concatenation.\n\nIf L1 = Regular Language and L2 = Regular Language then L1 . L2 = Regular Language.\n\nExample:\n\nL1 = ${\\mathrm{a}}^{\\mathrm{n}}$ and L2 = ${\\mathrm{a}}^{2\\mathrm{n}}$ then L = L1. L2 = ${\\mathrm{a}}^{\\mathrm{n}}$ . ${\\mathrm{a}}^{2\\mathrm{n}}$ = Regular Language\n\n4. Regular Language closed under Complement.\n\nIf  L = Regular Language then ${\\mathrm{L}}^{\\mathrm{C}}$ = Regular Language\n\nExample:\n\nL = {At least three a i.e  |a| ≥ 3 }  then,\n\n${\\mathrm{L}}^{\\mathrm{C}}$ =  = {At most two a i.e. |a| < 3 or |a| ≤ 2}\n\n{At most two a i.e. |a| < 3 or |a| ≤ 2} = Regular Language\n\n5.  Regular Language closed under Kleene star operator.\n\nIf L = Regular Language then L*= Regular Language\n\nExample:\n\nL = ${\\mathrm{a}}^{\\mathrm{n}}$  then L* = ${\\left({\\mathrm{a}}^{\\mathrm{n}}\\right)}^{*}$ = Regular Language\n\n6. Regular Language closed under Set Difference.\n\nIf L1 = Regular Language and L2 = Regular Language then,\n\n= Regular Language.\n\nExample:\n\nL1 = Mod 2 = {2, 4, 6, 8, 10, 12, 14, 16, 20…} and L2 = Mod 4 = {4, 8, 12, 16, 20….}\n\nNow L = L1 - L2 = {2, 6, 14, ….} = Regular Language\n\nRegular Expression Closed Under:\n\nUnion (U), Intersection (), Concatenation (.), Complement, Kleene star operator (*), Set Difference, Symmetric Difference (⊕), NOR, XNOR, Reversal, Homomorphism, Inverse, Homomorphism." ]
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https://www.gradesaver.com/textbooks/math/algebra/algebra-2-1st-edition/chapter-9-quadratic-relations-and-conic-sections-9-1-apply-the-distance-and-midpoint-formulas-9-1-exercises-skill-practice-page-618/43
[ "## Algebra 2 (1st Edition)\n\nPublished by McDougal Littell\n\n# Chapter 9 Quadratic Relations and Conic Sections - 9.1 Apply the Distance and Midpoint Formulas - 9.1 Exercises - Skill Practice - Page 618: 43\n\n#### Answer\n\n$x=\\pm6-4$\n\n#### Work Step by Step\n\nThe distance formula from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is $d=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Hence here: $\\sqrt{(x-(-4))^2+(7-1)^2}=6\\sqrt{2}\\\\(x+4)^2+36=72\\\\(x+4)^2=36\\\\x+4=\\pm6\\\\x=\\pm6-4$\n\nAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback." ]
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{"ft_lang_label":"__label__en","ft_lang_prob":0.76229143,"math_prob":0.98908395,"size":477,"snap":"2021-04-2021-17","text_gpt3_token_len":176,"char_repetition_ratio":0.09936575,"word_repetition_ratio":0.0,"special_character_ratio":0.3962264,"punctuation_ratio":0.0754717,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9986859,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-20T09:49:06Z\",\"WARC-Record-ID\":\"<urn:uuid:301f67ef-9ec0-4d88-a457-d66d24fb5528>\",\"Content-Length\":\"96539\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7fc0d4ad-085b-46b4-89a4-1b766e526f7f>\",\"WARC-Concurrent-To\":\"<urn:uuid:cf436b8d-4b0d-4efa-b02d-664780b15926>\",\"WARC-IP-Address\":\"52.86.130.234\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/algebra/algebra-2-1st-edition/chapter-9-quadratic-relations-and-conic-sections-9-1-apply-the-distance-and-midpoint-formulas-9-1-exercises-skill-practice-page-618/43\",\"WARC-Payload-Digest\":\"sha1:FLBG3RJKSW4IVPAU23NWCLPTHLGQBMJU\",\"WARC-Block-Digest\":\"sha1:E6MV3P465NBFDPE6Z3NFSC6EUIEVRQ2C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618039388763.75_warc_CC-MAIN-20210420091336-20210420121336-00049.warc.gz\"}"}
http://mslc.ctf.su/wp/leet-more-2010-time-traveller-writeup/
[ "Sep\n15\n\n## Leet More 2010 Time Traveller writeup\n\nA scientist who worked on the issue of space-time continuum, suddenly disappeared.\nHe left only\na mysterious drawing in a notebook.\nThere is a suspicion that he traveled back in time. In what year did he travel? And what is his name?", null, "There are only 2 breaks in this maze. Let’s try to find the way. Ascii of lines length don’t mean anything, but turns do. Each turn is a bit. Just experiement to find that turn right = 1, turn left = 0. Here is a script to collect bits:\n\n<?php\n\n$im = imagecreatefrompng($argv);\nif (!$im) die(\"can't open image\\n\");$right1 = 1; #if turn right = 1\n$sx =$sy = 512;\n\n#start coordinates\n$x = 256;$y = 246;\n$angle = 270;$key = '';\nwhile (1) {\n$cos = intval(cos(deg2rad($angle)));\n$sin = intval(sin(deg2rad($angle)));\n$c = imagecolorat($im, $x+$cos, $y-$sin);\nif ($c) #clear pixels for doctor's name imagesetpixel($im, $x+$cos, $y-$sin, 0x30);\nif (!$c) {$ar = ($angle + 270 ) % 360;$al = ($angle + 90 ) % 360;$xr = $x+intval(cos(deg2rad($ar)));\n$yr =$y-intval(sin(deg2rad($ar)));$xl = $x+intval(cos(deg2rad($al)));\n$yl =$y-intval(sin(deg2rad($al)));$cr = imagecolorat($im,$xr, $yr);$cl = imagecolorat($im,$xl, $yl); if ($cl && $cr) die(\"Picture failish\\n\"); if (!$cl && !$cr) break; if ($cr) {\n$angle =$ar;\n$x =$xr;\n$y =$yr;\n}\nelse {\n$angle =$al;\n$x =$xl;\n$y =$yl;\n}\n$key .= (!!($cr) ^ $right1) ? 1 : 0; } else {$x += $cos;$y -= $sin; //axes differ } }$a = str_split($key, 8); foreach ($a as $b) { echo chr(bindec($b));\n}\necho \"\\n\";\n\nimagepng($im, \"out.png\"); ?> $ php solve.php traveller.png\nTh1RtY_e1gHT_5ev3nTY_0Ne_A.D.\n\nout.png contains a shadowed path and we can see the scientist’s name:", null, "So, the answer to Time Traveller 2 was “Dr Leet”\n\n1.", null, "##### unkn0w says:\n\ninteresting challenge, but the question is how we can build such as image ?\nis there some trick using grafis editor or it just with the code ?\nif you please let me know ?\n\n2.", null, "##### hellman says:\n\nI built it with a script on php. It generates 100 random pics with the hidden text. So you can choose a nice one.\n\n“Dr Leet” text was added later manually.\n\n1.", null, "##### unkn0w says:\n\nhow we add the Dr Leet text ?\nfirst we add the text to an image or text added after we generated an image ?\n\n1.", null, "##### hellman says:\n\nFirst we generate the image, then we add Dr Leet text\n\n1.", null, "##### unkn0w says:\n\nthanks sir, i have try it and it so awesome, but a little hard to add the text on that image so that people cant notice there is secret text inside an image, i use photoshop to add the text, but mine not look so awesome as your sir, may be i should to find some font type or draw it by my self,\n\nthanks again sir :)\n\n1.", null, "##### hellman says:\n\nYes, we drew it manually, line by line in paint :)" ]
[ null, "http://leetmore.ctf.su/wp-content/uploads/2010/09/traveller-300x300.png", null, "http://leetmore.ctf.su/wp-content/uploads/2010/09/out-300x300.png", null, "http://1.gravatar.com/avatar/ac33af68f138e4368f291ae8a62609b9", null, "http://0.gravatar.com/avatar/6f090a8f95a8cb4d87b416fa5420227c", null, "http://0.gravatar.com/avatar/962cb8618e21c96441a1063d50ffdae2", null, "http://0.gravatar.com/avatar/6f090a8f95a8cb4d87b416fa5420227c", null, "http://0.gravatar.com/avatar/962cb8618e21c96441a1063d50ffdae2", null, "http://0.gravatar.com/avatar/6f090a8f95a8cb4d87b416fa5420227c", null ]
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https://www.ruby-forum.com/t/treetop-equal-precedence/127930
[ "# Treetop equal precedence\n\nHow do I make two rules with equal precedence. The obvious example is\ntrue||false&&false\nshould return false because the true||false is evaluated first, then\n&&false.\nbut also\ntrue&&false||true\nshould return true because true&&false is false, but then the ||true is\nevaluated.\n\n[email protected] wrote:\n\n[Note: parts of this message were removed to make it a legal post.]\n\nHow do I make two rules with equal precedence. The obvious example is\ntrue||false&&false\nshould return false because the true||false is evaluated first, then &&false.\nbut also\ntrue&&false||true\nshould return true because true&&false is false, but then the ||true is evaluated.\n\nI don’t understand how your example relates to the way you worded your\nquestion,\nbut if you have two or more operators at the same level of precedence,\njust use\na sequence. For example, a sum of 1 or more terms can be expressed as:\n\nrule sum\nterm ( (’+’/’-’) term )*\nend\n\n(with white-space skipping stripped out). If you want to evaluate the\nresult,\nsay by providing and calling a value() method, here’s the idiom I use:\n\n‘+’ { def operate(a, b); a+b; end }\n/ ‘-’ { def operate(a, b); a-b; end }\nend\n\nrule sum" ]
[ null ]
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http://www.nematrian.com/ERMForPensionFunds20110927
[ "/\n\n### var x2=document.getElementById(\"RandomWalkHyperlink\"); x2.setAttribute(\"width\",\"250\"); x2.setAttribute(\"height\",\"30\"); x2.setAttribute(\"style\",\"border: 1px solid black\"); var c2=x2.getContext(\"2d\"); var sigma=.06; var mu=0; var y=new Array; var r=new Array; var ylength=100; var i; var xplotlow=2; var xplothigh=80; var yplotlow=x2.height-2; var yplothigh=6; var frameRate=100; var lineColour=\"red\" y=1; for (i=1;i<ylength;i++) { r[i]=inverseNormal(Math.random()); y[i]=y[i-1]*Math.exp(mu+sigma*r[i]); } projectLineChartOntoCanvas(c2,y,xplotlow,xplothigh,yplotlow,yplothigh,lineColour); animateRandomWalk(x2,c2,y,xplotlow,xplothigh,yplotlow,yplothigh,lineColour,mu,sigma,frameRate) function animateRandomWalk(canvas,ctx,y,xplotlow,xplothigh,yplotlow,yplothigh,strokeStyle,mu,sigma,frameRate) { var i; var plotID=null; plotIncrement(); plotID=setInterval(plotIncrement,frameRate); function plotIncrement() { ctx.fillStyle=\"white\"; ctx.fillRect(0,0,canvas.width,canvas.height); ctx.clearRect(0,0,canvas.width,canvas.height); var i; var ylength=y.length; for (i=0;i<ylength-1;i++) { y[i]=y[i+1]; } y[ylength-1]=y[ylength-2]*Math.exp(mu+sigma*inverseNormal(Math.random())); ctx.beginPath(); projectLineChartOntoCanvas(ctx,y,xplotlow,xplothigh,yplotlow,yplothigh,strokeStyle); c2.fillStyle=\"maroon\"; c2.font=\"16px Arial\"; c2.fillText(\"ERM Resources\",110,21); } } function projectLineChartOntoCanvas(ctx,y,xplotlow,xplothigh,yplotlow,yplothigh,strokeStyle) { var i,ylow,yhigh,xplotscale,yplotscale; var xplot=new Array; var yplot=new Array; ylength=y.length; ylow=0; yhigh=0; for (i=0;i<ylength;i++) { if (y[i]<ylow) { ylow=y[i];} if (y[i] > yhigh) { yhigh=y[i];} } xplotscale=(xplothigh-xplotlow)/(ylength-1); yplotscale=(yplothigh-yplotlow)/(yhigh-ylow); for (i=0;i<ylength;i++) { xplot[i]=xplotlow+i*xplotscale; yplot[i]=yplotlow+y[i]*yplotscale; } ctx.beginPath(); ctx.strokeStyle=strokeStyle; ctx.moveTo(xplot,yplot); for (i=1;i<ylength;i++) { ctx.lineTo(xplot[i],yplot[i]); } ctx.stroke(); ctx.beginPath(); ctx.strokeStyle=\"green\"; ctx.lineWidth=1; ctx.strokeRect(xplotlow,Math.min(yplotlow,yplothigh)-4,xplothigh-xplotlow,Math.abs(yplothigh-yplotlow)+4); ctx.stroke(); } function inverseNormal(x){ // Adapted from Peter Acklam's \"An algorithm for computing the inverse normal cumulative distribution function\" var a1=-39.6968302866538; var a2=220.946098424521; var a3=-275.928510446969; var a4=138.357751867269; var a5=-30.6647980661472; var a6=2.50662827745924; var b1=-54.4760987982241; var b2=161.585836858041; var b3=-155.698979859887; var b4=66.8013118877197; var b5=-13.2806815528857; var c1=-0.00778489400243029; var c2=-0.322396458041136; var c3=-2.40075827716184; var c4=-2.54973253934373; var c5=4.37466414146497; var c6=2.93816398269878; var d1=0.00778469570904146; var d2=0.32246712907004; var d3=2.445134137143; var d4=3.75440866190742; var x_low=0.02425; var x_high=1-x_low; var q,r,ans; if (x <= 0) { throw \"InverseNormal: argument outside valid range\" } else if (x<x_low) { q=Math.sqrt(-2*Math.log(x)) return (((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q+c6)/ ((((d1*q+d2)*q+d3)*q+d4)*q+1) } else if (x <= x_high) { q=x-0.5 r=q*q return (((((a1*r+a2)*r+a3)*r+a4)*r+a5)*r+a6)*q/ (((((b1*r+b2)*r+b3)*r+b4)*r+b5)*r+1) } else if (x<1) { q=Math.sqrt(-2*Math.log(1-x)) return -(((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q+c6)/ ((((d1*q+d2)*q+d3)*q+d4)*q+1) } else { throw \"InverseNormal: argument outside valid range\" } } ERM For Pension Funds and their sponsors\n\nThis presentation (for a pension fund actuarial audience) covers ERM: what is it and why the current interest, enhancing pension scheme modelling and enhancing pension scheme governance.\n\n[as pdf]\n\nSlides\n 0 ERM for pension funds and their sponsors 1 Agenda 2 ERM: what is it and why the current interest 3 ERM versus other types of Risk Management 4 Why the current interest? 5 Some say ERM is for insurance/banks, not pensions 6 Kemp & Patel (2011) 7 Enhancing pension scheme modelling 8 Model Example (1) 9 Model Example (2) 10 Model Example (3) 11 Enhancing pension scheme governance 12 Example ERM framework for a large financial 13 Example ERM framework for a non-financial firm 14 Governance challenges for pension funds 15 Summary 16 Important Information" ]
[ null ]
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http://www.ccsenet.org/journal/index.php/mas/article/view/2775
[ "### Modeling the Bi-directional DC-DC Converter for HEV's\n\n•  Chongwu Wang\n•  Xiangzhong Meng\n•  Xiaowei Guo\n\n#### Abstract\n\nHybrid Electrical Vehicles-HEV!?s are the importnt ways to improve vehicle performance. The transformer isolated\nbi-directional DC-DC converters are the key components of the traction system in HEV!?s. This paper presents adetail\nmathematic model of isolated bi-directional DC-DC converter for HEV!?s. Approximate models are important\nmathematic methods especially for analysis and closed-loop control design converter circuits.  These differential\nequations, which govern the converter operation, change periodically among a set of linear differential equations\nbecause of the switch effect. Basing on the time-scale the state variables was separate as fast-scale and slow-scale\nvariables. The fast changing variable of the leakage inductor was eliminated by substitute the fast-scale variable into\nslow-scale variable equations, resulting in reduced order differential equations. From this set of  reduced order\ndifferential equations the completely averaged model of the isolated DC/DC converter was derived. The simulated\nresults reveal that the circuit and mathematical model are consistent very well. The averaged state variables can be\ntreated as a small component plus a DC component, so the averaged model can be separated a dynamic small signal part and a DC part. This linearized small signal model is suit for control design and analysis at a steady point that is decided by the DC component. As an example a PI controller was design basing on the linear model.", null, "This work is licensed under a Creative Commons Attribution 4.0 License.\n• ISSN(Print): 1913-1844\n• ISSN(Online): 1913-1852\n• Started: 2007\n• Frequency: monthly\n\n### Journal Metrics\n\n(The data was calculated based on Google Scholar Citations)\n\nh-index (January 2018): 30\n\ni10-index (January 2018): 163\n\nh5-index (January 2018): 19\n\nh5-median(January 2018): 25" ]
[ null, "data:image/png;base64,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", null ]
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https://alison.com/course/introduction-to-quadratic-equations-and-inequalities-for-general-studies
[ "Alison's New App is now available on iOS and Android!\n\n# Introduction to Quadratic Equations and Inequalities for General Studies\n\n## The free online course teaches you about quadratic equations and inequalities, as well as various exponential functions.\n\nPublisher: ADU\nIf you are a professional, a student or someone who has a keen interest in understanding quadratic equations and inequalities, this free online course will help you. Study the discriminant of roots and nature of roots, before moving on to look at quadratic-linear systems of equations. The solving of quadratic inequalities algebraically and by number line analysis, as well as properties of exponential functions will also be covered in the course.\n\n4-5 Hours\n\n23\n\nCPD\n\n## Description\n\nQuadratic equations and inequalities for General Studies is a free online course that has been specifically prepared to teach you about quadratic functions and the different methods of solving quadratic equations. When working with quadratic functions, you should take time to learn about how to solve a quadratic equation by factoring. This course also highlights how to graph a quadratic function. Do you know that quadratic equations can be solved by graphing and by completing the square? Prepare yourself to learn about the various steps involved in the derivation of the quadratic formula and how it's used to solve problems. It is also important that you learn about the discriminant of roots, as well as how to find the sum and product of the roots. You will learn about the relationship between the sum and product of the roots and coefficients of the equation. If you are asked about writing a quadratic equation given its roots, you should know that understanding the nature of roots and the coefficient is important. Are you aware that quadratic equations can also be solved by maximizing area and using the Pythagorean Theorem?\n\nIf you want to learn about other methods of solving quadratic equations such as frame problems and projectile motion, then you should complete this course. While going through this course, you will learn about the two methods of solving quadratic-linear systems which include; solving quadratic-linear systems graphically and algebraically. You will also learn about the concepts of quadratic inequalities, as well as how to solve quadratic inequalities. Did you know that quadratic inequalities can be solved using algebraic methods of set theory and number line analysis? To gain a better understanding, you should know the conditions involved in using these methods. You will also be able to identify the concepts of transcendental and trigonometric functions. This course can also help you understand the concepts, definition and properties of exponential functions. The graphing, applications and inverse of exponential functions will be covered extensively in this course. You will become familiar with Type I and Type II exponential functions. It is also imperative that you learn the two methods used to solve exponential equations; either algebraically or graphically.\n\nFurthermore, you can also learn about the definition and properties of logarithmic functions. Do you know that there are two types of logarithms? To gain more insight on this, you will need to understand the concepts of logarithms. You will learn about the five laws of logarithms and natural logarithms. You will also learn about how to plot the graph of a logarithmic function. You will gain insight on how to change between exponential, as well as logarithmic forms and vice versa. You will also be familiar with ways to manipulate logarithmic functions. The derivation of the change of base formula and its applications will be covered in this course. This course will help you understand how to solve logarithmic equations both algebraically and graphically. The application of the logarithmic scale in measuring the acidity of a solution and measuring the intensity of sound waves will also be covered in this course. This course will be of great interest to students, researchers, and anyone with an interest in understanding quadratic equations and inequalities. So, register for this course and start your next learning journey today.\n\nStart Course Now" ]
[ null ]
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https://thoughtbot.com/blog/come-correct-with-inject-and-collect
[ "# Come Correct with Inject and Collect\n\nHere’s a refactoring example for a simple Ruby math problem using the `inject` method.\n\nThe goal is to generate an n by n multiplication matrix. Pretty straightforward. Let’s make a first pass:\n\n``````def multiplication_table(n)\nresults = []\n\n(1..n).each do |row_index|\nrow = []\n(1..n).each { |column_index| row << row_index * column_index }\nresults << row\nend\n\nresults.each do |row|\nheader = '%-3s ' * row.length\nend\nend\n\nmultiplication_table(7)\n1 2 3 4 5 6 7\n2 4 6 8 10 12 14\n3 6 9 12 15 18 21\n4 8 12 16 20 24 28\n5 10 15 20 25 30 35\n6 12 18 24 30 36 42\n7 14 21 28 35 42 49\n``````\n\nIt does the job, but it’s nothing to look at. We can condense using in-line blocks and fancy curly braces, but first let’s try using `inject`.\n\nQuick background: Inject iterates over a set using a block with a collector, which is a variable whose value is passed back each round, making it good for iterative uses. The block’s return value is passed into the collector (make sure you return something or you’ll get a nil). Also, the return value of the whole inject block is the final collector value.\n\nSimple example from the docs:\n\n``````(5..10).inject {|sum, n| sum + n } #=> 45\n``````\n\nThe inject method takes a parameter, which initializes the collector value (default is to set to the first value). You can pass in an empty array and add values:\n\n``````def multiplication_table(n)\nresults = (1..n).map do |row_index|\n(1..n).inject([]) { |row, n| row + [row_index * n] }\nend\n\nresults.each { |row| puts '%-3s ' * row.length % row }\nend\n``````\n\nSo that’s inject with the iterative collect (Whoo-aaaa - got you all in check)\n\nNote: For a more in-depth discussion of `inject`, read Mike Burns’ recent post." ]
[ null ]
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https://chem.libretexts.org/Courses/Colorado_State_University_Pueblo/Elementary_Concepts_in_Physics_and_Chemistry/09%3A_Chapter_9_-_Waves/9.02%3A_Sound
[ "# 9.2: Sound\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\n• Define sound and hearing.\n• Describe sound as a longitudinal wave.\n\nSound can be used as a familiar illustration of waves. Because hearing is one of our most important senses, it is interesting to see how the physical properties of sound correspond to our perceptions of it. Hearing is the perception of sound, just as vision is the perception of visible light. But sound has important applications beyond hearing. Ultrasound, for example, is not heard but can be employed to form medical images and is also used in treatment.", null, "Figure $$\\PageIndex{1}$$: This glass has been shattered by a high-intensity sound wave of the same frequency as the resonant frequency of the glass. While the sound is not visible, the effects of the sound prove its existence. (credit: ||read||, Flickr)\n\nThe physical phenomenon of sound is defined to be a disturbance of matter that is transmitted from its source outward. Sound is a wave. On the atomic scale, it is a disturbance of atoms that is far more ordered than their thermal motions. In many instances, sound is a periodic wave, and the atoms undergo simple harmonic motion. In this text, we shall explore such periodic sound waves.\n\nA vibrating string produces a sound wave as illustrated in Figures $$\\PageIndex{2}$$-$$\\PageIndex{4}$$. As the string oscillates back and forth, it transfers energy to the air, mostly as thermal energy created by turbulence. But a small part of the string’s energy goes into compressing and expanding the surrounding air, creating slightly higher and lower local pressures. These compressions (high pressure regions) and rarefactions (low pressure regions) move out as longitudinal pressure waves having the same frequency as the string—they are the disturbance that is a sound wave. (Sound waves in air and most fluids are longitudinal, because fluids have almost no shear strength. In solids, sound waves can be both transverse and longitudinal.) Figure $$\\PageIndex{4}$$ shows a graph of gauge pressure versus distance from the vibrating string.", null, "Figure $$\\PageIndex{2}$$: A vibrating string moving to the right compresses the air in front of it and expands the air behind it.", null, "Figure $$\\PageIndex{3}$$: As the string moves to the left, it creates another compression and rarefaction as the ones on the right move away from the string.", null, "Figure $$\\PageIndex{4}$$: After many vibrations, there are a series of compressions and rarefactions moving out from the string as a sound wave. The graph shows gauge pressure versus distance from the source. Pressures vary only slightly from atmospheric for ordinary sounds.\n\nThe amplitude of a sound wave decreases with distance from its source, because the energy of the wave is spread over a larger and larger area. But it is also absorbed by objects, such as the eardrum in Figure $$\\PageIndex{5}$$, and converted to thermal energy by the viscosity of air. In addition, during each compression a little heat transfers to the air and during each rarefaction even less heat transfers from the air, so that the heat transfer reduces the organized disturbance into random thermal motions. (These processes can be viewed as a manifestation of the second law of thermodynamics presented in Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency.) Whether the heat transfer from compression to rarefaction is significant depends on how far apart they are—that is, it depends on wavelength. Wavelength, frequency, amplitude, and speed of propagation are important for sound, as they are for all waves.", null, "Figure $$\\PageIndex{5}$$: Sound wave compressions and rarefactions travel up the ear canal and force the eardrum to vibrate. There is a net force on the eardrum, since the sound wave pressures differ from the atmospheric pressure found behind the eardrum. A complicated mechanism converts the vibrations to nerve impulses, which are perceived by the person.\n\nPHET EXPLORATIONS: WAVE INTERFERENCE\n\nMake waves with a dripping faucet, audio speaker, or laser! Add a second source or a pair of slits to create an interference pattern.", null, "Figure $$\\PageIndex{6}$$: Wave Interference\n\n## Summary\n\n• Sound is a disturbance of matter that is transmitted from its source outward.\n• Sound is one type of wave.\n• Hearing is the perception of sound.\n\n## Glossary\n\nsound\na disturbance of matter that is transmitted from its source outward\nhearing\nthe perception of sound" ]
[ null, "https://phys.libretexts.org/@api/deki/files/6072/Figure_18_01_01a.jpg", null, "https://phys.libretexts.org/@api/deki/files/6073/Figure_18_01_02aa.jpg", null, "https://phys.libretexts.org/@api/deki/files/6074/Figure_18_01_02ba.jpg", null, "https://phys.libretexts.org/@api/deki/files/6075/Figure_18_01_02c.jpg", null, "https://phys.libretexts.org/@api/deki/files/6076/Figure_18_01_03a.jpg", null, "https://phys.libretexts.org/@api/deki/files/7641/PhET_Icon.png", null ]
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https://www.softmath.com/math-com-calculator/adding-matrices/monomials-calculator.html
[ "English | Español\n\n# Try our Free Online Math Solver!", null, "Online Math Solver\n\n Depdendent Variable\n\n Number of equations to solve: 23456789\n Equ. #1:\n Equ. #2:\n\n Equ. #3:\n\n Equ. #4:\n\n Equ. #5:\n\n Equ. #6:\n\n Equ. #7:\n\n Equ. #8:\n\n Equ. #9:\n\n Solve for:\n\n Dependent Variable\n\n Number of inequalities to solve: 23456789\n Ineq. #1:\n Ineq. #2:\n\n Ineq. #3:\n\n Ineq. #4:\n\n Ineq. #5:\n\n Ineq. #6:\n\n Ineq. #7:\n\n Ineq. #8:\n\n Ineq. #9:\n\n Solve for:\n\n Please use this form if you would like to have this math solver on your website, free of charge. 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https://beta.geogebra.org/m/nycuhsgc
[ "# Lesson 96- Effects of Changing Dimension\n\nHow does changing one dimension affect the area of a figure?\n\nIf you double just the base or the height of a rectangle, what do you think will happen to the area?\n\n1. Choose a base and a height\n2. Double one, either base or height\n3. How did the area change?\n\n## Rectangle\n\nGive an example of what happened:\n\n3. What was the area after you doubled either base or height?\n4. Describe the change in area.\n\nIf you double just the base or the height of a triangle, what do you think will happen to the area?\n\n1. Choose a base and a height\n2. Double one, either base or height\n3. How did the area change?\n• ## Triangle\n\nGive an example of what happened:\n\n3. What was the area after you doubled either base or height?\n4. Describe the change in area.\n\nIf you change the side length of a square or the radius of a circle, how will the area change?\n\n## Square\n\nGive an example of what happened:\n\n3. What was the area after you doubled either base or height?\n4. Describe the change in area.\n\n## Comparing two different dimensions verses two of the same.\n\nDoes changing just base or height affect area the same as changing a side in a square or radius in a circle?" ]
[ null ]
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https://www.jiskha.com/questions/1471606/a-parachutist-of-total-mass-75-kg-jumps-from-an-aeroplane-moving-at-a-speed-of-60m-s-at-a
[ "# pyhsics\n\na parachutist of total mass 75 kg jumps from an aeroplane moving at a speed of 60m/s at a height of 900 m above the ground. Her parachute reduce the speed of descent to 5m/s. calculate the decrease in her gravitational potential energy store as a result of her descent.\n\n1. 👍\n2. 👎\n3. 👁\n1. PE = mgh\n\nh = 900-60t\n\n1. 👍\n2. 👎\n\n## Similar Questions\n\n1. ### Physics\n\nA white billiard ball with mass mw = 1.43 kg is moving directly to the right with a speed of v = 3.4 m/s and collides elastically with a black billiard ball with the same mass mb = 1.43 kg that is initially at rest. The two\n\n2. ### physics\n\nan aeroplane is travelling horizontally at a speed of 80ms and drops a crate of emergency supplies.To avoid damage,the max vertical speed of the crate on landing is 20ms. a)calc d max height of the aeroplane when the crate is\n\n3. ### physics\n\nAn aeroplane is travelling horizontally at a speed of 80ms and drops a crate of emergency supplies.To avoid damage,the maximum vertical speed of the crate on landing is 20ms. a)the aeroplane is travelling at the maximum permitted\n\n4. ### maths\n\nan aeroplane takes 40 minutes less to fly 3600km with the wind blowing at 30 km/hr than the time it takes to fly against the same wind .Find the actual speed of the aeroplane when there is no wind.\n\n1. ### Physics\n\nA car of mass m moving at a speed v1 collides and couples with the back of a truck of mass 3m moving initially in the same direction as the car at a lower speed v2. (Use any variable or symbol stated above as necessary.) (b) What\n\n2. ### physics\n\nCalculate the magnitude of the linear momentum for the following cases. (a) a proton with mass 1.67 10-27 kg, moving with a speed of 4.00 106 m/s (b) a 16.5 g bullet moving with a speed of 270 m/s (c) a 70.5 kg sprinter running\n\n3. ### Math\n\nAn aeroplane flies from town A(20°N,60°E) to townB (20°N,20°E) if the journey takes 6 hours Calculate correct to 3 significant figures, the average speed of the aeroplane If it then flies due north from town B to town C 420km\n\n4. ### science\n\nA parachutist jumps from height 100m. He wants to reach at ground with zero velocity. For this purpose he switches on a parachute propeller after falling freely for certain height. Given that the parachute propeller is switched on\n\n1. ### physics\n\nA body of mass 5kg moving with a speed of 3m/s collides head on with a body of mass 3kg moving in the opposite direction at speed of 2m/s The first body stops after the collision The final velocity of the second body is Ans:3m/s\n\n2. ### Science\n\nAn aeroplane flies at 720km/h in an easterly direction.A passenger walks to the back of the plane at 3m/s. Calculate 1.The velocity of the aeroplane in m/s . 2.The resultant velocity of the passenger in m/s 3. The distance the\n\n3. ### Physics\n\nA parachutist relies on air resistance (mainly on her parachute) to decrease her downward velocity. She and her parachute have a mass of 55.5kg and air resistance exerts a total upward force of 620N on her and her parachute. What\n\n4. ### Mathematics\n\nAn aeroplane leave Bibiani at 10:10pm and reaches Accra 4415km away at 5:50am the next morning. Find correct to the nearest whole number the average speed of the aeroplane in km/h." ]
[ null ]
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https://www.physicsforums.com/search/4135838/
[ "# Search results\n\n1. ### Galois Theory question\n\nHomework Statement Let L/K be a Galois extension with Galois group isomorphic to A4. Let g(x) ϵ K [x] be an irreducible polynomial that is degree 3 that splits in L. Show that the Galois group of g(x) over K is cyclic. Homework Equations The Attempt at a Solution I know...\n2. ### Help with complex integral\n\nThanks....I think that helps!\n3. ### Help with complex integral\n\nNo, not sure how to...\n4. ### Help with complex integral\n\nso the integral would be zero in this case since the residues are -i and i?\n5. ### Help with complex integral\n\nHow can I use these facts to evaluate the integral?\n6. ### Complex analysis question\n\nIs it just as simple as applying the Cauchy Integral formula? ie. it follows directly from the CIF?\n7. ### Help with complex integral\n\nHomework Statement Evaluate the integral along the path given: integral(along a(t) of (b^2-1)/(b^2+1) db ) where a(t)=2*e^(it) , 0 <= t <= 2*pi Homework Equations none The Attempt at a Solution I am thinking of using the Residue Theorem. I think there are poles at -i...\n8. ### Ideal help\n\nHomework Statement Show that the ideal J=(a^2, abc, ac^2, c^3) cannot be generated by less than 4 monomials. Homework Equations None The Attempt at a Solution I was thinking of computer a Groebner basis for this (which is what I ended up doing) However, I'm not sure how I can...\n9. ### Complex analysis question\n\nInteresting ...I'll reread my notes. Thanks!\n10. ### Complex analysis question\n\nHomework Statement If an analytic function vanishes on the boundary of a closed disc in its domain , show it vanishes on the full disc Homework Equations CR equations? The Attempt at a Solution Not sure how to start this one.\n11. ### Hamming metric\n\nI have a new question. How would I show that the metric space defined by the Hamming metric is complete?\n12. ### What does the following subring of the complex numbers look like\n\nI was trying to figure out a way of writing things not in the subring, other than the way already written in the question\n13. ### What does the following subring of the complex numbers look like\n\nthe things you described like i/(x)*(x+i)\n14. ### What does the following subring of the complex numbers look like\n\nI'm not sure how to describe polynomials of this form\n15. ### What does the following subring of the complex numbers look like\n\nThe only difference I can see is things not in the subring don't contain i's, constant terms, or combinations of them\n16. ### Domain question\n\nah...very useful hint I solved for a before a in ak+lb=1...and that's what made a mess ...this hint 'solved' it - thanks!\n17. ### What does the following subring of the complex numbers look like\n\n...how does knowing this help?\n18. ### Domain question\n\ncare to give another hint? I plugged that into one of my equations and just got a big mess\n19. ### Domain question\n\ninteresting...I'll give it a shot -- I know the result but not the name...until now\n20. ### What does the following subring of the complex numbers look like\n\nah...anything with complex #'s... (1+i),x+i, etc..?\n21. ### Domain question\n\nI'm getting then (c^a)*(d^b)-(c^b)*(d^a)=0 I sbustituted in c^b=d^b to get (c^a)*(d^b)-(d^b)*(d^a)=0 but that gets me back to where I started...\n22. ### What does the following subring of the complex numbers look like\n\noh..I guess constants? 1, 5, etc\n23. ### Domain question\n\nactually...maybe I'm wrong, now I'm thinking to consider (c^a)/(d^a)=(c^b)/(d^b) (given since non-zero) ... I'm thinking if one messes around with this ...I'll get the answer. Does this seem on the right track?\n24. ### What does the following subring of the complex numbers look like\n\nI know (x) is (x) = xR = {r ϵ R | r = at for some t ϵ R} Not sure how to find some element not in (x)\n25. ### Domain question\n\nHomework Statement Let c and d be two non-zero elements of a domain D. If a and b are integers s.t gcd(a,b)=1, a>0, b > 0. If we know c^a=d^a and c^b=d^b, does it follow that c=d? Homework Equations The Attempt at a Solution I'm thinking divinding the two might be...\n26. ### What does the following subring of the complex numbers look like\n\nI mean, because x and x^2 are in (x)\n27. ### What does the following subring of the complex numbers look like\n\nBecause they are in (x)?\n28. ### What does the following subring of the complex numbers look like\n\nsome elements could be x^3+1/x, x^5+2/x^2, etc...right?\n29. ### Fractional field\n\nJust know the definition : Fraction field for integral domain = {a/b | a, b are elements of D, b not equal to zero}\n30. ### Fractional field\n\ndo you know the name of this theorem so I could look it up and see the proof?" ]
[ null ]
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https://rdrr.io/cran/osqp/f/README.md
[ "# R interface for OSQP", null, "", null, "Provides R-bindings to OSQP: the Operator Splitting QP Solver.\n\nThe OSQP (Operator Splitting Quadratic Program) solver is a numerical optimization package for solving problems in the form\n\n``````minimize 0.5 x' P x + q' x\n\nsubject to l <= A x <= u\n``````\n\nwhere `x in R^n` is the optimization variable. The objective function is defined by a positive semidefinite matrix `P in S^n_+` and vector `q in R^n`. The linear constraints are defined by matrix `A in R^{m x n}` and vectors `l in R^m U {-inf}^m`, `u in R^m U {+inf}^m`.\n\n## Documentation\n\nThe interface is documented here.\n\n## Try the osqp package in your browser\n\nAny scripts or data that you put into this service are public.\n\nosqp documentation built on Dec. 11, 2021, 9:25 a.m." ]
[ null, "https://travis-ci.org/oxfordcontrol/osqp-r.svg", null, "https://ci.appveyor.com/api/projects/status/bx1navxa474nhlpd/branch/master", null ]
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http://sim.okawa-denshi.jp/en/RLCbekeisan.htm
[ "", null, "# RLC Band-Stop Filter Design Tool\n\nThis page is a web application that design a RLC band-stop filter. Use this utility to simulate the Transfer Function for filters at a given frequency, damping ratio ζ, Q or values of R, L and C. The response of the filter is displayed on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response.\n\n## Calculate the transfer function for RLC band-stop filter with R, L and C values\n\n Vin(s)→", null, "→Vout(s)\nTransfer function", null, "R=Ω L=H C=F\np:pico, n:nano, u:micro, k:kilo, M:mega\n\n### Frequency analysis\n\nBode diagram\nPhase  Group delay\nNyquist diagram\nPole, zero\nPhase margin\nOscillation analysis\n\nUpper and lower frequency limits:\nf1= - f2=[Hz] (frequency limits are optional)\n\n### Transient analysis\n\nStep response\nImpulse response\nOvershoot\nFinal value of the step response\n\nSimulation time:\n0 - [sec] (optional)\n\n## Calculate the R, L and C values for the RLC band-stop filter at a given frequency and Q factor\n\n Vin(s)→", null, "→Vout(s)\nRejection frequency", null, "Transfer function", null, "### Q factor | Damping ratio ζ\n\nQuality factor Q =\nDamping ratio ζ =\n f0= Hz L = H C = F\nGive two values from three parameters of f0 ,L, C.\n\nSelect Capacitor Sequence:\nSelect Resistor Sequence:\nSelect Inductance Sequence:\n\n### Frequency analysis\n\nBode diagram\nPhase  Group delay\nNyquist diagram\nPole, zero\nPhase margin\nOscillation analysis\n\nUpper and lower frequency limits:\nf1= - f2=[Hz] (frequency limits are optional)\n\n### Transient analysis\n\nStep response\nImpulse response\nOvershoot\nFinal value of the step response\n\nSimulation time:\n0 - [sec] (optional)" ]
[ null, "http://sim.okawa-denshi.jp/images/ok-logo.jpg", null, "http://sim.okawa-denshi.jp/images/RLCBePass.png", null, "http://sim.okawa-denshi.jp/images/RLCBeD.gif", null, "http://sim.okawa-denshi.jp/images/RLCBePass.png", null, "http://sim.okawa-denshi.jp/images/RLCBpf0.gif", null, "http://sim.okawa-denshi.jp/images/RLCBeDf0zeta.gif", null ]
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https://gis.stackexchange.com/questions/88830/overlaying-spatial-polygon-with-grid-and-checking-in-which-grid-element-specific/89226
[ "# Overlaying spatial polygon with grid and checking in which grid element specific coordinates are located using R [closed]\n\nHow can one use R to\n\n1. split a shapefile in 200 meter squares/sub-polygons,\n2. plot this grid (incl. ID numbers for each square) over the original map below, and\n3. evaluate in which square specific geographic coordinates are located.\n\nI am a beginner in GIS and this is perhaps a basic question, but I haven't found a tutorial on how to do this in R.\n\nWhat I have done so far is loading a shapefile of NYC and plotting some exemplary geographic coordinates.\n\nI am looking for an example (R code) how to this with the data below.\n\n``````# Load packages\nlibrary(maptools)\n\n# OLD URL (no longer working)\n\ntmp <- tempfile(fileext=\".zip\")\nfiles <- unzip(tmp, exdir=getwd())\n\nplot(shp)\n\n# Define coordinates\npoints_of_interest <- data.frame(y=c(919500, 959500, 1019500, 1049500, 1029500, 989500),\nx =c(130600, 150600, 180600, 198000, 248000, 218000),\nid =c(\"A\"), stringsAsFactors=F)\n\n# Plot coordinates\npoints(points_of_interest\\$y, points_of_interest\\$x, pch=19, col=\"red\")\n``````", null, "Here is an example using a `SpatialGrid` object:\n\n``````### read shapefile\nlibrary(\"rgdal\")\n\nproj4string(shp) # units us-ft\n# \"+proj=lcc +lat_1=40.66666666666666 +lat_2=41.03333333333333\n# +lat_0=40.16666666666666 +lon_0=-74 +x_0=300000 +y_0=0 +datum=NAD83\n# +units=us-ft +no_defs +ellps=GRS80 +towgs84=0,0,0\"\n\n### define coordinates and convert to SpatialPointsDataFrame\npoi <- data.frame(x=c(919500, 959500, 1019500, 1049500, 1029500, 989500),\ny=c(130600, 150600, 180600, 198000, 248000, 218000),\nid=\"A\", stringsAsFactors=F)\ncoordinates(poi) <- ~ x + y\nproj4string(poi) <- proj4string(shp)\n\n### define SpatialGrid object\nbb <- bbox(shp)\ncs <- c(3.28084, 3.28084)*6000 # cell size 6km x 6km (for illustration)\n# 1 ft = 3.28084 m\ncc <- bb[, 1] + (cs/2) # cell offset\ncd <- ceiling(diff(t(bb))/cs) # number of cells per direction\ngrd <- GridTopology(cellcentre.offset=cc, cellsize=cs, cells.dim=cd)\ngrd\n# cellcentre.offset 923018 129964\n# cellsize 19685 19685\n# cells.dim 8 8\n\nsp_grd <- SpatialGridDataFrame(grd,\ndata=data.frame(id=1:prod(cd)),\nproj4string=CRS(proj4string(shp)))\nsummary(sp_grd)\n# Object of class SpatialGridDataFrame\n# Coordinates:\n# min max\n# x 913175 1070655\n# y 120122 277602\n# Is projected: TRUE\n# ...\n``````\n\nNow you can use the implemented `over`-method to obtain the cell IDs:\n\n``````over(poi, sp_grd)\n# id\n# 1 57\n# 2 51\n# 3 38\n# 4 39\n# 5 14\n# 6 28\n``````\n\nTo plot the shapefile and the grid with the cell IDs:\n\n``````library(\"lattice\")\nspplot(sp_grd, \"id\",\npanel = function(...) {\npanel.gridplot(..., border=\"black\")\nsp.polygons(shp)\nsp.points(poi, cex=1.5)\npanel.text(...)\n})\n``````", null, "or without colour/colour key:\n\n``````library(\"lattice\")\nspplot(sp_grd, \"id\", colorkey=FALSE,\npanel = function(...) {\npanel.gridplot(..., border=\"black\", col.regions=\"white\")\nsp.polygons(shp)\nsp.points(poi, cex=1.5)\npanel.text(..., col=\"red\")\n})\n``````", null, "• This looks like an answer to me, but in case you are looking for something different. Try the r tag in stackoverflow stackoverflow.com/search?q=R+tag – Brad Nesom Mar 14 '14 at 2:26\n• @rcs this code looks just like what I am trying to do but my shapefile is in a different projection: `proj4string (DK_reg1) \"+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0\"` does anyone have any suggestions on how to break this shapefiles of this projection to 1000 equal sized grid cells? and then randomly select 100 of them and highlight them? – I Del Toro Sep 13 '14 at 11:34\n\nThe New York dataset provided in the question is no longer available for download. I use the nc dataset from sf package to demonstrate a solution using sf package:\n\n``````library(sf)\nlibrary(ggplot2)\n\n# read nc polygon data and transform to UTM\nnc <- st_read(system.file('shape/nc.shp', package = 'sf')) %>%\nst_transform(32617)\n\n# random sample of 5 points\npts <- st_sample(nc, size = 5) %>% st_sf\n\n# create 50km grid - here you can substitute 200 for 50000\ngrid_50 <- st_make_grid(nc, cellsize = c(50000, 50000)) %>%\nst_sf(grid_id = 1:length(.))\n\n# create labels for each grid_id\ngrid_lab <- st_centroid(grid_50) %>% cbind(st_coordinates(.))\n\n# view the sampled points, polygons and grid\nggplot() +\ngeom_sf(data = nc, fill = 'white', lwd = 0.05) +\ngeom_sf(data = pts, color = 'red', size = 1.7) +\ngeom_sf(data = grid_50, fill = 'transparent', lwd = 0.3) +\ngeom_text(data = grid_lab, aes(x = X, y = Y, label = grid_id), size = 2) +\ncoord_sf(datum = NA) +\nlabs(x = \"\") +\nlabs(y = \"\")\n\n# which grid square is each point in?\npts %>% st_join(grid_50, join = st_intersects) %>% as.data.frame\n\n#> grid_id geometry\n#> 1 55 POINT (359040.7 3925435)\n#> 2 96 POINT (717024 4007464)\n#> 3 91 POINT (478906.6 4037308)\n#> 4 40 POINT (449671.6 3901418)\n#> 5 30 POINT (808971.4 3830231)\n``````", null, "• Thanks. I updated the link in my question to relfect the changes on their webpage. Now it should work again. – majom Mar 5 '18 at 15:18\n• I really need to start using the `sf` package. This is awesome! – philiporlando Mar 23 '18 at 20:41\n• Is there an easy way to only plot the grid cells that intersect with the state polygon? – philiporlando Mar 23 '18 at 22:09\n• st_intersection(grid_50, nc) should do it – sebdalgarno Mar 24 '18 at 23:18\n• Is there a way to replicate the same, but the points in the centre of each grid, so a grid is being drawn with the lat/long as the centre of the grid @sebdalgarno – Vijay Ramesh Aug 15 '19 at 17:58\n\nIf you have not looked at the R raster package, it has tools to convert to/from vector GIS objects so you should be able to a) create a raster (grid) with 200x200m cells and b) convert it to a set of polygons with a logical id of some kind. From there I would look at the sp package to help with intersecting the points and the polygon grid. This http://cran.r-project.org/web/packages/sp/vignettes/over.pdf page might be a good start. Wandering through the sp package docs you might be able to start with the SpatialGrid-class and just skip the raster part entirely.\n\nThe \"GIS universe\" is complex and have many standards that your data must be compliant. All \"GIS tools\" interoperates by GIS-standards. All \"serious GIS data\" today (2014) are stored in a database.\n\nThe best way to \"use R\" in a GIS context, with other FOSS tools, is embedded into SQL. The best tools are PostgreSQL 9.X (see PL/R) and PostGIS.\n\n• To import/export shape files: use `shp2pgsql` and `pgsql2shp`.\n• To \"split a shape file in 200 meter squares/sub-polygons\": see `ST_SnapToGrid()`, `ST_AsRaster()`, etc. We need understand better your needs to express into a \"recipe\".\n• you say that need \"geographic coordinates are located\" .. perhaps `ST_Centroid()` of the squares (?)... You can express \"more mathematically\" so I understand.\nA primitive way is use R without PL/R, in a your usual external compiler: only convert your polygons and export as shape or as WKT (see `ST_AsText`), then convert data with awk or another filter to the R format.\n• Thanks for your help. However, I would strongly prefer a solution which relies completely on R and existing packages. When I am able to split the shape file in 200m*200m subpolygons I can check with `point.in.polygon` which coordinates are in which polygons. My problem is to split the original shapefile in those sub-polygons. – majom Mar 9 '14 at 21:38" ]
[ null, "https://i.stack.imgur.com/NENNt.jpg", null, "https://i.stack.imgur.com/NSsCk.png", null, "https://i.stack.imgur.com/jRYFl.png", null, "https://i.stack.imgur.com/NsejX.png", null ]
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https://www.vertica.com/blog/extending-vertica-with-python-functions-adding-numpy-fft-as-a-udx/
[ "", null, "User-Defined Transform Function (UDTF) support for Python UDx were added back in Vertica 9.1, allowing you to add a much greater range of existing libraries and functions to Vertica. In this example, I’ll add Fast Fourier Transform (FFT) from the NumPy package.\n\nFFT is a way to transform time-domain data into frequency-domain data. My test dataset is a complex sine wave inserted into Vertica as X,Y float coordinates of amplitude versus time. Here’s a table extract and graph of the curve:\n\n```=> select * from t limit 5; time |     amplitude -------+------------------- 0 |                 0 0.001 | 0.516358837261612 0.002 | 0.933821744458138 0.003 |   1.1803794797964 0.004 |  1.22967657062023```", null, "My UDTF consists of a factory class “pyFFTFactory” that defines the input and output types of my function and returns instances of my function, as well as the class “pyFFT” that actually defines my function, converting input tuples to a format NumPy can work with, running the calculation, and returning the result set as tuples that Vertica can use. See the Python code at https://github.com/bryanherger/vertica-python-fft/blob/master/pyFFT.py\n\nNow I can call my Python code from SQL and store the result set in a new table:\n`CREATE TABLE t_fft AS SELECT pyFFT(a, b) OVER() FROM t;`\n\nThis produces output of amplitude vs. frequency as X,Y float coordinates shown in the following table extract and graph:\n\n```=> select * from t_fft limit 5; frequency     |    amplitude -------------------+------------------ 0 | 1.82150253105139 0 | 1.82150253105139 0.781860828772479 | 1.82391772795915 0.781860828772479 | 1.82391772795915 1.56372165754496 |  1.8311636695427```", null, "My original sine wave function, seen in the sample SQL, was y = sin(40 * 2 * 3.14 * x) + 0.5 * sin(90 * 2 * 3.14 * x), reflected here in the transform as (scaled) 1x peak at 40 and a 0.5x peak at 90.\n\nYou can find the full example Python and SQL and setup notes at https://github.com/bryanherger/vertica-python-fft\n\nThis should apply to many more functions as long as you define correct input and output types and column counts. You can even distribute processing across nodes using partitions in the OVER() clause – something I’ll cover in a future blog post." ]
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https://brainmass.com/math/geometry-and-topology/proofs-give-indirect-proof-theorem-189894
[ "Explore BrainMass\nShare\n\n# Geometry\n\nThis content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!\n\nGive an indirect proof of the theorem.\n1. If two lines are parallel to a third line then they are parallel to each other\n\n2. Solve the equation S=(n-2) 180 degrees for n when S is a given value. Find the number of sides of the polygon ( if possible) if the given value corresponds to the number of degrees in the sum of the interior angles of a polygon.\n\nhttps://brainmass.com/math/geometry-and-topology/proofs-give-indirect-proof-theorem-189894\n\n#### Solution Preview\n\n(1) Let the two lines be AB and CD, and let the third line be EF.\n\nGiven: AB || EF and CD || EF\n\nTo Prove: AB || CD\n\nProof: If possible, assume that AB and CD are not ...\n\n#### Solution Summary\n\nThe expert gives an indirect proof of the theorem. Neat, step-by-step solution is provided.\n\n\\$2.19" ]
[ null ]
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http://omvc.arqp.pw/line-equation-in-python.html
[ "# Line Equation In Python\n\nI'm running a python script in Nvidia xavier board using a pyqtgraph. Then, plug the slope into the slope formula, y = mx + b, where m is the slope. PDE solvers written in Python can then work with one API for creating matrices and solving linear systems. Finding eigenvalues, eigenvectors. Then we created to SymPy equation objects and solved two equations for two unknowns using SymPy's solve() function. I don't know if others coding in different language or python is facing the same problem. Linear Algebra with SciPy. 6 installed with Python 2. Expand source code class Constraint(object): r\"\"\" The class for constraints of a Mathematical Programming (MP) model. We gloss over their pros and cons, and show their relative computational complexity measure. Matrix methods represent multiple linear equations in a compact manner while using the existing matrix library functions. In my dataset I have two variables where I am interested at and I looking a function that gives me the value the free variables that I use in the equation. linear (min =-15, max = 15)) g. solve() function. This idea is not new and has been explored in many C++ libraries, e. Quick background on Rule of Sarrus and Cramer's Rule Rule of Sarrus computes the determinant of a 3x3 matrix. This handout will walk you through solving a simple. This equation might look duanting, but it is literally just straight-from-a-textbook material on these things. 24 or later; Once you have these you can begin with installation. The Jupyter Notebook is an open-source web application that allows you to create and share documents that contain live code, equations, visualizations and narrative text. MATLAB/Octave Python Description; doc help -i % browse with Info: {\\cdot}aewline (solve linear equations) vdot(a,b) Vector dot product: cross(a,b) Cross. For example, many applied problems in economics and finance require the solution of a linear system of equations, such as \\begin{aligned} y_1 = a x_1 + b x_2 \\\\ y_2 = c x_1 + d x_2 \\end{aligned} or, more generally,. Derivation of the Normal Equation for linear regression December 22, 2014 at 20:50 Tags Math , Machine Learning I was going through the Coursera \"Machine Learning\" course, and in the section on multivariate linear regression something caught my eye. Multiple Linear Regression using Python Machine Learning for predicting NPP (Net Primary Productivity, a Major Ecosystem Health Indicator) Structural Equation Modeling (SEM) is a statistical. This data also contains power line harmonics (i. We will solve many types of equations like polynomial, cubic, quadratic, linear, and etc. Using symbolic math, we can define expressions and equations exactly in terms of symbolic variables. In the book, we often had to do so because of layout reasons even though the statement may not have exceeded 80 characters, and in your projects you will want to do it so that your statements are easier to read and on the average all lines have a similar length. Python is one of high-level programming languages that is gaining momentum in scientific computing. x2 defines the point to perform the interpolation. Matplotlib is a plotting library for the Python programming language and its numerical mathematics extension numpy. Need advice on what which course to take? Email us (ourcourses \"at\" statistics. The equation shows that the element stiffness matrix for the linear spring element is a 2 ×2 matrix. Python Courses. What linear regression is, the assumptions, and how to implement/interpret a linear regression model. In this brief blog post I post a small code that can be used to solve a system of linear equations using SciPy package of Python and in particular the linalg module within the SciPy package. pyro: hydro by example A tutorial code and set of notes to introduce new students into computational hydrodynamics. Linear Regression is one of the easiest algorithms in machine learning. $$\\frac{dy(t)}{dt} = -k \\; y(t)$$ The Python code first imports the needed Numpy, Scipy, and Matplotlib packages. We gloss over their pros and cons, and show their relative computational complexity measure. $$3x + 4y - 12z = 35$$ NumPy's np. This is one of the most basic problems in linear algebra. solve() are below: Create NumPy array A as a 3 by 3 array of the coefficients; Create a NumPy array b as the right-hand side of the equations. While a linear model would take the form: A polynomial regression instead could look like: These types of equations can be extremely useful. find the line that best explains the observed data. A common use of least-squares minimization is curve fitting, where one has a parametrized model function meant to explain some phenomena and wants to adjust the numerical values for the model so that it most closely matches some data. Use Python to solve each problem. How to conduct linear regression, check regression assumptions, and interpret the results using Python. book on Linear Algebra starts off with, solving systems of linear equations. Linear Algebra with Python and NumPy (II)¶ This post is a continuation of the previous post on using Python and NumPy package for linear algebra. 6; Need help with constant movement; How to solve a linear two variable equation system? Need help trying to open a web page in python [split] solving linear equation; I need help stopping the loop and prompting user. (Updated 11/10/2005) The entire Dive into Python book is available online he re. As the name suggests this algorithm is applicable for Regression problems. Prompt the user, and obtain data from the keyboard (line 11). close() deleteLine(). In this tutorial, you. Use Python to solve various challenging slope and y-intercept exercises. The odeint () works in a two-state-space representation of : state one is function the way we want it and state two is a first derivative of. Welcome to the 9th part of our machine learning regression tutorial within our Machine Learning with Python tutorial series. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. Need advice on what which course to take? Email us (ourcourses \"at\" statistics. The documentation for numpy. Since our logistic regression will be only be able to find a linear decision boundary, we will have to fit the data in a better way. root with method=lm and explicit jacobian in input is the best solver for my specific problem (quadratic non linear systems with a few dozens of equations). Python NumPy サンプルコード: 線形連立方程式をヤコビ法で解く 今回は、線形方程式の数値計算法の ヤコビ法 を紹介します。 Python で線形連立方程式を反復法で解く. Quick background on Rule of Sarrus and Cramer's Rule Rule of Sarrus computes the determinant of a 3x3 matrix. I managed to convert the equations into matrix form below: For example the first line of the equation would be v0 = ps0,0 * rs0. 5) and (2, 2. The equation has the form Y= a + bX, where Y is the dependent variable (that's the variable that goes on the Y axis), X is the independent variable (i. ! to demonstrate how to solve a partial equation numerically. Linear algebra is essential to machine learning. The line with the minimum value of the sum of square is the best-fit regression line. The matrix rank will tell us that. If all entries of A below the main diagonal are zero, A is called an upper triangular matrix. In this example, we'll show you how to use Python to solve one of the more well-known mathematical equations: the quadratic equation (ax 2 + bx + c = 0). And there's a couple of ways that you could do this. In cell D1 Type your First Name Last Name and ID number. Then, you can import everything from both modules with the Python statements: from sympy import * from gravipy import * This way, you will have access to all of the functionality from these modules within the namespace of your own Python code. OLS(y, xelimination). Learn Least Square Regression Line Equation - Definition, Formula, Example Definition Least square regression is a method for finding a line that summarizes the relationship between the two variables, at least within the domain of the explanatory variable x. The code creates a line plot in a graphical desktop window. This vignette illustrates the ideas behind solving systems of linear equations of the form $$\\mathbf{A x = b}$$ where. Setting up an Environment for pyMOR Development. It is also a good general reference on the Python language. If a = 0 then the equation is linear, not quadratic. Linear Regression with Python. These curves are the graphical representation of the Fresnel equations. 5 5 0 100% of 2 4 raulbc777. Abstract: Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. Solving equations and inequalities. Algebraic equations consist of two mathematical quantities, such as polynomials, being equated to each other. 5) and (2, 2. Find number of solutions of a linear equation of n variables Given a linear equation of n variables, find number of non-negative integer solutions of it. The degree of a polynomial function is the highest degree among those in its terms. linalg or numpy. Linear algebra with Scipy module. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. The solution will involve eigenvectors and eigenvalues, so let's put our sleeves up and get to work! Solving coupled differential equations In contrast to the first system of linear equations above where Romeo and Juliet did not communicate with each other, the system now is coupled: Romeo's feelings influence Juliet's and vice versa. In this example, we have provided an optional argument kind that specifies the type of interpolation procedure. The equation has the form Y= a + bX, where Y is the dependent variable (that’s the variable that goes on the Y axis), X is the independent variable (i. Here is a gaussian elimination implementation in Python, written by me from scatch for 6. graphxy class. Although Python began as a classic computer language in which source files are written and then tested, a relatively new Python project named IPython supports user. First, select the range B6:D8. Regression equations are frequently used by scientists, engineers, and other professionals to predict a result given an input. We gloss over their pros and cons, and show their relative computational complexity measure. The solution will involve eigenvectors and eigenvalues, so let's put our sleeves up and get to work! Solving coupled differential equations In contrast to the first system of linear equations above where Romeo and Juliet did not communicate with each other, the system now is coupled: Romeo's feelings influence Juliet's and vice versa. In my previous post, I explained the concept of linear regression using R. I have a class Point, consisting of a point with x and y coordinates, and I have to write a method that computes and returns the equation of a straight line joining a Point object and another Point object that is passed as an argument (my_point. Python Problem: Anagram Tester. Linear algebra with Scipy module. Linear and nonlinear equations can also be solved with Excel and MATLAB. Linear Regression is essentially just a best fit line. Testing with the next pair of equations: 3 * x1 + 2 * x2 = 18 (-1) * x1 + 2 * x2 = 2. py: Calculate and display a Hertzsprung–Russell diagram for a catalog of nearby stars. The primary focus of this post is to illustrate how to implement the normal equation without getting bogged down with a complex data set. Non-Linear Least-Squares Minimization and Curve-Fitting for Python, Release 0. These functions cannot be used with complex numbers; use the functions of the same name from the cmath module if you require support for complex numbers. TO READ Time-stepping Newton’s equations of motion (17. In this post, we will see how to solve a Linear Program (LP) in Python. This page lists a number of packages related to numerics, number crunching, signal processing, financial modeling, linear programming, statistics, data structures, date-time processing, random number generation, and crypto. In our previous Machine Learning blog we have discussed about SVM (Support Vector Machine) in Machine Learning. How can I do this in Python, either solve equations, or calculating intersection points some other way? > > > Just solve the equations ahead of time by using generic ones. 4, the line would be a rough approximation for your data. Start by adding 10 to both sides. + Read More. This video is unavailable. You might recall from math calss that the equation 2x + 5 = 13 is an example of a first-degree equation, because the. Linear regression is a standard tool for analyzing the relationship between two or more variables. Clearly, it is nothing but an extension of Simple linear regression. the code below is stored in the repo as System_of_Eqns_WITH_Numpy-Scipy. NumPy has a lot of methods that are already made and optimized to solve a system of linear equations. I want to solve the following 3 non linear equations , and for 46 8 day time steps. Let's go back to basics and write out the regression equation that this model. 13, 2015 There will be several instances in this course when you are asked to numerically find the solu-tion of a differential equation (“diff-eq’s”). Problem: Show that it is possible to buy exactly 50, 51, 52, 53, 54, and 55 chicken nuggets, by finding solutions to the Diophantine equation. All these functions expect the same parameter list, and all function return values also follow a common standard. Give it a try!. Standard form also has some distinct uses, but more on that later. Conclusion A Monte Carlo simulation is a useful tool for predicting future results by calculating a formula multiple times with different random inputs. JupyterLab is the new interface for Jupyter notebooks and is ready for general use. You might also recognize the equation as the slope formula. solve() which solves a linear matrix equation, or system of linear scalar equation. startswith(str): output. In this tutorial, we’ll be calculating a best-fit line and using the equation of that line to model the linear relationship between the independent and dependent variables. In this example, we have provided an optional argument kind that specifies the type of interpolation procedure. Let's read those into our pandas data frame. close() deleteLine(). The equation above is a partial differential equation (PDE) called the wave equation and can be used to model different phenomena such as vibrating strings and propagating waves. It is developed and maintained by Matthias Heil and Andrew Hazel of the School of Mathematics at The University of Manchester, along with many other contributors. In this brief blog post I post a small code that can be used to solve a system of linear equations using SciPy package of Python and in particular the linalg module within the SciPy package. Solve the given system of m linear equations in n unknowns. 0 International License. To interpolate the y2 value: x1, x3, y1 and y3 need to be entered/copied from the table. The equations to solve are F = 0 for all components of F. CVXOPT is a free software package for convex optimization based on the Python programming language. However, the optimal regression line is the one for which the sum of the squared differences (vertical distances) or the sum of squared errors or SSE between the ‘y’ values predicted by the regression equation/line and the actual ‘y’ values is minimal. I have the following system of 3 nonlinear equations that I need to solve in python: 7 = -10zt + 4yzt - 5yt + 4tz^2 3 = 2yzt + 5yt 1 = - 10t + 2yt + 4zt How to solve a system of nonlinear equations in python | Physics Forums. Here the red line illustrates the left side of the equation while the yellow bold line represents the right side of the equation. Using the inverse matrix to solve equations Introduction One of the most important applications of matrices is to the solution of linear simultaneous equations. More Spirals top If you replace the term r(t)=at of the Archimedean spiral by other terms, you get a number of new spirals. The class contains:. Good for: Python implementation. raw download clone embed report print Python 1. If a set of systematic linear equations has constraints that are deterministic, we can represent the problem as matrices and apply matrix algebra. The “square” here refers to squaring the distance between a data point and the regression line. It includes its meaning along with assumptions related to the linear regression technique. Algebraic equations consist of two mathematical quantities, such as polynomials, being equated to each other. I would like to solve a system of linear equations, such as four equations with four unknowns. However, the optimal regression line is the one for which the sum of the squared differences (vertical distances) or the sum of squared errors or SSE between the ‘y’ values predicted by the regression equation/line and the actual ‘y’ values is minimal. Using Python to Solve Partial Differential Equations This article describes two Python modules for solving partial differential equations (PDEs): PyCC is designed as a Matlab-like environment for writing algorithms for solving PDEs, and SyFi creates matrices based on symbolic mathematics, code generation, and the finite element method. In this tutorial, you. py, which is not the most recent version. Decibels are logarithmic, not linear. In this case, the equation is -2. You can write Python code with either tabs or spaces indicating indentation. OK, I Understand. line, each data point is represented as a vertex (which location is given by the x and y columns) of a polyline mark in 2D space. Solving equations and inequalities. When doing non-linear curve fitting, it is helpful to give the program as much information as possible. py output You can clearly see in the histogram what colors are present, blue is there, yellow is there, and some white due to chessboard(it is part of that sample code) is there. The last line uses np. I've tried proving this to myself by showing the the resulting curve is a great circle. Simple linear regression is a great first machine learning algorithm to implement as it requires you to estimate properties from your training dataset, but is simple enough for beginners to understand. When doing non-linear curve fitting, it is helpful to give the program as much information as possible. I don't know if others coding in different language or python is facing the same problem. Solving equations and inequalities. The slope of the line is b, and a is the intercept (the value of y when x = 0). Just click on the link below. These functions are very quick, require, very little code, and provides us with a number of diagnostic statistics, including , t-statistics, and p-values. Interested in learning how to solve partial differential equations with numerical methods and how to turn them into python codes? This course provides you with a basic introduction how to apply methods like the finite-difference method, the pseudospectral method, the linear and spectral element method to the 1D (or 2D) scalar wave equation. Solving Linear Systems import numpy as np import matplotlib. I wrote this equation parser and solver, I feel like it is well documented and tested: import doctest def swap_sign(num): \"\"\" Swaps the sign of a number-representing string. Feel free to propose a chart or report a bug. y = cos(x) (x,y) coordinates using Python Turtle? On the Python trinket used below the turtle screen is 400. 1) 6 r + 7 = 13 + 7r 2) 13 − 4x = 1 − x. 5 in Jupyter (formerly iPython). Excel has many features which can perform different tasks. Linear regression is the simplest machine learning model you can learn, yet there is so much depth that you'll be returning to it for years to come. solve() which solves a linear matrix equation, or system of linear scalar equation. Solving Systems of Linear Equations. The slope of the line is b, and a is the intercept (the value of y when x = 0). Thus, the regression line minimizes the SSE. I would like to solve a system of linear equations, such as four equations with four unknowns. How to break a long equation? [duplicate] Ask Question For example a line should have the form `\\left( \\ldots \\right. All these functions expect the same parameter list, and all function return values also follow a common standard. First, select the range B6:D8. 3, the initial condition y 0 =5 and the following differential equation. I'm gonna be honest and say I'm so stuck on this assignment - I really need help! I've took on a third year computational physics course last year - turn your weaknesses into strengths someone told me. Python Programming Problem: Read in an input file – first line contains one word. graphxy class. linalg module; Solving linear systems: A x = b with A as a matrix and x, b as vectors. The vars argument has a default value of ['x', 'y'] but this only works if A is a 2×2 matrix. This page demonstrates three different ways to calculate a linear regression from python: Pure Python - Gary Strangman's linregress function; R from Python - R's lsfit function (Least Squares Fit) R from Python - R's lm function (Linear Model) Pure Python - Gary Strangman's linregress function. Update: a much better solution is to use CVXOPT. It has many important applications. Breaking long lines in Python. It is handled nicely in MATLAB, MATrix LABratory. However, using the Fusion 360 API you can create close approximations of equation curves. As the name suggests this algorithm is applicable for Regression problems. The linear splines have low precision, it should also be noted that they do not even provide first derivative continuity. Plot the curves of the exact solution and the approximated solution obtained with the function odeint on the same graph. If you find this content useful, please consider supporting the work by buying the book!. Python file method readline()reads one entire line from the file. In numerical linear algebra, the Gauss-Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a linear system of equations. In this article I show you how easy it is to create a simple linear regression equation from a small set of data. Python; GUI Tk / Alarm 1: Animation 3: Pmw Multi line label 2: Pmw OptionMenu 4: Pmw Password 1: Pmw. The data will be loaded using Python Pandas, a data analysis module. Another way to solve an equation like 2x + 5 = 13 is to create a general formula for this type of equation. Help me please, I'm looking for the solution how to automate spice simulation with python on MacOS, currently, I'm thinking to use LTspice. Linear algebra with Scipy module. I have the following system of 3 nonlinear equations that I need to solve in python: 7 = -10zt + 4yzt - 5yt + 4tz^2 3 = 2yzt + 5yt 1 = - 10t + 2yt + 4zt How to solve a system of nonlinear equations in python | Physics Forums. \" The standard form of a linear equation looks like + =, where , and are integers. In The GNU Linear Programming Kit, Part 1, the author uses glpk to solve this problem. The modulus r is the distance from z to the origin, while the phase phi is the counterclockwise angle, measured in radians, from the positive x-axis to the line segment that joins the origin to z. Combining Difference Equations: Difference equations can sometimes be easily combined by means of algebra. Scikit-learn is a powerful Python module for machine learning and it comes with default data sets. These functions are very quick, require, very little code, and provides us with a number of diagnostic statistics, including , t-statistics, and p-values. The equation of a straight line is y=mx+c, where m is the gradient and c is the y-intercept. It's not the fanciest machine learning technique, but it is a crucial technique to learn for many reasons:. Skip navigation Sign in. 4, the line would be a rough approximation for your data. Therefore, scientific computing with Python still goes mostly with version 2. Why linear algebra?. How to run Linear regression in Python scikit-Learn Posted on Mar 5, 2018 Dec 26, 2018 Author Manu Jeevan Y ou know that linear regression is a popular technique and you might as well seen the mathematical equation of linear regression. It can be useful to confirm there should be a solution, e. + Read More. In the book, we often had to do so because of layout reasons even though the statement may not have exceeded 80 characters, and in your projects you will want to do it so that your statements are easier to read and on the average all lines have a similar length. In order to do this, we assume that the input X, and the output Y have a linear relationship. Take examplesAdd an extra column (x 0 feature)Construct a matrix (X - the design matrix) which contains all the training data features in an [m x n+1] matrixDo something similar for y; Construct a column vector y vector [m x 1] matrixUsing the following equation (X transpose * X) inverse times X transpose y. We consider. Let's begin with a quick review of NumPy arrays. Basic Algebra and Calculus¶ Sage can perform various computations related to basic algebra and calculus: for example, finding solutions to equations, differentiation, integration, and Laplace transforms. express¶ Plotly Express is the easy-to-use, high-level interface to Plotly, which operates on \"tidy\" data. The class contains:. Just click on the link below. Trying to understand from linear algebra, what does the last equation mean? Why is the general solution of Schroedinger's equation a linear combination of the eigenfunctions?. x2 defines the point to perform the interpolation. In this article, I will show you solving equations in Excel. It is developed and maintained by Matthias Heil and Andrew Hazel of the School of Mathematics at The University of Manchester, along with many other contributors. Suppose you are the product manager of the factory and you have the test results for some microships of two different tests. It is pronounced \"pipes-ah\". Polynomial Models with Python 2 1 General Forms of Polynomial Functions Linear and quadratic equations are special cases of polynomial functions. 1 Line plots The basic syntax for creating line plots is plt. Learn how to solve linear equation using python numpy. This vignette illustrates the ideas behind solving systems of linear equations of the form $$\\mathbf{A x = b}$$ where. In this example, we have provided an optional argument kind that specifies the type of interpolation procedure. You may already be familiar with the \"y=mx+b\" form (called the slope-intercept form of the equation of a line). Since the given equation clearly shows how values of y are related to values of x, it seems reasonable to start by assigning several different numbers to x and then find the corresponding values of y to get points that lie on the graph. It seems like the Blender developers are working on such a f. However, we can extend it over to multiple lines using the line continuation character (\\). The set of solutions in R2 of a linear equation in two variables is a 1-dimensional line. Creating small projects and doing them will push you to become a better programmer and grow professionally. Solving Linear Systems import numpy as np import matplotlib. So let's learn Linear algebra with Scipy module in Python with examples. The Python programming language has no built-in support for linear algebra, but it is fairly straightforward to write code which will implement as much as you need. Linear equations with two variables may appear in the form Ax + By = C, and the resulting graph is always a straight line. If you're familiar with linear algebra, you may be aware that there's another way to find the optimal parameters for a linear model called the \"normal equation\" which basically solves the problem at once using a series of matrix calculations. These functions cannot be used with complex numbers; use the functions of the same name from the cmath module if you require support for complex numbers. This page lists a number of packages related to numerics, number crunching, signal processing, financial modeling, linear programming, statistics, data structures, date-time processing, random number generation, and crypto. Solving equations yields a solution for the independent variables, either symbolic or numeric. Linear Regression is one of the easiest algorithms in machine learning. It is a simple model but everyone needs to master it as it lays the foundation for other…. Engineering - Interpolator Formula. The steps to solve the system of linear equations with np. In this course, you'll hone your problem-solving skills through learning to find numerical solutions to systems of differential equations. This last equation doesn't make any sense to me. The SciPy library is one of the core packages for scientific computing that provides mathematical algorithms and convenience functions built on the NumPy extension of Python. Let's begin with a quick review of NumPy arrays. We will be using NumPy (a good tutorial here) and SciPy (a reference guide here). Given a set of data the algorithm will create a best fit line through those data points. 303 Linear Partial Differential Equations Matthew J. Inside the python interpreter, documentation on functions and variable types can be found using the function help(). This page will help you draw the graph of a line. Solving Systems of Linear Equations. Where we left off, we had just realized that we needed to replicate some non-trivial algorithms into Python code in an attempt to calculate a best-fit line for a given dataset. CG is a Python library which implements a simple version of the conjugate gradient (CG) method for solving a system of linear equations of the form A*x=b, suitable for situations in which the matrix A is positive definite (only real, positive eigenvalues) and symmetric. So if I wanted to plot Sin(x) my equation is simply y = np. Cramer's Rule For Solving a Linear System Of n Equations With n Variables. In order to use Linear Regression, we need to import it: from sklearn. 5 in Jupyter (formerly iPython). It draws straight line segments between these successive points on the circle. However, I'm open to any proposal. startswith(str): output. , diffusion-reaction, mass-heattransfer, and fluid flow. The code below uses np. Here's the full description: \"Write a class for linear equations. Intuition tells me that it is probably just\\theta = k\\phi + \\alpha$and$\\phi\\$ as a free parameter. opengl and I installed python3-pyqt5 (5. the blog is about Machine Learning with Python - Linear Regression #Python it is useful for students and Python Developers for more updates on python follow the link Python Online Training For more info on other technologies go with below links tableau online training hyderabad ServiceNow Online Training mulesoft Online Training. I have written a program that simulates protein cleavage but I need to modify it so that it produces fasta formatted output. Scikit Learn is awesome tool when it comes to machine learning in Python. Multiple linear regression attempts to model the relationship between two or more features and a response by fitting a linear equation to observed data. Linear and nonlinear equations can also be solved with Excel and MATLAB. Linear Regression (Python Implementation) This article discusses the basics of linear regression and its implementation in Python programming language. But, if you’re using Python 3, you must be consistent with your choice. This matrix can be formed using the vander function in Numpy. Problem: Show that it is possible to buy exactly 50, 51, 52, 53, 54, and 55 chicken nuggets, by finding solutions to the Diophantine equation. Now we are going to provide you a detailed description of SVM Kernel and Different Kernel Functions and its examples such as linear, nonlinear, polynomial, Gaussian kernel, Radial basis function (RBF), sigmoid etc. The situation goes worst when I try to do my Circuit Theory tutorial, in which I need to solve many simultaneous equations. \" The standard form of a linear equation looks like + =, where , and are integers. import numpy as np. We will spend some time looking at these solutions. Along the way, we'll discuss a variety of topics, including. SciPy is a Python library of mathematical routines. Here, The left hand side of the equation is the value of q that's going to minimize the cost function. A forward di erence approximation occurs if we set i min = 0 and i max = d+p 1. Just click on the link below. Introduction to Linear Programming with Python and PuLP. And the plotted points form a line on which every possible pair of x and y values for the equation can be found. (Note that operations which share a table row are performed from left to right. go for Python 3, because this is the version that will be developed in the future. Solving Systems of Linear Equations. So if I wanted to plot Sin(x) my equation is simply y = np. If the optional sizehint argument is present, instead of reading up to EOF, whole lines totalling approximately sizehint bytes (possibly after rounding up to an internal buffer size) are read. With Python fast emerging as the de-facto programming language of choice, it is critical for a data scientist to be aware of all the various methods he or she can use to quickly fit a linear model to a fairly large data set and assess the relative importance of each feature in the outcome of the process. Trying to understand from linear algebra, what does the last equation mean? Why is the general solution of Schroedinger's equation a linear combination of the eigenfunctions?. By the way, in the Console, you can show a Python prompt and enter the Python commands. Loop Analysis of Electric Circuits. Python Control Systems Library¶ The Python Control Systems Library (python-control) is a Python package that implements basic operations for analysis and design of feedback control systems. In this lecture, we’ll use the Python package statsmodels to estimate, interpret, and visualize linear regression models. Matrix methods represent multiple linear equations in a compact manner while using the existing matrix library functions. 5 in Jupyter (formerly iPython). However, using the Fusion 360 API you can create close approximations of equation curves. csv\" which has all of the data you need in order to plot the linear regression in Python. See http. We then plot these points and connect them with a smooth curve. But simple Euclidean distance doesn’t cut it since we have to deal with a sphere, or an oblate spheroid to be exact. The last line uses np. We will focus on: Linear equations: y = ax + b Quadratic equations: y = ax2 + bx + c Trigonometric functions: e. \" The final fit looks good:. Example4: Write the equation of the line with a slope of (-3/4 ) that passes through the point (0,6) in standard form. py, which is not the most recent version. a 21 x 1 + a 22 x 2 + … + a 2n x n = c 2 a n1 x 1 + a n2 x 2 + … + a nn x n = c n where x i are unknowns and a ij are coefficients of unknowns and c i are equations’ constants. The essential difference between linear and logistic regression is that Logistic regression is used when the dependent variable is binary in nature." ]
[ null ]
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https://trycolors.com/colors/CE4A2C
[ "", null, "WORKSPACE\nACCOUNT\nGALLERY\nVersion: 3.4.0\nMix & Match #CE4A2C\nSearch colors...\n#CE4A2C\nValencia\n\n## Mix\n\n#CE4A2C can be mixed using 30% of YELLOW, 30% of RED, 21% of MAGENTA, 4% of BLUE, 15% of BLACK.\n\n## Match\n\nWe found 50 paints that are close to #CE4A2C from brands like Ameritone Devoe, Devoe Fuller, ICI, Horn Textiles, RAL Design, Glidden.\n\nMix guide\n\n#CE4A2C\n#CE4A2C match: 100%\nYELLOW\nRED\nMAGENTA\nBLUE\nBLACK\nMixing process step by step\n\n1\n=\n1\n+\n1\n=\n1\n+\n2\n=\n1\n+\n3\n=\n1\n+\n4\n=\n1\n+\n5\n=\n1\n+\n6\n=\n1\n+\n7\n=\n1\n+\n8\n=\n1\n+\n9\n=\n1\n+\n10\n=\n1\n+\n11\n=\n1\n+\n12\n=\n1\n+\n13\n=\n1\n+\n14\n=\n1\n+\n15\n=\n1\n+\n16\n=\n1\n+\n17\n=\n1\n+\n18\n=\n1\n+\n19\n=\n1\n+\n20\n=\n1\n+\n21\n=\n1\n+\n22\n=\n1\n+\n23\n=\n1\n+\n24\n=\n1\n+\n25\n=\n1\n+\n26\n=\n1\n+\n27\n=\n1\n+\n28\n=\n1\n+\n29\n=\n1\n+\n30\n=\n1\n+\n31\n=\n1\n+\n32\n=\n1\n+\n33\n=\n1\n+\n34\n=\n1\n+\n35\n=\n1\n+\n36\n=\n1\n+\n37\n=\n1\n+\n38\n=\n1\n+\n39\n=\n1\n+\n40\n=\n1\n+\n41\n=\n1\n+\n42\n=\n1\n+\n43\n=\n1\n+\n44\n=\n1\n+\n45\n=\n1\n+\n46\n=\nConversion table\n\nHEX\n#CE4A2C\n\nHSV\n11°, 79, 81\n\nHSL\n11°, 65, 49\n\nCIE Lab\n49.74, 50.73, 44.7\n\nRGB decimal\n206, 74, 44\n\nRGB percent\n80.8%, 29%, 17.3%\n\nCMYK\n0, 64, 79, 19\n\nColor name\nValencia" ]
[ null, "https://trycolors.com/_next/image", null ]
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https://reactdatagrid.io/docs/footer
[ "DataGrid - Footer\n\n# Footer\n\nThe `<ReactDataGrid />` supports showing a grid footer, which can be used to display a summary - using the same reducer strategy being used for group summaries.\nSee the snippet below for a demo and make sure you read about summary reducers here.\nFor the footer area, you can have multiple `footerRows` which allow you to render whathever you decide.\nYou have to use `footerRow.render` in order to tell the `DataGrid` what to render for the cells inside the footer.\nThe `footerRow.render` can be an object with keys corresponding to columns, while values can be functions or `ReactNode` values. Using a function gives you the flexibility to decide what to render at run-time - for example, the first argument will have a `summary` property which will hold the value computed via the configured `summaryReducer`.\n\n# Using the summary\n\nBy using the summary reducer, you have the flexibility of computing all kind of summaries based on the available data.\nWe introduced the concept of `summaryReducer` - which are simple objects with the following props:\n• `initialValue` - the initial value to be used for the summary computation - generally a number/string/etc\n• `reducer(accumulator, currentItem)` - the reducer function - basically computes the summary from the accumulated value (at first call, this will equal the `initialValue`) and the current item at which we are doing the computation\n• `complete(accumulatedValue, array)` - can be used for doing one last computation at the end of the iteration - for example useful for computing the average of a value. The first argument is the accumulated value, while the second is the array on which the summary was computed against\nIn the snippet below, we display `min`, `max` and `average` values for the population column.\nThe example above shows the summaries for the population in one cell - see the demo below to display multiple footer rows, one for each summary type.\n\n# Customizing the footer\n\nThere are multiple ways to customize the footer rows - here are just a few:\n• Display additional information from the grid computed properties by using `footerRow.render` function\n• Use colspan to stretch footer cells across multiple columns\n• Customize `footer cell styling`\nSee the demo below for an example of each of the above.\nFooter rows are not limited to the height of grid rows, but they adjust to the natural height of their content.\nThe code above shows using `footerRow.colspan` - the value used for the `colspan` can be an object or a function. In case it's defined as an object, each key should correspond to a column, while the value determines the amount of the colspan. In case it's a function, the first argument has a `column` property, which you can use to decide how much colspan you want the footer cell to have.\nFor styling the footer row cells, you can use any of the following:\nAll of the above are called with the exact same arguments. The first argument is an object containing properties for , `columnIndex` and `summary`, while the second argument is the computed grid props.\nTop" ]
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https://in.mathworks.com/help/sltest/ref/triangle.html
[ "# triangle\n\nTriangle wave test signal\n\n## Syntax\n\n``triangle(x)``\n\n## Description\n\n````triangle(x)` creates a triangle wave with a period of 1 and range -1 to 1. In the interval 0 <= x < 0.5, `triangle(x)` increases. The difference between triangle waves and sawtooth waves is that a triangle wave has equal rise and fall times.", null, "To specify the number of triangle wave cycles within a test step, use this operator with the elapsed time (`et`) operator.```\n\n## Examples\n\n### Create a Triangle Wave\n\nCreate a triangle wave with a period of 10.\n\n`triangle(et/10)`\n\n## Tips\n\n`triangle` signal generation statements can be used in the Test Sequence and Test Assessment blocks and in Stateflow® charts." ]
[ null, "https://in.mathworks.com/help/sltest/ref/operator_triangle.png", null ]
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https://www.jpost.com/israel-news/labor-gesher-calls-to-increase-health-basket-spending-606304
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[ null ]
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https://itl.nist.gov/div898/handbook/eda/section3/compdeam.htm
[ "", null, "1. Exploratory Data Analysis\n1.3. EDA Techniques\n1.3.3. Graphical Techniques: Alphabetic\n\n## Complex Demodulation Amplitude Plot\n\nPurpose:\nDetect Changing Amplitude in Sinusoidal Models\nIn the frequency analysis of time series models, a common model is the sinusoidal model:\n$Y_{i} = C + \\alpha\\sin{(2\\pi\\omega t_{i} + \\phi)} + E_{i}$\nIn this equation, α is the amplitude, φ is the phase shift, and ω is the dominant frequency. In the above model, α and φ are constant, that is they do not vary with time, ti.\n\nThe complex demodulation amplitude plot (Granger, 1964) is used to determine if the assumption of constant amplitude is justifiable. If the slope of the complex demodulation amplitude plot is not zero, then the above model is typically replaced with the model:\n\n$Y_{i} = C + \\alpha_{i}\\sin{(2\\pi\\omega t_{i} + \\phi)} + E_{i}$\nwhere $$\\hat{\\alpha}_{i}$$ is some type of linear model fit with standard least squares. The most common case is a linear fit, that is the model becomes\n$Y_{i} = C + (B_0 + B_1*t_{i}) \\sin{(2\\pi\\omega t_{i} + \\phi)} + E_{i}$\nQuadratic models are sometimes used. Higher order models are relatively rare.\nSample Plot:", null, "This complex demodulation amplitude plot of the LEW.DAT data set shows that:\n\n• the amplitude is fixed at approximately 390;\n• there is a start-up effect; and\n• there is a change in amplitude at around x = 160 that should be investigated for an outlier.\nDefinition:\nThe complex demodulation amplitude plot is formed by:\n• Vertical axis: Amplitude\n• Horizontal axis: Time\nThe mathematical computations for determining the amplitude are beyond the scope of the Handbook. Consult Granger (Granger, 1964) for details.\nQuestions The complex demodulation amplitude plot answers the following questions:\n1. Does the amplitude change over time?\n2. Are there any outliers that need to be investigated?\n3. Is the amplitude different at the beginning of the series (i.e., is there a start-up effect)?\nImportance:\nAssumption Checking\nAs stated previously, in the frequency analysis of time series models, a common model is the sinusoidal model:\n$Y_{i} = C + \\alpha\\sin{(2\\pi\\omega t_{i} + \\phi)} + E_{i}$\nIn this equation, α is assumed to be constant, that is it does not vary with time. It is important to check whether or not this assumption is reasonable.\n\nThe complex demodulation amplitude plot can be used to verify this assumption. If the slope of this plot is essentially zero, then the assumption of constant amplitude is justified. If it is not, α should be replaced with some type of time-varying model. The most common cases are linear (B0 + B1*t) and quadratic (B0 + B1*t + B2*t2).\n\nRelated Techniques Spectral Plot\nComplex Demodulation Phase Plot\nNon-Linear Fitting\nCase Study The complex demodulation amplitude plot is demonstrated in the beam deflection data case study.\nSoftware Complex demodulation amplitude plots are available in some, but not most, general purpose statistical software programs.", null, "" ]
[ null, "https://itl.nist.gov/div898/handbook/gifs/nvgtbr.gif", null, "https://itl.nist.gov/div898/handbook/eda/gif/cdampplo.gif", null, "https://itl.nist.gov/div898/handbook/gifs/nvgbrbtm.gif", null ]
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http://herkimershideaway.org/writings/unbiae.htm
[ "Sanderson M. Smith\n\nUNBIASED ESTIMATORS\n\nConsider the number set P = {2,4,6}.\n\nIf P is a population, then\n\nMean = m = (2+4+6)/3 = 4.\n\nVariance = s2 = [(2-4)2 + (4-4)2 + (6-4)2]/3 = 8/3 = 2.666667.\n\nStandard deviation = sqrt(s2) = sqrt(8/3) = s = 1.632993.\n\nNOTE: The formula for s2 involves dividing by the population size n. In this case, n = 3.\n\nIf P is a sample, then\n\nSample mean = x(bar) = (2+4+6)/2 = 4.\n\nSample variance = s2 = [(2-4)2 + (4-4)2 + (6-4)2]/2 = 8/2 = 4.\n\nSample standard deviation = sqrt(s2) = sqrt(4) = s = 2.\n\nNOTE: The formula for s2 involves dividing by n-1. In the case, n=3. Hence n-1 = 2.\n\nNow, let's consider P to be a population.\n\nThe table below shows all possible samples of size 2 chosen from P, with replacement. There would be 3x3 = 9 samples.\n\n Sample x(bar) for sample s2 for sample s for sample s2 for sample s for sample 2,2 2 0 0 0 0 2,4 3 2 1.414214 1 1 2,6 4 8 2.828427 4 2 4,2 3 2 1.414214 1 1 4,4 4 0 0 0 0 4,6 5 2 1.414214 1 1 6,2 4 8 2.828427 4 2 6,4 5 2 1.414214 1 1 6,6 6 0 0 0 0 Column Means 4 2.666667 1.257079 1.333333 0.888889\n\nTo summarize, we have listed all samples of size 2 (with replacement) from a population P of size 3. We have calculated statistics for each sample of size 2. Here is an important definition:\n\nA statistic used to estimate a population parameter is unbiased if the mean of the sampling distribution of the statistic is equal to the true value of the parameter being estimated.\n\nNote that\n\nThe mean of the sample means (4) is equal to m, the mean of the population P. This illustrates that a sample mean x(bar) is an unbiased statistic. It is sometimes stated that x(bar) is an unbiased estimator for the population parameter m .\n\nThe mean of the sample values of s2 (2.666667) is equal to s2 , the variance of the population P. This illustrates that the sample variance s2 is an unbiased statistic. It is sometimes stated that s2 is an unbiased estimator for the population variance s2.\n\nNote carefully that the sample statistic s is not an unbiased statistic. That is, the mean of the s column in the table (1.257079) is not equal to the population parameter s = 1.632993.\n\nAlso, if you use the s2 formula for samples, the resulting statistics are not unbiased estimates for a population parameter. Note that the means for the last two columns in the table are not equal to population parameters.\n\nIn summary, the sample statistics x(bar) and s2 are unbiased estimators for the population mean m and population variance s2, respectively." ]
[ null ]
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http://forums.wolfram.com/mathgroup/archive/1998/Jun/msg00287.html
[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Re: How to Extract a common factor from a Sum\n\n• To: mathgroup at smc.vnet.net\n• Subject: [mg12963] Re: How to Extract a common factor from a Sum\n• From: colin at tri.org.au (Colin Rose)\n• Date: Sun, 28 Jun 1998 02:51:52 -0400\n• Organization: Theoretical Research Institute\n• References: <6mq9k4\\$2pi@smc.vnet.net>\n• Sender: owner-wri-mathgroup at wolfram.com\n\n```loewenthal at iap.unibe.ch (Frank Loewenthal) wrote:\n\n> I have a symbolical sum like\n\nexpr = Sum[ a f[k], {k,1,N}]\n\n> and I want to force Mathematica to write this as\n\nexpr = a Sum[f[k], {k,1,N}]\n\n> What ever I tried it did not work.\n> Does anyone knows a solution?\n\nMyRule := Sum[u_. w_,{k_,a_,b_}] :> u Sum[w,{k,a,b}] /;\nFreeQ[u,k]==True\n\nExample:\n\nIn[] expr = Sum[a b c f[k], {k, 1, n}];\n\nIn[] expr //. MyRule\n\nOut[] a b c Sum[f[k], {k, 1, n}]\n\nHope this helps\n\nCheerio\n\nColin\n\nColin Rose\ntr(I) - Theoretical Research Institute\n__________________________________________ colin at tri.org.au\nhttp://www.tri.org.au/\n\n```\n\n• Prev by Date: Re: Maximize\n• Next by Date: HTMLSave\n• Previous by thread: Re: How to Extract a common factor from a Sum\n• Next by thread: Re: How to Extract a common factor from a Sum" ]
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https://brilliant.org/practice/inscribed-and-circumscribed-figures-level-3-4/?subtopic=circles&amp;chapter=inscribed-and-circumscribed-figures
[ "", null, "Geometry\n\n# Inscribed and Circumscribed Figures: Level 4 Challenges", null, "In the right triangle above and altitude is drawn from the right angle to the hypotenuse. Circles are inscribed within each of the smaller triangles.\n\nWhat is the distance between the centers of these circles?", null, "A chord of a circle divides the circle into two parts such that the squares inscribed in the two parts have areas 16 and 144, respectively.\n\nThe radius of the circle is $\\text{\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_}.$", null, "The 5 circles have the same size. If the side of the large square is 1, what is the radius of each circle (to 3 decimal places)?", null, "Triangle $ABC$ is such that $AB = 13, BC = 14,$ and $CA = 15.$ A point $D$ on $BC$ is placed such that $AB + BD = AC + CD.$ Let $X$ be the intersection of $AD$ with the incircle of $ABC$ closest to $A.$ Find the length of $BX.$", null, "Find the value of $x$.\n\n×" ]
[ null, "https://ds055uzetaobb.cloudfront.net/brioche/chapter/Inscribed%20and%20Circumscribed%20Figures-1EHKIC.png", null, "https://ds055uzetaobb.cloudfront.net/brioche/solvable/b35fd0e040.e929b44699.iCD1bA.png", null, "https://ds055uzetaobb.cloudfront.net/brioche/uploads/LmAWVS24Jw-46559.svg", null, "https://ds055uzetaobb.cloudfront.net/brioche/uploads/c7pnzH4R3H-23535.svg", null, "https://ds055uzetaobb.cloudfront.net/brioche/uploads/QuT8jxaxKy-35768.svg", null, "https://ds055uzetaobb.cloudfront.net/brioche/uploads/NQ8E6f4wGZ-bm5iv1h.png", null ]
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https://answers.everydaycalculation.com/multiply-fractions/50-5-times-30-35
[ "Solutions by everydaycalculation.com\n\n## Multiply 50/5 with 30/35\n\n1st number: 10 0/5, 2nd number: 30/35\n\nThis multiplication involving fractions can also be rephrased as \"What is 50/5 of 30/35?\"\n\n50/5 × 30/35 is 60/7.\n\n#### Steps for multiplying fractions\n\n1. Simply multiply the numerators and denominators separately:\n2. 50/5 × 30/35 = 50 × 30/5 × 35 = 1500/175\n3. After reducing the fraction, the answer is 60/7\n4. In mixed form: 84/7\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:\nAndroid and iPhone/ iPad\n\n×" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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https://origin.geeksforgeeks.org/java-program-to-print-all-duplicate-characters-in-a-string/
[ "", null, "Open in App\nNot now\n\n# Java program to print all duplicate characters in a string\n\n• Difficulty Level : Medium\n• Last Updated : 07 Aug, 2022\n\nGiven a string, the task is to write Java program to print all the duplicate characters with their frequency Example:\n\nInput: str = “geeksforgeeks” Output: s : 2 e : 4 g : 2 k : 2 Input: str = “java” Output: a : 2\n\n## Recommended: Please try your approach on {IDE} first, before moving on to the solution.\n\nApproach: The idea is to do hashing using HashMap.\n\n• Create a hashMap of type {char, int}.\n• Traverse the string, check if the hashMap already contains the traversed character or not.\n• If it is present, then increment the count or else insert the character in the hashmap with frequency = 1.\n• Now traverse through the hashmap and look for the characters with frequency more than 1. Print these characters with their respective frequencies.\n\nBelow is the implementation of the above approach:\n\n## Java\n\n `// Java program for the above approach` `import` `java.util.*;` `class` `GFG {`   `    ``// Function to print all duplicate` `    ``// characters in string using HashMap` `    ``public` `static` `void` `    ``countDuplicateCharacters(String str)` `    ``{`   `        ``// Creating a HashMap containing char` `        ``// as a key and occurrences as a value` `        ``Map map` `            ``= ``new` `HashMap();`   `        ``// Converting given string into` `        ``// a char array` `        ``char``[] charArray = str.toCharArray();`   `        ``// Checking each character` `        ``// of charArray` `        ``for` `(``char` `c : charArray) {`   `            ``if` `(map.containsKey(c)) {`   `                ``// If character is present` `                ``// in map incrementing it's` `                ``// count by 1` `                ``map.put(c, map.get(c) + ``1``);` `            ``}` `            ``else` `{`   `                ``// If character is not present` `                ``// in map putting this` `                ``// character into map with` `                ``// 1 as it's value.` `                ``map.put(c, ``1``);` `            ``}` `        ``}`   `        ``// Traverse the HashMap, check` `        ``// if the count of the character` `        ``// is greater than 1 then print` `        ``// the character and its frequency` `        ``for` `(Map.Entry entry :` `             ``map.entrySet()) {`   `            ``if` `(entry.getValue() > ``1``) {` `                ``System.out.println(entry.getKey()` `                                   ``+ ``\" : \"` `                                   ``+ entry.getValue());` `            ``}` `        ``}` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `    ``main(String args[])` `    ``{` `        ``// Given String str` `        ``String str = ``\"geeksforgeeks\"``;`   `        ``// Function Call` `        ``countDuplicateCharacters(str);` `    ``}` `}`\n\nOutput:\n\n```s : 2\ne : 4\ng : 2\nk : 2```\n\nTime Complexity: O(NlogN)\n\nAuxiliary Space: O(N) since using Map\n\nMy Personal Notes arrow_drop_up\nRelated Articles" ]
[ null, "https://media.geeksforgeeks.org/gfg-gg-logo.svg", null ]
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https://www.thomas-cokelaer.info/tutorials/python/frozensets.html
[ "# 4.6. Frozensets¶\n\nSets are mutable, and may therefore not be used, for example, as keys in dictionaries.\n\nAnother problem is that sets themselves may only contain immutable (hashable) values, and thus may not contain other sets.\n\nBecause sets of sets often occur in practice, there is the frozenset type, which represents immutable (and, therefore, hashable) sets.\n\n## 4.6.1. Quick Example¶\n\n```>>> a = frozenset([1, 2, 3])\n>>> b = frozenset([2, 3, 4])\n>>> a.union(b)\nfrozenset([1, 2, 3, 4])\n```\n\n## 4.6.2. Set of Sets¶\n\nSets may only contain immutable (hashable) values, and thus may not contain other sets, in which case frozensets can be useful. Consider the following example:\n\n```>>> a = set([1, 2, 3])\n>>> b = set([2, 3, 4])\n```\n\n## 4.6.3. Using set as key in a dictionary¶\n\nIf you want to use a set as a key dictionary, you will need frozenset:\n\n```>>> fa = {frozenset([1,2]): 1}\n>>> fa[ frozenset([1,2]) ]\n1\n```\n\n## 4.6.4. Methods¶\n\nfrozensets have less methods than sets.\n\nThere are some operators similar to sets (intersection(), union(), symmetric_difference(), difference(), issubset(), isdisjoint(), issuperset()) and a copy() method." ]
[ null ]
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https://worldbuilding.stackexchange.com/questions/167877/how-do-i-calculate-the-hours-of-daylight-on-an-arbitrary-planet-for-a-given-day
[ "How do I calculate the hours of daylight on an arbitrary planet for a given day at a given latitude?\n\nI want to be able to graph the change in daylight hours across the year for a given latitude, to get an idea of what kind of cycle in available daylight people at that latitude would live through and adapt to. I'm assuming \"daylight hours\" is the time between the two periods the top of the star is tangent with the horizon in a solar day (sunrise/sunset), assuming the horizon is flat.\n\nThe problem is I have no background in mathematics or astrophysics, and all the answers I've found so far seem to assume I know a bunch of terms and formulas off-hand. I'm asking about an arbitrary planet because I can't even find a clear answer on what information about my planet I even need to consider, thus I've no idea what information I should be giving.\n\n...and it reads: Here's how I'd go at it:\n\n1) For a given orbit day (elapsed planetary days since perihelion, for simplicity) calculate the true anomaly.\n\n2) From the true anomaly, calculate the orbital angular velocity.\n\n3) From the orbital angular velocity and the rotation angular velocity, calculate the mean angular velocity of the sun across the sky.\n\n4) From the latitude, axial tilt and [true anomaly-solstice anomaly], calculate the angular length of sun's path in the sky at the required latitude.\n\n5) From 3) and 4), derive the day length.\n\nNow thru google and wikipedia I've learned enough (I think) to make it past step 2. However, \"rotation angular velocity\" is not a a specific term I can find any info on. I ASSUME it's the angular velocity for the spin of the planet, but I'm not really sure... and then we have \"calculate the mean angular velocity of the sun across the sky\", which sounds like something that translates to a fairly long equation that clearly isn't given here, nor anywhere else I've searched. Am I supposed to just average the 2 other angular velocities in this step? That doesn't seem right.\n\nSteps 4 and 5 utterly defeat me. If I knew what equations to plug those values into, I don't think I would need to ask this question at all. \"solstice anomaly\" is another term that seems to exist nowhere else but in this post. Another problem is that these angular values can be expressed in radians or degrees, and I have no idea how those wildly different values should factor into the equation, which I should use, how it would change the final answer...\n\nIn essence, I just wanna know what numbers I need to know about my planet and what formulas to plug them into to get a basic idea of what the damn sun is doing. I'm aware that doing this at multiple latitudes for every day will be hilariously tedious, but as long as I know the process, I can at least get started.\n\nI'll also have to calculate the movement of multiple celestial objects eventually, as the movement of particular planets/stars/constellations tends to have a notable effect on what traits/gods people ascribe to them, so I might as well start off relatively easy...\n\n• Welcome to Worldbuilding! This is a good first question (my opinion!). In future, be careful of supplement info like your closing paragraph. If you veer off to tangents, it can often lead to less on-topic answers. Always ask just one question per post... you can always post follow-up questions later in a new post. Here’s hoping your first question draws some useful answers for you!\n– SRM\nFeb 8 '20 at 13:47\n• The answer to this question is highly dependent on how accurate you want to be. Do you want a simple model that gives a rough approximation, or a complex model that gives a detailed approximation? Feb 8 '20 at 16:02\n\nA graphical method\n\nSometimes a graphical method may be easier to understand and remember.\n\nOne year is the time required for the planet to complete one full orbit around its primary. You decide how long a year is; it could be shorter than an Earth year, it could be longer; but if the star is similar to our Sun, and the planet is supposed to be habitable for life as we know it, it cannot be all that much shorter or all that much longer.\n\nA day can be reckoned in two ways.\n\n• The simplest way is the time required for the planet to complete a full rotation around its axis; this is called a sidereal day, because it is the time between two culminations of any given star. (\"Sidera\" means stars in Latin.)\n\nYou choose the length of the sidereal day. It can shorter than an Earth day, it can be longer. There is no relationship between the length of the year and the length of the sidereal day.\n\n• The more complicated, but more useful way is to reckon the time between two culminations of the planet's sun, that is, the time from one noon to the next; this is called a solar day, and it is a bit longer than a sidereal day, and can be calculated as the duration of one sidereal day plus a fraction of the sidereal day equal to the ratio between the sideral day and the year.\n\n• For Earth, a sidereal day is 23 hours 56 minutes, and an average solar day is 24 hours. (The current definition of the second was chosen very carefully, so that the mean solar day computed for 1 January 1900 is almost exactly 24 hours.)\n\n(The solar day is longer than the sidereal day because by the time the planet has completed one rotation around the axis it has also advanced a little bit on its orbit, and it must rotate a little bit more to bring the sun in the same position.)\n\n(Of course, if the planet rotates in the opposite direction of its revolution around the primary, the solar day will be shorter than the sidereal day, with the same amount. Most planets don't do this -- they rotate around the axis and revolve around the primary in the same direction.)\n\nAs the planet revolves around its primary there are four important points on the orbit:\n\n1. At one point, the axis of rotation appears to be tilted towards the primary at a maximum, equal to the obliquity. This is the northern solstice, which is the summer solstice for people in the northern hemisphere. At the northern solstice, at all places on the planet north of the northern polar circle, that is, the northern parallel of 90° less the axial tilt, the sun doesn't set; and at all places on the planet south of the southern polar circle, that is, the southern parallel of 90° less the axial tilt, the sun doesn't rise.\n\n2. Then comes a point where the axis of rotation is perpendicular to the radius of the orbit; this is an equinox. At equinoxes, days and nights are equal at all latitudes.\n\n3. Then comes a point where the axis of rotation appears to be tilted away from primary at a maximum, equal to the obliquity. This is the southern solstice, which is the winter solstice for people in the northern hemisphere. At the southern solstice, at all places on the planet north of the northern polar circle, that is, the northern parallel of 90° less the axial tilt, the sun doesn't rise; and at all places on the planet south of the southern polar circle, that is, the southern parallel of 90° less the axial tilt, the sun doesn't set.\n\n4. Finally, a second point where the axis of rotation is perpendicular to the radius of the orbit; this is an equinox. At equinoxes, days and nights are equal at all latitudes. Then the cycle repeats.\n\nAssumming that the planet has a circular or almost circular orbit around its primary, the four points (two solstices and two equinoxes) are almost equally spaced within the year.\n\nWhat you want to do is compute the duration of daylight for a given latitude at the northern solstice; then you can estimate the duration of daylight for that latitude at any time in the year.", null, "How to compute the duration of day and night at summer or winter solstice for a given latitude using a graphical method. Own work, available on Flickr under the Creative Commons Attribution 2.0 Generic license.\n\n1. Draw the planet tilted towards the Sun.\n\n2. Draw the equator; notice that on the equator the days and nights are of equal length at all times.\n\n3. Draw the polar circles as lines parallel to the equator starting from the topmost and bottommost points on the planet.\n\n4. Draw the terminator, that is, the line separating day from night. Note the position of the terminator with respect to the lines representing the polar circles.\n\n5. With a protractor, identify your parallel of interest. In the picture, the parallel of interest is at 30°.\n\n6. Now measure how much of that parallel is in the illuminated part of the planet, and how much is in the shadow.\n\n• ”but if the star is similar to our Sun, it cannot be all that much shorter or all that much longer.” Add “if the planet is to be habitable.”\n– SRM\nFeb 8 '20 at 16:03\n• @SRM: Oh, yes. Added. Feb 8 '20 at 16:04\n• @AlexP: I assume you'd calculate the day length for your Parallel of Interest at some other point of the year by linear interpolation, as you'd know the min and max day length? Feb 8 '20 at 16:42\n• @Kyyshak: Yes, true. Won't be exact, but it won't be wildly off -- good enough for government work, as they say. Feb 8 '20 at 17:19\n• It might be worth noting that the length of a year is a function of the mass of the star and the distance of the planet from it. For a more massive star than our sun, a planet will have a year equal to an Earth year at a distance further from the star than Earth is from the sun. For a less massive star, a closer planet will have a year equal to an Earth year.\n– Him\nFeb 8 '20 at 20:53\n\nTL;DR: you need to compute solar declination given your axial tilt, current true anomaly and the true anomaly of the winter solstice. You can feed that and your latitude into the sunrise equation.\n\nHere's a complete worked example though, mostly for my own edification but others might find it helpul or useful.\n\n(and for future readers, the date it was written was the date used to compute various numbers, and was 2020-02-08)\n\n1) For a given orbit day (elapsed planetary days since perihelion, for simplicity) calculate the true anomaly.\n\nEarth's perihelion in 2020 was on the 5th of January, so we're on day 34 of our current orbit. If we say the year length is 365 days and perihelion was precisely at midnight, that makes the current Mean Anomaly 33.5° (something like wolfram alpha will give you a more accurate value, but this'll do for an example).\n\nIf Earth had a perfectly circular orbit, the true anomaly would be exactly the same as the mean anomaly. Alas, real life is irrational and unhelpful, and so we do not have a nice tractable circular orbit.\n\nWe can compute the True Anomaly via this nice simple equation:\n\n$$\\nu = M + \\left(2e - \\frac{1}{4} e^3\\right) \\sin M + \\frac{5}{4} e^2 \\sin 2M + \\frac{13}{12} e^3 \\sin 3M + \\cdots$$\n\nwhere $$e$$ is the eccentricity of the orbit, which for Earth is ~0.0167, and $$M$$ is the mean anomaly we computed above. Using just these first three terms of the series expansion, we get a true anomaly $$\\nu$$ of ~35.63° (and if you wanted more terms, you can have a read of this). Again, a slightly more reputable source than \"some person on the internet\" will give you a better value, but we're still close enough to see that this simple(ish) example isn't totally wrong.\n\n2) From the true anomaly, calculate the orbital angular velocity.\n\nThe orbital velocity of a body changes as it procedes around its orbit... it will be fastest at perihelion, and slowest at aphelion. It is the rate of change of the true anomaly.\n\nFor a perfectly circular orbit, it would be simple: about .986° per day, or ~1.1416x10-5 degrees per second.\n\nAs before, ellipses ruin everything. You get the the specific relative angular momentum of an orbit where the orbiting body masses much less than the orbited body (as is the case with Earth and the Sun, for example) via this equation:\n\n$$h = \\sqrt{GM_sa(1-e^2)}$$\n\nwhere $$M_s$$ is the mass of the Sun and $$a$$ is the semi-major axis of the planet and $$e$$ is still its orbital eccentricity. Courtesy of this handy answer on physics.SE, you can see that angular velocity $$\\omega$$, the rate of change of true anomaly, can be obtained from $$h = \\omega r^2$$.\n\nYou can get $$r$$ from $$\\nu$$ like this:\n\n$$r = \\frac{a(1-e^2)}{1 + e \\cos(\\nu)}$$\n\nSo, today's value of $$r$$ is approximately 1.4755x1011m, giving us a current angular velocity of about 1.1724x10-5 degrees per second. As expected, this is a little faster than the circular equivalent, because we're closer to Earth's perihelion than the aphelion and so our orbital speed is a little higher than average.\n\n3) From the orbital angular velocity and the rotation angular velocity, calculate the mean angular velocity of the sun across the sky.\n\nIn a circular orbit, if the rotational angular velocity were equal to the orbital angular velocty the world would be tidally locked and the sun would never appear to move. That would make the question a little too easy to answer, though.\n\nThe rotational period of the earth (the sidereal day) is a little shorter than the average 24 hour day (the solar day), which is the length of time between the sun reaching its zenith point in successive cycles. There's a handy answer on this very site for computing the solar day length: How to calculate the solar day from sidereal day and sidereal orbital period?\n\nThis of course gives you an average solar day length, which isn't quite right as the day length changes slightly due to orbital and rotational inconveniences. I'm going to skip handling the equation of time for now, and cheat by assuming an average 24 day which gives us the mean angular velocity of ~0.0042°/s. I might revisit this later, but don't hold your breath.\n\n3) From the latitude, axial tilt and [true anomaly-solstice anomaly], calculate the angular length of sun's path in the sky at the required latitude.\n\nThe solstice anomaly mentioned here is presumably the true anomaly of the planet when it was last at a solstice, that being the point at which a pole is closest to (or further from) the sun. Again, we live on an inconvenient planet where the solstices do not coincide with the apsides (though for various reasons the gap between them changes over time in multi-millenia cycles which I shall ignore entirely. They've coincided in the past, will in the future, and could coincide for your fictional worlds, too). The last winter solstice was roughly at day 350 of last year, and you can compute its true anomaly using the method in step (1), giving $$\\nu_w$$ of approximately 343.98°.\n\nSolar declination declination is the angle between the sun's current zenith, and its zenith during the equinoxes, and you can compute it from your planet's axial tilt and the length of time since the last solstice:\n\n$$\\delta_\\odot = \\theta_a \\cdot \\cos(\\nu - \\nu_w)$$\n\nwhere $$\\theta_a$$ is the Earth's axial tilt, about -23.44°. Today's declination is therefore approximately -14.55°.\n\nMy latitude $$\\Phi$$ is about 52° north. You can use the sunrise equation to find the hour angle of sunrise and sunset:\n\n$$\\pm \\cos \\omega_0 = -\\tan \\Phi \\tan \\delta_\\odot$$\n\nWhere sunrise has the positive hour angle and sunset has the negative. The day length is then the sunrise angle minus the sunset angle... in this case about 141 degrees.\n\n(This does assume that the Sun is a point source of light instead of a disc, and atmospheric refraction of light from an over-the-horizon sun is also ignored. You can use a more generalised equation which has an additional term to take these things into account)\n\nNote that when $$\\Phi$$ becomes large enough you will find that sunrise and sunset times become no longer defined. This is a sign that the latitude you're looking at is in a period of 24 hour night or day, where it will remain until $$\\delta_\\odot$$ has moved a bit closer to zero. 75.4N is roughly the limit for a sunrise at the moment, which is why places like Svalbard don't manage a proper daytime right now.\n\nIf $$\\delta_\\odot$$ is zero, then the day has the same length regardless of latitude. This happens on the equinoxes. If axial tilt is zero then on every day of the year the day length will be the same regardless of latitude (though one day might have a slightly different length than the next, depending on your planet's orbital eccentricity).\n\n5) From 3) and 4), derive the day length.\n\nDivide the day length angle from (4) by the angular velocity in (3). In my case, this ands up being approximately 33890 seconds, or a bit over 9 hours and 24 minutes. This is within a few minutes of the actual day length according to timeanddate.com, which is a nice result.\n\nEasy as that!\n\nNote: Handling the difference between civil twilight, nautical twilight, astronomical twilight and night will be left as an exercise for the reader. The additional complexity is minimal ;-)\n\n• I get a solstice anomaly of 343.68, not 343.98. I'm not sufficiently confident in my math to make the edit for you, but any chance you made a typo? Feb 9 '20 at 20:20\n• @Kofthefens I've not been very thorough with the quality of my numbers. Even in the first paragraph in section (1) I admit to using a year length of 365 days ;-) I wouldn't worry about whether your numbers match mine; I'm reasonably happy that the formulae and methods are correct, though (and those bits at least have references). Feb 9 '20 at 20:51\n• Here's an implementation of these formulas in javascript for anyone who wants to use this answer but doesn't want to go through the math by hand: github.com/KMarshland/hours-of-daylight/blob/master/…. I'll slowly be going through and removing the simplifying assumptions. Feb 9 '20 at 20:55\n• @Kofthefens good stuff. I was intending to do something similar myself; its nice that I can take the lazy option! Feb 9 '20 at 20:56\n\n$$h=\\frac{2\\cdot\\left|\\cos^{-1}\\left(-\\tan l\\left(-a\\left(\\cos\\left(\\frac{360d}{y}\\right)\\right)\\right)\\right)\\right|}{15}*\\frac{1}{r÷24}$$\n\n• h = hours of daylight\n• l = latitude (in degrees)\n• a = axial tilt of the planet (in degrees)\n• d = number of days (local days, not Earth days) since the planet's spring solstice in its Northern Hemisphere\n• y = number of days (local days, not Earth days) in a year on the planet\n• r = length of local day in decimal Earth hours\n\nThis formula calculates the length of day in decimal Earth hours (not including astronomical refraction (which causes twilight), solar disc diameter, or elevation of the observer) for planets (not including moons) with day lengths shorter than their year lengths that are not tidally locked. However, the influence of the above three factors is very minimal.\n\nAstronomical refraction cannot be calculated unless you know the exact atmospheric composition of the observer. Solar disc diameter requires knowledge of the diameter of the planet's star and the distance of the planet from the star. The length of day on moons is a lot more difficult to calculate because they require calculation of the moon's orbit around its planet. Tidally locked worlds have the same amount of daylight throughout the year except for a few seasonal changes caused by axial tilt.\n\nNote: This answer will give you the number of hours as a decimal. For example, 2 hours and 12 minutes will come out as 2.2. To convert this number into hours, minutes, and seconds; go here: https://unitconverter.net/decimal-to-time-calculator\n\nThis answer is adapted from the Sunrise equation1 and the Declination equation2.\n\n• This also does not calculate for true anomaly, but the margin of error is very small. Mar 26 '20 at 23:47\n• Very nice equation! However, am I missing something or is l never used? Also, my own research (checked tidally locked planets/moons in our solar system) suggests axial tilt is very low in tidally locked planets. At least in our glorious sample of 1 solar system... :)\n– Erk\nAug 6 '20 at 21:10\n• @Erk, there was an error in the formula. It's now fixed. Aug 17 '20 at 23:03\n• @Galactic, how would this formula be written out for a Google or Excel spreadsheet? I don't quite understand the mathematical symbols but I think this is exactly what I'm hunting for... just need to figure out how to translate it... Thanks! Sep 24 '20 at 0:52\n\nHere is a mostly \"simple\" formula. It is from an article in Ecological Modeling, volume 80 (1995) pp. 87-95, called \"A Model Comparison for Daylength as a Function of Latitude and Day of the Year.\"\n\nD = daylength\n\nL = latitude\n\nJ = day of the year\n\nP = asin[.39795 * cos(.2163108 + 2 * atan{.9671396 * tan[.00860(J - 186)]})]\n\nXX = sin(0.8333 * pi / 180) + sin(L * pi / 180) * sin(P)\n\nYY = cos(L * pi / 180) * cos(P)\n\nD = 24 - (24 / pi) * acos(XX / YY)\n\nThe latitude should be entered in degrees.\n\nThe model error is less than one minute within 40 degrees of the equator, and less than seven minutes within 60 degrees and usually within two minutes for these latitudes. It is not 100% accurate because the Earth bulges in the center.\n\nEDIT: This reference website will walk you through more math than you might like on this challenge. It explains why the formulas are more complex than given. It also gives examples that extend it to other orbiting bodies. http://www.analemma.com/Pages/framesPage.html\n\n• Whilst the answer is valid for Earth, it isn't obviously that useful for an arbitrary planet (as requested by the OP) because it has magic numbers instead of sensible parameters like orbital semimajor axis, eccentricity, period, planetary rotational period and axial tilt. Feb 8 '20 at 14:53\n• It’s a great answer if we could get info for where the magic constants came from. Does the citation source include that info?\n– SRM\nFeb 8 '20 at 16:02\n• Those constants are calculations that address the Earth bias challenges. For example, if the Earth were a perfect sphere, and the sun was shining on it perfectly centered on the equator, the formula is solving for the arc from where the sun rises to where it sets. When you move north or south, the sun doesn't shine exactly perpendicular, so there is an angle with that latitude that the sun is off from being directly perpendicular. This and other oddities are in the magic numbers. I only have the reference and the final formula, so I don't know if it has the magic number detail.\n– user72081\nFeb 8 '20 at 16:09\n• @castlewrks Makes sense. Thanks for replying... this answer may serve people working on Earth easier than the general solution.\n– SRM\nFeb 8 '20 at 17:20\n• See the EDIT link... it gives more detail including applying the math to other planetary bodies. Too complex to post here. It is a great site explaining the complex math involved.\n– user72081\nFeb 8 '20 at 17:24\n\nAlex P's answer says in part:\n\nOne year is the time required for the planet to complete one full orbit around its primary. You decide how long a year is; it could be shorter than an Earth year, it could be longer; but if the star is similar to our Sun, and the planet is supposed to be habitable for life as we know it, it cannot be all that much shorter or all that much longer.\n\nThat is correct in stating that the length of a habitable planet's year should not be too much longer than an Earth year.\n\nStars that are much brighter than the Sun would have inner and outer edges of their habitable zones much farther out than the inner and outer edges of the Sun's habitable zone. So planets in the habitable zones of extremely bright stars could have years hundreds or thousands of Earth years long.\n\nBut stars much more massive and much brighter than the Sun would use up their nuclear fuel so fast that it would not last long enough for planet in their habitable zones to become habitable for humans, which would take billions of years of planetary evolution. So I think that planets with multi celled lifeforms, or habitable for humans, should only have years a few times as long as Earth years, maybe five or ten Earth years long at most.\n\nBut on the other hand, it may be possible for habitable planets to orbit stars much dimmer than the Sun very closely and to have years much shorter than Earth years.\n\nIn Wikipedia's List of Potentially Habitable Exoplanets, exoplanets which orbit within the habitable zones of their planets, the one with the shortest day is TRAPPIST--1 d, which has a year 4.05 Earth days long.\n\nThe same is true in The Habitable Exoplanets Catalog, which also lists Teegarden's Star b as having a year 4.9 Earth days long.\n\nSo there are two known exoplanets in the habitable zones of their stars which have years less than 0.013 Earth years long. And there are three others listed with years less than 0.02 Earth years long.\n\nOne problem with the habitability of planets with such short years would be that tidal effects on planets that close to their stars would cause the planets to quickly (in astronomical and geological time scales) become tidally locked to their planets. So one side of the planet would always face the Sun and become very hot and one side of the planet would be in eternal darkness and get very cold. Such a planet's water and atmosphere might quickly freeze on the dark side and never melt.\n\nHowever, some calculations indicate that a planet with enough water and atmosphere might circulate heat from the light side to the dark side and equalize temperatures enough to avoid freezing out the water and air.\n\nSo if a tidally locked planet in the habitable zone of a dim star can still be habitable, the minimum year length for a habitable planet could be as little as 4 Earth days.\n\nIf a tidally locked planet can never be habitable, the minimum year length of a habitable planet would be many times longer, probable several Earth months long.\n\nAnd another way to have habitable worlds very close to a dim star would be to have them be giant moons of a giant planet orbiting close to the dim star. The moons of a giant planet would become tidally locked to the planet, and not to the star, and so they would have days equal to their periods of rotation around the giant planet.\n\nIf the orbital period, and thus the day, of a hypothetical habitable exomoon was in the range of the Galilean moons of Jupiter or of Titan, it would between about 1.5 and 17 Earth days long, and so the moon might avoid too drastic heating and cooling during its daily cycle.\n\nThe orbital period of the planet around its star would have to be at least nine times the length of the orbital period of the moon around its planet, so that the year of a habitable exomoon of a giant planet in the habitable On zone of its star should be at least 13.5 to 153 Earth days long.\n\nSo depending on the correctness of various speculations and calculations, the minimum possible year length of a habitable exoplanet might be:\n\n1) Several Earth months.\n\n2) 13.5 Earth days.\n\n3) 4.00 Earth days.\n\nI have been trying to implement Starfish Prime;s algorithm, above, in C++. I'm convinced he knows his subject, but I'm a programmer, not a physicist. So here are some questions (and complaints):\n\nYou go out of your way to compute w, r and h. They never get used. I feel like I'm missing something here.\n\nYou talk about days since winter solstice and days since LAST solstice. I think you always meant last winter solstice (implying shortest day), but then I don't think the negation before tan*tan is correct.\n\nUnits! No one is going to implement this on paper, and software likes radians. Knowing which units were intended for the sun's mass, gravity etc (if they matter) would save some hair-pulling.\n\nClarity appreciated! (and to make this an \"answer\", I'll post code once I'm sure it's right.)" ]
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http://www.tutorialspoint.com/cprogramming/c_quick_guide.htm
[ "C - Quick Guide\n\nC is a general-purpose, high-level language that was originally developed by Dennis M. Ritchie to develop the UNIX operating system at Bell Labs. C was originally first implemented on the DEC PDP-11 computer in 1972.\n\nIn 1978, Brian Kernighan and Dennis Ritchie produced the first publicly available description of C, now known as the K&R standard.\n\nThe UNIX operating system, the C compiler, and essentially all UNIX application programs have been written in C. C has now become a widely used professional language for various reasons −\n\n• Easy to learn\n• Structured language\n• It produces efficient programs\n• It can handle low-level activities\n• It can be compiled on a variety of computer platforms\n\n• C was invented to write an operating system called UNIX.\n\n• C is a successor of B language which was introduced around the early 1970s.\n\n• The language was formalized in 1988 by the American National Standard Institute (ANSI).\n\n• The UNIX OS was totally written in C.\n\n• Today C is the most widely used and popular System Programming Language.\n\n• Most of the state-of-the-art software have been implemented using C.\n\n• Today's most popular Linux OS and RDBMS MySQL have been written in C.\n\nWhy use C?\n\nC was initially used for system development work, particularly the programs that make-up the operating system. C was adopted as a system development language because it produces code that runs nearly as fast as the code written in assembly language. Some examples of the use of C might be −\n\n• Operating Systems\n• Language Compilers\n• Assemblers\n• Text Editors\n• Print Spoolers\n• Network Drivers\n• Modern Programs\n• Databases\n• Language Interpreters\n• Utilities\n\nC Programs\n\nA C program can vary from 3 lines to millions of lines and it should be written into one or more text files with extension \".c\"; for example, hello.c. You can use \"vi\", \"vim\" or any other text editor to write your C program into a file.\n\nThis tutorial assumes that you know how to edit a text file and how to write source code inside a program file.\n\nC - Environment Setup\n\nLocal Environment Setup\n\nIf you want to set up your environment for C programming language, you need the following two software tools available on your computer, (a) Text Editor and (b) The C Compiler.\n\nText Editor\n\nThis will be used to type your program. Examples of few a editors include Windows Notepad, OS Edit command, Brief, Epsilon, EMACS, and vim or vi.\n\nThe name and version of text editors can vary on different operating systems. For example, Notepad will be used on Windows, and vim or vi can be used on windows as well as on Linux or UNIX.\n\nThe files you create with your editor are called the source files and they contain the program source codes. The source files for C programs are typically named with the extension \".c\".\n\nBefore starting your programming, make sure you have one text editor in place and you have enough experience to write a computer program, save it in a file, compile it and finally execute it.\n\nThe C Compiler\n\nThe source code written in source file is the human readable source for your program. It needs to be \"compiled\", into machine language so that your CPU can actually execute the program as per the instructions given.\n\nThe compiler compiles the source codes into final executable programs. The most frequently used and free available compiler is the GNU C/C++ compiler, otherwise you can have compilers either from HP or Solaris if you have the respective operating systems.\n\nThe following section explains how to install GNU C/C++ compiler on various OS. We keep mentioning C/C++ together because GNU gcc compiler works for both C and C++ programming languages.\n\nInstallation on UNIX/Linux\n\nIf you are using Linux or UNIX, then check whether GCC is installed on your system by entering the following command from the command line −\n\n\\$ gcc -v\n\nIf you have GNU compiler installed on your machine, then it should print a message as follows −\n\nUsing built-in specs.\nTarget: i386-redhat-linux\nConfigured with: ../configure --prefix=/usr .......\ngcc version 4.1.2 20080704 (Red Hat 4.1.2-46)\n\nIf GCC is not installed, then you will have to install it yourself using the detailed instructions available at https://gcc.gnu.org/install/\n\nThis tutorial has been written based on Linux and all the given examples have been compiled on the Cent OS flavor of the Linux system.\n\nInstallation on Mac OS\n\nIf you use Mac OS X, the easiest way to obtain GCC is to download the Xcode development environment from Apple's web site and follow the simple installation instructions. Once you have Xcode setup, you will be able to use GNU compiler for C/C++.\n\nXcode is currently available at developer.apple.com/technologies/tools/.\n\nInstallation on Windows\n\nWhile installing Min GW, at a minimum, you must install gcc-core, gcc-g++, binutils, and the MinGW runtime, but you may wish to install more.\n\nAdd the bin subdirectory of your MinGW installation to your PATH environment variable, so that you can specify these tools on the command line by their simple names.\n\nAfter the installation is complete, you will be able to run gcc, g++, ar, ranlib, dlltool, and several other GNU tools from the Windows command line.\n\nC - Program Structure\n\nBefore we study the basic building blocks of the C programming language, let us look at a bare minimum C program structure so that we can take it as a reference in the upcoming chapters.\n\nHello World Example\n\nA C program basically consists of the following parts −\n\n• Preprocessor Commands\n• Functions\n• Variables\n• Statements & Expressions\n\nLet us look at a simple code that would print the words \"Hello World\" −\n\n#include <stdio.h>\n\nint main() {\n/* my first program in C */\nprintf(\"Hello, World! \\n\");\n\nreturn 0;\n}\n\nLet us take a look at the various parts of the above program −\n\n• The first line of the program #include <stdio.h> is a preprocessor command, which tells a C compiler to include stdio.h file before going to actual compilation.\n\n• The next line int main() is the main function where the program execution begins.\n\n• The next line /*...*/ will be ignored by the compiler and it has been put to add additional comments in the program. So such lines are called comments in the program.\n\n• The next line printf(...) is another function available in C which causes the message \"Hello, World!\" to be displayed on the screen.\n\n• The next line return 0; terminates the main() function and returns the value 0.\n\nCompile and Execute C Program\n\nLet us see how to save the source code in a file, and how to compile and run it. Following are the simple steps −\n\n• Open a text editor and add the above-mentioned code.\n\n• Save the file as hello.c\n\n• Open a command prompt and go to the directory where you have saved the file.\n\n• Type gcc hello.c and press enter to compile your code.\n\n• If there are no errors in your code, the command prompt will take you to the next line and would generate a.out executable file.\n\n• Now, type a.out to execute your program.\n\n• You will see the output \"Hello World\" printed on the screen.\n\n\\$ gcc hello.c\n\\$ ./a.out\nHello, World!\n\nMake sure the gcc compiler is in your path and that you are running it in the directory containing the source file hello.c.\n\nC - Basic Syntax\n\nYou have seen the basic structure of a C program, so it will be easy to understand other basic building blocks of the C programming language.\n\nTokens in C\n\nA C program consists of various tokens and a token is either a keyword, an identifier, a constant, a string literal, or a symbol. For example, the following C statement consists of five tokens −\n\nprintf(\"Hello, World! \\n\");\n\nThe individual tokens are −\n\nprintf\n(\n\"Hello, World! \\n\"\n)\n;\n\nSemicolons\n\nIn a C program, the semicolon is a statement terminator. That is, each individual statement must be ended with a semicolon. It indicates the end of one logical entity.\n\nGiven below are two different statements −\n\nprintf(\"Hello, World! \\n\");\nreturn 0;\n\nComments are like helping text in your C program and they are ignored by the compiler. They start with /* and terminate with the characters */ as shown below −\n\n/* my first program in C */\n\nYou cannot have comments within comments and they do not occur within a string or character literals.\n\nIdentifiers\n\nA C identifier is a name used to identify a variable, function, or any other user-defined item. An identifier starts with a letter A to Z, a to z, or an underscore '_' followed by zero or more letters, underscores, and digits (0 to 9).\n\nC does not allow punctuation characters such as @, \\$, and % within identifiers. C is a case-sensitive programming language. Thus, Manpower and manpower are two different identifiers in C. Here are some examples of acceptable identifiers −\n\nmohd zara abc move_name a_123\nmyname50 _temp j a23b9 retVal\n\nKeywords\n\nThe following list shows the reserved words in C. These reserved words may not be used as constants or variables or any other identifier names.\n\n auto else long switch break enum register typedef case extern return union char float short unsigned const for signed void continue goto sizeof volatile default if static while do int struct _Packed double\n\nWhitespace in C\n\nA line containing only whitespace, possibly with a comment, is known as a blank line, and a C compiler totally ignores it.\n\nWhitespace is the term used in C to describe blanks, tabs, newline characters and comments. Whitespace separates one part of a statement from another and enables the compiler to identify where one element in a statement, such as int, ends and the next element begins. Therefore, in the following statement −\n\nint age;\n\nthere must be at least one whitespace character (usually a space) between int and age for the compiler to be able to distinguish them. On the other hand, in the following statement −\n\nfruit = apples + oranges; // get the total fruit\n\nno whitespace characters are necessary between fruit and =, or between = and apples, although you are free to include some if you wish to increase readability.\n\nC - Data Types\n\nData types in c refer to an extensive system used for declaring variables or functions of different types. The type of a variable determines how much space it occupies in storage and how the bit pattern stored is interpreted.\n\nThe types in C can be classified as follows −\n\nSr.No. Types & Description\n1\n\nBasic Types\n\nThey are arithmetic types and are further classified into: (a) integer types and (b) floating-point types.\n\n2\n\nEnumerated types\n\nThey are again arithmetic types and they are used to define variables that can only assign certain discrete integer values throughout the program.\n\n3\n\nThe type void\n\nThe type specifier void indicates that no value is available.\n\n4\n\nDerived types\n\nThey include (a) Pointer types, (b) Array types, (c) Structure types, (d) Union types and (e) Function types.\n\nThe array types and structure types are referred collectively as the aggregate types. The type of a function specifies the type of the function's return value. We will see the basic types in the following section, where as other types will be covered in the upcoming chapters.\n\nInteger Types\n\nThe following table provides the details of standard integer types with their storage sizes and value ranges −\n\nType Storage size Value range\nchar 1 byte -128 to 127 or 0 to 255\nunsigned char 1 byte 0 to 255\nsigned char 1 byte -128 to 127\nint 2 or 4 bytes -32,768 to 32,767 or -2,147,483,648 to 2,147,483,647\nunsigned int 2 or 4 bytes 0 to 65,535 or 0 to 4,294,967,295\nshort 2 bytes -32,768 to 32,767\nunsigned short 2 bytes 0 to 65,535\nlong 8 bytes -9223372036854775808 to 9223372036854775807\nunsigned long 8 bytes 0 to 18446744073709551615\n\nTo get the exact size of a type or a variable on a particular platform, you can use the sizeof operator. The expressions sizeof(type) yields the storage size of the object or type in bytes. Given below is an example to get the size of various type on a machine using different constant defined in limits.h header file −\n\n#include <stdio.h>\n#include <stdlib.h>\n#include <limits.h>\n#include <float.h>\n\nint main(int argc, char** argv) {\n\nprintf(\"CHAR_BIT : %d\\n\", CHAR_BIT);\nprintf(\"CHAR_MAX : %d\\n\", CHAR_MAX);\nprintf(\"CHAR_MIN : %d\\n\", CHAR_MIN);\nprintf(\"INT_MAX : %d\\n\", INT_MAX);\nprintf(\"INT_MIN : %d\\n\", INT_MIN);\nprintf(\"LONG_MAX : %ld\\n\", (long) LONG_MAX);\nprintf(\"LONG_MIN : %ld\\n\", (long) LONG_MIN);\nprintf(\"SCHAR_MAX : %d\\n\", SCHAR_MAX);\nprintf(\"SCHAR_MIN : %d\\n\", SCHAR_MIN);\nprintf(\"SHRT_MAX : %d\\n\", SHRT_MAX);\nprintf(\"SHRT_MIN : %d\\n\", SHRT_MIN);\nprintf(\"UCHAR_MAX : %d\\n\", UCHAR_MAX);\nprintf(\"UINT_MAX : %u\\n\", (unsigned int) UINT_MAX);\nprintf(\"ULONG_MAX : %lu\\n\", (unsigned long) ULONG_MAX);\nprintf(\"USHRT_MAX : %d\\n\", (unsigned short) USHRT_MAX);\n\nreturn 0;\n}\n\nWhen you compile and execute the above program, it produces the following result on Linux −\n\nCHAR_BIT : 8\nCHAR_MAX : 127\nCHAR_MIN : -128\nINT_MAX : 2147483647\nINT_MIN : -2147483648\nLONG_MAX : 9223372036854775807\nLONG_MIN : -9223372036854775808\nSCHAR_MAX : 127\nSCHAR_MIN : -128\nSHRT_MAX : 32767\nSHRT_MIN : -32768\nUCHAR_MAX : 255\nUINT_MAX : 4294967295\nULONG_MAX : 18446744073709551615\nUSHRT_MAX : 65535\n\nFloating-Point Types\n\nThe following table provide the details of standard floating-point types with storage sizes and value ranges and their precision −\n\nType Storage size Value range Precision\nfloat 4 byte 1.2E-38 to 3.4E+38 6 decimal places\ndouble 8 byte 2.3E-308 to 1.7E+308 15 decimal places\nlong double 10 byte 3.4E-4932 to 1.1E+4932 19 decimal places\n\nThe header file float.h defines macros that allow you to use these values and other details about the binary representation of real numbers in your programs. The following example prints the storage space taken by a float type and its range values −\n\n#include <stdio.h>\n#include <stdlib.h>\n#include <limits.h>\n#include <float.h>\n\nint main(int argc, char** argv) {\n\nprintf(\"Storage size for float : %d \\n\", sizeof(float));\nprintf(\"FLT_MAX : %g\\n\", (float) FLT_MAX);\nprintf(\"FLT_MIN : %g\\n\", (float) FLT_MIN);\nprintf(\"-FLT_MAX : %g\\n\", (float) -FLT_MAX);\nprintf(\"-FLT_MIN : %g\\n\", (float) -FLT_MIN);\nprintf(\"DBL_MAX : %g\\n\", (double) DBL_MAX);\nprintf(\"DBL_MIN : %g\\n\", (double) DBL_MIN);\nprintf(\"-DBL_MAX : %g\\n\", (double) -DBL_MAX);\nprintf(\"Precision value: %d\\n\", FLT_DIG );\n\nreturn 0;\n}\n\nWhen you compile and execute the above program, it produces the following result on Linux −\n\nStorage size for float : 4\nFLT_MAX : 3.40282e+38\nFLT_MIN : 1.17549e-38\n-FLT_MAX : -3.40282e+38\n-FLT_MIN : -1.17549e-38\nDBL_MAX : 1.79769e+308\nDBL_MIN : 2.22507e-308\n-DBL_MAX : -1.79769e+308\nPrecision value: 6\n\nThe void Type\n\nThe void type specifies that no value is available. It is used in three kinds of situations −\n\nSr.No. Types & Description\n1\n\nFunction returns as void\n\nThere are various functions in C which do not return any value or you can say they return void. A function with no return value has the return type as void. For example, void exit (int status);\n\n2\n\nFunction arguments as void\n\nThere are various functions in C which do not accept any parameter. A function with no parameter can accept a void. For example, int rand(void);\n\n3\n\nPointers to void\n\nA pointer of type void * represents the address of an object, but not its type. For example, a memory allocation function void *malloc( size_t size ); returns a pointer to void which can be casted to any data type.\n\nC - Variables\n\nA variable is nothing but a name given to a storage area that our programs can manipulate. Each variable in C has a specific type, which determines the size and layout of the variable's memory; the range of values that can be stored within that memory; and the set of operations that can be applied to the variable.\n\nThe name of a variable can be composed of letters, digits, and the underscore character. It must begin with either a letter or an underscore. Upper and lowercase letters are distinct because C is case-sensitive. Based on the basic types explained in the previous chapter, there will be the following basic variable types −\n\nSr.No. Type & Description\n1\n\nchar\n\nTypically a single octet(one byte). It is an integer type.\n\n2\n\nint\n\nThe most natural size of integer for the machine.\n\n3\n\nfloat\n\nA single-precision floating point value.\n\n4\n\ndouble\n\nA double-precision floating point value.\n\n5\n\nvoid\n\nRepresents the absence of type.\n\nC programming language also allows to define various other types of variables, which we will cover in subsequent chapters like Enumeration, Pointer, Array, Structure, Union, etc. For this chapter, let us study only basic variable types.\n\nVariable Definition in C\n\nA variable definition tells the compiler where and how much storage to create for the variable. A variable definition specifies a data type and contains a list of one or more variables of that type as follows −\n\ntype variable_list;\n\nHere, type must be a valid C data type including char, w_char, int, float, double, bool, or any user-defined object; and variable_list may consist of one or more identifier names separated by commas. Some valid declarations are shown here −\n\nint i, j, k;\nchar c, ch;\nfloat f, salary;\ndouble d;\n\nThe line int i, j, k; declares and defines the variables i, j, and k; which instruct the compiler to create variables named i, j and k of type int.\n\nVariables can be initialized (assigned an initial value) in their declaration. The initializer consists of an equal sign followed by a constant expression as follows −\n\ntype variable_name = value;\n\nSome examples are −\n\nextern int d = 3, f = 5; // declaration of d and f.\nint d = 3, f = 5; // definition and initializing d and f.\nbyte z = 22; // definition and initializes z.\nchar x = 'x'; // the variable x has the value 'x'.\n\nFor definition without an initializer: variables with static storage duration are implicitly initialized with NULL (all bytes have the value 0); the initial value of all other variables are undefined.\n\nVariable Declaration in C\n\nA variable declaration provides assurance to the compiler that there exists a variable with the given type and name so that the compiler can proceed for further compilation without requiring the complete detail about the variable. A variable definition has its meaning at the time of compilation only, the compiler needs actual variable definition at the time of linking the program.\n\nA variable declaration is useful when you are using multiple files and you define your variable in one of the files which will be available at the time of linking of the program. You will use the keyword extern to declare a variable at any place. Though you can declare a variable multiple times in your C program, it can be defined only once in a file, a function, or a block of code.\n\nExample\n\nTry the following example, where variables have been declared at the top, but they have been defined and initialized inside the main function −\n\n#include <stdio.h>\n\n// Variable declaration:\nextern int a, b;\nextern int c;\nextern float f;\n\nint main () {\n\n/* variable definition: */\nint a, b;\nint c;\nfloat f;\n\n/* actual initialization */\na = 10;\nb = 20;\n\nc = a + b;\nprintf(\"value of c : %d \\n\", c);\n\nf = 70.0/3.0;\nprintf(\"value of f : %f \\n\", f);\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nvalue of c : 30\nvalue of f : 23.333334\n\nThe same concept applies on function declaration where you provide a function name at the time of its declaration and its actual definition can be given anywhere else. For example −\n\n// function declaration\nint func();\n\nint main() {\n\n// function call\nint i = func();\n}\n\n// function definition\nint func() {\nreturn 0;\n}\n\nLvalues and Rvalues in C\n\nThere are two kinds of expressions in C −\n\n• lvalue − Expressions that refer to a memory location are called \"lvalue\" expressions. An lvalue may appear as either the left-hand or right-hand side of an assignment.\n\n• rvalue − The term rvalue refers to a data value that is stored at some address in memory. An rvalue is an expression that cannot have a value assigned to it which means an rvalue may appear on the right-hand side but not on the left-hand side of an assignment.\n\nVariables are lvalues and so they may appear on the left-hand side of an assignment. Numeric literals are rvalues and so they may not be assigned and cannot appear on the left-hand side. Take a look at the following valid and invalid statements −\n\nint g = 20; // valid statement\n\n10 = 20; // invalid statement; would generate compile-time error\n\nC - Constants and Literals\n\nConstants refer to fixed values that the program may not alter during its execution. These fixed values are also called literals.\n\nConstants can be of any of the basic data types like an integer constant, a floating constant, a character constant, or a string literal. There are enumeration constants as well.\n\nConstants are treated just like regular variables except that their values cannot be modified after their definition.\n\nInteger Literals\n\nAn integer literal can be a decimal, octal, or hexadecimal constant. A prefix specifies the base or radix: 0x or 0X for hexadecimal, 0 for octal, and nothing for decimal.\n\nAn integer literal can also have a suffix that is a combination of U and L, for unsigned and long, respectively. The suffix can be uppercase or lowercase and can be in any order.\n\nHere are some examples of integer literals −\n\n212 /* Legal */\n215u /* Legal */\n0xFeeL /* Legal */\n078 /* Illegal: 8 is not an octal digit */\n032UU /* Illegal: cannot repeat a suffix */\n\nFollowing are other examples of various types of integer literals −\n\n85 /* decimal */\n0213 /* octal */\n30 /* int */\n30u /* unsigned int */\n30l /* long */\n30ul /* unsigned long */\n\nFloating-point Literals\n\nA floating-point literal has an integer part, a decimal point, a fractional part, and an exponent part. You can represent floating point literals either in decimal form or exponential form.\n\nWhile representing decimal form, you must include the decimal point, the exponent, or both; and while representing exponential form, you must include the integer part, the fractional part, or both. The signed exponent is introduced by e or E.\n\nHere are some examples of floating-point literals −\n\n3.14159 /* Legal */\n314159E-5L /* Legal */\n510E /* Illegal: incomplete exponent */\n210f /* Illegal: no decimal or exponent */\n.e55 /* Illegal: missing integer or fraction */\n\nCharacter Constants\n\nCharacter literals are enclosed in single quotes, e.g., 'x' can be stored in a simple variable of char type.\n\nA character literal can be a plain character (e.g., 'x'), an escape sequence (e.g., '\\t'), or a universal character (e.g., '\\u02C0').\n\nThere are certain characters in C that represent special meaning when preceded by a backslash for example, newline (\\n) or tab (\\t).\n\nFollowing is the example to show a few escape sequence characters −\n\n#include <stdio.h>\n\nint main() {\nprintf(\"Hello\\tWorld\\n\\n\");\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nHello World\n\nString Literals\n\nString literals or constants are enclosed in double quotes \"\". A string contains characters that are similar to character literals: plain characters, escape sequences, and universal characters.\n\nYou can break a long line into multiple lines using string literals and separating them using white spaces.\n\nHere are some examples of string literals. All the three forms are identical strings.\n\n\"hello, dear\"\n\n\"hello, \\\n\ndear\"\n\n\"hello, \" \"d\" \"ear\"\n\nDefining Constants\n\nThere are two simple ways in C to define constants −\n\n• Using #define preprocessor.\n\n• Using const keyword.\n\nThe #define Preprocessor\n\nGiven below is the form to use #define preprocessor to define a constant −\n\n#define identifier value\n\nThe following example explains it in detail −\n\n#include <stdio.h>\n\n#define LENGTH 10\n#define WIDTH 5\n#define NEWLINE '\\n'\n\nint main() {\nint area;\n\narea = LENGTH * WIDTH;\nprintf(\"value of area : %d\", area);\nprintf(\"%c\", NEWLINE);\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nvalue of area : 50\n\nThe const Keyword\n\nYou can use const prefix to declare constants with a specific type as follows −\n\nconst type variable = value;\n\nThe following example explains it in detail −\n\n#include <stdio.h>\n\nint main() {\nconst int LENGTH = 10;\nconst int WIDTH = 5;\nconst char NEWLINE = '\\n';\nint area;\n\narea = LENGTH * WIDTH;\nprintf(\"value of area : %d\", area);\nprintf(\"%c\", NEWLINE);\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nvalue of area : 50\n\nNote that it is a good programming practice to define constants in CAPITALS.\n\nC - Storage Classes\n\nA storage class defines the scope (visibility) and life-time of variables and/or functions within a C Program. They precede the type that they modify. We have four different storage classes in a C program −\n\n• auto\n• register\n• static\n• extern\n\nThe auto Storage Class\n\nThe auto storage class is the default storage class for all local variables.\n\n{\nint mount;\nauto int month;\n}\n\nThe example above defines two variables with in the same storage class. 'auto' can only be used within functions, i.e., local variables.\n\nThe register Storage Class\n\nThe register storage class is used to define local variables that should be stored in a register instead of RAM. This means that the variable has a maximum size equal to the register size (usually one word) and can't have the unary '&' operator applied to it (as it does not have a memory location).\n\n{\nregister int miles;\n}\n\nThe register should only be used for variables that require quick access such as counters. It should also be noted that defining 'register' does not mean that the variable will be stored in a register. It means that it MIGHT be stored in a register depending on hardware and implementation restrictions.\n\nThe static Storage Class\n\nThe static storage class instructs the compiler to keep a local variable in existence during the life-time of the program instead of creating and destroying it each time it comes into and goes out of scope. Therefore, making local variables static allows them to maintain their values between function calls.\n\nThe static modifier may also be applied to global variables. When this is done, it causes that variable's scope to be restricted to the file in which it is declared.\n\nIn C programming, when static is used on a global variable, it causes only one copy of that member to be shared by all the objects of its class.\n\n#include <stdio.h>\n\n/* function declaration */\nvoid func(void);\n\nstatic int count = 5; /* global variable */\n\nmain() {\n\nwhile(count--) {\nfunc();\n}\n\nreturn 0;\n}\n\n/* function definition */\nvoid func( void ) {\n\nstatic int i = 5; /* local static variable */\ni++;\n\nprintf(\"i is %d and count is %d\\n\", i, count);\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\ni is 6 and count is 4\ni is 7 and count is 3\ni is 8 and count is 2\ni is 9 and count is 1\ni is 10 and count is 0\n\nThe extern Storage Class\n\nThe extern storage class is used to give a reference of a global variable that is visible to ALL the program files. When you use 'extern', the variable cannot be initialized however, it points the variable name at a storage location that has been previously defined.\n\nWhen you have multiple files and you define a global variable or function, which will also be used in other files, then extern will be used in another file to provide the reference of defined variable or function. Just for understanding, extern is used to declare a global variable or function in another file.\n\nThe extern modifier is most commonly used when there are two or more files sharing the same global variables or functions as explained below.\n\nFirst File: main.c\n\n#include <stdio.h>\n\nint count ;\nextern void write_extern();\n\nmain() {\ncount = 5;\nwrite_extern();\n}\n\nSecond File: support.c\n\n#include <stdio.h>\n\nextern int count;\n\nvoid write_extern(void) {\nprintf(\"count is %d\\n\", count);\n}\n\nHere, extern is being used to declare count in the second file, where as it has its definition in the first file, main.c. Now, compile these two files as follows −\n\n\\$gcc main.c support.c\n\nIt will produce the executable program a.out. When this program is executed, it produces the following result −\n\ncount is 5\n\nC - Operators\n\nAn operator is a symbol that tells the compiler to perform specific mathematical or logical functions. C language is rich in built-in operators and provides the following types of operators −\n\n• Arithmetic Operators\n• Relational Operators\n• Logical Operators\n• Bitwise Operators\n• Assignment Operators\n• Misc Operators\n\nWe will, in this chapter, look into the way each operator works.\n\nArithmetic Operators\n\nThe following table shows all the arithmetic operators supported by the C language. Assume variable A holds 10 and variable B holds 20 then −\n\nShow Examples\n\nOperator Description Example\n+ Adds two operands. A + B = 30\nSubtracts second operand from the first. A − B = -10\n* Multiplies both operands. A * B = 200\n/ Divides numerator by de-numerator. B / A = 2\n% Modulus Operator and remainder of after an integer division. B % A = 0\n++ Increment operator increases the integer value by one. A++ = 11\n-- Decrement operator decreases the integer value by one. A-- = 9\n\nRelational Operators\n\nThe following table shows all the relational operators supported by C. Assume variable A holds 10 and variable B holds 20 then −\n\nShow Examples\n\nOperator Description Example\n== Checks if the values of two operands are equal or not. If yes, then the condition becomes true. (A == B) is not true.\n!= Checks if the values of two operands are equal or not. If the values are not equal, then the condition becomes true. (A != B) is true.\n> Checks if the value of left operand is greater than the value of right operand. If yes, then the condition becomes true. (A > B) is not true.\n< Checks if the value of left operand is less than the value of right operand. If yes, then the condition becomes true. (A < B) is true.\n>= Checks if the value of left operand is greater than or equal to the value of right operand. If yes, then the condition becomes true. (A >= B) is not true.\n<= Checks if the value of left operand is less than or equal to the value of right operand. If yes, then the condition becomes true. (A <= B) is true.\n\nLogical Operators\n\nFollowing table shows all the logical operators supported by C language. Assume variable A holds 1 and variable B holds 0, then −\n\nShow Examples\n\nOperator Description Example\n&& Called Logical AND operator. If both the operands are non-zero, then the condition becomes true. (A && B) is false.\n|| Called Logical OR Operator. If any of the two operands is non-zero, then the condition becomes true. (A || B) is true.\n! Called Logical NOT Operator. It is used to reverse the logical state of its operand. If a condition is true, then Logical NOT operator will make it false. !(A && B) is true.\n\nBitwise Operators\n\nBitwise operator works on bits and perform bit-by-bit operation. The truth tables for &, |, and ^ is as follows −\n\np q p & q p | q p ^ q\n0 0 0 0 0\n0 1 0 1 1\n1 1 1 1 0\n1 0 0 1 1\n\nAssume A = 60 and B = 13 in binary format, they will be as follows −\n\nA = 0011 1100\n\nB = 0000 1101\n\n-----------------\n\nA&B = 0000 1100\n\nA|B = 0011 1101\n\nA^B = 0011 0001\n\n~A = 1100 0011\n\nThe following table lists the bitwise operators supported by C. Assume variable 'A' holds 60 and variable 'B' holds 13, then −\n\nShow Examples\n\nOperator Description Example\n& Binary AND Operator copies a bit to the result if it exists in both operands. (A & B) = 12, i.e., 0000 1100\n| Binary OR Operator copies a bit if it exists in either operand. (A | B) = 61, i.e., 0011 1101\n^ Binary XOR Operator copies the bit if it is set in one operand but not both. (A ^ B) = 49, i.e., 0011 0001\n~ Binary One's Complement Operator is unary and has the effect of 'flipping' bits. (~A ) = ~(60), i.e,. -0111101\n<< Binary Left Shift Operator. The left operands value is moved left by the number of bits specified by the right operand. A << 2 = 240 i.e., 1111 0000\n>> Binary Right Shift Operator. The left operands value is moved right by the number of bits specified by the right operand. A >> 2 = 15 i.e., 0000 1111\n\nAssignment Operators\n\nThe following table lists the assignment operators supported by the C language −\n\nShow Examples\n\nOperator Description Example\n= Simple assignment operator. Assigns values from right side operands to left side operand C = A + B will assign the value of A + B to C\n+= Add AND assignment operator. It adds the right operand to the left operand and assign the result to the left operand. C += A is equivalent to C = C + A\n-= Subtract AND assignment operator. It subtracts the right operand from the left operand and assigns the result to the left operand. C -= A is equivalent to C = C - A\n*= Multiply AND assignment operator. It multiplies the right operand with the left operand and assigns the result to the left operand. C *= A is equivalent to C = C * A\n/= Divide AND assignment operator. It divides the left operand with the right operand and assigns the result to the left operand. C /= A is equivalent to C = C / A\n%= Modulus AND assignment operator. It takes modulus using two operands and assigns the result to the left operand. C %= A is equivalent to C = C % A\n<<= Left shift AND assignment operator. C <<= 2 is same as C = C << 2\n>>= Right shift AND assignment operator. C >>= 2 is same as C = C >> 2\n&= Bitwise AND assignment operator. C &= 2 is same as C = C & 2\n^= Bitwise exclusive OR and assignment operator. C ^= 2 is same as C = C ^ 2\n|= Bitwise inclusive OR and assignment operator. C |= 2 is same as C = C | 2\n\nMisc Operators ↦ sizeof & ternary\n\nBesides the operators discussed above, there are a few other important operators including sizeof and ? : supported by the C Language.\n\nShow Examples\n\nOperator Description Example\nsizeof() Returns the size of a variable. sizeof(a), where a is integer, will return 4.\n& Returns the address of a variable. &a; returns the actual address of the variable.\n* Pointer to a variable. *a;\n? : Conditional Expression. If Condition is true ? then value X : otherwise value Y\n\nOperators Precedence in C\n\nOperator precedence determines the grouping of terms in an expression and decides how an expression is evaluated. Certain operators have higher precedence than others; for example, the multiplication operator has a higher precedence than the addition operator.\n\nFor example, x = 7 + 3 * 2; here, x is assigned 13, not 20 because operator * has a higher precedence than +, so it first gets multiplied with 3*2 and then adds into 7.\n\nHere, operators with the highest precedence appear at the top of the table, those with the lowest appear at the bottom. Within an expression, higher precedence operators will be evaluated first.\n\nShow Examples\n\nCategory Operator Associativity\nPostfix () [] -> . ++ - - Left to right\nUnary + - ! ~ ++ - - (type)* & sizeof Right to left\nMultiplicative * / % Left to right\nAdditive + - Left to right\nShift << >> Left to right\nRelational < <= > >= Left to right\nEquality == != Left to right\nBitwise AND & Left to right\nBitwise XOR ^ Left to right\nBitwise OR | Left to right\nLogical AND && Left to right\nLogical OR || Left to right\nConditional ?: Right to left\nAssignment = += -= *= /= %=>>= <<= &= ^= |= Right to left\nComma , Left to right\n\nC - Decision Making\n\nDecision making structures require that the programmer specifies one or more conditions to be evaluated or tested by the program, along with a statement or statements to be executed if the condition is determined to be true, and optionally, other statements to be executed if the condition is determined to be false.\n\nShow below is the general form of a typical decision making structure found in most of the programming languages −", null, "C programming language assumes any non-zero and non-null values as true, and if it is either zero or null, then it is assumed as false value.\n\nC programming language provides the following types of decision making statements.\n\nSr.No. Statement & Description\n1 if statement\n\nAn if statement consists of a boolean expression followed by one or more statements.\n\n2 if...else statement\n\nAn if statement can be followed by an optional else statement, which executes when the Boolean expression is false.\n\n3 nested if statements\n\nYou can use one if or else if statement inside another if or else if statement(s).\n\n4 switch statement\n\nA switch statement allows a variable to be tested for equality against a list of values.\n\n5 nested switch statements\n\nYou can use one switch statement inside another switch statement(s).\n\nThe ? : Operator\n\nWe have covered conditional operator ? : in the previous chapter which can be used to replace if...else statements. It has the following general form −\n\nExp1 ? Exp2 : Exp3;\n\nWhere Exp1, Exp2, and Exp3 are expressions. Notice the use and placement of the colon.\n\nThe value of a ? expression is determined like this −\n\n• Exp1 is evaluated. If it is true, then Exp2 is evaluated and becomes the value of the entire ? expression.\n\n• If Exp1 is false, then Exp3 is evaluated and its value becomes the value of the expression.\n\nC - Loops\n\nYou may encounter situations, when a block of code needs to be executed several number of times. In general, statements are executed sequentially: The first statement in a function is executed first, followed by the second, and so on.\n\nProgramming languages provide various control structures that allow for more complicated execution paths.\n\nA loop statement allows us to execute a statement or group of statements multiple times. Given below is the general form of a loop statement in most of the programming languages −", null, "C programming language provides the following types of loops to handle looping requirements.\n\nSr.No. Loop Type & Description\n1 while loop\n\nRepeats a statement or group of statements while a given condition is true. It tests the condition before executing the loop body.\n\n2 for loop\n\nExecutes a sequence of statements multiple times and abbreviates the code that manages the loop variable.\n\n3 do...while loop\n\nIt is more like a while statement, except that it tests the condition at the end of the loop body.\n\n4 nested loops\n\nYou can use one or more loops inside any other while, for, or do..while loop.\n\nLoop Control Statements\n\nLoop control statements change execution from its normal sequence. When execution leaves a scope, all automatic objects that were created in that scope are destroyed.\n\nC supports the following control statements.\n\nSr.No. Control Statement & Description\n1 break statement\n\nTerminates the loop or switch statement and transfers execution to the statement immediately following the loop or switch.\n\n2 continue statement\n\nCauses the loop to skip the remainder of its body and immediately retest its condition prior to reiterating.\n\n3 goto statement\n\nTransfers control to the labeled statement.\n\nThe Infinite Loop\n\nA loop becomes an infinite loop if a condition never becomes false. The for loop is traditionally used for this purpose. Since none of the three expressions that form the 'for' loop are required, you can make an endless loop by leaving the conditional expression empty.\n\n#include <stdio.h>\n\nint main () {\n\nfor( ; ; ) {\nprintf(\"This loop will run forever.\\n\");\n}\n\nreturn 0;\n}\n\nWhen the conditional expression is absent, it is assumed to be true. You may have an initialization and increment expression, but C programmers more commonly use the for(;;) construct to signify an infinite loop.\n\nNOTE − You can terminate an infinite loop by pressing Ctrl + C keys.\n\nC - Functions\n\nA function is a group of statements that together perform a task. Every C program has at least one function, which is main(), and all the most trivial programs can define additional functions.\n\nYou can divide up your code into separate functions. How you divide up your code among different functions is up to you, but logically the division is such that each function performs a specific task.\n\nA function declaration tells the compiler about a function's name, return type, and parameters. A function definition provides the actual body of the function.\n\nThe C standard library provides numerous built-in functions that your program can call. For example, strcat() to concatenate two strings, memcpy() to copy one memory location to another location, and many more functions.\n\nA function can also be referred as a method or a sub-routine or a procedure, etc.\n\nDefining a Function\n\nThe general form of a function definition in C programming language is as follows −\n\nreturn_type function_name( parameter list ) {\nbody of the function\n}\n\nA function definition in C programming consists of a function header and a function body. Here are all the parts of a function −\n\n• Return Type − A function may return a value. The return_type is the data type of the value the function returns. Some functions perform the desired operations without returning a value. In this case, the return_type is the keyword void.\n\n• Function Name − This is the actual name of the function. The function name and the parameter list together constitute the function signature.\n\n• Parameters − A parameter is like a placeholder. When a function is invoked, you pass a value to the parameter. This value is referred to as actual parameter or argument. The parameter list refers to the type, order, and number of the parameters of a function. Parameters are optional; that is, a function may contain no parameters.\n\n• Function Body − The function body contains a collection of statements that define what the function does.\n\nExample\n\nGiven below is the source code for a function called max(). This function takes two parameters num1 and num2 and returns the maximum value between the two −\n\n/* function returning the max between two numbers */\nint max(int num1, int num2) {\n\n/* local variable declaration */\nint result;\n\nif (num1 > num2)\nresult = num1;\nelse\nresult = num2;\n\nreturn result;\n}\n\nFunction Declarations\n\nA function declaration tells the compiler about a function name and how to call the function. The actual body of the function can be defined separately.\n\nA function declaration has the following parts −\n\nreturn_type function_name( parameter list );\n\nFor the above defined function max(), the function declaration is as follows −\n\nint max(int num1, int num2);\n\nParameter names are not important in function declaration only their type is required, so the following is also a valid declaration −\n\nint max(int, int);\n\nFunction declaration is required when you define a function in one source file and you call that function in another file. In such case, you should declare the function at the top of the file calling the function.\n\nCalling a Function\n\nWhile creating a C function, you give a definition of what the function has to do. To use a function, you will have to call that function to perform the defined task.\n\nWhen a program calls a function, the program control is transferred to the called function. A called function performs a defined task and when its return statement is executed or when its function-ending closing brace is reached, it returns the program control back to the main program.\n\nTo call a function, you simply need to pass the required parameters along with the function name, and if the function returns a value, then you can store the returned value. For example −\n\n#include <stdio.h>\n\n/* function declaration */\nint max(int num1, int num2);\n\nint main () {\n\n/* local variable definition */\nint a = 100;\nint b = 200;\nint ret;\n\n/* calling a function to get max value */\nret = max(a, b);\n\nprintf( \"Max value is : %d\\n\", ret );\n\nreturn 0;\n}\n\n/* function returning the max between two numbers */\nint max(int num1, int num2) {\n\n/* local variable declaration */\nint result;\n\nif (num1 > num2)\nresult = num1;\nelse\nresult = num2;\n\nreturn result;\n}\n\nWe have kept max() along with main() and compiled the source code. While running the final executable, it would produce the following result −\n\nMax value is : 200\n\nFunction Arguments\n\nIf a function is to use arguments, it must declare variables that accept the values of the arguments. These variables are called the formal parameters of the function.\n\nFormal parameters behave like other local variables inside the function and are created upon entry into the function and destroyed upon exit.\n\nWhile calling a function, there are two ways in which arguments can be passed to a function −\n\nSr.No. Call Type & Description\n1 Call by value\n\nThis method copies the actual value of an argument into the formal parameter of the function. In this case, changes made to the parameter inside the function have no effect on the argument.\n\n2 Call by reference\n\nThis method copies the address of an argument into the formal parameter. Inside the function, the address is used to access the actual argument used in the call. This means that changes made to the parameter affect the argument.\n\nBy default, C uses call by value to pass arguments. In general, it means the code within a function cannot alter the arguments used to call the function.\n\nC - Scope Rules\n\nA scope in any programming is a region of the program where a defined variable can have its existence and beyond that variable it cannot be accessed. There are three places where variables can be declared in C programming language −\n\n• Inside a function or a block which is called local variables.\n\n• Outside of all functions which is called global variables.\n\n• In the definition of function parameters which are called formal parameters.\n\nLet us understand what are local and global variables, and formal parameters.\n\nLocal Variables\n\nVariables that are declared inside a function or block are called local variables. They can be used only by statements that are inside that function or block of code. Local variables are not known to functions outside their own. The following example shows how local variables are used. Here all the variables a, b, and c are local to main() function.\n\n#include <stdio.h>\n\nint main () {\n\n/* local variable declaration */\nint a, b;\nint c;\n\n/* actual initialization */\na = 10;\nb = 20;\nc = a + b;\n\nprintf (\"value of a = %d, b = %d and c = %d\\n\", a, b, c);\n\nreturn 0;\n}\n\nGlobal Variables\n\nGlobal variables are defined outside a function, usually on top of the program. Global variables hold their values throughout the lifetime of your program and they can be accessed inside any of the functions defined for the program.\n\nA global variable can be accessed by any function. That is, a global variable is available for use throughout your entire program after its declaration. The following program show how global variables are used in a program.\n\n#include <stdio.h>\n\n/* global variable declaration */\nint g;\n\nint main () {\n\n/* local variable declaration */\nint a, b;\n\n/* actual initialization */\na = 10;\nb = 20;\ng = a + b;\n\nprintf (\"value of a = %d, b = %d and g = %d\\n\", a, b, g);\n\nreturn 0;\n}\n\nA program can have same name for local and global variables but the value of local variable inside a function will take preference. Here is an example −\n\n#include <stdio.h>\n\n/* global variable declaration */\nint g = 20;\n\nint main () {\n\n/* local variable declaration */\nint g = 10;\n\nprintf (\"value of g = %d\\n\", g);\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nvalue of g = 10\n\nFormal Parameters\n\nFormal parameters, are treated as local variables with-in a function and they take precedence over global variables. Following is an example −\n\n#include <stdio.h>\n\n/* global variable declaration */\nint a = 20;\n\nint main () {\n\n/* local variable declaration in main function */\nint a = 10;\nint b = 20;\nint c = 0;\n\nprintf (\"value of a in main() = %d\\n\", a);\nc = sum( a, b);\nprintf (\"value of c in main() = %d\\n\", c);\n\nreturn 0;\n}\n\n/* function to add two integers */\nint sum(int a, int b) {\n\nprintf (\"value of a in sum() = %d\\n\", a);\nprintf (\"value of b in sum() = %d\\n\", b);\n\nreturn a + b;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nvalue of a in main() = 10\nvalue of a in sum() = 10\nvalue of b in sum() = 20\nvalue of c in main() = 30\n\nInitializing Local and Global Variables\n\nWhen a local variable is defined, it is not initialized by the system, you must initialize it yourself. Global variables are initialized automatically by the system when you define them as follows −\n\nData Type Initial Default Value\nint 0\nchar '\\0'\nfloat 0\ndouble 0\npointer NULL\n\nIt is a good programming practice to initialize variables properly, otherwise your program may produce unexpected results, because uninitialized variables will take some garbage value already available at their memory location.\n\nC - Arrays\n\nArrays a kind of data structure that can store a fixed-size sequential collection of elements of the same type. An array is used to store a collection of data, but it is often more useful to think of an array as a collection of variables of the same type.\n\nInstead of declaring individual variables, such as number0, number1, ..., and number99, you declare one array variable such as numbers and use numbers, numbers, and ..., numbers to represent individual variables. A specific element in an array is accessed by an index.\n\nAll arrays consist of contiguous memory locations. The lowest address corresponds to the first element and the highest address to the last element.", null, "Declaring Arrays\n\nTo declare an array in C, a programmer specifies the type of the elements and the number of elements required by an array as follows −\n\ntype arrayName [ arraySize ];\n\nThis is called a single-dimensional array. The arraySize must be an integer constant greater than zero and type can be any valid C data type. For example, to declare a 10-element array called balance of type double, use this statement −\n\ndouble balance;\n\nHere balance is a variable array which is sufficient to hold up to 10 double numbers.\n\nInitializing Arrays\n\nYou can initialize an array in C either one by one or using a single statement as follows −\n\ndouble balance = {1000.0, 2.0, 3.4, 7.0, 50.0};\n\nThe number of values between braces { } cannot be larger than the number of elements that we declare for the array between square brackets [ ].\n\nIf you omit the size of the array, an array just big enough to hold the initialization is created. Therefore, if you write −\n\ndouble balance[] = {1000.0, 2.0, 3.4, 7.0, 50.0};\n\nYou will create exactly the same array as you did in the previous example. Following is an example to assign a single element of the array −\n\nbalance = 50.0;\n\nThe above statement assigns the 5th element in the array with a value of 50.0. All arrays have 0 as the index of their first element which is also called the base index and the last index of an array will be total size of the array minus 1. Shown below is the pictorial representation of the array we discussed above −", null, "Accessing Array Elements\n\nAn element is accessed by indexing the array name. This is done by placing the index of the element within square brackets after the name of the array. For example −\n\ndouble salary = balance;\n\nThe above statement will take the 10th element from the array and assign the value to salary variable. The following example Shows how to use all the three above mentioned concepts viz. declaration, assignment, and accessing arrays −\n\n#include <stdio.h>\n\nint main () {\n\nint n[ 10 ]; /* n is an array of 10 integers */\nint i,j;\n\n/* initialize elements of array n to 0 */\nfor ( i = 0; i < 10; i++ ) {\nn[ i ] = i + 100; /* set element at location i to i + 100 */\n}\n\n/* output each array element's value */\nfor (j = 0; j < 10; j++ ) {\nprintf(\"Element[%d] = %d\\n\", j, n[j] );\n}\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nElement = 100\nElement = 101\nElement = 102\nElement = 103\nElement = 104\nElement = 105\nElement = 106\nElement = 107\nElement = 108\nElement = 109\n\nArrays in Detail\n\nArrays are important to C and should need a lot more attention. The following important concepts related to array should be clear to a C programmer −\n\nSr.No. Concept & Description\n1 Multi-dimensional arrays\n\nC supports multidimensional arrays. The simplest form of the multidimensional array is the two-dimensional array.\n\n2 Passing arrays to functions\n\nYou can pass to the function a pointer to an array by specifying the array's name without an index.\n\n3 Return array from a function\n\nC allows a function to return an array.\n\n4 Pointer to an array\n\nYou can generate a pointer to the first element of an array by simply specifying the array name, without any index.\n\nC - Pointers\n\nPointers in C are easy and fun to learn. Some C programming tasks are performed more easily with pointers, and other tasks, such as dynamic memory allocation, cannot be performed without using pointers. So it becomes necessary to learn pointers to become a perfect C programmer. Let's start learning them in simple and easy steps.\n\nAs you know, every variable is a memory location and every memory location has its address defined which can be accessed using ampersand (&) operator, which denotes an address in memory. Consider the following example, which prints the address of the variables defined −\n\n#include <stdio.h>\n\nint main () {\n\nint var1;\nchar var2;\n\nprintf(\"Address of var1 variable: %x\\n\", &var1 );\nprintf(\"Address of var2 variable: %x\\n\", &var2 );\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nWhat are Pointers?\n\nA pointer is a variable whose value is the address of another variable, i.e., direct address of the memory location. Like any variable or constant, you must declare a pointer before using it to store any variable address. The general form of a pointer variable declaration is −\n\ntype *var-name;\n\nHere, type is the pointer's base type; it must be a valid C data type and var-name is the name of the pointer variable. The asterisk * used to declare a pointer is the same asterisk used for multiplication. However, in this statement the asterisk is being used to designate a variable as a pointer. Take a look at some of the valid pointer declarations −\n\nint *ip; /* pointer to an integer */\ndouble *dp; /* pointer to a double */\nfloat *fp; /* pointer to a float */\nchar *ch /* pointer to a character */\n\nThe actual data type of the value of all pointers, whether integer, float, character, or otherwise, is the same, a long hexadecimal number that represents a memory address. The only difference between pointers of different data types is the data type of the variable or constant that the pointer points to.\n\nHow to Use Pointers?\n\nThere are a few important operations, which we will do with the help of pointers very frequently. (a) We define a pointer variable, (b) assign the address of a variable to a pointer and (c) finally access the value at the address available in the pointer variable. This is done by using unary operator * that returns the value of the variable located at the address specified by its operand. The following example makes use of these operations −\n\n#include <stdio.h>\n\nint main () {\n\nint var = 20; /* actual variable declaration */\nint *ip; /* pointer variable declaration */\n\nip = &var; /* store address of var in pointer variable*/\n\nprintf(\"Address of var variable: %x\\n\", &var );\n\n/* address stored in pointer variable */\nprintf(\"Address stored in ip variable: %x\\n\", ip );\n\n/* access the value using the pointer */\nprintf(\"Value of *ip variable: %d\\n\", *ip );\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nAddress stored in ip variable: bffd8b3c\nValue of *ip variable: 20\n\nNULL Pointers\n\nIt is always a good practice to assign a NULL value to a pointer variable in case you do not have an exact address to be assigned. This is done at the time of variable declaration. A pointer that is assigned NULL is called a null pointer.\n\nThe NULL pointer is a constant with a value of zero defined in several standard libraries. Consider the following program −\n\n#include <stdio.h>\n\nint main () {\n\nint *ptr = NULL;\n\nprintf(\"The value of ptr is : %x\\n\", ptr );\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nThe value of ptr is 0\n\nIn most of the operating systems, programs are not permitted to access memory at address 0 because that memory is reserved by the operating system. However, the memory address 0 has special significance; it signals that the pointer is not intended to point to an accessible memory location. But by convention, if a pointer contains the null (zero) value, it is assumed to point to nothing.\n\nTo check for a null pointer, you can use an 'if' statement as follows −\n\nif(ptr) /* succeeds if p is not null */\nif(!ptr) /* succeeds if p is null */\n\nPointers in Detail\n\nPointers have many but easy concepts and they are very important to C programming. The following important pointer concepts should be clear to any C programmer −\n\nSr.No. Concept & Description\n1 Pointer arithmetic\n\nThere are four arithmetic operators that can be used in pointers: ++, --, +, -\n\n2 Array of pointers\n\nYou can define arrays to hold a number of pointers.\n\n3 Pointer to pointer\n\nC allows you to have pointer on a pointer and so on.\n\n4 Passing pointers to functions in C\n\nPassing an argument by reference or by address enable the passed argument to be changed in the calling function by the called function.\n\n5 Return pointer from functions in C\n\nC allows a function to return a pointer to the local variable, static variable, and dynamically allocated memory as well.\n\nC - Strings\n\nStrings are actually one-dimensional array of characters terminated by a null character '\\0'. Thus a null-terminated string contains the characters that comprise the string followed by a null.\n\nThe following declaration and initialization create a string consisting of the word \"Hello\". To hold the null character at the end of the array, the size of the character array containing the string is one more than the number of characters in the word \"Hello.\"\n\nchar greeting = {'H', 'e', 'l', 'l', 'o', '\\0'};\n\nIf you follow the rule of array initialization then you can write the above statement as follows −\n\nchar greeting[] = \"Hello\";\n\nFollowing is the memory presentation of the above defined string in C/C++ −", null, "Actually, you do not place the null character at the end of a string constant. The C compiler automatically places the '\\0' at the end of the string when it initializes the array. Let us try to print the above mentioned string −\n\n#include <stdio.h>\n\nint main () {\n\nchar greeting = {'H', 'e', 'l', 'l', 'o', '\\0'};\nprintf(\"Greeting message: %s\\n\", greeting );\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nGreeting message: Hello\n\nC supports a wide range of functions that manipulate null-terminated strings −\n\nSr.No. Function & Purpose\n1\n\nstrcpy(s1, s2);\n\nCopies string s2 into string s1.\n\n2\n\nstrcat(s1, s2);\n\nConcatenates string s2 onto the end of string s1.\n\n3\n\nstrlen(s1);\n\nReturns the length of string s1.\n\n4\n\nstrcmp(s1, s2);\n\nReturns 0 if s1 and s2 are the same; less than 0 if s1<s2; greater than 0 if s1>s2.\n\n5\n\nstrchr(s1, ch);\n\nReturns a pointer to the first occurrence of character ch in string s1.\n\n6\n\nstrstr(s1, s2);\n\nReturns a pointer to the first occurrence of string s2 in string s1.\n\nThe following example uses some of the above-mentioned functions −\n\n#include <stdio.h>\n#include <string.h>\n\nint main () {\n\nchar str1 = \"Hello\";\nchar str2 = \"World\";\nchar str3;\nint len ;\n\n/* copy str1 into str3 */\nstrcpy(str3, str1);\nprintf(\"strcpy( str3, str1) : %s\\n\", str3 );\n\n/* concatenates str1 and str2 */\nstrcat( str1, str2);\nprintf(\"strcat( str1, str2): %s\\n\", str1 );\n\n/* total lenghth of str1 after concatenation */\nlen = strlen(str1);\nprintf(\"strlen(str1) : %d\\n\", len );\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nstrcpy( str3, str1) : Hello\nstrcat( str1, str2): HelloWorld\nstrlen(str1) : 10\n\nC - Structures\n\nArrays allow to define type of variables that can hold several data items of the same kind. Similarly structure is another user defined data type available in C that allows to combine data items of different kinds.\n\nStructures are used to represent a record. Suppose you want to keep track of your books in a library. You might want to track the following attributes about each book −\n\n• Title\n• Author\n• Subject\n• Book ID\n\nDefining a Structure\n\nTo define a structure, you must use the struct statement. The struct statement defines a new data type, with more than one member. The format of the struct statement is as follows −\n\nstruct [structure tag] {\n\nmember definition;\nmember definition;\n...\nmember definition;\n} [one or more structure variables];\n\nThe structure tag is optional and each member definition is a normal variable definition, such as int i; or float f; or any other valid variable definition. At the end of the structure's definition, before the final semicolon, you can specify one or more structure variables but it is optional. Here is the way you would declare the Book structure −\n\nstruct Books {\nchar title;\nchar author;\nchar subject;\nint book_id;\n} book;\n\nAccessing Structure Members\n\nTo access any member of a structure, we use the member access operator (.). The member access operator is coded as a period between the structure variable name and the structure member that we wish to access. You would use the keyword struct to define variables of structure type. The following example shows how to use a structure in a program −\n\n#include <stdio.h>\n#include <string.h>\n\nstruct Books {\nchar title;\nchar author;\nchar subject;\nint book_id;\n};\n\nint main( ) {\n\nstruct Books Book1; /* Declare Book1 of type Book */\nstruct Books Book2; /* Declare Book2 of type Book */\n\n/* book 1 specification */\nstrcpy( Book1.title, \"C Programming\");\nstrcpy( Book1.author, \"Nuha Ali\");\nstrcpy( Book1.subject, \"C Programming Tutorial\");\nBook1.book_id = 6495407;\n\n/* book 2 specification */\nstrcpy( Book2.title, \"Telecom Billing\");\nstrcpy( Book2.author, \"Zara Ali\");\nstrcpy( Book2.subject, \"Telecom Billing Tutorial\");\nBook2.book_id = 6495700;\n\n/* print Book1 info */\nprintf( \"Book 1 title : %s\\n\", Book1.title);\nprintf( \"Book 1 author : %s\\n\", Book1.author);\nprintf( \"Book 1 subject : %s\\n\", Book1.subject);\nprintf( \"Book 1 book_id : %d\\n\", Book1.book_id);\n\n/* print Book2 info */\nprintf( \"Book 2 title : %s\\n\", Book2.title);\nprintf( \"Book 2 author : %s\\n\", Book2.author);\nprintf( \"Book 2 subject : %s\\n\", Book2.subject);\nprintf( \"Book 2 book_id : %d\\n\", Book2.book_id);\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nBook 1 title : C Programming\nBook 1 author : Nuha Ali\nBook 1 subject : C Programming Tutorial\nBook 1 book_id : 6495407\nBook 2 title : Telecom Billing\nBook 2 author : Zara Ali\nBook 2 subject : Telecom Billing Tutorial\nBook 2 book_id : 6495700\n\nStructures as Function Arguments\n\nYou can pass a structure as a function argument in the same way as you pass any other variable or pointer.\n\n#include <stdio.h>\n#include <string.h>\n\nstruct Books {\nchar title;\nchar author;\nchar subject;\nint book_id;\n};\n\n/* function declaration */\nvoid printBook( struct Books book );\n\nint main( ) {\n\nstruct Books Book1; /* Declare Book1 of type Book */\nstruct Books Book2; /* Declare Book2 of type Book */\n\n/* book 1 specification */\nstrcpy( Book1.title, \"C Programming\");\nstrcpy( Book1.author, \"Nuha Ali\");\nstrcpy( Book1.subject, \"C Programming Tutorial\");\nBook1.book_id = 6495407;\n\n/* book 2 specification */\nstrcpy( Book2.title, \"Telecom Billing\");\nstrcpy( Book2.author, \"Zara Ali\");\nstrcpy( Book2.subject, \"Telecom Billing Tutorial\");\nBook2.book_id = 6495700;\n\n/* print Book1 info */\nprintBook( Book1 );\n\n/* Print Book2 info */\nprintBook( Book2 );\n\nreturn 0;\n}\n\nvoid printBook( struct Books book ) {\n\nprintf( \"Book title : %s\\n\", book.title);\nprintf( \"Book author : %s\\n\", book.author);\nprintf( \"Book subject : %s\\n\", book.subject);\nprintf( \"Book book_id : %d\\n\", book.book_id);\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nBook title : C Programming\nBook author : Nuha Ali\nBook subject : C Programming Tutorial\nBook book_id : 6495407\nBook title : Telecom Billing\nBook author : Zara Ali\nBook subject : Telecom Billing Tutorial\nBook book_id : 6495700\n\nPointers to Structures\n\nYou can define pointers to structures in the same way as you define pointer to any other variable −\n\nstruct Books *struct_pointer;\n\nNow, you can store the address of a structure variable in the above defined pointer variable. To find the address of a structure variable, place the '&'; operator before the structure's name as follows −\n\nstruct_pointer = &Book1;\n\nTo access the members of a structure using a pointer to that structure, you must use the → operator as follows −\n\nstruct_pointer->title;\n\nLet us re-write the above example using structure pointer.\n\n#include <stdio.h>\n#include <string.h>\n\nstruct Books {\nchar title;\nchar author;\nchar subject;\nint book_id;\n};\n\n/* function declaration */\nvoid printBook( struct Books *book );\nint main( ) {\n\nstruct Books Book1; /* Declare Book1 of type Book */\nstruct Books Book2; /* Declare Book2 of type Book */\n\n/* book 1 specification */\nstrcpy( Book1.title, \"C Programming\");\nstrcpy( Book1.author, \"Nuha Ali\");\nstrcpy( Book1.subject, \"C Programming Tutorial\");\nBook1.book_id = 6495407;\n\n/* book 2 specification */\nstrcpy( Book2.title, \"Telecom Billing\");\nstrcpy( Book2.author, \"Zara Ali\");\nstrcpy( Book2.subject, \"Telecom Billing Tutorial\");\nBook2.book_id = 6495700;\n\n/* print Book1 info by passing address of Book1 */\nprintBook( &Book1 );\n\n/* print Book2 info by passing address of Book2 */\nprintBook( &Book2 );\n\nreturn 0;\n}\n\nvoid printBook( struct Books *book ) {\n\nprintf( \"Book title : %s\\n\", book->title);\nprintf( \"Book author : %s\\n\", book->author);\nprintf( \"Book subject : %s\\n\", book->subject);\nprintf( \"Book book_id : %d\\n\", book->book_id);\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nBook title : C Programming\nBook author : Nuha Ali\nBook subject : C Programming Tutorial\nBook book_id : 6495407\nBook title : Telecom Billing\nBook author : Zara Ali\nBook subject : Telecom Billing Tutorial\nBook book_id : 6495700\n\nBit Fields\n\nBit Fields allow the packing of data in a structure. This is especially useful when memory or data storage is at a premium. Typical examples include −\n\n• Packing several objects into a machine word. e.g. 1 bit flags can be compacted.\n\n• Reading external file formats -- non-standard file formats could be read in, e.g., 9-bit integers.\n\nC allows us to do this in a structure definition by putting :bit length after the variable. For example −\n\nstruct packed_struct {\nunsigned int f1:1;\nunsigned int f2:1;\nunsigned int f3:1;\nunsigned int f4:1;\nunsigned int type:4;\nunsigned int my_int:9;\n} pack;\n\nHere, the packed_struct contains 6 members: Four 1 bit flags f1..f3, a 4-bit type and a 9-bit my_int.\n\nC automatically packs the above bit fields as compactly as possible, provided that the maximum length of the field is less than or equal to the integer word length of the computer. If this is not the case, then some compilers may allow memory overlap for the fields while others would store the next field in the next word.\n\nC - Unions\n\nA union is a special data type available in C that allows to store different data types in the same memory location. You can define a union with many members, but only one member can contain a value at any given time. Unions provide an efficient way of using the same memory location for multiple-purpose.\n\nDefining a Union\n\nTo define a union, you must use the union statement in the same way as you did while defining a structure. The union statement defines a new data type with more than one member for your program. The format of the union statement is as follows −\n\nunion [union tag] {\nmember definition;\nmember definition;\n...\nmember definition;\n} [one or more union variables];\n\nThe union tag is optional and each member definition is a normal variable definition, such as int i; or float f; or any other valid variable definition. At the end of the union's definition, before the final semicolon, you can specify one or more union variables but it is optional. Here is the way you would define a union type named Data having three members i, f, and str −\n\nunion Data {\nint i;\nfloat f;\nchar str;\n} data;\n\nNow, a variable of Data type can store an integer, a floating-point number, or a string of characters. It means a single variable, i.e., same memory location, can be used to store multiple types of data. You can use any built-in or user defined data types inside a union based on your requirement.\n\nThe memory occupied by a union will be large enough to hold the largest member of the union. For example, in the above example, Data type will occupy 20 bytes of memory space because this is the maximum space which can be occupied by a character string. The following example displays the total memory size occupied by the above union −\n\n#include <stdio.h>\n#include <string.h>\n\nunion Data {\nint i;\nfloat f;\nchar str;\n};\n\nint main( ) {\n\nunion Data data;\n\nprintf( \"Memory size occupied by data : %d\\n\", sizeof(data));\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nMemory size occupied by data : 20\n\nAccessing Union Members\n\nTo access any member of a union, we use the member access operator (.). The member access operator is coded as a period between the union variable name and the union member that we wish to access. You would use the keyword union to define variables of union type. The following example shows how to use unions in a program −\n\n#include <stdio.h>\n#include <string.h>\n\nunion Data {\nint i;\nfloat f;\nchar str;\n};\n\nint main( ) {\n\nunion Data data;\n\ndata.i = 10;\ndata.f = 220.5;\nstrcpy( data.str, \"C Programming\");\n\nprintf( \"data.i : %d\\n\", data.i);\nprintf( \"data.f : %f\\n\", data.f);\nprintf( \"data.str : %s\\n\", data.str);\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\ndata.i : 1917853763\ndata.f : 4122360580327794860452759994368.000000\ndata.str : C Programming\n\nHere, we can see that the values of i and f members of union got corrupted because the final value assigned to the variable has occupied the memory location and this is the reason that the value of str member is getting printed very well.\n\nNow let's look into the same example once again where we will use one variable at a time which is the main purpose of having unions −\n\n#include <stdio.h>\n#include <string.h>\n\nunion Data {\nint i;\nfloat f;\nchar str;\n};\n\nint main( ) {\n\nunion Data data;\n\ndata.i = 10;\nprintf( \"data.i : %d\\n\", data.i);\n\ndata.f = 220.5;\nprintf( \"data.f : %f\\n\", data.f);\n\nstrcpy( data.str, \"C Programming\");\nprintf( \"data.str : %s\\n\", data.str);\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\ndata.i : 10\ndata.f : 220.500000\ndata.str : C Programming\n\nHere, all the members are getting printed very well because one member is being used at a time.\n\nC - Bit Fields\n\nSuppose your C program contains a number of TRUE/FALSE variables grouped in a structure called status, as follows −\n\nstruct {\nunsigned int widthValidated;\nunsigned int heightValidated;\n} status;\n\nThis structure requires 8 bytes of memory space but in actual, we are going to store either 0 or 1 in each of the variables. The C programming language offers a better way to utilize the memory space in such situations.\n\nIf you are using such variables inside a structure then you can define the width of a variable which tells the C compiler that you are going to use only those number of bytes. For example, the above structure can be re-written as follows −\n\nstruct {\nunsigned int widthValidated : 1;\nunsigned int heightValidated : 1;\n} status;\n\nThe above structure requires 4 bytes of memory space for status variable, but only 2 bits will be used to store the values.\n\nIf you will use up to 32 variables each one with a width of 1 bit, then also the status structure will use 4 bytes. However as soon as you have 33 variables, it will allocate the next slot of the memory and it will start using 8 bytes. Let us check the following example to understand the concept −\n\n#include <stdio.h>\n#include <string.h>\n\n/* define simple structure */\nstruct {\nunsigned int widthValidated;\nunsigned int heightValidated;\n} status1;\n\n/* define a structure with bit fields */\nstruct {\nunsigned int widthValidated : 1;\nunsigned int heightValidated : 1;\n} status2;\n\nint main( ) {\nprintf( \"Memory size occupied by status1 : %d\\n\", sizeof(status1));\nprintf( \"Memory size occupied by status2 : %d\\n\", sizeof(status2));\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nMemory size occupied by status1 : 8\nMemory size occupied by status2 : 4\n\nBit Field Declaration\n\nThe declaration of a bit-field has the following form inside a structure −\n\nstruct {\ntype [member_name] : width ;\n};\n\nThe following table describes the variable elements of a bit field −\n\nSr.No. Element & Description\n1\n\ntype\n\nAn integer type that determines how a bit-field's value is interpreted. The type may be int, signed int, or unsigned int.\n\n2\n\nmember_name\n\nThe name of the bit-field.\n\n3\n\nwidth\n\nThe number of bits in the bit-field. The width must be less than or equal to the bit width of the specified type.\n\nThe variables defined with a predefined width are called bit fields. A bit field can hold more than a single bit; for example, if you need a variable to store a value from 0 to 7, then you can define a bit field with a width of 3 bits as follows −\n\nstruct {\nunsigned int age : 3;\n} Age;\n\nThe above structure definition instructs the C compiler that the age variable is going to use only 3 bits to store the value. If you try to use more than 3 bits, then it will not allow you to do so. Let us try the following example −\n\n#include <stdio.h>\n#include <string.h>\n\nstruct {\nunsigned int age : 3;\n} Age;\n\nint main( ) {\n\nAge.age = 4;\nprintf( \"Sizeof( Age ) : %d\\n\", sizeof(Age) );\nprintf( \"Age.age : %d\\n\", Age.age );\n\nAge.age = 7;\nprintf( \"Age.age : %d\\n\", Age.age );\n\nAge.age = 8;\nprintf( \"Age.age : %d\\n\", Age.age );\n\nreturn 0;\n}\n\nWhen the above code is compiled it will compile with a warning and when executed, it produces the following result −\n\nSizeof( Age ) : 4\nAge.age : 4\nAge.age : 7\nAge.age : 0\n\nC - typedef\n\nThe C programming language provides a keyword called typedef, which you can use to give a type a new name. Following is an example to define a term BYTE for one-byte numbers −\n\ntypedef unsigned char BYTE;\n\nAfter this type definition, the identifier BYTE can be used as an abbreviation for the type unsigned char, for example..\n\nBYTE b1, b2;\n\nBy convention, uppercase letters are used for these definitions to remind the user that the type name is really a symbolic abbreviation, but you can use lowercase, as follows −\n\ntypedef unsigned char byte;\n\nYou can use typedef to give a name to your user defined data types as well. For example, you can use typedef with structure to define a new data type and then use that data type to define structure variables directly as follows −\n\n#include <stdio.h>\n#include <string.h>\n\ntypedef struct Books {\nchar title;\nchar author;\nchar subject;\nint book_id;\n} Book;\n\nint main( ) {\n\nBook book;\n\nstrcpy( book.title, \"C Programming\");\nstrcpy( book.author, \"Nuha Ali\");\nstrcpy( book.subject, \"C Programming Tutorial\");\nbook.book_id = 6495407;\n\nprintf( \"Book title : %s\\n\", book.title);\nprintf( \"Book author : %s\\n\", book.author);\nprintf( \"Book subject : %s\\n\", book.subject);\nprintf( \"Book book_id : %d\\n\", book.book_id);\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nBook title : C Programming\nBook author : Nuha Ali\nBook subject : C Programming Tutorial\nBook book_id : 6495407\n\ntypedef vs #define\n\n#define is a C-directive which is also used to define the aliases for various data types similar to typedef but with the following differences −\n\n• typedef is limited to giving symbolic names to types only where as #define can be used to define alias for values as well, q., you can define 1 as ONE etc.\n\n• typedef interpretation is performed by the compiler whereas #define statements are processed by the pre-processor.\n\nThe following example shows how to use #define in a program −\n\n#include <stdio.h>\n\n#define TRUE 1\n#define FALSE 0\n\nint main( ) {\nprintf( \"Value of TRUE : %d\\n\", TRUE);\nprintf( \"Value of FALSE : %d\\n\", FALSE);\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nValue of TRUE : 1\nValue of FALSE : 0\n\nC - Input and Output\n\nWhen we say Input, it means to feed some data into a program. An input can be given in the form of a file or from the command line. C programming provides a set of built-in functions to read the given input and feed it to the program as per requirement.\n\nWhen we say Output, it means to display some data on screen, printer, or in any file. C programming provides a set of built-in functions to output the data on the computer screen as well as to save it in text or binary files.\n\nThe Standard Files\n\nC programming treats all the devices as files. So devices such as the display are addressed in the same way as files and the following three files are automatically opened when a program executes to provide access to the keyboard and screen.\n\nStandard File File Pointer Device\nStandard input stdin Keyboard\nStandard output stdout Screen\n\nThe file pointers are the means to access the file for reading and writing purpose. This section explains how to read values from the screen and how to print the result on the screen.\n\nThe getchar() and putchar() Functions\n\nThe int getchar(void) function reads the next available character from the screen and returns it as an integer. This function reads only single character at a time. You can use this method in the loop in case you want to read more than one character from the screen.\n\nThe int putchar(int c) function puts the passed character on the screen and returns the same character. This function puts only single character at a time. You can use this method in the loop in case you want to display more than one character on the screen. Check the following example −\n\n#include <stdio.h>\nint main( ) {\n\nint c;\n\nprintf( \"Enter a value :\");\nc = getchar( );\n\nprintf( \"\\nYou entered: \");\nputchar( c );\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it waits for you to input some text. When you enter a text and press enter, then the program proceeds and reads only a single character and displays it as follows −\n\n\\$./a.out\nEnter a value : this is test\nYou entered: t\n\nThe gets() and puts() Functions\n\nThe char *gets(char *s) function reads a line from stdin into the buffer pointed to by s until either a terminating newline or EOF (End of File).\n\nThe int puts(const char *s) function writes the string 's' and 'a' trailing newline to stdout.\n\nNOTE: Though it has been deprecated to use gets() function, Instead of using gets, you want to use fgets().\n\n#include <stdio.h>\nint main( ) {\n\nchar str;\n\nprintf( \"Enter a value :\");\ngets( str );\n\nprintf( \"\\nYou entered: \");\nputs( str );\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it waits for you to input some text. When you enter a text and press enter, then the program proceeds and reads the complete line till end, and displays it as follows −\n\n\\$./a.out\nEnter a value : this is test\nYou entered: this is test\n\nThe scanf() and printf() Functions\n\nThe int scanf(const char *format, ...) function reads the input from the standard input stream stdin and scans that input according to the format provided.\n\nThe int printf(const char *format, ...) function writes the output to the standard output stream stdout and produces the output according to the format provided.\n\nThe format can be a simple constant string, but you can specify %s, %d, %c, %f, etc., to print or read strings, integer, character or float respectively. There are many other formatting options available which can be used based on requirements. Let us now proceed with a simple example to understand the concepts better −\n\n#include <stdio.h>\nint main( ) {\n\nchar str;\nint i;\n\nprintf( \"Enter a value :\");\nscanf(\"%s %d\", str, &i);\n\nprintf( \"\\nYou entered: %s %d \", str, i);\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it waits for you to input some text. When you enter a text and press enter, then program proceeds and reads the input and displays it as follows −\n\n\\$./a.out\nEnter a value : seven 7\nYou entered: seven 7\n\nHere, it should be noted that scanf() expects input in the same format as you provided %s and %d, which means you have to provide valid inputs like \"string integer\". If you provide \"string string\" or \"integer integer\", then it will be assumed as wrong input. Secondly, while reading a string, scanf() stops reading as soon as it encounters a space, so \"this is test\" are three strings for scanf().\n\nC - File I/O\n\nThe last chapter explained the standard input and output devices handled by C programming language. This chapter cover how C programmers can create, open, close text or binary files for their data storage.\n\nA file represents a sequence of bytes, regardless of it being a text file or a binary file. C programming language provides access on high level functions as well as low level (OS level) calls to handle file on your storage devices. This chapter will take you through the important calls for file management.\n\nOpening Files\n\nYou can use the fopen( ) function to create a new file or to open an existing file. This call will initialize an object of the type FILE, which contains all the information necessary to control the stream. The prototype of this function call is as follows −\n\nFILE *fopen( const char * filename, const char * mode );\n\nHere, filename is a string literal, which you will use to name your file, and access mode can have one of the following values −\n\nSr.No. Mode & Description\n1\n\nr\n\nOpens an existing text file for reading purpose.\n\n2\n\nw\n\nOpens a text file for writing. If it does not exist, then a new file is created. Here your program will start writing content from the beginning of the file.\n\n3\n\na\n\nOpens a text file for writing in appending mode. If it does not exist, then a new file is created. Here your program will start appending content in the existing file content.\n\n4\n\nr+\n\nOpens a text file for both reading and writing.\n\n5\n\nw+\n\nOpens a text file for both reading and writing. It first truncates the file to zero length if it exists, otherwise creates a file if it does not exist.\n\n6\n\na+\n\nOpens a text file for both reading and writing. It creates the file if it does not exist. The reading will start from the beginning but writing can only be appended.\n\nIf you are going to handle binary files, then you will use following access modes instead of the above mentioned ones −\n\n\"rb\", \"wb\", \"ab\", \"rb+\", \"r+b\", \"wb+\", \"w+b\", \"ab+\", \"a+b\"\n\nClosing a File\n\nTo close a file, use the fclose( ) function. The prototype of this function is −\n\nint fclose( FILE *fp );\n\nThe fclose(-) function returns zero on success, or EOF if there is an error in closing the file. This function actually flushes any data still pending in the buffer to the file, closes the file, and releases any memory used for the file. The EOF is a constant defined in the header file stdio.h.\n\nThere are various functions provided by C standard library to read and write a file, character by character, or in the form of a fixed length string.\n\nWriting a File\n\nFollowing is the simplest function to write individual characters to a stream −\n\nint fputc( int c, FILE *fp );\n\nThe function fputc() writes the character value of the argument c to the output stream referenced by fp. It returns the written character written on success otherwise EOF if there is an error. You can use the following functions to write a null-terminated string to a stream −\n\nint fputs( const char *s, FILE *fp );\n\nThe function fputs() writes the string s to the output stream referenced by fp. It returns a non-negative value on success, otherwise EOF is returned in case of any error. You can use int fprintf(FILE *fp,const char *format, ...) function as well to write a string into a file. Try the following example.\n\nMake sure you have /tmp directory available. If it is not, then before proceeding, you must create this directory on your machine.\n\n#include <stdio.h>\n\nmain() {\nFILE *fp;\n\nfp = fopen(\"/tmp/test.txt\", \"w+\");\nfprintf(fp, \"This is testing for fprintf...\\n\");\nfputs(\"This is testing for fputs...\\n\", fp);\nfclose(fp);\n}\n\nWhen the above code is compiled and executed, it creates a new file test.txt in /tmp directory and writes two lines using two different functions. Let us read this file in the next section.\n\nGiven below is the simplest function to read a single character from a file −\n\nint fgetc( FILE * fp );\n\nThe fgetc() function reads a character from the input file referenced by fp. The return value is the character read, or in case of any error, it returns EOF. The following function allows to read a string from a stream −\n\nchar *fgets( char *buf, int n, FILE *fp );\n\nThe functions fgets() reads up to n-1 characters from the input stream referenced by fp. It copies the read string into the buffer buf, appending a null character to terminate the string.\n\nIf this function encounters a newline character '\\n' or the end of the file EOF before they have read the maximum number of characters, then it returns only the characters read up to that point including the new line character. You can also use int fscanf(FILE *fp, const char *format, ...) function to read strings from a file, but it stops reading after encountering the first space character.\n\n#include <stdio.h>\n\nmain() {\n\nFILE *fp;\nchar buff;\n\nfp = fopen(\"/tmp/test.txt\", \"r\");\nfscanf(fp, \"%s\", buff);\nprintf(\"1 : %s\\n\", buff );\n\nfgets(buff, 255, (FILE*)fp);\nprintf(\"2: %s\\n\", buff );\n\nfgets(buff, 255, (FILE*)fp);\nprintf(\"3: %s\\n\", buff );\nfclose(fp);\n\n}\n\nWhen the above code is compiled and executed, it reads the file created in the previous section and produces the following result −\n\n1 : This\n2: is testing for fprintf...\n\n3: This is testing for fputs...\n\nLet's see a little more in detail about what happened here. First, fscanf() read just This because after that, it encountered a space, second call is for fgets() which reads the remaining line till it encountered end of line. Finally, the last call fgets() reads the second line completely.\n\nBinary I/O Functions\n\nThere are two functions, that can be used for binary input and output −\n\nsize_t fread(void *ptr, size_t size_of_elements, size_t number_of_elements, FILE *a_file);\n\nsize_t fwrite(const void *ptr, size_t size_of_elements, size_t number_of_elements, FILE *a_file);\n\nBoth of these functions should be used to read or write blocks of memories - usually arrays or structures.\n\nC - Preprocessors\n\nThe C Preprocessor is not a part of the compiler, but is a separate step in the compilation process. In simple terms, a C Preprocessor is just a text substitution tool and it instructs the compiler to do required pre-processing before the actual compilation. We'll refer to the C Preprocessor as CPP.\n\nAll preprocessor commands begin with a hash symbol (#). It must be the first nonblank character, and for readability, a preprocessor directive should begin in the first column. The following section lists down all the important preprocessor directives −\n\nSr.No. Directive & Description\n1\n\n#define\n\nSubstitutes a preprocessor macro.\n\n2\n\n#include\n\nInserts a particular header from another file.\n\n3\n\n#undef\n\nUndefines a preprocessor macro.\n\n4\n\n#ifdef\n\nReturns true if this macro is defined.\n\n5\n\n#ifndef\n\nReturns true if this macro is not defined.\n\n6\n\n#if\n\nTests if a compile time condition is true.\n\n7\n\n#else\n\nThe alternative for #if.\n\n8\n\n#elif\n\n#else and #if in one statement.\n\n9\n\n#endif\n\nEnds preprocessor conditional.\n\n10\n\n#error\n\nPrints error message on stderr.\n\n11\n\n#pragma\n\nIssues special commands to the compiler, using a standardized method.\n\nPreprocessors Examples\n\nAnalyze the following examples to understand various directives.\n\n#define MAX_ARRAY_LENGTH 20\n\nThis directive tells the CPP to replace instances of MAX_ARRAY_LENGTH with 20. Use #define for constants to increase readability.\n\n#include <stdio.h>\n\nThese directives tell the CPP to get stdio.h from System Libraries and add the text to the current source file. The next line tells CPP to get myheader.h from the local directory and add the content to the current source file.\n\n#undef FILE_SIZE\n#define FILE_SIZE 42\n\nIt tells the CPP to undefine existing FILE_SIZE and define it as 42.\n\n#ifndef MESSAGE\n#define MESSAGE \"You wish!\"\n#endif\n\nIt tells the CPP to define MESSAGE only if MESSAGE isn't already defined.\n\n#ifdef DEBUG\n/* Your debugging statements here */\n#endif\n\nIt tells the CPP to process the statements enclosed if DEBUG is defined. This is useful if you pass the -DDEBUG flag to the gcc compiler at the time of compilation. This will define DEBUG, so you can turn debugging on and off on the fly during compilation.\n\nPredefined Macros\n\nANSI C defines a number of macros. Although each one is available for use in programming, the predefined macros should not be directly modified.\n\nSr.No. Macro & Description\n1\n\n__DATE__\n\nThe current date as a character literal in \"MMM DD YYYY\" format.\n\n2\n\n__TIME__\n\nThe current time as a character literal in \"HH:MM:SS\" format.\n\n3\n\n__FILE__\n\nThis contains the current filename as a string literal.\n\n4\n\n__LINE__\n\nThis contains the current line number as a decimal constant.\n\n5\n\n__STDC__\n\nDefined as 1 when the compiler complies with the ANSI standard.\n\nLet's try the following example −\n\n#include <stdio.h>\n\nint main() {\n\nprintf(\"File :%s\\n\", __FILE__ );\nprintf(\"Date :%s\\n\", __DATE__ );\nprintf(\"Time :%s\\n\", __TIME__ );\nprintf(\"Line :%d\\n\", __LINE__ );\nprintf(\"ANSI :%d\\n\", __STDC__ );\n\n}\n\nWhen the above code in a file test.c is compiled and executed, it produces the following result −\n\nFile :test.c\nDate :Jun 2 2012\nTime :03:36:24\nLine :8\nANSI :1\n\nPreprocessor Operators\n\nThe C preprocessor offers the following operators to help create macros −\n\nThe Macro Continuation (\\) Operator\n\nA macro is normally confined to a single line. The macro continuation operator (\\) is used to continue a macro that is too long for a single line. For example −\n\n#define message_for(a, b) \\\nprintf(#a \" and \" #b \": We love you!\\n\")\n\nThe Stringize (#) Operator\n\nThe stringize or number-sign operator ( '#' ), when used within a macro definition, converts a macro parameter into a string constant. This operator may be used only in a macro having a specified argument or parameter list. For example −\n\n#include <stdio.h>\n\n#define message_for(a, b) \\\nprintf(#a \" and \" #b \": We love you!\\n\")\n\nint main(void) {\nmessage_for(Carole, Debra);\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nCarole and Debra: We love you!\n\nThe Token Pasting (##) Operator\n\nThe token-pasting operator (##) within a macro definition combines two arguments. It permits two separate tokens in the macro definition to be joined into a single token. For example −\n\n#include <stdio.h>\n\n#define tokenpaster(n) printf (\"token\" #n \" = %d\", token##n)\n\nint main(void) {\nint token34 = 40;\ntokenpaster(34);\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\ntoken34 = 40\n\nIt happened so because this example results in the following actual output from the preprocessor −\n\nprintf (\"token34 = %d\", token34);\n\nThis example shows the concatenation of token##n into token34 and here we have used both stringize and token-pasting.\n\nThe Defined() Operator\n\nThe preprocessor defined operator is used in constant expressions to determine if an identifier is defined using #define. If the specified identifier is defined, the value is true (non-zero). If the symbol is not defined, the value is false (zero). The defined operator is specified as follows −\n\n#include <stdio.h>\n\n#if !defined (MESSAGE)\n#define MESSAGE \"You wish!\"\n#endif\n\nint main(void) {\nprintf(\"Here is the message: %s\\n\", MESSAGE);\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nHere is the message: You wish!\n\nParameterized Macros\n\nOne of the powerful functions of the CPP is the ability to simulate functions using parameterized macros. For example, we might have some code to square a number as follows −\n\nint square(int x) {\nreturn x * x;\n}\n\nWe can rewrite above the code using a macro as follows −\n\n#define square(x) ((x) * (x))\n\nMacros with arguments must be defined using the #define directive before they can be used. The argument list is enclosed in parentheses and must immediately follow the macro name. Spaces are not allowed between the macro name and open parenthesis. For example −\n\n#include <stdio.h>\n\n#define MAX(x,y) ((x) > (y) ? (x) : (y))\n\nint main(void) {\nprintf(\"Max between 20 and 10 is %d\\n\", MAX(10, 20));\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nMax between 20 and 10 is 20\n\nA header file is a file with extension .h which contains C function declarations and macro definitions to be shared between several source files. There are two types of header files: the files that the programmer writes and the files that comes with your compiler.\n\nYou request to use a header file in your program by including it with the C preprocessing directive #include, like you have seen inclusion of stdio.h header file, which comes along with your compiler.\n\nIncluding a header file is equal to copying the content of the header file but we do not do it because it will be error-prone and it is not a good idea to copy the content of a header file in the source files, especially if we have multiple source files in a program.\n\nA simple practice in C or C++ programs is that we keep all the constants, macros, system wide global variables, and function prototypes in the header files and include that header file wherever it is required.\n\nInclude Syntax\n\nBoth the user and the system header files are included using the preprocessing directive #include. It has the following two forms −\n\n#include <file>\n\nThis form is used for system header files. It searches for a file named 'file' in a standard list of system directories. You can prepend directories to this list with the -I option while compiling your source code.\n\n#include \"file\"\n\nThis form is used for header files of your own program. It searches for a file named 'file' in the directory containing the current file. You can prepend directories to this list with the -I option while compiling your source code.\n\nInclude Operation\n\nThe #include directive works by directing the C preprocessor to scan the specified file as input before continuing with the rest of the current source file. The output from the preprocessor contains the output already generated, followed by the output resulting from the included file, followed by the output that comes from the text after the #include directive. For example, if you have a header file header.h as follows −\n\nchar *test (void);\n\nand a main program called program.c that uses the header file, like this −\n\nint x;\n\nint main (void) {\nputs (test ());\n}\n\nthe compiler will see the same token stream as it would if program.c read.\n\nint x;\nchar *test (void);\n\nint main (void) {\nputs (test ());\n}\n\nIf a header file happens to be included twice, the compiler will process its contents twice and it will result in an error. The standard way to prevent this is to enclose the entire real contents of the file in a conditional, like this −\n\n#endif\n\nThis construct is commonly known as a wrapper #ifndef. When the header is included again, the conditional will be false, because HEADER_FILE is defined. The preprocessor will skip over the entire contents of the file, and the compiler will not see it twice.\n\nComputed Includes\n\nSometimes it is necessary to select one of the several different header files to be included into your program. For instance, they might specify configuration parameters to be used on different sorts of operating systems. You could do this with a series of conditionals as follows −\n\n#if SYSTEM_1\n# include \"system_1.h\"\n#elif SYSTEM_2\n# include \"system_2.h\"\n#elif SYSTEM_3\n...\n#endif\n\nBut as it grows, it becomes tedious, instead the preprocessor offers the ability to use a macro for the header name. This is called a computed include. Instead of writing a header name as the direct argument of #include, you simply put a macro name there −\n\n#define SYSTEM_H \"system_1.h\"\n...\n#include SYSTEM_H\n\nSYSTEM_H will be expanded, and the preprocessor will look for system_1.h as if the #include had been written that way originally. SYSTEM_H could be defined by your Makefile with a -D option.\n\nC - Type Casting\n\nType casting is a way to convert a variable from one data type to another data type. For example, if you want to store a 'long' value into a simple integer then you can type cast 'long' to 'int'. You can convert the values from one type to another explicitly using the cast operator as follows −\n\n(type_name) expression\n\nConsider the following example where the cast operator causes the division of one integer variable by another to be performed as a floating-point operation −\n\n#include <stdio.h>\n\nmain() {\n\nint sum = 17, count = 5;\ndouble mean;\n\nmean = (double) sum / count;\nprintf(\"Value of mean : %f\\n\", mean );\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nValue of mean : 3.400000\n\nIt should be noted here that the cast operator has precedence over division, so the value of sum is first converted to type double and finally it gets divided by count yielding a double value.\n\nType conversions can be implicit which is performed by the compiler automatically, or it can be specified explicitly through the use of the cast operator. It is considered good programming practice to use the cast operator whenever type conversions are necessary.\n\nInteger Promotion\n\nInteger promotion is the process by which values of integer type \"smaller\" than int or unsigned int are converted either to int or unsigned int. Consider an example of adding a character with an integer −\n\n#include <stdio.h>\n\nmain() {\n\nint i = 17;\nchar c = 'c'; /* ascii value is 99 */\nint sum;\n\nsum = i + c;\nprintf(\"Value of sum : %d\\n\", sum );\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nValue of sum : 116\n\nHere, the value of sum is 116 because the compiler is doing integer promotion and converting the value of 'c' to ASCII before performing the actual addition operation.\n\nUsual Arithmetic Conversion\n\nThe usual arithmetic conversions are implicitly performed to cast their values to a common type. The compiler first performs integer promotion; if the operands still have different types, then they are converted to the type that appears highest in the following hierarchy −", null, "The usual arithmetic conversions are not performed for the assignment operators, nor for the logical operators && and ||. Let us take the following example to understand the concept −\n\n#include <stdio.h>\n\nmain() {\n\nint i = 17;\nchar c = 'c'; /* ascii value is 99 */\nfloat sum;\n\nsum = i + c;\nprintf(\"Value of sum : %f\\n\", sum );\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nValue of sum : 116.000000\n\nHere, it is simple to understand that first c gets converted to integer, but as the final value is double, usual arithmetic conversion applies and the compiler converts i and c into 'float' and adds them yielding a 'float' result.\n\nC - Error Handling\n\nAs such, C programming does not provide direct support for error handling but being a system programming language, it provides you access at lower level in the form of return values. Most of the C or even Unix function calls return -1 or NULL in case of any error and set an error code errno. It is set as a global variable and indicates an error occurred during any function call. You can find various error codes defined in <error.h> header file.\n\nSo a C programmer can check the returned values and can take appropriate action depending on the return value. It is a good practice, to set errno to 0 at the time of initializing a program. A value of 0 indicates that there is no error in the program.\n\nerrno, perror(). and strerror()\n\nThe C programming language provides perror() and strerror() functions which can be used to display the text message associated with errno.\n\n• The perror() function displays the string you pass to it, followed by a colon, a space, and then the textual representation of the current errno value.\n\n• The strerror() function, which returns a pointer to the textual representation of the current errno value.\n\nLet's try to simulate an error condition and try to open a file which does not exist. Here I'm using both the functions to show the usage, but you can use one or more ways of printing your errors. Second important point to note is that you should use stderr file stream to output all the errors.\n\n#include <stdio.h>\n#include <errno.h>\n#include <string.h>\n\nextern int errno ;\n\nint main () {\n\nFILE * pf;\nint errnum;\npf = fopen (\"unexist.txt\", \"rb\");\n\nif (pf == NULL) {\n\nerrnum = errno;\nfprintf(stderr, \"Value of errno: %d\\n\", errno);\nperror(\"Error printed by perror\");\nfprintf(stderr, \"Error opening file: %s\\n\", strerror( errnum ));\n} else {\n\nfclose (pf);\n}\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nValue of errno: 2\nError printed by perror: No such file or directory\nError opening file: No such file or directory\n\nDivide by Zero Errors\n\nIt is a common problem that at the time of dividing any number, programmers do not check if a divisor is zero and finally it creates a runtime error.\n\nThe code below fixes this by checking if the divisor is zero before dividing −\n\n#include <stdio.h>\n#include <stdlib.h>\n\nmain() {\n\nint dividend = 20;\nint divisor = 0;\nint quotient;\n\nif( divisor == 0){\nfprintf(stderr, \"Division by zero! Exiting...\\n\");\nexit(-1);\n}\n\nquotient = dividend / divisor;\nfprintf(stderr, \"Value of quotient : %d\\n\", quotient );\n\nexit(0);\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nDivision by zero! Exiting...\n\nProgram Exit Status\n\nIt is a common practice to exit with a value of EXIT_SUCCESS in case of program coming out after a successful operation. Here, EXIT_SUCCESS is a macro and it is defined as 0.\n\nIf you have an error condition in your program and you are coming out then you should exit with a status EXIT_FAILURE which is defined as -1. So let's write above program as follows −\n\n#include <stdio.h>\n#include <stdlib.h>\n\nmain() {\n\nint dividend = 20;\nint divisor = 5;\nint quotient;\n\nif( divisor == 0) {\nfprintf(stderr, \"Division by zero! Exiting...\\n\");\nexit(EXIT_FAILURE);\n}\n\nquotient = dividend / divisor;\nfprintf(stderr, \"Value of quotient : %d\\n\", quotient );\n\nexit(EXIT_SUCCESS);\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nValue of quotient : 4\n\nC - Recursion\n\nRecursion is the process of repeating items in a self-similar way. In programming languages, if a program allows you to call a function inside the same function, then it is called a recursive call of the function.\n\nvoid recursion() {\nrecursion(); /* function calls itself */\n}\n\nint main() {\nrecursion();\n}\n\nThe C programming language supports recursion, i.e., a function to call itself. But while using recursion, programmers need to be careful to define an exit condition from the function, otherwise it will go into an infinite loop.\n\nRecursive functions are very useful to solve many mathematical problems, such as calculating the factorial of a number, generating Fibonacci series, etc.\n\nNumber Factorial\n\nThe following example calculates the factorial of a given number using a recursive function −\n\n#include <stdio.h>\n\nunsigned long long int factorial(unsigned int i) {\n\nif(i <= 1) {\nreturn 1;\n}\nreturn i * factorial(i - 1);\n}\n\nint main() {\nint i = 12;\nprintf(\"Factorial of %d is %d\\n\", i, factorial(i));\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\nFactorial of 12 is 479001600\n\nFibonacci Series\n\nThe following example generates the Fibonacci series for a given number using a recursive function −\n\n#include <stdio.h>\n\nint fibonacci(int i) {\n\nif(i == 0) {\nreturn 0;\n}\n\nif(i == 1) {\nreturn 1;\n}\nreturn fibonacci(i-1) + fibonacci(i-2);\n}\n\nint main() {\n\nint i;\n\nfor (i = 0; i < 10; i++) {\nprintf(\"%d\\t\\n\", fibonacci(i));\n}\n\nreturn 0;\n}\n\nWhen the above code is compiled and executed, it produces the following result −\n\n0\n1\n1\n2\n3\n5\n8\n13\n21\n34\n\nC - Variable Arguments\n\nSometimes, you may come across a situation, when you want to have a function, which can take variable number of arguments, i.e., parameters, instead of predefined number of parameters. The C programming language provides a solution for this situation and you are allowed to define a function which can accept variable number of parameters based on your requirement. The following example shows the definition of such a function.\n\nint func(int, ... ) {\n.\n.\n.\n}\n\nint main() {\nfunc(1, 2, 3);\nfunc(1, 2, 3, 4);\n}\n\nIt should be noted that the function func() has its last argument as ellipses, i.e. three dotes (...) and the one just before the ellipses is always an int which will represent the total number variable arguments passed. To use such functionality, you need to make use of stdarg.h header file which provides the functions and macros to implement the functionality of variable arguments and follow the given steps −\n\n• Define a function with its last parameter as ellipses and the one just before the ellipses is always an int which will represent the number of arguments.\n\n• Create a va_list type variable in the function definition. This type is defined in stdarg.h header file.\n\n• Use int parameter and va_start macro to initialize the va_list variable to an argument list. The macro va_start is defined in stdarg.h header file.\n\n• Use va_arg macro and va_list variable to access each item in argument list.\n\n• Use a macro va_end to clean up the memory assigned to va_list variable.\n\nNow let us follow the above steps and write down a simple function which can take the variable number of parameters and return their average −\n\n#include <stdio.h>\n#include <stdarg.h>\n\ndouble average(int num,...) {\n\nva_list valist;\ndouble sum = 0.0;\nint i;\n\n/* initialize valist for num number of arguments */\nva_start(valist, num);\n\n/* access all the arguments assigned to valist */\nfor (i = 0; i < num; i++) {\nsum += va_arg(valist, int);\n}\n\n/* clean memory reserved for valist */\nva_end(valist);\n\nreturn sum/num;\n}\n\nint main() {\nprintf(\"Average of 2, 3, 4, 5 = %f\\n\", average(4, 2,3,4,5));\nprintf(\"Average of 5, 10, 15 = %f\\n\", average(3, 5,10,15));\n}\n\nWhen the above code is compiled and executed, it produces the following result. It should be noted that the function average() has been called twice and each time the first argument represents the total number of variable arguments being passed. Only ellipses will be used to pass variable number of arguments.\n\nAverage of 2, 3, 4, 5 = 3.500000\nAverage of 5, 10, 15 = 10.000000\n\nC - Memory Management\n\nThis chapter explains dynamic memory management in C. The C programming language provides several functions for memory allocation and management. These functions can be found in the <stdlib.h> header file.\n\nSr.No. Function & Description\n1\n\nvoid *calloc(int num, int size);\n\nThis function allocates an array of num elements each of which size in bytes will be size.\n\n2\n\nThis function releases a block of memory block specified by address.\n\n3\n\nvoid *malloc(size_t size);\n\nThis function allocates an array of num bytes and leave them uninitialized.\n\n4\n\nThis function re-allocates memory extending it upto newsize.\n\nAllocating Memory Dynamically\n\nWhile programming, if you are aware of the size of an array, then it is easy and you can define it as an array. For example, to store a name of any person, it can go up to a maximum of 100 characters, so you can define something as follows −\n\nchar name;\n\nBut now let us consider a situation where you have no idea about the length of the text you need to store, for example, you want to store a detailed description about a topic. Here we need to define a pointer to character without defining how much memory is required and later, based on requirement, we can allocate memory as shown in the below example −\n\n#include <stdio.h>\n#include <stdlib.h>\n#include <string.h>\n\nint main() {\n\nchar name;\nchar *description;\n\nstrcpy(name, \"Zara Ali\");\n\n/* allocate memory dynamically */\ndescription = malloc( 200 * sizeof(char) );\n\nif( description == NULL ) {\nfprintf(stderr, \"Error - unable to allocate required memory\\n\");\n} else {\nstrcpy( description, \"Zara ali a DPS student in class 10th\");\n}\n\nprintf(\"Name = %s\\n\", name );\nprintf(\"Description: %s\\n\", description );\n}\n\nWhen the above code is compiled and executed, it produces the following result.\n\nName = Zara Ali\nDescription: Zara ali a DPS student in class 10th\n\nSame program can be written using calloc(); only thing is you need to replace malloc with calloc as follows −\n\ncalloc(200, sizeof(char));\n\nSo you have complete control and you can pass any size value while allocating memory, unlike arrays where once the size defined, you cannot change it.\n\nResizing and Releasing Memory\n\nWhen your program comes out, operating system automatically release all the memory allocated by your program but as a good practice when you are not in need of memory anymore then you should release that memory by calling the function free().\n\nAlternatively, you can increase or decrease the size of an allocated memory block by calling the function realloc(). Let us check the above program once again and make use of realloc() and free() functions −\n\n#include <stdio.h>\n#include <stdlib.h>\n#include <string.h>\n\nint main() {\n\nchar name;\nchar *description;\n\nstrcpy(name, \"Zara Ali\");\n\n/* allocate memory dynamically */\ndescription = malloc( 30 * sizeof(char) );\n\nif( description == NULL ) {\nfprintf(stderr, \"Error - unable to allocate required memory\\n\");\n} else {\nstrcpy( description, \"Zara ali a DPS student.\");\n}\n\n/* suppose you want to store bigger description */\ndescription = realloc( description, 100 * sizeof(char) );\n\nif( description == NULL ) {\nfprintf(stderr, \"Error - unable to allocate required memory\\n\");\n} else {\nstrcat( description, \"She is in class 10th\");\n}\n\nprintf(\"Name = %s\\n\", name );\nprintf(\"Description: %s\\n\", description );\n\n/* release memory using free() function */\nfree(description);\n}\n\nWhen the above code is compiled and executed, it produces the following result.\n\nName = Zara Ali\nDescription: Zara ali a DPS student.She is in class 10th\n\nYou can try the above example without re-allocating extra memory, and strcat() function will give an error due to lack of available memory in description.\n\nC - Command Line Arguments\n\nIt is possible to pass some values from the command line to your C programs when they are executed. These values are called command line arguments and many times they are important for your program especially when you want to control your program from outside instead of hard coding those values inside the code.\n\nThe command line arguments are handled using main() function arguments where argc refers to the number of arguments passed, and argv[] is a pointer array which points to each argument passed to the program. Following is a simple example which checks if there is any argument supplied from the command line and take action accordingly −\n\n#include <stdio.h>\n\nint main( int argc, char *argv[] ) {\n\nif( argc == 2 ) {\nprintf(\"The argument supplied is %s\\n\", argv);\n}\nelse if( argc > 2 ) {\nprintf(\"Too many arguments supplied.\\n\");\n}\nelse {\nprintf(\"One argument expected.\\n\");\n}\n}\n\nWhen the above code is compiled and executed with single argument, it produces the following result.\n\n\\$./a.out testing\nThe argument supplied is testing\n\nWhen the above code is compiled and executed with a two arguments, it produces the following result.\n\n\\$./a.out testing1 testing2\nToo many arguments supplied.\n\nWhen the above code is compiled and executed without passing any argument, it produces the following result.\n\n\\$./a.out\nOne argument expected\n\nIt should be noted that argv holds the name of the program itself and argv is a pointer to the first command line argument supplied, and *argv[n] is the last argument. If no arguments are supplied, argc will be one, and if you pass one argument then argc is set at 2.\n\nYou pass all the command line arguments separated by a space, but if argument itself has a space then you can pass such arguments by putting them inside double quotes \"\" or single quotes ''. Let us re-write above example once again where we will print program name and we also pass a command line argument by putting inside double quotes −\n\n#include <stdio.h>\n\nint main( int argc, char *argv[] ) {\n\nprintf(\"Program name %s\\n\", argv);\n\nif( argc == 2 ) {\nprintf(\"The argument supplied is %s\\n\", argv);\n}\nelse if( argc > 2 ) {\nprintf(\"Too many arguments supplied.\\n\");\n}\nelse {\nprintf(\"One argument expected.\\n\");\n}\n}\n\nWhen the above code is compiled and executed with a single argument separated by space but inside double quotes, it produces the following result.\n\n\\$./a.out \"testing1 testing2\"\n\nProgranm name ./a.out\nThe argument supplied is testing1 testing2" ]
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https://papers.nips.cc/paper_files/paper/2011/hash/58c54802a9fb9526cd0923353a34a7ae-Abstract.html
[ "#### Authors\n\nPablo Olmos, Luis Salamanca, Juan Fuentes, Fernando Pérez-Cruz\n\n#### Abstract\n\nWe show an application of a tree structure for approximate inference in graphical models using the expectation propagation algorithm. These approximations are typically used over graphs with short-range cycles. We demonstrate that these approximations also help in sparse graphs with long-range loops, as the ones used in coding theory to approach channel capacity. For asymptotically large sparse graph, the expectation propagation algorithm together with the tree structure yields a completely disconnected approximation to the graphical model but, for for finite-length practical sparse graphs, the tree structure approximation to the code graph provides accurate estimates for the marginal of each variable." ]
[ null ]
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https://npg.copernicus.org/articles/29/265/2022/npg-29-265-2022.html
[ "Nonlin. Processes Geophys., 29, 265–277, 2022\nhttps://doi.org/10.5194/npg-29-265-2022\nNonlin. Processes Geophys., 29, 265–277, 2022\nhttps://doi.org/10.5194/npg-29-265-2022\nResearch article | 05 Jul 2022", null, "# Empirical adaptive wavelet decomposition (EAWD): an adaptive decomposition for the variability analysis of observation time series in atmospheric science\n\nEmpirical adaptive wavelet decomposition (EAWD): an adaptive decomposition for the variability analysis of observation time series in atmospheric science\nOlivier Delage1, Thierry Portafaix1, Hassan Bencherif1,2, Alain Bourdier3, and Emma Lagracie1,4 Olivier Delage et al.\n• 1Laboratoire de l'Atmosphère et des Cyclones, (LACy, UMR 8105 CNRS, Université de la Réunion, Météo-France), Université de La Réunion, 97400 Saint-Denis de La Réunion, France\n• 2School of Chemistry and Physics, University of KwaZulu-Natal, Westville, Durban 4041, South Africa\n• 3Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA\n• 4École Nationale Supérieure des Techniques Avancées, 91120, Palaiseau, France\n\nCorrespondence: Olivier Delage (olivier.delage@univ-reunion.fr)\n\nAbstract\n\nMost observational data sequences in geophysics can be interpreted as resulting from the interaction of several physical processes at several timescales and space scales. In consequence, measurement time series often have characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at different timescales. The application of decomposition methods is an important step in the analysis of time series variability, allowing patterns and behaviour to be extracted as components providing insight into the mechanisms producing the time series. This study introduces empirical adaptive wavelet decomposition (EAWD), a new adaptive method for decomposing non-linear and non-stationary time series into multiple empirical modes with non-overlapping spectral contents. The method takes its origin from the coupling of two widely used decomposition techniques: empirical mode decomposition (EMD) and empirical wavelet transformation (EWT). It thus combines the advantages of both methods and can be interpreted as an optimization of EMD. Here, through experimental time series applications, EAWD is shown to accurately retrieve different physically meaningful components concealed in the original signal.\n\nShare\n1 Introduction\n\nMost geophysical systems are complex and the variability of the corresponding observation time series is characterized by large fluctuations at different timescales. To analyse these fluctuations and the associated multi-scale dynamics, some specific methods have been developed. Empirical mode decomposition (EMD) is part of a more general signal processing method called the Hilbert–Huang transform (Huang et al., 1998) and consists in decomposing a signal in a self-adaptive way into a sum of oscillating components named IMFs (intrinsic mode functions). Each IMF captures the repeating signal behaviour at some particular timescale. Like the wavelet transform, the EMD techniques reduce a time signal to a set of basis signals; unlike the wavelet transform, the basic functions are derived from the signal itself. The main advantages of the EMD method are that it is fully adaptive, data-driven, and, indeed, close to the observed dynamics. As the EMD acts as a bank of bandpass filters (Flandrin et al., 2004), the main limiting factor is the frequency resolution, which may give rise to the mode-mixing phenomenon where the spectral contents of some IMFs overlap each other (Gao et al., 2008).\n\nAlthough several techniques exist to overcome this problem (Fosso and Molinas, 2017; Delage et al., 2019), Gilles (2013) proposed an alternative entitled empirical wavelet transform (EWT), which builds a wavelet filter bank from the segmentation of the original signal's Fourier spectrum. This approach is similar to that used in the construction of both Littlewood–Paley and Meyers wavelets (Meyer, 1997). The heart of the EWT method is the segmentation of the Fourier spectrum based on the detection of local maxima in order to obtain a set of non-overlapping segments. Because it is linked to the Fourier spectrum, the frequency resolution provided by the EWT is higher than that provided by the EMD and therefore allows the mode-mixing problem to be overcome. Although the EWT technique enables detection of the relevant frequencies involved in the original time series fluctuations, such a technique does not enable the detected frequencies to be associated with a specific mode of variability as EMD does. Because the EMD is closer to the observed dynamics than EWT, in the present work, we developed a new approach called EAWD (empirical adaptive wavelet decomposition) based on the coupling of the EMD and EWT techniques. We use the spectral content of the IMFs retrieved by EMD to optimize the segmentation of the original time series Fourier spectrum required by EWT. This document is structured around four sections. The first section is devoted to the EMD and EWT techniques. In the second one, the new adaptive decomposition EAWD is described and it is explained why such a method can be considered to be an optimization of the EMD. In the third section, two observation time series are analysed by using EMD and EAWD techniques, and the corresponding results are presented. Finally, the results obtained respectively with the EMD and EAWD techniques are compared and discussed.\n\n2 The existing approaches\n\n## 2.1 EMD\n\nHuang et al. (1998) proposed an original method called EMD, which adaptively decomposes any signal into oscillatory contributions. In a nutshell, EMD can be summarized as an iterative method where the signal is considered the superimposition of high- and low-frequency oscillations. At each iteration, high-frequency oscillation components are separated from the low-frequency oscillations and then re-injected as a new signal in the following iteration. The EMD is thus directly controlled by the signal itself and not by some filtering operations as in the wavelet decomposition. More precisely, the decomposition is carried out at the scale of local oscillations, the low-frequency modes being obtained as the mean value of an upper and a lower envelope computed as cubic spline interpolations between maxima and minima respectively. By subtracting this component from the original signal, we obtain what is called an IMF. The procedure is then applied to the low-frequency part as a new signal to be decomposed and successive oscillatory components are iteratively extracted from the original signal. The original time series x(t) can finally be expressed as the sum of a finite number, N, of IMFs and a residual term, R, which cannot be assimilated to an oscillation.\n\n$\\begin{array}{}\\text{(1)}& x\\left(t\\right)={\\sum }_{i=\\mathrm{1}}^{N}{\\text{IMF}}_{i}\\left(t\\right)+R\\left(t\\right)\\end{array}$\n\nThe interesting fact about this algorithm is that it is highly adaptable and is able to extract the non-stationary part of the original signal. However, in practice, the EMD technique presents some limiting factors. For example, some problems appear when a certain amount of noise is present in the signal. To deal with this problem, Wu and Wang (2009) introduced an EMD optimization entitled ensemble empirical-mode decomposition (EEMD). The principle behind EEMD is to average the modes obtained by EMD after several realizations of Gaussian white noise that are added to the original signal. This approach seems to stabilize the decomposition obtained.\n\n## 2.2 Wavelet approaches\n\nWavelets are commonly used to analyse the variability of a signal. In the temporal domain, a wavelet basis is defined as the mother wavelet ψ of zero mean, dilated with a parameter s>0 and translated by uR:\n\n$\\begin{array}{}\\text{(2)}& {\\mathit{\\psi }}_{u,s}\\left(t\\right)=\\frac{\\mathrm{1}}{\\sqrt{s}}\\mathit{\\psi }\\left(\\frac{t-u}{s}\\right).\\end{array}$\n\nFor the wavelet decomposition of a time series x(ti), the most widely used case is the dyadic one, s=2j. Then the wavelet decomposition of x is obtained by computing the inner products Wx(kj) as\n\n$\\begin{array}{}\\text{(3)}& \\begin{array}{rl}& {W}_{x}\\left(k,j\\right)=〈x,{\\mathit{\\psi }}_{k,j}〉,\\\\ & \\text{with}\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}{\\mathit{\\psi }}_{k,j}\\left(t\\right)=\\frac{\\mathrm{1}}{\\sqrt{{\\mathrm{2}}^{j}}}\\mathit{\\psi }\\left(\\frac{t-k}{{\\mathrm{2}}^{j}}\\right),\\phantom{\\rule{0.25em}{0ex}}k\\in Z\\phantom{\\rule{0.125em}{0ex}},\\end{array}\\end{array}$\n\nwhere j represents the resolution level. The decomposition is then similar to a multi-resolution analysis carrying out successive projections of x on a sequence of nested subspaces ${V}_{j}\\in {L}^{\\mathrm{2}}\\left(R\\right)j=\\left[\\mathrm{0},n\\right]$, which leads to increasingly coarse approximations of x as j increases. The difference between two successive approximations, resulting from projections of x on Vj−1 and Vj, contains the information of “details”, which existed at the scale 2j−1 but which is lost at the scale 2j. This information is contained in the subspace Wj orthogonal to Vj such that ${V}_{j-\\mathrm{1}}={V}_{j}\\oplus {W}_{j}$, where denotes the direct sum of vector subspaces. The orthogonal projection of x on Wj gives the information of “details” at the resolution level j. Wavelets $\\left\\{{\\mathit{\\psi }}_{k,j}\\left(t\\right),k\\in Z\\right\\}$ form a basis of Wj. According to the definition of a multi-resolution analysis, there exists a function ϕ(t), called a scaling function, such that $\\left\\{\\mathit{\\phi }\\left(t-k\\right),k\\in Z\\right\\}$ form a basis of V0 corresponding to the coarsest approximation of x. The reconstruction of x is obtained from\n\n$\\begin{array}{}\\text{(4)}& x\\left(t\\right)=〈x\\left(t\\right),\\mathit{\\phi }\\left(t\\right)〉\\cdot \\mathit{\\phi }\\left(t\\right)+{\\sum }_{j=\\mathrm{1}}^{N}〈x\\left(t\\right),{\\mathit{\\psi }}_{k,j}\\left(t\\right)〉\\cdot {\\mathit{\\psi }}_{k,j}\\left(t\\right)\\phantom{\\rule{0.125em}{0ex}},\\end{array}$\n\nwhere 〈 〉 represents the inner products. The approximation coefficients corresponding to the coarsest resolution level are given by x,φ and the detail coefficients corresponding to the successively decreasing resolution level are given by $〈x,{\\mathit{\\psi }}_{k,j}〉$ as follows:\n\n$\\begin{array}{}\\text{(5)}& \\begin{array}{rl}& 〈x\\left(t\\right),\\mathit{\\psi }\\left(t\\right)〉=\\int x\\left(\\mathit{\\tau }\\right)\\stackrel{\\mathrm{‾}}{\\mathit{\\phi }\\left(\\mathit{\\tau }-t\\right)}\\mathrm{d}\\mathit{\\tau }\\phantom{\\rule{0.125em}{0ex}},\\\\ & 〈x\\left(t\\right),{\\mathit{\\psi }}_{k,j}\\left(t\\right)〉=\\int x\\left(\\mathit{\\tau }\\right)\\stackrel{\\mathrm{‾}}{{\\mathit{\\psi }}_{k,j}\\left(\\mathit{\\tau }-t\\right)}\\mathrm{d}\\mathit{\\tau }\\phantom{\\rule{0.125em}{0ex}}.\\end{array}\\end{array}$\n\n## 2.3 Empirical wavelets – EWT\n\nThe essence of EMD is that the functions into which a signal is decomposed are all in the time domain have the same length as the original signal, allowing time-varying frequencies to be preserved. In this context, Flandrin et al. (2004) described the EMD as behaving as a dyadic filter bank like those involved in the multi-resolution analysis. This can be interpreted as the presence of several filters of overlapping frequency content that may give rise to the mode-mixing phenomenon, which is defined as a single IMF consisting either of widely disparate scales or of similar scales residing in different IMFs. In that case, the spectral contents of some IMFs overlap each other. To overcome this problem, Gilles (2013) proposed an alternative named the EWT. As the EMD technique acts as a filter bank in the spectral domain, the method proposed by Gilles (2013) designs an appropriate wavelet filter bank from the segmentation of the original signal's Fourier spectrum. The Fourier support [0,π] is segmented into N contiguous segments denoted ${\\mathrm{\\Delta }}_{n}=\\left[{\\mathit{\\omega }}_{n-\\mathrm{1}},{\\mathit{\\omega }}_{n}\\right]$.\n\nThe filter bank (Meyer, 1997; Jaffard et al., 2001) is defined by the empirical scaling function and the empirical wavelets on each Δn through Eqs. (6) and (7) respectively:\n\nThe function β(x) is an arbitrary Ck([0,1]) function defined as\n\nMany functions satisfy this property, and the one most used in the literature (Daubechies, 1992) is\n\n$\\begin{array}{}\\text{(9)}& \\mathit{\\beta }\\left(x\\right)={x}^{\\mathrm{4}}\\left(\\mathrm{35}-\\mathrm{84}x+\\mathrm{70}{x}^{\\mathrm{2}}-\\mathrm{20}{x}^{\\mathrm{3}}\\right).\\end{array}$\n\nThe parameter γ is chosen to satisfy the following criterion:\n\n$\\begin{array}{}\\text{(10)}& \\mathit{\\gamma }<{\\text{Min}}_{n}\\left(\\frac{{\\mathit{\\omega }}_{n+\\mathrm{1}}-{\\mathit{\\omega }}_{n}}{{\\mathit{\\omega }}_{n+\\mathrm{1}}+{w}_{n}}\\right).\\end{array}$\n\nThe details and approximation coefficients are calculated by using Eqs. (6) and (7) and are respectively given by inner products with the empirical wavelets ψn and the scaling function ϕ1\n\n$\\begin{array}{}\\text{(11)}& {W}_{x}\\left(n,t\\right)=〈x\\left(t\\right),{\\mathit{\\psi }}_{n}〉=\\text{IFFT}\\left(X\\left(\\mathit{\\omega }\\right)\\cdot \\stackrel{\\mathrm{‾}}{\\stackrel{\\mathrm{^}}{{\\mathit{\\psi }}_{n}}\\left(\\mathit{\\omega }\\right)}\\right)\\phantom{\\rule{0.125em}{0ex}},\\text{(12)}& {W}_{x}\\left(\\mathrm{1},t\\right)=〈x\\left(t\\right),{\\mathit{\\varphi }}_{\\mathrm{1}}〉=\\text{IFFT}\\left(X\\left(\\mathit{\\omega }\\right)\\stackrel{\\mathrm{‾}}{\\stackrel{\\mathrm{^}}{{\\mathit{\\phi }}_{\\mathrm{1}}}\\left(\\mathit{\\omega }\\right)}\\right)\\phantom{\\rule{0.125em}{0ex}},\\end{array}$\n\nwhere X is the Fourier transform of the original signal x, ${}^{\\stackrel{\\mathrm{‾}}{\\phantom{\\rule{0.25em}{0ex}}}}$ represents the complex conjugate, IFFT represents the inverse Fourier transform, and ψn and ϕ1 are the results of the inverse Fourier transforms of $\\stackrel{\\mathrm{^}}{{\\mathit{\\psi }}_{n}}$ and $\\stackrel{\\mathrm{^}}{{\\mathit{\\varphi }}_{\\mathrm{1}}}$ respectively.\n\nThe heart of the empirical wavelet transform is the segmentation of the original signal's Fourier spectrum. In order to obtain a set of non-overlapping segments, the Fourier spectrum local maxima are detected. Each segment is centred around a group of one or more local maxima. The limit between two contiguous segments, each of them characterized by a group of local maxima, is determined as the local minimum closest to the midpoint between the two local maximum groups. Many of the detected local maxima are irrelevant as their contributions to the variability of the original time series are negligible. Selecting the relevant local maxima requires the setting of a threshold, which is not always possible.\n\n3 The empirical adaptive wavelet decomposition (EAWD)\n\nThe EMD enables an observation data sequence to be decomposed into multiple empirical modes of variability, each of them reflecting the observed dynamics at a specific timescale. However, in some cases, the frequency resolution provided by EMD does not allow IMFs with disjoint spectral support to be retrieved.\n\nThe adaptive wavelet transform (EWT) is one of several interesting methods pursuing the same goal as EMD, which allows the mode-mixing problem to be overcome. This method relies on robust pre-processing for peak detection, then performs original signal Fourier spectrum segmentation based on detected maxima, and then constructs a corresponding wavelet filter bank.\n\nThe main idea of the proposed EAWD method is to combine EMD and EWT techniques by setting non-overlapping groups of local maxima from the spectral contents of the IMFs returned by the EMD technique.\n\nEach IMF local maximum group will be associated with a segment of the original signal Fourier spectrum segmentation. The boundaries of each of these segments will be set as the local minima located between local maximum groups of two consecutive IMFs. As the EMD acts like a bank of dyadic band-pass filters, the result of each of these filters, in the frequency domain, is composed of a set of local maxima relative to a specific timescale in which the resolution is divided by 2 in comparison with the timescale immediately above it. Considering that a timescale is characterized by the set of values in the range of $\\left[{\\mathrm{2}}^{n},{\\mathrm{2}}^{n+\\mathrm{1}}\\right]$, to carry out a segmentation of the Fourier spectrum, it is necessary to distribute the local maximum groups relative to a grid $\\left[{\\mathrm{2}}^{i},{\\mathrm{2}}^{i+\\mathrm{1}}\\right]$, $i\\in \\left[\\mathrm{2},J\\right]$ with $J=\\text{int}\\left(\\frac{\\mathrm{log}\\left(N\\right)}{\\mathrm{log}\\left(\\mathrm{2}\\right)}\\right)-\\mathrm{1}$, where N is the size of the original time series.\n\nThe proposed Fourier spectrum segmentation algorithm is based on two main points.\n\n1. The spectrum of two consecutive IMFs contains at most two different dominant frequencies. Relative to the spectral content of an IMF, the frequency with the greatest spectral density is called the dominant frequency.\n\n2. The local maximum list of the spectra of two consecutive IMFs is subdivided into three groups: the local maxima belonging to the IMFi spectrum, ML1, the local maxima belonging to the intersection of IMFi and IMFi+1 spectra, MLINTER, and the local maxima belonging to the IMFi+1 spectrum, ML2.\n\nThe proposed EAWD algorithm is composed of three steps as described in the diagrams below (see Figs. 1–3).", null, "Figure 1Estimation of the spectral density for each IMF spectrum and selection of significant local maxima whose energy contribution >1 %.", null, "Figure 2Calculation of the MLTAB matrix. Each row of MLTAB contains the list of significant local maxima present in the spectrum of an IMF. The rows of MLTAB have no common elements, and therefore MLTAB can be seen as a set of non-overlapping local maximum groups and represents a segmentation of the original signal Fourier spectrum.", null, "Figure 3Calculation of the BOUNDARY vector representing the boundaries between the local maximum groups contained in the MLTAB matrix. The EWT technique is run from BOUNDARY.\n\n“Size” represents the length of list1 and “cut” is the boundary between two consecutive local maximum groups MLi and MLi+1.\n\nThe parameter k can be interpreted as the ratio between the number of scales contained in list1 and the number of scales in the interval [fdi, fdi+1] of two consecutive dominant frequencies.\n\n4 Time series analysis and results\n\nThe EMD and EAWD techniques presented above have been applied to two experimental time series of observations. The first time series was a series of monthly total columns of ozone (TCO) in Dobson units (DU), recorded over 41 years, from January 1979 to December 2019, by a SAOZ (Zenithal Observation Analysis System) spectrometer on the Moufia University Campus, Saint-Denis, Réunion (21 S, 55.5 E).\n\nThis TCO time series was elaborated by merging satellite data (OMI and TOMS) and ground-based observations recorded by a SAOZ spectrometer (Pommereau and Goutail, 1988) installed in Saint-Denis, Réunion, in 1993. The method used for merging satellite and ground data to obtain a homogeneous series is explained in Pastel et al. (2014).\n\nDespite its low abundance, ozone plays an important role in the Earth's atmosphere. It is mainly produced in the tropical stratosphere and transported to higher latitudes by the large-scale circulation called the Brewer–Dobson circulation. In the stratosphere, ozone acts like a filter and prevents incident solar ultraviolet (UV) radiation from reaching the ground, thus protecting the biosphere. The significant depletion of the ozone layer since the late 1970s has revealed the importance of ozone in the climate system and the associated environmental and health risks. The TCO is a parameter that measures the abundance of ozone over a given location. It is given in DU and consists of ∼90 % stratospheric ozone and ∼10 % tropospheric ozone.\n\nThe second time series comprised 57 years of monthly rainfall measurements recorded at the Conakry (Guinea) meteorological station from 1961 to 2017.\n\nThe resulting original time series of total ozone columns and rainfall measurements are displayed in Figs. 4 and 5 respectively.", null, "Figure 4Monthly time series of total ozone columns in Dobson units (DU) over Réunion from 1979 to 2019. The time axis is expressed in years.", null, "Figure 5Monthly rainfall record time series recorded in Conakry (Guinea) from 1960 to 2019. The time axis is expressed in years.\n\nVery often, noise is present in the original time series. To deal with this problem, the authors suggest computing an EEMD (Wu and Wang, 2009). This approach seems to reduce the noise present in the original signal. Generally, some of the IMFs returned by the EEMD technique present poor correlations with the original signal and therefore make a weak contribution to the variability of the original series. Such IMFs are qualified as irrelevant. Relevant IMFs are discriminated from the irrelevant ones by means of two criteria. The first of these criteria uses Pearson's correlation to estimate the degree of correlation of each IMF with the original signal by setting a threshold. A threshold commonly used in the literature (Ayenu-Prah and Attoh-Okine, 2010) can be expressed as:\n\n$\\begin{array}{}\\text{(13)}& \\mathit{\\tau }=\\frac{max\\left(\\text{Cor}\\left({\\text{IMF}}_{i},x\\right)\\right)}{\\left(\\mathrm{10}×max\\left(\\text{Cor}\\left({\\text{IMF}}_{i},x\\right)\\right)\\right)-\\mathrm{3}}.\\end{array}$\n\nIn Eq. (13), Cor(IMFi,x) stands for the Pearson correlation coefficient between the ith IMF and the original signal x(t), i.e.\n\n$\\begin{array}{}\\text{(14)}& \\text{Cor}\\left({\\text{IMF}}_{i},x\\right)=\\frac{\\text{Cov}\\left({\\text{IMF}}_{i},x\\right)}{\\text{SD}\\left({\\text{IMF}}_{i}\\right)×\\text{SD}\\left(x\\right)}\\phantom{\\rule{0.125em}{0ex}},\\end{array}$\n\nwhere SD represents the standard deviation and Cov the covariance.\n\nThe second criterion determines the energy contribution of each IMF compared with the energy contained in the original signal. The energy contribution of each IMF is calculated as a percentage as follows:\n\n$\\begin{array}{}\\text{(15)}& \\text{CENR}=\\left(\\frac{{E}_{i}}{{E}_{x}}\\right)×\\mathrm{100}=\\frac{\\text{var}\\left({\\text{IMF}}_{i}\\right)}{\\text{var}\\left(x-\\stackrel{\\mathrm{‾}}{x}\\right)}×\\mathrm{100}\\phantom{\\rule{0.125em}{0ex}},\\end{array}$\n\nwhere ${E}_{i}={\\sum }_{\\mathrm{1}}^{N}{\\text{IMF}}_{i}^{\\mathrm{2}}\\left(t\\right)=\\text{var}\\left({\\text{IMF}}_{i}\\right)$ because each IMF is a zero-mean function by construction. ${E}_{x}={\\sum }_{\\mathrm{1}}^{N}{x}^{\\mathrm{2}}\\left(t\\right)=\\text{var}\\left(x-\\stackrel{\\mathrm{‾}}{x}\\right)$.\n\nThe threshold set for this second criterion is 1 %.\n\nIMFs with a degree of correlation less than τ and for which the energy contribution is less than 1 % are said to be irrelevant. The irrelevant IMFs are added to the residual mode R returned by the EEMD to form the trend of the original signal. For such IMFs to be part of the trend of the observed dynamics, they must not be too oscillating and are therefore contiguous to the residue.\n\nWhen EEMD was applied to the Réunion TCO time series presented in Fig. 4, seven IMFs were found in addition to the residual mode. Taking account of the selection procedure mentioned above, the first five of the seven IMFs initially identified were relevant, and IMFs 6 and 7 were added to the residual mode. Results are displayed in Fig. 6 below.", null, "Figure 6Relevant IMFs and trend from the EEMD applied to time series of Réunion total columns of ozone from 1979 to 2019.", null, "Figure 7TCO IMF1 (black line), IMF2 (green line) and IMF3 (blue line) spectral contents.\n\nFor each IMF, the cycle defined as the period associated with the dominant frequency is specified. Mode mixing occurs in IMF2 and IMF3 as they have the same 1-year oscillation cycle. As shown in Fig. 7, the IMF2 spectrum contains ${F}_{\\mathrm{1}}=\\mathrm{1}/\\mathrm{6}$ and ${F}_{\\mathrm{2}}=\\mathrm{1}/\\mathrm{12}$ frequencies, and F2 is contained in both IMF2 and IMF3.\n\nTo estimate the accuracy of the residual returned by the EEMD, it is compared with the trend of the original signal obtained from a moving window with a size set at the maximum of the relevant IMF cycles, i.e. 125 months (10.4 years).", null, "Figure 8Trend obtained from the EEMD technique (black curve). The trend of the original signal obtained from a moving window (blue curve) with a 125-month size (i.e. 10.4 years).\n\nThe accuracy of the residual, R, returned by the EEMD and compared with the trend of the original signal by using a moving window, Tmb, was estimated using the following expression:\n\n$\\begin{array}{}\\text{(16)}& \\begin{array}{rl}{\\mathit{Pr}}_{\\mathrm{EEMD}}& =\\sqrt{\\frac{\\left({\\sum }_{i=\\mathrm{1}}^{N}{\\left(R\\left(i\\right)-\\text{Tmb}\\left(i\\right)\\right)}^{\\mathrm{2}}\\right)/N}{\\stackrel{\\mathrm{‾}}{\\text{Tmb}}}}×\\mathrm{100}\\\\ & =\\mathrm{0.7}\\phantom{\\rule{0.125em}{0ex}}\\mathit{%}\\phantom{\\rule{0.125em}{0ex}},\\end{array}\\end{array}$\n\nwhere N is the original time series length and $\\stackrel{\\mathrm{‾}}{.}$ represents the mean operator.\n\nTo overcome the mixing mode occurring in IMFs 2 and 3 returned by the EEMD technique, we applied the EAWD technique to the Réunion TCO time series. The results obtained with EAWD are displayed in Fig. 9 below.\n\nAs shown in Fig. 10 below, the 6-month and 1-year cycles relating respectively to EAWD1 and EAWD2 are correctly separated, and the mode mixing occurring in the EEMD results has been removed.\n\nSimilarly, the accuracy of the residual returned by the EAWD technique was estimated and compared with that returned by the EEMD.", null, "Figure 11The residual TrendEAWD returned by the EAWD technique (red curve), the trend of the original signal obtained from a moving window (blue curve) with a size fixed at 125 (i.e. 10.4 years), and the residual returned by the EEMD technique (black curve).\n\nLikewise, the accuracy of the residual returned by the EAWD technique was estimated using Eq. (16): PrEAWD=0.3 %.\n\nThe EAWD trend expressed in DU per decade is shown in Fig. 12.\n\nResults in Fig. 12 show that ozone levels in Réunion decreased from 1981, stopped decreasing in 1992, and started rising again from 2002.\n\nThe accuracy of the DU per decade EAWD trend in Fig. 12 was calculated as PrEAWD, i.e. 0.6 %.\n\nEEMD was applied to the rainfall time series measurements, and relevant IMFs were selected. Results are represented in Fig. 13 below.", null, "Figure 13Relevant IMFs and trend from the EEMD applied to the Conakry rainfall time series from 1960 to 2019.\n\nMode mixing occurs in IMF2 and IMF3 as they have the same 1-year oscillation cycle. As shown in Fig. 14 below, frequency ${F}_{\\mathrm{1}}=\\mathrm{1}/\\mathrm{6}$ is contained in both IMF1 and IMF2, while ${F}_{\\mathrm{2}}=\\mathrm{1}/\\mathrm{12}$ is contained in IMF1, IMF2, and IMF3.", null, "Figure 14Rainfall IMF1 (black line), IMF2 (green line), and IMF3 (blue line) spectral contents.\n\nThe accuracy of the trend calculated from EEMD results is compared below with the trend of the original signal obtained from a moving window with its size set at the maximum of the relevant IMF cycles, i.e. 144 months (12 years).", null, "Figure 15Trend obtained from the EEMD technique (black curve) with the trend of the original signal obtained from a moving window (blue curve) with a size of 144 months (i.e. 12 years).\n\nThe accuracy of the residual returned by the EEMD technique was estimated using Eq. (16): PrEEMD=15 %.\n\nResults obtained with EAWD are displayed in Fig. 16 below.\n\nThe 6-month and 1-year cycles relating respectively to EAWD1 and EAWD2 are correctly separated, and the mode mixing occurring in the EEMD results has been removed (see Fig. 17).\n\nThe accuracy of the residual returned by the EAWD technique was estimated at PrEAWD=0.9 %.", null, "Figure 18The residual TrendEAWD returned by the EAWD technique (red curve), the trend of the original signal obtained from a moving window (blue curve) with a size fixed at 144 (i.e. 12 years), and the residual returned by the EEMD technique (black curve).\n\nThe EAWD trend represented by an annual average of rainfall (in millimetres) is shown in Fig. 19 below.\n\nThe results reported in Fig. 19 show that the rainfall average amount decreased by 2.3 mm yr−1 in the period [1960, 1984], then increased by 1 mm yr−1 in the period [1984, 2003], and decreased again, by 0.7 mm yr−1, in the period [2003, 2020].\n\n5 Consistency of the EAWD method\n\nThe method commonly employed in atmospheric physics to determine the variability and trend of observation time series is to use a multi-linear regression model. This type of approach has been used very often (Randel and Thompson, 2011; Bourassa et al., 2014; Toihir et al., 2018).\n\nThe main requirement of this method is the a priori knowledge of the atmospheric climate forcings that control the variability of the time series studied. The ozone–QBO (Quasi-Biennial Oscillation) relationship has been discussed in several papers, as has the influence of ENSO (El Niño–Southern Oscillation) on ozone variability (Butchart et al., 2003; Brunner et al., 2006; Randel and Thompson, 2011). Other papers have shown the role played by solar flux in the temporal variability of ozone (Randel and Wu, 2007).\n\nTo validate results obtained with the EAWD method on the TCO time series for Réunion, we used the TREND-RUN multi-linear regression model developed at the University of Réunion and already applied in many studies (Bencherif et al., 2006; Bègue et al., 2010; Toihir et al., 2018).\n\nClimate forcings used as input to the TREND-RUN model were QBO, ENSO, and solar flux. A linear function was used to estimate the long-term linear trend of the series. The trend was then estimated by calculating the slope of the normalized linear function. As the variability of ozone is also affected by the annual and semi-annual oscillations (AO and SAO), these two analytic oscillations were also used as input to the model. The TREND-RUN model and the climate forcings used (such as ENSO, QBO, and solar flux at 10.7 cm) are described in detail in Toihir et al. (2018).\n\nThe results obtained here with TREND-RUN on the 1979–2019 Réunion TCO time series are consistent with those obtained by Toihir et al. (2018) on a shorter total ozone series at Réunion (1998–2013).\n\nThe trend obtained from the TREND-RUN model over the whole monthly mean ozone series from 1979 to 2019 is $-\\mathrm{1.11}±\\mathrm{0.19}$ % per decade. The error is estimated from the SD of the residual found by the model.\n\nThe variability components returned by the EAWD method are in agreement with the climatic forcings used as input to the TREND-RUN model, and the energy contributions respectively estimated by the TREND-RUN model and the EAWD technique are reported in Table 1.\n\nTable 1Comparison of total ozone variability in Réunion (from 1979 to 2019) obtained with the TREND-RUN model and the EAWD method.", null, "The main advantage of the EAWD technique for analysing the ozone variability from an observational time series is that it auto-adaptively extracts the modes of variability implicitly contained in the original time series without requiring any a priori knowledge of the atmospheric forcings controlling the ozone variability. It can be seen that the results returned by the EAWD method are in complete agreement with those returned by the TREND-RUN model. On the other hand, the energy contributions of the various modes of variability obtained with the EAWD method are compatible with those obtained with the TREND-RUN method (Table 1).\n\nIn contrast to the trend returned by the TREND-RUN model, which is linear over the whole duration of the series, the EAWD technique enables the evolution of the trend to be visualized over the whole period studied.\n\nTREND-RUN has not been applied to the Conakry rainfall time series as it contains intermittent processes, which makes use of multi-linear methods inappropriate.\n\n6 Conclusion\n\nEMD is a method for breaking down a signal without leaving the time domain. It can be compared with other analysis methods, such as Fourier transforms and wavelet decomposition, and the process is very useful for analysing raw signals, which are most often non-linear and non-stationary. Even though the EMD adaptability seems useful for many applications, the major drawback with EMD lies in the mode mixing, where the spectral contents of IMFs overlap each other. To overcome this problem, the EWT technique proposes a new approach, introducing a way of building adaptive wavelets and thus of extracting the different oscillatory modes from a signal by designing an appropriate filter bank. At the heart of the EWT technique lies the segmentation of the Fourier spectrum of the original signal. The main idea of the proposed EAWD technique is to use the results provided by EMD to segment the Fourier spectrum of the original signal. The algorithm implemented uses the spectral contents of the IMFs and ensures that their supports do not overlap, so that they can constitute a segmentation of the Fourier spectrum of the original signal. In another way, the method most commonly used to analyse the variability of observation time series is based on a multi-linear regression model. If we look at the results obtained with the TREND-RUN model on Réunion TCO time series, the variability modes returned by the EAWD are in good agreement with those obtained with the TREND-RUN multi-linear regression model.\n\nFrom a comparison between the results obtained with the EMD and EAWD techniques, it emerges that the EAWD technique enables the mode-mixing problem to be overcome while providing a trend with better accuracy than that obtained with the EMD technique. Thanks to the rigour of the EWT, the EAWD keeps the behaviour of the signal in the timescales returned by the EMD. In this context, the EAWD technique can be seen as an optimization of the EMD.\n\nCode availability\n\nThe first version of the EAWD method was written in R and is currently a beta version of the code and still requires some validation so that it can run on any time series before being included in an R package.\n\nData availability\n\nThe data are available from Thierry Portafaix and Hassan Bencherif at LACy UMR 8105 University of Reunion.\n\nAuthor contributions\n\nOD and AB developed and implemented the EAWD method. EL conducted the test and numerical validation. TP and HB conducted physical validation and comparison between the EAWD results with those obtained with a multilinear regression model.\n\nCompeting interests\n\nThe contact author has declared that neither they nor their co-authors have any competing interests.\n\nDisclaimer\n\nPublisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\nFinancial support\n\nThis study has been funded by the LEFE French National programme.\n\nReview statement\n\nThis paper was edited by Norbert Marwan and reviewed by two anonymous referees.\n\nReferences\n\nAyenu-Prah, A. Y. and Attoh-Okine, N.: A Criterion for Selecting Relevant Intrinsic Mode Functions in Empirical Mode Decomposition, Advances in Adaptive Data Analysis, 2, 1–24, https://doi.org/10.1142/S1793536910000367, 2010.\n\nBègue, N., Bencherif, H., Sivakumar, V., Kirgis, G., Mze, N., and Leclair de Bellevue, J.: Temperature variability and trends in the UT-LS over a subtropical site: Reunion (20.8 S, 55.5 E), Atmos. Chem. Phys., 10, 8563–8574, https://doi.org/10.5194/acp-10-8563-2010, 2010.\n\nBencherif, H., Diab, R. D., Portafaix, T., Morel, B., Keckhut, P., and Moorgawa, A.: Temperature climatology and trend estimates in the UTLS region as observed over a southern subtropical site, Durban, South Africa, Atmos. Chem. Phys., 6, 5121–5128, https://doi.org/10.5194/acp-6-5121-2006, 2006.\n\nBourassa, A. E., Degenstein, D. A., Randel, W. J., Zawodny, J. M., Kyrölä, E., McLinden, C. A., Sioris, C. E., and Roth, C. Z.: Trends in stratospheric ozone derived from merged SAGE II and Odin-OSIRIS satellite observations, Atmos. Chem. Phys., 14, 6983–6994, https://doi.org/10.5194/acp-14-6983-2014, 2014.\n\nBrunner, D., Staehelin, J., Maeder, J. A., Wohltmann, I., and Bodeker, G. E.: Variability and trends in total and vertically resolved stratospheric ozone based on the CATO ozone data set, Atmos. Chem. Phys., 6, 4985–5008, https://doi.org/10.5194/acp-6-4985-2006, 2006.\n\nButchart, N., Scaife, A. A., Austin, J., Hare, S. H. E., and Knight, J. R.: Quasi-biennial oscillation in ozone in a coupled chemistry-climate model, J. Geophys. Res., 108, 4486, https://doi.org/10.1029/2002JD003004, 2003,\n\nDaubechies, I.: Ten Lectures on Wavelets, in: CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, ISBN: 978-0-89871-274-2, 1992.\n\nDelage, O., Portafaix, T., Bencheriff, H., Guimbretière, G., and Loua, R. T.: Multi-scale Variability Analysis of Time Series in Geophysics by using the Empirical Mode Decomposition, Processing SAGA, https://hal.archives-ouvertes.fr/hal-02363170, last access: 6 October 2019.\n\nFlandrin, P., Rilling, G., and Gonçalvès, P.: Empirical Mode Decomposition as a filter bank, IEEE Signal Proc. Let., 11, 112–114, 2004.\n\nFosso, O. B. and Molinas, M.: Method for mode mixing separation in Empirical Mode decomposition, arXiv [preprint], arXiv:1709.05547v1, 16 September 2017.\n\nGao, Y., Ge, G., Sheng, Z., and Sang, E.: Analysis and solution to the mode mixing phenomenon in EMD, in: 2008 Congress on Image and Signal Processing, Sanya, China, 27–30 May 2008, https://doi.org/10.1109/CISP.2008.193, 2008.\n\nGilles, J.: Empirical Wavelet Transform, IEEE T. Signal Proces., 61, 3999–4010, https://doi.org/10.1109/TSP.2013.2265222, February 2013.\n\nHuang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N.-C., Tung, C. C., and Liu, H. H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, P. Roy. Soc. Lond. A, 454, 903–995, 1998.\n\nJaffard, S., Meyer, Y., and Ryan, R. D.: Wavelets: Tools for Science and Technology, SIAM, ISBN: 0898714486, 2001.\n\nMeyer, Y.: Wavelets, Vibrations and Scaling, American Mathematical Society, Centre de Recherches Mathématiques, ISBN: 978-0821806852, 1997.\n\nPastel, M., Pommereau, J.-P., Goutail, F., Richter, A., Pazmiño, A., Ionov, D., and Portafaix, T.: Construction of merged satellite total O3 and NO2 time series in the tropics for trend studies and evaluation by comparison to NDACC SAOZ measurements, Atmos. Meas. Tech., 7, 3337–3354, https://doi.org/10.5194/amt-7-3337-2014, 2014.\n\nPommereau, J.-P. and Goutail, F.: Ground-based measurements by visible spectrometry during Arctic Winter and Spring, Geophys. Res. Lett., 15, 891–894, https://doi.org/10.1029/GL015i008p00891, 1988.\n\nRandel, W. J. and Thompson, A. M.: Interannual variability and trends in tropical ozone derived from SAGE II satellite data and SHADOZ ozonesondes, J. Geophys. Res., 116, D07303, https://doi.org/10.1029/2010JD015195, 2011.\n\nRandel, W. J. and Wu, F.: A stratospheric ozone profile data set for 1979–2005: Variability, Trends and comparison with column ozone data, J. Geophys. Res., 112, D06313, https://doi.org/10.1029/2006jd007339, 2007.\n\nToihir, A. M., Portafaix, T., Sivakumar, V., Bencherif, H., Pazmiño, A., and Bègue, N.: Variability and trend in ozone over the southern tropics and subtropics, Ann. Geophys., 36, 381–404, https://doi.org/10.5194/angeo-36-381-2018, 2018.\n\nWu, Z. and Huang, N. E.: Ensemble empirical mode decomposition: A noise-assisted data analysis method, Advances in Adaptive Data Analysis, 1, 1–41, https://doi.org/10.1142/S1793536909000047, 2009." ]
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https://odederell3d.blog/2020/06/18/writing-a-basic-osl-color-shader/
[ "# Writing a basic OSL color shader\n\nThe following is an introduction to basic OSL shader syntax using a simple color blending shader example. a more general explanation of the subject can be read here.\n\nNotes:\n> It’s highly recommended to get acquainted with basic C language syntax, since it’s the basis for common shading languages like OSL, HLSL and GLSL.\n> More detailed information about writing OSL shaders can be found in the osl-languagespec PDF document from ImageWorks’s OSL GitHub.\n\nThis example shader blends 2 color sources according to the surface viewing angle (aka “facing ratio” or “incident angle” or “Perpendicular-Parallel”). the user can choose a facing (“front”) color or texture, a side color or texture, and the shader’s output bell be a mix of the these 2 inputs that depends on the angle the surface is viewed at.\n\n``` #include \"stdosl.h\"\n\n[[ string help = \"Blend colors by view angle\" ]]\n(\ncolor facing_color = color(0, 0, 0)\n[[ string help = \"The color (or texture) that will appear at perpendicular view angle\" ]],\ncolor side_color = color(1, 1, 1)\n[[ string help = \"The color (or texture) that will appear at grazing view angle\" ]],\nfloat base_blend = 0.0\n[[ string help = \"The percent of side_color that is mixed with facing_color at perpendicular view angle\",\nfloat min = 0.0, float max = 1.0]],\nfloat curve_exponent = 1.0\n[[ string help = \"A power exponent value by which the blend value is raised to control the blend curve\",\nfloat min = 0.001, float max = 10.0]],\noutput color color_out = color(1, 1, 1))\n{\n// calculate the linear facing ratio:\nfloat facing_ratio = acos(abs(dot(-I,N))) / M_PI_2;\n// calculate the curve facing ratio:\nfloat final_blend_ratio = pow(facing_ratio , curve_exponent);\n// blend the facing color:\ncolor final_facing_color = (facing_color * (1 - base_blend)) + (side_color * base_blend);\n// blend and output the final color:\ncolor_out = ((final_facing_color * (1 - final_blend_ratio)) + (side_color * final_blend_ratio));\n}```\n\nThe first statment:\n\n`#include \"stdosl.h\"`\n\nThe #include statement is a standard C compiler directive to link the OSL source code library code file stdosl.h to the shader’s code, so that the OSL data types and functions in the code will be recognized.\n* Some systems compile the code successfully without this statement. I’m not sure if their compiler links stdosl.h automatically or not.\n\nThe double-square bracketed statements provide both help annotations and value range limits for the shader parameters:\n\n`[[ string help = \"The percent of side_color that is mixed with facing_color at perpendicular view angle\", float min = 0.0, float max = 1.0]]`\n\nNote that these statements are appended to single parameters in the shader right before the comma character that ends the parameter statement.\n* Not all shading systems that supprt OSL also implement the annotations in the shader’s interface generated by the host software (the shader will work, but it’s parameters wont be described and limited to the defined value range).\n\nRemoving the #include statement, annotations and comments,\nWe can see that the OSL shader structure is very similar to a C function:\n\n```shader cglColorAngleBlend\n(\ncolor facing_color = color(0, 0, 0),\ncolor side_color = color(1, 1, 1),\nfloat base_blend = 0.0,\nfloat curve_exponent = 1.0,\noutput color color_out = color(1, 1, 1)\n)\n{\nfloat facing_ratio = acos(abs(dot(-I,N))) / M_PI_2;\nfloat final_blend_ratio = pow(facing_ratio , curve_exponent);\ncolor final_facing_color = (facing_color * (1 - base_blend)) + (side_color * base_blend);\ncolor_out = ((final_facing_color * (1 - final_blend_ratio)) + (side_color * final_blend_ratio));\n}```\n\nFirst the data type, in this case shader, followed by the shader identifier, in this case “cglColorAngleBlend”:\n\n`shader cglColorAngleBlend`\n\nAfter the shader’s type and identifier, a list of parameters is defined within parentheses, separated by comma’s. these parameters define the shader’s input’s, outputs, and default values. Output parameters are preceded by the output modifier.\n\n(\n<parameter type> <parameter identifier> = <parameter default value>,\n<parameter type> <parameter identifier> = <parameter default value>,\noutput <parameter type> <parameter identifier> = <parameter default value>\n)\n\n```(\ncolor facing_color = color(0, 0, 0),\ncolor side_color = color(1, 1, 1),\nfloat base_blend = 0.0,\nfloat curve_exponent = 1.0,\noutput color color_out = color(1, 1, 1)\n)```\n\nIn this case the shader has 4 user input parameters, and 1 output parameter.\n2 color type parameters, “facing_color” and “side_color” for the facing and side color that will be blended together, a float* parameter “base_blend” that specifies how much of the side color will be mixed with the facing color regardless of view angle, and a second float parameter “curve_exponent” specifying a power exponent by which the blend value will be raised to create a non-linear blend curve.\nThe output parameter “color_out” is a color that will calculated by the shader.\n* Note that even though the the output parameter will be calculated by the shader, it is required to define a default value for it for the shader to compile.\n\nAfter the shader parameters, enclosed within curly braces is the actual body of the shader code, containing the instructions, each ending by a semicolon ; character:\n\n{\n<instruction>;\n<instruction>;\n…..\n}\n\n```{\nfloat facing_ratio = acos(abs(dot(-I,N))) / M_PI_2;\nfloat final_blend_ratio = pow(facing_ratio , curve_exponent);\ncolor final_facing_color = (facing_color * (1 - base_blend)) + (side_color * base_blend);\ncolor_out = ((final_facing_color * (1 - final_blend_ratio)) + (side_color * final_blend_ratio));\n}```\n\nI the case of our shader the first code instruction is to define a new float internal variable named “facing_ratio”, calculate the surface/view angle and assign the resulting value to it:\n\n`float facing_ratio = acos(abs(dot(-I,N))) / M_PI_2;`\n\nThe expression:\n\nacos( abs( dot( -I, N ) ) )  / M_PI_2\n\ncalculates incident angle, i.e. angle between 2 vectors, originating at the surface shading point, one pointing towards the origin of the incoming ray, and the other the surface normal, as a factor of 0 to 1 representing 0 – 90 degrees.\nThese 2 vector are easily obtained through the built in OSL global variables N and I. N is the surface normal at the shading point, and I is the incoming ray vector pointing to the shading point which is inverted in this case to point backwards by  typing a minus before it: -I.\nThe incident angle is calculated in radians as the arc-cosine of the dot-product of N and -I and then divided by half a π to convert it to a linear factor of 0 to 1 representing 0 to 90 degrees in radians, M_PI_2 being a convenient half π constant.\n* M_PI being a full π, M_2PI being 2π representing 180 degrees in radians and 360 degrees respectively (OSL provides there are more constants in this series).\n\nThe second instruction raises the facing ratio that was calculated in the previous instruction by a power value provided by the curve_exponent input parameter, to create a non linear angle/color blend in values other than 1.0.\nThe resulting modified blend value is stored in a new internal variable final_blend_ratio:\n\n`float final_blend_ratio = pow(facing_ratio , curve_exponent);`\n\nNote:\nWe could avoid setting a new variable by modifying the value of  the facing_ratio variable, and we could also combine the these 2 instruction into 1 bigger expression like this:\n\npow( acos( abs( dot( -I, N ) ) ) / M_PI_2 , curve_exponent )\n\nBut I decided to keep it separated into 2 variable and 2 instructions for clarity.\n* try modifying the code as an exercise\n\nThe third instruction modifies the input color facing_color by premixing it with the input side_color according to the percent give by the input parameter base_blend and assigns the resulting color to a new internal variable named final_facing_color:\n\n`color final_facing_color = (facing_color * (1 - base_blend)) + (side_color * base_blend);`\n\nThe expression:\n\n( facing_color * ( 1 – base_blend ) ) + ( side_color * base_blend )\n\nCalculates a linear combination** (linear interpolation) between the 2 input colors using the base_blend as a 0 – 1 factor between them.\n* Note that OSL allows to define arithmatic operations freely between colors and floats.\n\nThe forth and final instruction creates the final mix between the modified facing color stored in final_facing_color variable and the side color given by the input color parameter side_color, by again, calculating a linear combination between the 2 colors, this time using final_blend_ratio variable value we calculated previously as the combination factor, and very importantly, finally, assigning the mixed result to the shader output parameter color_out so it will be the final output of the shader:\n\n`color_out = ((final_facing_color * (1 - final_blend_ratio)) + (side_color * final_blend_ratio));`\n\nThis screen capture shows this shader at work in Blender and Cycles, connected to a Principled BSDF shader as it’s base color source:", null, "Thats it! 🙂\n\nClarifications:\n\n* A “float” data type is simply the the computer-science geeky way of saying “accurate non-integer number”. when we have to store numbers that can describe geometry and color, we need a data type that isn’t limited to integers so for that purpose we use float values. there’s actually a lot more to the float formal definition in computer science, but for our purpose here this will suffice.\n\n** A Linear Combination, or Linear interpolation (lerp) is one of the most useful numerical operations in 3D geometry and color processing (vector math):\nA * ( 1 – t ) +  B * t\nA and B being your source and target locations or colors or any other value you need to interpolate and t being the blending factor from 0 – 1.\n\nRelated posts:\n\n## 7 thoughts on “Writing a basic OSL color shader”\n\n1.", null, "san2008 D says:\n\nThanks Oded for such useful information. I just starting learning Blender and I know something of C, so it helps me to understand more of Blender.\n\n1.", null, "Oded Erell says:\n\nGlad you found this useful! 🙂" ]
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https://gambit-ksiazki.pl/books/9783211994313/66026/Maple-and-Mathematica-2nd-ed.-2009-ISBN-9783211994313
[ "### Logowanie\n\nZapomniałeś hasła?\nNowy klient\n\nJeżeli nie znalazłeś poszukiwanej książki, skontaktuj się z nami wypełniając formularz kontaktowy.\n\nTa strona używa plików cookies, by ułatwić korzystanie z serwisu. Mogą Państwo określić warunki przechowywania lub dostępu do plików cookies w swojej przeglądarce zgodnie z polityką prywatności.\n\n### Informacje szczegółowe o książce", null, "# Maple and Mathematica, 2nd ed. 2009\n\n##### ISBN 9783211994313\n\nAutor: Inna K. Shingareva\n\nWydawca: Springer\n\nDostępność: Wysyłka w ciągu 2-3 dni\n\nCena: 313,95 zł\n\n ISBN13: 9783211994313 ISBN10: 3211994319 Autor: Inna K. Shingareva Oprawa: Paperback Rok Wydania: 2009-09-01 Numer Wydania: 2 Ilość stron: 484\n\nThe first book to compare the main two computer algebra systems (CAS), Maple and Mathematica used by students, mathematicians, scientists, and engineers. Both systems are presented in parallel so that Mathematica users can learn Maple quickly by finding the Maple equivalent to Mathematica functions, and vice versa. This student reference handbook consists of core material for incorporating Maple and Mathematica as a working tool into different undergraduate mathematical courses (abstract and linear algebra, geometry, calculus and analysis, complex functions, special functions, integral and discrete transforms, algebraic and transcendental equations, ordinary and partial differential equations, integral equations, numerical analysis and scientific computing). The book also contains applications from various areas of mathematics, physics, and music theory and can be useful for graduate students, professors, and researchers in science and engineering.\nOne of the goals of this book is to develop problem-solving skills (that are most useful for solving sophisticated research problems) finding solutions with Maple and Mathematica and not to depend on a specific version of both systems (Maple 12 and Mathematica 6 and 7 are considered).\n\nPart I, describes the foundations of Maple and Mathematica (with equivalent problems and solutions). Part II, describes Mathematics with Maple and Mathematica by using equivalent problems.\nFinally, this book is ideal for scientists who want to corroborate their Maple and Mathematica work with independent verification provided by another CAS.\nJ. Carter, SIAM Review 50: 149-152 (2008).\n\nPreface.- Foundations of Maple and Mathematica: Maple; Mathematica.- Mathematics: Maple and Mathematica: Graphics; Algebra; Linear Algebra; Geometry; Calculus and Analysis; Complex Functions; Special Functions and Orthogonal Polynomials; Integral and Discrete Transforms; Mathematical Equations; Numerical Analysis and Scientific Computing.-\n\nReferences.- General Index.- Maple Index.- Mathematica Index.- CD-ROM Contents.\n\n### Koszyk\n\nKsiążek w koszyku: 0 szt.\n\nWartość zakupów: 0,00 zł\n\n### Kontakt\n\nGambit\nCentrum Oprogramowania\ni Szkoleń Sp. z o.o.\n\nAl. Pokoju 29b/22-24\n\n31-564 Kraków\n\n+48 12 414 3791\n\n+48 12 414 3387\n\nSiedziba Księgarni\n\nul. Kordylewskiego 1\n\n31-542 Kraków\n\n+48 12 410 5989\n\n+48 12 414 3767\n\nWyślij e-mail\n\n### Subskrypcje\n\nAdministratorem danych osobowych jest firma Gambit COiS Sp. z o.o. Na podany adres będzie wysyłany wyłącznie biuletyn informacyjny.\n\n### Autoryzacja płatności", null, "" ]
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https://adriangcoder.medium.com/how-much-data-to-you-need-ba834d074f3a
[ "# How much data to you need?\n\nThe use of pre-trained language models is beginning to revolutionise applied NLP. Here I present some simple tests on language model and classification accuracy with and without pre-trained language models.", null, "Fig. 1. Comparison of accuracy of language model on pre-trained vs non pre-trained model.\n\nIn Figure 1 we can see the resulting accuracy of a LSTM RNN Encoder/Decoder language model for the imdb dataset with 100,000 texts in total. The blue line shows accuracy for a model pre-trained on the Wikitext 103 dataset and the orange curve shows results with pretraining. The x axis shows the decimation fraction of the data used for training. Eg for x=10, one tenth of the data ie 10,000 text units was used. Of the total number of text units used for each test, 90% were used for training and 10% used for testing.\n\nThe base code for the language model can be found here.\n\nWe can see that when the full dataset is used the wikitext pre-trained model performs slightly better than the non pre-trained model. However as the amount of data used for training decreases, the non pre-trained model decreases in accuracy rapidly, while the pre-trained model hits a plateau exhibiting a baseline language model performance essentially without any additional training data.", null, "Fig.2. Accuracy vs dataset decimation for pre-trained Wikitext 103 language model\n\nIn Figure 3 we see a zoom in of Figure 1 for the performance of the pre-trained Wikitext 103 language model on the imdb dataset. At c. 1/25th of the data (total of 4000 texts, of which 90% are used for training) we see a plateau in accuracy reached, below which a baseline accuracy of .26 to .27 is achieved on predicting the next word in a sentence.\n\nFor multi-class classification tasks I used the same architecture as per the imdb fastai code.", null, "Fig. 3. Multi-class classification confusion matrix for pre-trained wikitext-103 language model on the dbpedia dataset — the baseline.\n\nA baseline classification was run using a wikitext 103 pre trained model then trained on 90% of the dbpedia dataset (567,000 samples) to generate the confusion matrix show in Figure 4.\n\nThen a series of tests were made using a pre-trained wiki 103 language model on fractions of the dbpedia dataset used for training. The average F1 score of resulting classifications is shown against the number of training samples in Figure 4 below.", null, "Fig. 4. Average F1 score for all classes vs number of samples for classification results for the dbpedia dataset\n\nWhere:\n\n`F1 Score = 2*((Precision * Recall) / (Precision + Recall))Recall = True Positives / (True Positives + False Negatives)Precision = True Positives / (True Positives + False Positives)`\n\nWe can see that even with a very low number of training samples (630) we are still acheiving a respectable average F1 score (average of f1 score for each class) of ~0.94.", null, "Fig 5. Multi-class classification confusion matrix for pre-trained wikitext-103 language model on the dbpedia dataset trained on 1/1000th of the dataset.\n\nThe confusion matrix for classification results trained on just 1/1000th of the dataset is shown above.\n\nThe tests were repeated for the ag_news dataset (4 classes, 127600 total samples).", null, "Fig. 6. Multi-class classification confusion matrix for pre-trained wikitext-103 language model on the ag_news dataset — the baseline.\n\nAgain the average F1 score with different training dataset sizes is shown, here for the ag_news dataset.", null, "Fig. 7. Average F1 score for all classes vs number of samples for classification results for the ag_news dataset", null, "Fig 8. Multi-class classification confusion matrix for pre-trained wikitext-103 language model on the ag_news dataset trained on 1/1000th of the dataset.\n\nThe main take away from this work is that even with small datasets in the hundreds to few thousands of sample size range, one can get good results by using a pre-trained language model and subsequent fine tuning on a domain specific dataset.\n\nGeophysicist and Deep Learning Practitioner" ]
[ null, "https://miro.medium.com/max/1042/1*ROplwVb0e_HC2-9AhwIQeQ.png", null, "https://miro.medium.com/max/60/1*dXeaI58oM0Ipn0MUU-cPGg.png", null, "https://miro.medium.com/max/60/1*rUD9i_4E1pjBcPbMGWKm4Q.png", null, "https://miro.medium.com/max/60/1*wx1JUzSdJWjydMS7aPZloQ.png", null, "https://miro.medium.com/max/60/1*gONhwYyStIvYXkQLZx8cgQ.png", null, "https://miro.medium.com/max/60/1*I3K_1IuDL65MQKxpE7Tkxw.png", null, "https://miro.medium.com/max/60/1*_iCDXAwkx3jLodWdjnxzuA.png", null, "https://miro.medium.com/max/60/1*40lger5ufpMhA72qmhgIdA.png", null ]
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http://celsiusfahrenheit.co/104.3
[ "# 🌡104.3 C to F\n\n🔆🌡104.3 C to F. How many degrees Fahrenheit in a degree Celsius. °C to F Calculator.\n\n### Celsius to Fahrenheit\n\n Celsius Fahrenheit You can edit any of the fields below: = Detailed result here", null, "Change to Fahrenheit to Celsius\n\n## How to convert from Celsius to Fahrenheit\n\nIt is ease to convert a temperature value from Celsius to Fahrenheit by using the formula below:\n\n [°F] = [°C] × 9⁄5 + 32\nor\n Value in Fahrenheit = Value in Celsius × 9⁄5 + 32\n\nTo change 104.3° Celsius to Fahrenheit, just need to replace the value [°C] in the formula below and then do the math.\n\n### Step-by-step Solution:\n\n1. Write down the formula: [°F] = [°C] × 9⁄5 + 32\n2. Plug the value in the formula: 104.3 × 9⁄5 + 32\n3. Multiply by 9: 938.7⁄5 + 32\n4. Divide by 5: 187.74 + 32\n5. Add 32: 219.74° = Value in Fahrenheit (answer)\n\n### Values around 104.3 Celsius(s)\n\nCelsiusFahrenheitCelsiusFahrenheit\n103.439.7103.539.7\n103.639.8103.739.8\n103.839.9103.939.9\n10440.0104.140.1\n104.240.1104.340.2\n104.440.2104.540.3\n104.640.3104.740.4\n104.840.4104.940.5\n10540.6105.140.6\n105.240.7105.340.7" ]
[ null, "http://celsiusfahrenheit.co/images/calculator16x20.png", null ]
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http://www.java2s.com/Questions_And_Answers/Java-Data-Type/Integer/Integer-1.htm
[ "# Integer 1 « Integer « Java Data Type Q&A\n\n### 1. How to multiply 10 to an \"Integer\" object in Java?    stackoverflow.com\n\nHow do I multiply 10 to an Integer object and get back the Integer object? I am looking for the neatest way of doing this. I would probably do it this way: Get int ...\n\n### 2. Are Integers in Java little endian or big endian?    stackoverflow.com\n\nI ask because I am sending a byte stream from a C process to Java. On the C side the 32 bit integer has the LSB is the first byte and ...\n\n### 3. Left padding integers with zeros in Java    stackoverflow.com\n\nHow do you left pad an int with zeros in java when converting to a string? I'm basically looking to pad out integers up to 9999 with the leading zeros. E.g. 1 = ...\n\n### 4. How can I tell if a Java integer is null?    stackoverflow.com\n\nGreetings, I'm trying to validate whether my integer is null. If it is, I need to prompt the user to enter a value. My background is Perl, so my first ...\n\n### 5. Java: dividing 2 ints makes an int?    stackoverflow.com\n\nIn another Bruce Eckels exercise in calculating velocity, `v = s / t` where s and t are integers. How do I make it so the division cranks out a ...\n\n### 6. In Java, why is the call foo() not ambigious given 2 varags methods foo(int... ints) and foo(Object... objects)?    stackoverflow.com\n\nIf I declare just the 2 varargs methods as follows:\n\n``````public void foo(String... strings) {\nSystem.out.println(\"Foo with Strings\");\n}\n``````\nand\n``````public void foo(int... ints) {\nSystem.out.println(\"Foo with ints\");\n}\n``````\nand then ...\n\n### 7. 09 is not recognized where as 9 is recognized    stackoverflow.com\n\nI am using quartz for schedulling. TriggerUtils.getDateOf(0,40,18,09,06); it accept 5 parameter. (seconds, minutes, hours, daysOfMonth, month). When i pass fourth parameter as \"09\". Eclipse give me error \"The literal Octal 09 (digit 9) ...\n\n### 8. Pattern to create class instances by integer id?    stackoverflow.com\n\nI am reading a Stream, which provides an identifier (a simple int). Depending on the int different data follows, which i need to turn into objects. So far i created classes ...\n\n### 9. Problems with createImage(int width, int height)    stackoverflow.com\n\nI have the following code, which is run every 10ms as part of a game:\n\n``````private void gameRender()\n{\nif(dbImage == null)\n{\n...``````\n\n### 10. java int comparation    stackoverflow.com\n\nHow does Java know/evaluate the comparison of two `int` values; for example:\n\n``````int a=5;\nint b=10;\n``````\nHow does it evaluates whether `a > b` or `a == b` or `a < b` Please give an elaborate ...\n\n### 11. Integer Linear Programming Java: Multiple Open Source and Commercial tools are available. Which one to use?    stackoverflow.com\n\nI need to use Integer Linear Programming API/Tool for my application. Though my application is in Java but I don’t mind calling an EXE (Tool) from Java providing input using file ...\n\n### 12. How to enforce an integer limit in an argument hint in Java    stackoverflow.com\n\nI'm new to Java after working for a few years in PHP and I'm trying to get an idea of some of the best practices and norms when working with Java. I'm ...\n\n### 13. Integer counter - What to do when Max-Value?    stackoverflow.com\n\nHow do you solve the max value problem when using an integer counter, that looks like\n\n``````counter = counter + 1;\n``````\nWhen this reaches the max value, how do you know this happened? ...\n\n### 14. Integer as primitve type    stackoverflow.com\n\nWhy there is primitive type for integer(int) even though we have an object for integer as Integer.? but the same is not with string type. There is no such primitive type for ...\n\n### 15. Java object Equality    stackoverflow.com\n\nThe two cards c1 and c4 seem to be equal...but they are not why. I want them to be equal so that only one of them is allowed in the Set. ...\n\n### 16. Can an int be null in Java?    stackoverflow.com\n\nCan an `int` be `null` in Java? For example:\n\n``````int data = check(Node root);\n\nif ( data == null ) {\n// do something\n} else {\n// do something\n}\n``````\nMy goal is to write a ...\n\n### 17. A textbox class only accept integers in Java    stackoverflow.com\n\nI just want to do a textbox class only accepts integers.. I have done something, but ? think it's not enough. Can anyone help me, please? Thanks...\n\n``````import java.awt.TextField\npublic class textbox extends TextField{\n...``````\n\n### 18. What Java method takes an int and returns +1 or -1?    stackoverflow.com\n\nWhat Java method takes an `int` and returns +1 or -1? The criteria for this is whether or not the `int` is positive or negative. I looked through the documentation but ...\n\n### 19. Method return type    stackoverflow.com\n\nIn my company, a system is designed to have 3 layers. Layer1 is responsible for business logic handling. Layer3 is calling back end systems. Layer2 sits between the two layers so ...\n\n### 20. GMP Vs java BIG INTEGERS,,,    stackoverflow.com\n\nWhich tool is the best one for accesing large bit numbers for testing Crypto systems..either GMP library or JAVA big integers..?? in terms of speed, memory, functions, flexibility towards crptosystems(mathematical functions like ...\n\n### 21. JNI how to access Java Object (Integer)    stackoverflow.com\n\nI have a JNI method to access java method which returns an Integer object. I do not want to return the primitive int type because this code will be modified to ...\n\n### 22. Problem in inferring instances that have integer cardinality constraint    stackoverflow.com\n\nI have created an RDF/OWL file using Protege 4.1 alpha. I also created a defined class in Protege called CheapPhone. This class has a restriction which is shown below :\n\n``(hasPrice some ...``\n\n### 23. Integers caching in Java    stackoverflow.com\n\nPossible Duplicate:\nWeird Java Boxing\nHi guys, Recently I saw a presentation where was the following sample of Java code:\n``Integer a = 1000, b = 1000; ...``\n\n### 24. Integer Type && Null in java    stackoverflow.com\n\nI have a class such as :\n\n``````class node\n{\nInteger id ;\ndouble lon;\ndouble lat ;\n...``````\n\n### 25. problem with integers    stackoverflow.com\n\ncan anybody look at this code and tell me why the exception happens?\n\n``````public static void main(String[] args)\n{\nint total =100;\nint discount_Ammount = 20 ...``````\n\n### 26. Java : Best way to pass int by reference    stackoverflow.com\n\nI have a parsing function that parses an encoded length from a byte buffer, it returns the parsed length as an int, and takes an index into the buffer as an ...\n\n### 27. How can I pass an Integer class correctly by reference?    stackoverflow.com\n\nI am hoping that someone can clarify what is happening here for me. I dug around in the integer class for a bit but because integer is overriding the `+` ...\n\n### 28. int does not override Integer in Java    stackoverflow.com\n\nI had a function in Java with method signature\n\n``````public void myMethod (int someInt, String someString)\n``````\nin my abstract class and I had over-ridden it with method\n``public void myMethod (Integer ...``\n\n### 29. Basic question on Java's int    stackoverflow.com\n\nWhy does the below code prints 2147483647, the actual value being 2147483648?\n\n`````` i = (int)Math.pow(2,31) ;\nSystem.out.println(i);\n``````\nI understand that the max positive value that ...\n\n### 30. Getting a function to return two integers    stackoverflow.com\n\nI am writing a function and I want it two return two integers as results. However, I cannot get it to do this. Could someone help me? Here is my best ...\n\n### 31. Java Int & ASCII Question    stackoverflow.com\n\n``````String source = \"WEDGEZ\"\nchar letter = source.charAt(i);\nshift=5;\nfor (int i=0;i<source.length();i++){\nif (source.charAt(i) >=65 && source.charAt(i) <=90 )\nletterMix =(char)(('D' + (letter - 'D' + shift) % 26));\n}\n``````\nOk what I'm trying to do ...\n\n### 32. How to check whether a int is not null or empty?    stackoverflow.com\n\nI really dont know this is possible or not. But I am strucking in a place where i want to check a int value is `null` or not, to call different methods. Is ...\n\n### 33. Uninitialized int vs Integer    stackoverflow.com\n\nI was just studying up on my Java in preparation for an exam and I ran into a sort of problem with uninitialized int/Integer values.\n\n``````class A\n{\n...``````\n\n### 34. Function that swaps two integers    stackoverflow.com\n\nPossible Duplicate:\nHow to write a basic swap function in Java\nHi. I don't know java at all, and in the near future have no wish ...\n\n### 35. extending java Integer cahce    stackoverflow.com\n\nWhy YOU should use Integer.valueOf(int) In particular, why you should use Integer.valueOf(int) instead of new Integer(int): CACHING. But in JDK 5+, you should really use valueOf because Integer now caches Integer objects ...\n\n### 36. More about rotateLeft method in java    stackoverflow.com\n\nplease tell me examples of [rotateLeft] method of Integer class in java : http://download-llnw.oracle.com/javase/6/docs/api/java/lang/Integer.html#rotateLeft(int, int)\n\n### 37. Passing Integer to int and vice versa    stackoverflow.com\n\nJust wondered why is it possible to pass Integer as argument where method parameter is of int type and vice versa?\n\n``````public class Salmon {\n\npublic static Integer foo(Integer a, int b){\n...``````\n\n### 38. Can't check if int is null    stackoverflow.com\n\nI'm trying to use a dictionary. Whenever I want to check if an element is present in the dictionary, I do this:\n\n``````int value = results.get(\"aKeyThatMayOrMayNotBePresent\");\n\nif (value != null)\n// ...\n``````\nBut ...\n\n### 39. How to handle “int i != \"\"” or “int i != null” statements in Java?    stackoverflow.com\n\nAs we know int is a primitive data type and cannot be null. In my program i want to do a condition check like int i != \"\" but it says ...\n\n### 40. binarySearch method issue, not accepting int paramater    stackoverflow.com\n\nI am using the Java 2 Platform to practice different algorithms. I am getting two errors and I think the first one is that I am passing the integer \"5\" ...\n\n### 41. Is this Java program legitimate? /newbie    stackoverflow.com\n\ni'm doing some exercises in my Java book. I'm very new to programming. Therefore, notice (in the code) that i'm still on Chapter one. Now I already did everything, I just ...\n\n### 42. cannot find symbol-method add (java.lang.integer)..whats the problem actually?    stackoverflow.com\n\n``````public class ArrayList\n{\n// instance variables - replace the example below with your own\npublic void processinput (String s)\n{\n...``````\n\n### 43. Display three non-negative integers in increasing order    stackoverflow.com\n\nPrompt the user to type in three non-negative integers. Display the integers in an increasing order.\n\n``````import java.util.Scanner;\n\n{\nint number1,number2,number3;\nScanner ...``````\n\n### 44. common divisiors of two integers    stackoverflow.com\n\nin java, I want an efficient program to find all common divisors betwen two integers... for e.g. if there are two integers:- 30(2*3*5) and 45(5*3*3) Program should retrun 3, 5 which are common divisors between 30 ...\n\n### 45. Enumerations vs int flags?    stackoverflow.com\n\nJust wanted some opinions on the matter. I have always used int flags, and was just curious on possible performance of ease of use if I were to use enumerations? Thanks in ...\n\n### 46. Pointer to an Integer in Java    stackoverflow.com\n\nSo the problem is: I have a code like this\n\n``````int a,b;\nswitch(whatever){\ncase 1:\nlots_of_lines_dealing_with_variable_a;\ncase 2:\n...``````\n\n### 47. Does the \"switch\" statement in Java only work with integers?    stackoverflow.com\n\nPossible Duplicate:\nSwitch Statement With Strings in Java?\nDoes the \"switch\" statement in Java only work with integers ? Can't I write something like this instead ? switch(string) ...\n\n### 48. Cannot find symbol method drawImage(SlidingBlockModel, int, int, int, int, )    stackoverflow.com\n\nI'm trying to make a sliding block game. In this class I've used the drawImage method to display the blocks of the \"puzzle\", using the drawImage method of the Graphics object ...\n\n### 49. Java - Change int to ascii    stackoverflow.com\n\nIs there a way for java to convert int's to ascii symbols?\n\n### 50. Java integer list    stackoverflow.com\n\nI am trying to make java go trough a list of numbers. It chooses the first one, gives this as output, waits/sleeps like 2000 milliseconds and then give the next one as ...\n\n### 51. How to add a group of integers    stackoverflow.com\n\nCan some one tell me how to do this and explain it to me: Write a program that reads a text file that contains groups of integers that start with the ...\n\n### 52. (Java) Is Integer Immutable    stackoverflow.com\n\nI know this is probably very stupid, but a lot of places claim that the Integer class in Java is immutable, yet the following code:\n\n``````Integer a=3;\nInteger b=3;\na+=b;\nSystem.out.println(a);\n``````\nExecutes without any trouble giving ...\n\n### 53. Fastest method to calculate difference between two ARGB ints in Java?    stackoverflow.com\n\nGiven an int from a DataBuffer which has ARGB data packed in it with the masks A = 0xFF000000 R = 0xFF0000 G = 0xFF00 B = 0xFF I'm doing the following but wonder if there ...\n\n### 54. java integer handling    stackoverflow.com\n\nWhen I run this program, it outputs -43.\n\n``````public class Main {\npublic static void main(String[] args) {\nint a=053;\n...``````\n\n### 55. java vs c integer    stackoverflow.com\n\nPossible Duplicate:\n++i + ++i + ++i in Java vs C\nUsing Java:\n``````public class Main {\npublic static void main(String[] args) {\n...``````\n\n### 56. integer handaling in java    stackoverflow.com\n\nPossible Duplicate:\njava vs c integer\n``````public class Main {\npublic static void main(String[] args) {\n...``````\n\n### 57. Integer construction variations    stackoverflow.com\n\nHey all, I ran into an interesting occurrence and am looking for an explanation. In Java 1.6:\n\n``````Integer a = new Integer(5);\nInteger b = new Integer(5);\n\nSystem.out.println(a == b);\n\nInteger c = 5;\nInteger d = ...``````\n\n### 58. C like while in java with integer?    stackoverflow.com\n\nis it possible in java to have a C like syntax for this:\n\n`````` int counter = 10;\n...``````\n\n### 59. Best way to change an integer field in a compiled 1.6 Java class with no source    stackoverflow.com\n\nA class file that was compiled with java 1.6 settings has two fields which I need to set to higher values.\n\n``````private Integer days = 7;\nprivate Integer running = 30;\n``````\nunfortunately, I don't ...\n\n### 60. Java - Managing specific int[][]    stackoverflow.com\n\nLet's say I want to store three sets of 2D arrays that load up on `int[][] board`. An example set:\n\n``````{\n{ 67, 67, 118, 118, 118, 118, 118, 118, 118, 118, 118, 118, ...``````\n\n### 61. How to handle not being able to store time in an int?    stackoverflow.com\n\nIn some languages, time is stored as the number of seconds from the epoch and stored in an int (Correct me if I am wrong). So we will eventually hit a ...\n\n### 62. Help to transform int to bool conditions    stackoverflow.com\n\nI have realized some logic using integers\n\n``````import java.util.concurrent.locks.*;\n\npublic class MassageSalon implements Salon{\n\n//I want to transform this into bool\nprivate int customerOnCouch = 0;\n...``````\n\n### 63. Multiplication of two int's gets negativ    stackoverflow.com\n\nI'm currently coding a little download manager and I get a funny output when I try to calculate the download-progress in percent. This is what i use to calculate it:\n\n``int progress ...``\n\n### 64. How to push integer on Stack in BCEL    stackoverflow.com\n\nI am facing a problem in context of pushing a integer on stack in BCEL. I have a method _square of someClass i.e. \"mathClass\"\n\n`````` ilist = new InstructionList();\n...``````\n\n### 65. Integer and int duality?    stackoverflow.com\n\nCan someone explain me this\n\n`````` List<Integer> list = new LinkedList<Integer>();\n``````\nwhen I used\n`````` list.remove(1);\n``````\nthen 1st element got removed\n`````` list.remove(new Integer(\"1\"));\n``````\nthen 2nd element got removed. so, can you explain behavior ...\n\n### 66. How to left pad integers with a formatter with dots?    stackoverflow.com\n\nI know we can left-pad integers with a formatter like this:\n\n``````String.format(\"%7d\", 234); // \" 234\"\nString.format(\"%07d\", 234); // \"0000234\"\nString.format(\"%015d\", 234); // \"0000000000000234\"\n``````\nBut, how to replace the ...\n\n### 67. Why int[] a = new int instead of just int a?    stackoverflow.com\n\nIs there some hidden meaning in this code which I don't see in java? How can it be useful?\n\n``````int[] a = new int;\n``````\nthan just\n``````int a;\n``````\nbecause from my point of view it's ...\n\n### 68. Binding a Java Integer to JavaScriptEngine doesn't work    stackoverflow.com\n\nTo see how binding Java objects to symbols in a dynamic language works, I wrote the following spike test, binding a `java.lang.Integer` to the symbol `i` to be changed ...\n\n### 69. Having null safe checks using org.apache.commons.ObjectUtil class for custom objects    stackoverflow.com\n\nIve been searching for a robust way to compare my objects, I came across the ObjectUtils , and had the immidiate doubt that would it be able to compare it efficiently ...\n\n### 70. Hard to read integers in java? Is there any reason behind it?    stackoverflow.com\n\nI have to read integers more frequently in Java. So how i should do? What function i have to use? C/C++ too have buffering concepts but they has a single statement. But ...\n\n### 71. java Integer reference    stackoverflow.com\n\nI've got a question.\n\n``````public class Jaba {\n\npublic static void main(String args[]) {\nInteger i = new Integer(0); ...``````\n\n### 72. f(int x) { return x == 0 ? 0 : 1; } in Java without conditionals    stackoverflow.com\n\nI want to implement `f(int x) { return x == 0 ? 0 : 1; }` in Java. In C, I'd just \"`return !!x;`\", but `!` doesn't work like that in Java. ...\n\n### 73. Java method returning List and a integer    stackoverflow.com\n\nI have a method which reads a file and returns the contents of the text file in a list of `String` array. Find the implementation of the method and how I ...\n\n### 74. n Choose k using an integer type of n and k in java    stackoverflow.com\n\nI have been given a task that requires to use n and k to work out the n Choose k problem. The condition I have is I can not use other data ...\n\n### 75. Difference between System.exit(int code) and Runtime.getRuntime().exit(int code)    stackoverflow.com\n\nI'm working on the Java batch program that should exit with different codes based on various conditions. The program will be triggered and monitored by CA7 scheduler which will use exit ...\n\n### 76. JDK Issue with Integer Comparision    stackoverflow.com\n\nIn jdk 1.6.0_24 comparison of two Integer Objects with same int value is failing? Issue :\n\n``````Integer x = 2;\nInteger y = 2;\n\nIf(x != y){\n//Control should not come here, but ...``````\n\n### 77. Java Int to Represent an Class    stackoverflow.com\n\nI need to get an variable from one of the 100+ Classes I have. the Class from which I get the variable is determined by an Integer. I didn't find a ...\n\n### 78. Simple calculator program in Java. No. of integers read and Average    stackoverflow.com\n\nI have a task that requires me to print out the following quantities: I need to write a java program that can calculate: 1. the number of integers read in 2. the average value—which ...\n\n### 79. How does Robot's getPixelColor(int x, int y) method work?    stackoverflow.com\n\nHow exactly does the method `getPixelColor(int x,int y)` from the Robot class work? I tried this code fragment:\n\n``````try\n{\nRobot robos = ...``````\n\n### 80. int with leading 0's behave strangely    stackoverflow.com\n\nPossible Duplicate:\nInteger with leading zeroes\nCan someone please tell me what is going on here? When I initialize an int with leading zeroes the program ...\n\n### 81. using new(Integer) versus an int    stackoverflow.com\n\nIn my Java class, the professor uses something like:\n\n``````integerBox.add(new Integer(10));\n``````\nIs this the same as just doing:\n``````integerBox.add(10);\n``````\n? I've googled a bit but can't find out one way or the other, and the prof ...\n\n### 82. Java int equality inconsistency?    stackoverflow.com\n\nThis is driving me insane because it completely violates my attempts to de-buggify it:\n\n``````int k = keyCode; //keyCode being a variable declared by a keyPress\n//in the Processing library\n//k and keyCode are ...``````\n\n### 83. how to delimit integers in java?    stackoverflow.com\n\nI have a integer value coming from command line. Its like 12345 or 2343455435 without any delimit characters. How can I get individual pieces of that integer, say like for 12345 ...\n\n### 84. How can it be determined if one integer is divisble by another?    stackoverflow.com\n\nSo for this problem the question asks\n\na number x is divisible by y if the remainder after the division is zero. Write a program that tests whether one ...\n\n### 85. Java - Select object by int    stackoverflow.com\n\nHow do I select an object by the an int inside it? Here is code:\n\n``````String FolderName = result.getString (\"name\");\nString FolderId = result.getString (\"category_id\");\nString ParentId = result.getString (\"parent_id\");\nint intFolderId = Integer.parseInt(FolderId);\nint intParentId = ...``````\n\n### 86. Stack returning Objects instead of Integers    stackoverflow.com\n\nI'm trying to implement a program that involves an array of stacks. Each stack takes in Integer objects, but the problem is when I try to get an Integer object from ...\n\n### 87. Java ternary allows you to return an int or null. How is this correct?    stackoverflow.com\n\nPossible Duplicate:\nConversion from null to int possible?\nI found that the following expression compiles in java.\n``````int i = false ? 3 : null;\n``````\nWhen the ...\n\n### 88. Reading integers from a line    stackoverflow.com\n\nI'm trying to read two integers on the same line.\n\n``````Scanner a=new Scanner(System.in);\nx=a.nextInt();\ny=a.nextInt();\n``````\nNow, if I input\n3 4\n3 4\nx = 3 and y = 3. I ...\n\n### 89. Can JSON Object Attribute Names Be Integers?    stackoverflow.com\n\nI am just getting started with some Jackson JSON data here. This section is giving me trouble.\n\n``````\"pointData\":{\n\"1\":\"32.1093904, 66.7065216\",\n\"2\":\"33.1236854, 67.8128443\",\n...``````\n\n### 90. If ... is not an int {    stackoverflow.com\n\nI am trying to get the program to recognize if an int is not entered . I have seen everything from:\n\n`````` if (v % 1)\n``````\nto\n`` ...``\n\n### 91. Java: returning two ints from a method call    stackoverflow.com\n\nI do this a lot in my code that works with lots of 2 dimensional coordinates:\n\n``````int[] getSize() {\nint[] res = {gridRows, gridColumns};\nreturn res;\n}\n``````\nI ...\n\n### 92. Integer manipulation in Java    stackoverflow.com\n\nI have an assignment to be done in college, a piece asks for the instructions below to be done. Please don't give away the answer, simply leading me in the right ...\n\n### 93. Resolving \"The method must return a result of type int\" in Java    stackoverflow.com\n\nI'm very new to Java. Eclipse is giving me the error\n\nThe method must return a result of type int\nfor the following code:\n``````public class firstprog {\npublic ...``````\n\n### 94. Int Nullpointerexception Java    stackoverflow.com\n\nI have the below code running and it is throwing a nullpointerexception on the if statement line.\n\n``````int answered;\n...``````\n\n### 95. Returning an int[] from java to C using JNI    stackoverflow.com\n\nI have a C program that invokes a java program but I have a problem: my java program returns an int [], how can I use JNI to get the result ...\n\n### 96. Integer class object    stackoverflow.com\n\nI'd a code snippet:\n\n``````public class Test{\npublic static void main(String args[]){\nInteger a = 100;\n...``````\n\n### 97. Big Integer - What is this code doing?    stackoverflow.com\n\nI understand this questions is strange, not my usual style. I am currently doing a project using a chord implementation in peersim. The code below shows a big integer and some ...\n\n### 98. How do I express NaN for integer types in Java?    stackoverflow.com\n\nI have a method returning `long` and there are cases where a valid result can not be computed. `Double` has the `NaN` constant, which is not expressable in `long`. I can think ...\n\n### 99. Transfer of Integer!    bytes.com\n\nHello guys......I have a problem with my code, its more like I am stuck to continue further if I cannot find a way or an alternative. The problem is I have ...\n\n### 100. need program that finds smallest of several prompted integers    bytes.com\n\nI need to write a java application that finds the smallest of several integers. I need it to prompt the user for the number of integers that will be input, then ..." ]
[ null ]
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https://fr.slideserve.com/sheila/bullets-powerpoint-ppt-presentation
[ "", null, "Download", null, "Download Presentation", null, "Bullets\n\n# Bullets\n\nTélécharger la présentation", null, "## Bullets\n\n- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -\n##### Presentation Transcript\n\n1. Bullets Two bullets of equal mass are shot at equal speeds at blocks of wood on a smooth ice rink. One bullet, made of rubber bounces off of the wood. The other bullet, made of aluminum, burrows into the wood. In which case does the block of wood move faster? Explain.\n\n2. MOMENTUM\n\n3. What is a collision? A collision is a short duration interaction between two objects. An example of a collision includes a train car rolling toward an identical car at rest. The two cars couple together upon impact and then roll down the tracks together.\n\n4. ANOTHER COLLISION The collision between a tennis ball and racket may seem instantaneous to your eye, but that is a limitation of your perception. A careful look at this picture reveals that the right side of the ball is flattened and pressed up against the strings of the racket.\n\n5. The magnitude of the momentum is the product of the object’s mass and speed p=mv The momentum has the same sign as the object’s velocity.\n\n6. Ways to Increase Momentum • Increase velocity: • A fast moving object will have more momentum than a slow moving/still object. • Compare the momentum of a 40kg skateboarder moving 10m/s and a 150kg parked car. • Increase mass: • A larger massed object will have more momentum than a small massed object. • Compare the momentum of a 5kg dog and a 15kg dog both moving at 5 m/s.\n\n7. Summary • A heavy, fast moving object will have a lot of momentum • A light, slow moving object will have very little momentum.\n\n8. Practice Problem #1 • Describe a situation when two objects with very different masses can have similar momenta.(plural for momentum) • Yes…they must be moving….\n\n9. Impulse • A change in momentum is called an impulse or force applied over a time I = ΔFt • What is impulse’s derived unit?\n\n10. Practice Problem #2 • A professional boxer can punch with a force of 150N. When he uses gloves, the time of impact is .9s. However, when he does not use gloves the time of impact is .7s. Calculate the impulse for both punches.\n\n11. Impulse is also known as a change in momentum.\n\n12. THE IMPULSE-MOMENTUM THEOREM The stick exerts an impulse on the puck, changing its speed.\n\n13. The Law of Conservation of Momentum State: Total momentum of a system remains the same before an interaction (a collision or explosion) and after an interaction (a collision or explosion) Mathematically: Momentum before = momentum after pbefore = pafter (mv)before = (mv)after\n\n14. Collisions • Two types of collisions: • Elastic • Ex: • Inelastic • Ex: • Momentum is still conserved in collisions.\n\n16. Practice Problem #3 • A billiards ball, ball A, rolls towards a stationary billiards ball, ball B, with a velocity of 5 m/s. Both balls have a mass of 2kg. • Classify this collision. • Calculate the momentum before the collision. • Calculate the velocity of each ball after the collision. • What direction is each ball traveling in?\n\n17. Practice Problem #4 • A 50kg lineman running at 10m/s tackles a stationary 40kg quarterback. • Classify this collision. • Calculate the momentum before the collision. • Calculate the velocity of the players after the collision. • In what direction are the player traveling in after the collision?\n\n18. Explosions • Opposite of collisions • The particles of the system move apart after a brief, intense interaction • Exploding forces are usually internal\n\n19. 7.1 Momentum • Newton’s 1st Law is also called the Law of Inertia. • Inertia can be applied to objects in motion and at rest. • This chapter inertia is concerned with objects in motion, also called momentum. • Momentum = mass x velocity • An object can have a large momentum if it has a large mass, velocity, or both. • Which as more momentum a car or truck traveling at the same velocity? Why? Truck b/c it has a larger mass • Which has more momentum a car traveling at a faster velocity than a truck? Car b/c it has more velocity • How much momentum does an object at rest have? zero\n\n20. 7.2 Momentum • What has to change if the momentum of an object changes? Mass or velocity • A change is velocity means there is an acceleration. • What is the cause for acceleration? Force • The greater the force applied, the great the acceleration, which means a greater change in velocity, which mean a greater change in momentum. • A force sustained over a great period of time produces more change in momentum. • Both force and time are important in changing momentum. • Impulse = Force x time • The greater the impulse the greater the change in momentum. • You could write another equation: • Force x time = Δ (mass x velocity)\n\n21. 18. Case #1 • Example given: golfer or baseball player • Major Concepts: swinging through allows for more time and an applied force- change in force from instant to instant • Impact= Force (N) • Impulse= impact force x time (Ns) • Case #2 • Example given: hitting haystack instead of wall in a car • Major Concepts: extend impact time and reduce force • When you increase the time of impact, you decrease the force of impact.\n\n22. 7.3 Bouncing • Impulse are great when an object bounces. • The impulse required to bring an object to a stop and then to “throw it back again” is greater than the impulse required to bring the object to a stop. • Explain the physics behind Lester A. Pelton’s improved paddle wheel. • U- turn of paddle wheel • Water “bounce,” so impulse increased\n\n23. 7.4 Conservation of Momentum • Based on Newton’s 2nd Law: a net force produces an acceleration. • The chapter says the same thing only with different key terms. A change in momentum produces a impulse. • Both impulse and force must be exerted on the object by something outside the object, internal forces will not work. • Internal forces come in action/reaction pairs that are equal and opposite to each other in an object. • Newton’s 3rd Law: is about action and reaction forces.\n\n24. Use Newton’s 3rd Law to analyze a cannonball being fired from a cannon. • A. The cannon and cannonball are considered to be internal forces. • B. The momentum before and the momentum after are equal and opposite therefore they cancel each other. • C. The system does not gain ___________ ___________, therefore it does not gain momentum. • If no net force acts on a system, the momentum of that system cannot change. • The Law of Conservation of Momentum states: In the absence of an external force, the momentum of a system remains unchanged.\n\n25. 7.5 Momentum • Net momentum before = net momentum after. • Elastic Collisions = collision without permanently deforming or generating heat • Example: billiards • Inelastic Collisions = collision with deformation and generating heat Ex: a toy car hitting play dough\n\n26. 7.6 Momentum Vectors • Momentum is a vector quality. • Example:\n\n27. Review Questions • Skater has a faster velocity. • Same impulse because same momentum. Impact would be different. • Force and time are inversely related to time. • Yes, no acceleration means no net force which means no momentum. • Yes, because impulse is Ft, or change in momentum\n\n28. 6. Travel away from each other with the same velocity 7. Stick together and zero acceleration 8. The velocity is in the direction of motion, a decreasing to zero" ]
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https://dsp.stackexchange.com/tags/power-spectral-density
[ "# Questions tagged [power-spectral-density]\n\nThe Power Spectral Density (PSD) is the distribution of signal power over frequencies.\n\n563 questions\nFilter by\nSorted by\nTagged with\n95 views\n\n### What is the point of smoothing an FFT or spectral density plot, and how does that affect the noise floor?\n\nIt appears that smoothing the FFT or spectral density plots of a noisy signal is a common practice. I see that common tools like MATLAB and Python have functions built in to their FFT tools to do just ...\n54 views\n\n### How many bins to include when calculating SNR from FFT?\n\nI'm a scientist conducting an experiment that requires some signal processing. My expertise is not in signal processing, thus here I am. We've basically re-created an experiment conducted by other ...\n89 views\n\n### Is spectral density sometimes normalized by sampling rate rather than bin size?\n\nI'm a scientist conducting an experiment that requires some signal processing. My expertise is not in signal processing, thus here I am. We've basically re-created an experiment conducted by other ...\n30 views\n\n### Power spectrum of modified process\n\nSuppose there is a process $x(t)$ with power spectrum $$S_x(\\omega)=\\lim_{T\\to\\infty}\\frac{1}{T}\\left|\\int_{-T/2}^{T/2}\\mathrm{d}t\\,e^{j\\omega t}x(t)\\right|^2,$$ ignoring the expectation value for ...\n42 views\n\n### How to calculate PSD if i have power vs freq spectrum?\n\ni have a signal something like this how to calculate PSD? i have freq from 191000200 to 196500000 time gap or delta t = 1 or 2 sec, (what i mean is [tn] - [tn-1]) i will be computing in python any ...\n23 views\n\n### Why is the Periodogram Used as an Estimate of PSD?\n\nWhy is the periodogram method as given by Schuster (1898) - which is not a consistent estimate of the PSD - still used, as opposed to consistent non-parametric methods for estimating the PSD like ...\n20 views\n\n### Energy or power signal for continuous signal\n\nI have solved $w(t) = 1dt$ and determined it as power but when $w(t) =\\Pi\\left(\\frac{t}{T_0}\\right)$ it is energy." ]
[ null ]
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https://www.itutorialist.com/tutorials/machine-learning-and-training-neural-network-in-matlab-simpliv
[ "# Machine Learning and Training Neural Network in MATLAB - Simpliv\n\n( Report)\n\nMachine Learning is the up and upcoming branch of Artificial Intelligence and it holds great promises for the generations to come. In this course, we will talk about Machine Learning and Artificial Neural Networks and how you can implement a simple Machine Learning Model in MATLAB.\n\nWho this course is for:\n\n• Anyone who is interested in learning basic concepts of Machine Learning and Neural networks\n\nBasic knowledge\n\n• The course is beginner level for those who are interested in implementing Machine Learning in MATLAB. No prior technical Knowledge is required. However, if you are already familiar with MATLAB, it can be a plus point\n\nWhat you will learn\n\n• You will learn about Machine Learning and how you can train a simple Model in MATLAB on a simple Dataset. You will get to know some basics of MATLAB too and how you can write and run scripts in MATLAB. You will be able to import your own dataset and train it using different parameters to make some interactive prediction model" ]
[ null ]
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https://convertoctopus.com/26-2-ounces-to-pounds
[ "## Conversion formula\n\nThe conversion factor from ounces to pounds is 0.0625, which means that 1 ounce is equal to 0.0625 pounds:\n\n1 oz = 0.0625 lb\n\nTo convert 26.2 ounces into pounds we have to multiply 26.2 by the conversion factor in order to get the mass amount from ounces to pounds. We can also form a simple proportion to calculate the result:\n\n1 oz → 0.0625 lb\n\n26.2 oz → M(lb)\n\nSolve the above proportion to obtain the mass M in pounds:\n\nM(lb) = 26.2 oz × 0.0625 lb\n\nM(lb) = 1.6375 lb\n\nThe final result is:\n\n26.2 oz → 1.6375 lb\n\nWe conclude that 26.2 ounces is equivalent to 1.6375 pounds:\n\n26.2 ounces = 1.6375 pounds\n\n## Alternative conversion\n\nWe can also convert by utilizing the inverse value of the conversion factor. In this case 1 pound is equal to 0.61068702290076 × 26.2 ounces.\n\nAnother way is saying that 26.2 ounces is equal to 1 ÷ 0.61068702290076 pounds.\n\n## Approximate result\n\nFor practical purposes we can round our final result to an approximate numerical value. We can say that twenty-six point two ounces is approximately one point six three eight pounds:\n\n26.2 oz ≅ 1.638 lb\n\nAn alternative is also that one pound is approximately zero point six one one times twenty-six point two ounces.\n\n## Conversion table\n\n### ounces to pounds chart\n\nFor quick reference purposes, below is the conversion table you can use to convert from ounces to pounds\n\nounces (oz) pounds (lb)\n27.2 ounces 1.7 pounds\n28.2 ounces 1.763 pounds\n29.2 ounces 1.825 pounds\n30.2 ounces 1.888 pounds\n31.2 ounces 1.95 pounds\n32.2 ounces 2.013 pounds\n33.2 ounces 2.075 pounds\n34.2 ounces 2.138 pounds\n35.2 ounces 2.2 pounds\n36.2 ounces 2.263 pounds" ]
[ null ]
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https://blog.zwotausend.de/2014/12/using-ir-sensor-and-arduino.html
[ "# blog.zwotausend.de\n\n## 21.12.14\n\n### A different way to use an IR sensor and the Arduino microcontroller to measure infrared pulses/signals", null, "Arduino UNO - like microcontroller\nWith a microcontroller board like the Arduino UNO and a simple infrared light sensor you can read the signals and used pulse sequences from an IR remote control. Probably you've been looking at this website from adafruit.com already, so did I at the beginning. But I didn't want to believe that bypassing the board and using cryptic byte-commands is the only way to measure short pulses in the range of few microseconds, and in the following I will show you how to do the pulse measuring in a more understandable yet potentially more precise way. Among others we use the pulseIn() and the micros() function. See how to use the resulting pulse sequence to control IR equipment in this following article. If you want to control your arduino with an available IR remote, check this blogpost.\n\nLet's first have a look at the code first, afterwards we'll discuss and explain it.\n// THIS CODE WAS IMPLEMENTED BY PATRICK BAYER IN THE YEAR 2014. DO NOT CLAIM THIS CODE FOR YOUR OWN IN ANY WAY AND QUOTE THE SOURCE WHEN YOU USE IT.\n\n#define messart 2          // Matrix x-values\n#define valuepairs 100     // Matrix y-values -> should be bigger than amount of sent pulse-pairs by IR-remote; setting the value higher should not bring problems.\nint measuremethod1 = LOW;    // if value is LOW, pulseIn() waits for the pin to go LOW, starts timing, then waits for the pin to go HIGH and stops timing.\nint measuremethod2 = HIGH;   // if value is HIGH, pulseIn() waits for the pin to go HIGH, starts timing, then waits for the pin to go LOW and stops timing.\n// pulseIn() returns 0 if no pulse starts within a specified time out !!!\nint measureoutput;           // placeholder for serial output\nint irpin=2;               // IR Sensor position on Arduino\nint i;                     // used for different loops; can theoretically be implemented in the loops directly\nlong matrix[valuepairs][messart];    // definition of the matrix\nint ende;                  // variable integer for ending, cause matrix is normally not filled totally\nint changemethods=1;       // starting mode; in the loop sequence always HIGH,LOW,HIGH,LOW,... measure\nint sm=10;                 // round, for example on full hundreds, for this sm = 100\n\nvoid setup () {   Serial.begin(9600); }\n\nlong roundvalues(long rundwert){if(rundwert-rundwert/sm*sm>(sm/2)){return(rundwert/sm*sm+sm);}else{return(rundwert/sm*sm);}}   //  function to round values in the output\n\nvoid loop(){\n\nende=valuepairs;  // for resetting\n\nif(changemethods==1)                                     {\nfor(i=0;i<valuepairs;i++)                                                             {\nmatrix[i]=pulseIn(irpin, measuremethod1);\nmatrix[i]=micros();\nif(matrix[i]==0){ende=i; i=valuepairs; if(matrix>1){changemethods=0;}}     }\nmeasureoutput=measuremethod1;                          }\nelse                               {\nfor(i=0;i<valuepairs;i++)                                                             {\nmatrix[i]=pulseIn(irpin, measuremethod2);\nmatrix[i]=micros();\nif(matrix[i]==0){ende=i; i=valuepairs; if(matrix>1){changemethods=1;}}     }\nmeasureoutput=measuremethod2;    }\n\nif(ende>0)            {\n\nif(measureoutput==0){Serial.println(\"-------- New record: --------\");Serial.println(); Serial.println(\"| ON | OFF |          (whereby OFF was calculated with the micros() command)\");Serial.println();}\nelse              {Serial.println(\"-------- New record: --------\");Serial.println(); Serial.println(\"| OFF | ON |          (whereby ON was calculated with the micros() command)\");Serial.println();}\n\nfor(i=0;i<ende;i++)                      {\nSerial.print(matrix[i]);\nSerial.print(\",\");\nSerial.print(matrix[i+1]-matrix[i]-matrix[i+1]);\nSerial.print(\",\");\nSerial.println();                      }\nSerial.print(\"   Listing has ended, amount of pairs: \");Serial.println(ende);\n\nSerial.print(\"   CSV: \");\nfor(i=0;i<ende;i++)                      {\nSerial.print(matrix[i]);\nSerial.print(\",\");\nSerial.print(matrix[i+1]-matrix[i]-matrix[i+1]);\nSerial.print(\",\");                      }\nSerial.println();\n\nSerial.print(\"   CSV smooth: \");\nfor(i=0;i<ende;i++)                      {\nSerial.print(roundvalues(matrix[i]));\nSerial.print(\",\");\nSerial.print(roundvalues(matrix[i+1]-matrix[i]-matrix[i+1]));\nSerial.print(\",\");                      }\nSerial.println();\n\nSerial.print(\"   Method for measuring: (1=HIGH, 0=LOW):\"); Serial.println(measureoutput);\nSerial.println();  }\n\n}", null, "Screenshot of the output\nIn the following I'll try to explain how the pulse measuring works.\nOn the right you see a screenshot of the serial output, to see how a measured pulse signal actually looks like. Click the image to enlarge it.\nIR sensors can have a different allocation of output pins, so installing it on your Arduino relies on you. In many cases, this sensor outputs a high value (5V) when no IR signal is received, so a pulse of the remote is related to a low voltage on the receiving-pin, as shown in the pulse scheme later. This sensor outputs a low voltage when receiving a 38 kHz signal, what means the infrared LED in your remote goes for about 13 microseconds and out for about 13 microseconds, and this loops for e.g. 800 microseconds. These 800 microseconds are then one \"pulse\" as shown in the pulse scheme afterwards. So we do not measure those very little 38 kHz pulses with the Arduino, because this is done by the sensor itself. For more information visit this page, where you can see pictures of oscilloscope measurements on the topic of IR proximity detection.\n\nThe program is beginning with defining different integers, whereby this section is very well explained in the code itself. Maybe you wonder why some integers are defined using the method  #define. Look at this explanation for further information on this topic.\nIn a first step we have a function called roundvalues, we use long and not int for this because sometimes quite high times (f.ex. 40000 us, where us means microseconds) are in use, and with int we get a roll over - look here if you're interested why. So with roundvalues we can round the output pulse lengths - and they look more smoothly afterwards.\n\nOne basic problem stated on the adafruit page on the topic of reading IR signals was that digitalRead () is too slow for our purpose, and this is quite correct. But instead of measuring the time a certain pulse is high or low, a good idea is to measure the pulse length itself using the pulseIn() function. So one possibility would be to say pulseIn(irpin,HIGH) and afterwards pulseIn(irpin, LOW) and save the different times. But this is not what I did in the code above, for a good reason: pulseIn(irpin, HIGH) for example waits for a pulse to go high (so to 5V on the pin) and measures the time this high pulse is active in microseconds, up so several seconds.", null, "A typical pulse scheme\nBut using pulseIn(irpin, LOW) directly afterwards jumps over one pulse, because the low pulse already started. In the scheme on the right we see a pulse, x is the time axis. at the beginning we are at level 1(HIGH). Opening the pulseIn(irpin, HIGH) function gives us the length between b and c - we jump over our first pulse that is between a and b, what is not really good, and that's why we normally use the pulseIn(irpin, LOW) function at the beginning. But let's assume we started with the HIGH method, so now we get the length between b and c. The microcontroller is slightly after position c now, because it waited for the high pulse to end and additionally saved the pulse length for later. Next we want the length between c and d. But using pulseIn(irpin, LOW) now just gives us the length of the pulse beginning at e - because we are already in the LOW-phase and additionally, the pulseIn(irpin, LOW) function waits until a new low pulse begins - we jump over one full pulse, as said at the beginning.\n\nSo what we do is we use the micros() command to solve this problem. This function gives us the time in microseconds our program is running on the Arduino - at every place we want. So using this function we can save the time where the Arduino actually is executing our commands. So now we do not use the pulseIn(irpin, LOW) and pulseIn(irpin, HIGH) functions in a loop, we only use pulseIn(irpin, LOW) and directly afterwards the micros() command. The output times are stored in a matrix - a list with positions we can later on read out and store values in. To come back to the pulse sequence from above, we first get the length between a and b, the time-position of b, then the length between c and d, and the time-position of d, and so on. The high pulses are afterwards calculated, so for the first HIGH pulse we calculate d minus b minus length (a to b). That's it.", null, "Arduino, IR sensor and IR LED\nSome other things are implemented to make the output more beautiful, understandable and usable, like comma-separated values (CSV) when we later want to build up our own remote by copying the received pulse sequence. The ende integer is used to throw away unneeded values and get out of the procedure when no more LOW pulse is measured, then the pulseIn() function returns zero after some time. The measurement always switches between HIGH and LOW pulse measuring, and in the output you can see the first (low) pulse cannot be measured using the HIGH method, of course.\n\n#### Kommentar posten\n\nKommentare verfassen ist hier sehr einfach, man kann sogar ohne Anmeldung anonym Kommentare hinterlassen. Also, zeig' uns deine Meinung ...\n\nName\n\nE-Mail *\n\nNachricht *" ]
[ null, "https://4.bp.blogspot.com/-wh5FNwNU3qM/VJbf9fKKfKI/AAAAAAAAFO0/dYBqfkMEm5E/s1600/PC200103.jpg", null, "https://2.bp.blogspot.com/-Z9_XcK-rhJw/VJbjT317j0I/AAAAAAAAFPA/vO4VxDm3DAk/s1600/ir%2Breceive%2Bserial%2Bscreen.PNG", null, "https://4.bp.blogspot.com/-3gz8IfWiZfI/VJbqH_C4yLI/AAAAAAAAFPQ/pvvsGIILcOs/s1600/pulse.PNG", null, "https://1.bp.blogspot.com/-Vc_-l0ddp5o/VJbzCHkSraI/AAAAAAAAFPg/zrQlcJpIB-s/s1600/PC200104.jpg", null ]
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https://openmdao.readthedocs.io/en/1.7.3/usr-guide/examples/example_fd.html
[ "# Finite Difference¶\n\nOpenMDAO allows you to specify analytic derivatives for your models, but it is not a requirement. You can choose instead to allow any part or all of your model to be finite differenced to your specifications. Any System (i.e., Component or Group) has a set of options called deriv_options which can be used to turn on finite difference and control its settings. The following settings are available for all groups.\n\ntype : string\nDerivative calculation type (‘user’, ‘fd’, ‘cs’) Default is ‘user’, where derivative is calculated from user-supplied derivatives. Set to ‘fd’ to finite difference this system. Set to ‘cs’ to perform the complex step\nform : string\nFinite difference mode (‘forward’, ‘backward’, ‘central’)\nstep_size : float\nDefault finite difference stepsize\nstep_calc : string\nSet to ‘absolute’ or ‘relative’\n\nThe following examples will show you how to turn on finite difference for a Component, a Group, and a full model.\n\n## Finite Difference on a Component¶\n\nLet us define a simple component that takes an input and multiplies it by 3.0, and include analytic derivatives. We will insert some print statements so that we can watch what it does.\n\nfrom __future__ import print_function\n\nfrom openmdao.api import Component, Group, Problem, IndepVarComp\n\nclass SimpleComp(Component):\n\"\"\" A simple component that provides derivatives. \"\"\"\n\ndef __init__(self):\nsuper(SimpleComp, self).__init__()\n\n# Params\n\n# Unknowns\n\ndef solve_nonlinear(self, params, unknowns, resids):\n\"\"\" Doesn't do much. Just multiply by 3\"\"\"\nunknowns['y'] = 3.0*params['x']\nprint('Execute', self.name)\n\ndef linearize(self, params, unknowns, resids):\n\"\"\"Analytical derivatives.\"\"\"\n\nJ = {}\nJ[('y', 'x')] = 3.0\nprint('Calculate Derivatives:', self.name)\nreturn J\n\n\nNow let’s chain 4 of them together in series. OpenMDAO can calculate a gradient across the chain using all of the individual derivatives. However, let’s finite difference the 2nd and 4th component in the chain.\n\nclass Model(Group):\n\"\"\" Simple model to experiment with finite difference.\"\"\"\n\ndef __init__(self):\nsuper(Model, self).__init__()\n\nself.connect('px.x', 'comp1.x')\nself.connect('comp1.y', 'comp2.x')\nself.connect('comp2.y', 'comp3.x')\nself.connect('comp3.y', 'comp4.x')\n\n# Tell these components to finite difference\nself.comp2.deriv_options['type'] = 'fd'\nself.comp2.deriv_options['form'] = 'central'\nself.comp2.deriv_options['step_size'] = 1.0e-4\n\nself.comp4.deriv_options['type'] = 'fd'\nself.comp4.deriv_options['form'] = 'central'\nself.comp4.deriv_options['step_size'] = 1.0e-4\n\n\nTo do so, we set ‘type’ to ‘fd’ in comp2 and comp4. To further ilustrate setting options, we select central difference with a stepsize of 1.0e-4. Now let’s run the model.\n\n# Setup and run the model.\ntop = Problem()\ntop.root = Model()\ntop.setup()\ntop.run()\n\nprint ('-'*25)\n\nprint(J)\n\n\nWe get output that looks like this:\n\n...\n-------------------------\nCalculate Derivatives: comp1\nExecute comp2\nExecute comp2\nCalculate Derivatives: comp3\nExecute comp4\nExecute comp4\n[[ 81.]]\n\n\nThe output shows that comp2 and comp4 aren’t using their linearize function, but instead are executing twice, as would be expected when using central difference.\n\n## Complex Step on a Component¶\n\nIf you have a pure python component (or an external code that can support complex inputs and outputs) then you can also choose to use complex step to calculate the Jacobian of a component. This will give more accurate derivatives that are insensitive to the step size. Like finite difference, complex step runs your component using the apply_nonlinear or solve_nonlinear functions, but it applies a step in the complex direction. To activate it, you just need to set the “type” option on a Compontent’s deriv_options to “cs”:\n\nself.comp2.deriv_options['type'] = 'cs'\n\n\nIn many cases, this will require no other changes to your code, as long as all of the calculation in your solve_nonlinear and apply_nonlinear support complex numbers. During a complex step, the incoming params vector will return a complex number when a variable is being stepped. Likewise, the unknowns and resids vectors will accept complex values. If you are allocating temporary numpy arrays, remember to conditionally set their dtype based on the dtype in the unknowns vector.\n\nAt present, complex step is not supported on groups of components, so you will need to complex step the components in them individually.\n\n## Finite Difference on Groups of Components¶\n\nNext, we show how to finite difference a group of components together. For this example, let’s finite difference comp2 and comp3 as one entity. To do this, we need to add a Group to the model called ‘sub’ and place comp2 and comp3 in that group.\n\nclass Model(Group):\n\"\"\" Simple model to experiment with finite difference.\"\"\"\n\ndef __init__(self):\nsuper(Model, self).__init__()\n\n# 2 and 3 are in a sub Group\n\nself.connect('px.x', 'comp1.x')\nself.connect('comp1.y', 'sub.comp2.x')\nself.connect('sub.comp2.y', 'sub.comp3.x')\nself.connect('sub.comp3.y', 'comp4.x')\n\n# Tell the group with comps 2 and 3 to finite difference\nself.sub.deriv_options['type'] = 'fd'\nself.sub.deriv_options['step_size'] = 1.0e-4\n\n\nTo turn on finite difference, we have set ‘type’ to ‘fd’ in self.sub.\n\nThere is no change to the execution code. The result looks like this:\n\n...\n-------------------------\nCalculate Derivatives: comp1\nExecute comp2\nExecute comp3\nCalculate Derivatives: comp4\n[[ 81.]]\n\n\nHere we see that, instead of calling ‘linearize’, comp2 and comp3 execute during finite differnce of the group that owns them. This is as we expect.\n\n## Complex Step on Groups of Components¶\n\nComplex step on a sub-group of components is currently not supported, though support is planned. You can perform complex step on your whole model under certain conditions, as is explained later in this example.\n\n## Finite Difference on an Entire Model¶\n\nFinally, let’s finite difference the whole model in one operation. We tell OpenMDAO to do this by setting type to ‘fd’ in the top Group (problem.root).\n\nclass Model(Group):\n\"\"\" Simple model to experiment with finite difference.\"\"\"\n\ndef __init__(self):\nsuper(Model, self).__init__()\n\nself.connect('px.x', 'comp1.x')\nself.connect('comp1.y', 'comp2.x')\nself.connect('comp2.y', 'comp3.x')\nself.connect('comp3.y', 'comp4.x')\n\n# Tell the whole model to finite difference\nself.deriv_options['type'] = 'fd'\n\n\nNothing else changes in the original model. When we run it, we get:\n\n...\n-------------------------\nExecute comp1\nExecute comp2\nExecute comp3\nExecute comp4\n[[ 81.00000002]]\n\n\nSo here, linearize is never called in any component as the finite difference just executes the components in sequence. This is also as expected.\n\n## Complex Step on an Entire Model¶\n\nIf your model supports it, you can use complex step instead of finite difference in your root system to calculate the system gradient. Do this by setting the type in deriv_options of the top system to “cs”.\n\nclass Model(Group):\n\"\"\" Simple model to experiment with finite difference.\"\"\"\n\ndef __init__(self):\nsuper(Model, self).__init__()\n\nself.connect('px.x', 'comp1.x')\nself.connect('comp1.y', 'comp2.x')\nself.connect('comp2.y', 'comp3.x')\nself.connect('comp3.y', 'comp4.x')\n\n# Tell the whole model to complex step\nself.deriv_options['type'] = 'cs'\n\n\nNothing else changes in the original model. When we run it, we get:\n\n...\n-------------------------\nExecute comp1\nExecute comp2\nExecute comp3\nExecute comp4\n[[ 81.]]\n\n\nNotice that the derivative we get is exactly 81, highlighting the accuracy of complex step over finiite difference.\n\nHowever, you can only use complex step if your model is compatible:\n\nAll components must support complex calculations in solve_nonlinear:\nUnder complex step, a component’s params are complex, all stages of the calculation will operate on complex inputs to produce complex outputs, and the final value placed into unknowns is complex. Most Python functions already support complex numbers, so pure Python components will generally satisfy this requirement. Take care with functions like abs, which effectively squelches the complex part of the argument.\nSolvers like Newton that require gradients are not supported:\nComplex stepping a model causes it to run with complex inputs. When there is a nonlinear solver at some level, the solver must be able to converge. Some solvers such as NLGaussSeidel can handle this. However, the Newton solver must linearize and initiate a gradient solve about a complex point. This is not possible to do at present (though we are working on some ideas to make this work.)\n\n## Parallel Finite Difference¶\n\nSuppose you need to calculate a bunch of finite differences, either because you have a bunch of different design variables, or maybe just a single design variable that happens to be an array. OpenMDAO has a special Group called a ParallelFDGroup that will allow you to calculate multiple finite differences in parallel.\n\nLet’s start off our example by creating a Component that has array inputs and outputs.\n\nimport numpy\nimport time\nfrom openmdao.api import Problem, Component, ParallelFDGroup, IndepVarComp\nfrom openmdao.core.mpi_wrap import MPI\n\nclass ArrayFDComp(Component):\n\"\"\" A simple component takes an array input, produces\nan array output, and does not provide derivatives.\n\nArgs\n----\nsize : int\nThe size of the input and output variables.\n\ndelay : float\nThe number of seconds to sleep during the solve_nonlinear\ncall.\n\"\"\"\n\ndef __init__(self, size, delay):\nsuper(ArrayFDComp, self).__init__()\n\nself.delay = delay\n\n# Params\n\n# Unknowns\n\ndef solve_nonlinear(self, params, unknowns, resids):\n\"\"\" Doesn't do much. Just multiply by 3\"\"\"\ntime.sleep(self.delay)\nunknowns['y'] = 3.0*params['x']\n\n\nThe following check is only here so that our doc tests, which don’t run under MPI, will pass. If you use a ParallelFDGroup when you’re not running under MPI, it will behave like a regular Group.\n\nif MPI:\nfrom openmdao.api import PetscImpl as impl\nelse:\nfrom openmdao.api import BasicImpl as impl\n\nprob = Problem(impl=impl)\n\n\nFor this simple example, we’ll do parallel finite difference at the top level of our model, by using a ParallelFDGroup in place of a regular Group, but you can use ParallelFDGroup to replace other Groups inside of your model as well. ParallelFDGroup takes an argument that tells it how many finite differences to perform in parallel. In this case, we’ll do two parallel finite differences. The size of our design variable is 10, so we’ll perform 5 finite differences in each of our two processes. Note that the number of design variables doesn’t have to divide equally among the processes, but you’ll get the best speedup when it does.\n\n# Create a ParallelFDGroup that does 2 finite differences in parallel.\nprob.root = ParallelFDGroup(2)\n\n# let's use size 10 arrays and a delay of 0.1 seconds\nsize = 10\ndelay = 0.1\n\nprob.root.connect('P1.x', 'C1.x')\n\nprob.setup(check=False)\nprob.run()\n\n\nNow we’ll calculate the Jacobian using our parallel finite difference setup.\n\nJ = prob.calc_gradient(['P1.x'], ['C1.y'], mode='fd',\nreturn_format='dict')\n\nprint(J['C1.y']['P1.x'])\n\n\nWhen we’re done, our J should look like this:\n\n[[ 3. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n[ 0. 3. 0. 0. 0. 0. 0. 0. 0. 0.]\n[ 0. 0. 3. 0. 0. 0. 0. 0. 0. 0.]\n[ 0. 0. 0. 3. 0. 0. 0. 0. 0. 0.]\n[ 0. 0. 0. 0. 3. 0. 0. 0. 0. 0.]\n[ 0. 0. 0. 0. 0. 3. 0. 0. 0. 0.]\n[ 0. 0. 0. 0. 0. 0. 3. 0. 0. 0.]\n[ 0. 0. 0. 0. 0. 0. 0. 3. 0. 0.]\n[ 0. 0. 0. 0. 0. 0. 0. 0. 3. 0.]\n[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 3.]]\n\n\nYou can experiment with this example by changing the size of the arrays and the length of the delay. You’ll find that you get the most speedup from parallel finite difference when the delay is longer.\n\nTags" ]
[ null ]
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https://www.edplace.com/worksheet_info/maths/keystage2/year6/topic/877/4639/long-division-problems
[ "", null, "", null, "# Solve Problems Using Long Division\n\nIn this worksheet, students will solve problems involving dividing numbers up to four digits by a two-digit number using the formal written method of long division. There will be remainders, which should be interpreted correctly.", null, "Key stage:  KS 2\n\nCurriculum topic:   Number: Addition, Subtraction, Multiplication and Division\n\nCurriculum subtopic:   Divide to Four Digits (Long Division)\n\nDifficulty level:", null, "", null, "", null, "#### Worksheet Overview\n\nIn this activity, we will use long division to solve problems by dividing up to four digit numbers by two-digit numbers.\n\nWhen using long division, we need to recognise remainders and write them in the appropriate place.", null, "Example\n\n3,904 eggs are packed into boxes of 12.\n\nHow many boxes will there be and how many eggs will be left over?\n\nWe must do   3904 ÷ 12\n\nFirst, do  39 ÷ 12 = 3 rem 3 and bring down the 0.\n\nNext, do 30 ÷ 12 = 2 rem 6 and bring down the 4.\n\nLastly, divide 64 ÷ 12 = 5 rem 4.", null, "We have shown that 3,904 ÷ 12 = 325 r4\n\nThere will be 325 boxes and 4 eggs will be left over.\n\nShall we have a go at some questions now?", null, "### What is EdPlace?\n\nWe're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.\n\nGet started", null, "" ]
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https://mathoverflow.net/questions/220468/good-choice-of-extension-of-equivariant-map
[ "good choice of extension of equivariant map\n\nLet $K$ be a compact Lie group. Let $C_K$ denote the category whose objects are the compact lie groups containing $K$ and whose morphisms are inclusion of the groups. Let $Y$ be a $K-$space such that $Y^L$ is contractible for each closed subgroup $L$ of $K$ except $K$ itself and $Y^K$ is empty.\n\nLet $H\\leqslant G$ be two objects in $C_K$. By equivariant obstruction theory, each $K-$map $$f: H\\longrightarrow Y$$ can be extended to a $K-$map $$\\widetilde{f}: G\\longrightarrow Y$$ which is unique up to homotopy rel $H$.\n\nI wonder whether there is any specific construction of the extension $\\widetilde{f}$ such that we have a covariant functor from $C_K$ to the category of topological spaces, sending $G$ to $Map_K(G, Y)$, and a morphism $H\\hookrightarrow G$ to $f\\mapsto \\widetilde{f}$.\n\nObviously, we have a contravariant functor from $C_K$ to the category of topological spaces, sending $G$ to $Map_K(G, Y)$, and a morphism $H\\hookrightarrow G$ to $g\\mapsto g|_H$ where $g\\in Map_K(G, Y)$ and $g|_H$ is its restriction to $H$.\n\nBut I'm thinking about the other direction and don't have good idea how to find such a \"standard\" extension $\\widetilde{f}$." ]
[ null ]
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https://www.gamblingbonusoffers.com/plunged/big/how/581807958a79cb2f63440645
[ "This trifecta box costs \\$24 for 24 possible finishing combinations. A \\$2 box of two horses would be (2 x 1 x 2) = \\$4. The trifecta box costs more than a straight trifecta because you must pay for each possible finishing combination. 1-48 of 439 results for\"holmes fan parts\" Price and other details may vary based on product size and color. Essentially it would be the same as having 2 . Trifecta Box Cost. H = Total number of horses being boxed. The Trifecta 2.0 Tonneau Cover costs about \\$400, but the price depends on the year, length of the bed, model, and brand of your truck.\n\nHow much does a boxed trifecta with 5 horses cost? Quinella cost The cost of a quinella depends on how many selections are included to fill the first two places. How much does a 4 horse quinella box cost? Exacta Box 1,2. How much does a \\$2 trifecta box cost with 4 horses? Notes: Sportsbook will calculate box cost automatically. Let's continue by explaining how much does a trifecta pay. \\$1 Trifecta box of 4 horses = 24 possible combinations = \\$24. Common alternatives are the four and five-horse trifectas which cost more, but gives punters a better chance of success. \\$1 Trifecta box of 5 horses = 60 possible combinations = \\$60. Even though the minimum bet for a boxed trifecta is only \\$1, you will need to pay a minimum of \\$6 if you select three horses. \\$2 Exacta Box Costs. If 3 horses are selected, the quinella will cost \\$3, if 4 horses . A 4 Horse Trifecta Box on Horses 6-1-8-3 means you are betting \\$1 that any combination horses 6, 1, 8 or 3 will finish first, second and third in any order.\n\nThe formula for calculating the cost of an exacta box is (horses in box x (horses in box minus 1) x dollar amount of bet). A \\$2 box of four horses would be (4 x 3 x 2) = \\$24. Here's a way to bet the trifecta using four horses for \\$18. (H) x (H - 1) x (H - 2) x (C) A 3 horse trifecta box costs \\$6 for 6 combinations: 3 x 2 x 1 x \\$1. \\$12 (six combinations) To figure the cost: Multiply the number of horses used by the number of horses used less one. When using three or more horses in your Exacta Box, any two of your horses must finish first and second. X = size of the bet in dollars. The formula for calculating the cost of an exacta box is (horses in box x (horses in box minus 1) x dollar amount of bet). The 1 in this instance is the key, so it must finish in the top three positions. For example, a box trifecta with 5 selections has 60 (5 x 4 x 3) combinations. A \\$2 box of two horses would be (2 x 1 x 2) = \\$4. For example, Preakness trifecta box payout was 149.30 USD in 2019 for a 1 USD/3 horse bet. A \\$2 box of two horses would be (2 x 1 x 2) = \\$4.\n\nHow much does a boxed trifecta with 5 horses cost? First, select the horse you think will win. It should be at least 43x11x32. A \\$2 box of two horses would be (2 x 1 x 2) = \\$4. How much does a 3 horse box cost? A \\$2 box of three horses would be (3 x 2 x 2) = \\$12. Cost: \\$1 per Combination. \\$1 with 2,3,4: \\$6. Trifecta Box Cost. For example, Preakness trifecta box payout was 149.30 USD in 2019 for a 1 USD/3 horse bet. A \\$2 Trifecta wager 1/2,4,6,8 would cost \\$36. Let's continue by explaining how much does a trifecta pay. How much does it . a \\$2 Trifecta Key Box: 1/2,4,6,8 would cost \\$36; (the 1 is the\"KEY\" and must finish in the first three positions to have any chance of winning, and the other two trifecta positions must be filled by the 2,4,6 OR 8) Just so, how much does it cost to play a 10 cent superfecta box? How much does a \\$2 exacta box cost with 3 horses? C = Cost per Combination, usually \\$1. A \\$2 box of three horses would be (3 x 2 x 2) = \\$12. For a full \\$1 unit, this bet will cost \\$60. HYD-Parts 12inch 3 Speed Table Fan Floor Fan with Remote Control, Air-Circulator Home Fan Office Fan with Timer,Black 4.1 out of 5 stars135 \\$57.99\\$57.99 Get it Wed, Mar 2- Mon, Mar 7 FREE Shipping . Cost: \\$1 per Combination. What pays more exacta or Trifecta? This is the base bike box size. EZ Horse Betting Pro Play.\n\nThere are different types of trifectas, they include: normal trifecta, box trifecta, standout trifecta and roving banker trifecta. Trifecta Box Payouts. What does a \\$2 exacta box cost? You can box three or more horses on a single ticket and wager \\$1 (or more) on each combination. (H) x (H - 1) x (H - 2) x (C) A 3 horse trifecta box costs \\$6 for 6 combinations: 3 x 2 x 1 x \\$1. The trifecta box has a \\$1 minimum bet per combination -- \\$6 minimum total cost.\n\nThe trifecta box costs more than a straight trifecta because you must pay for each possible finishing combination. \\$1 Trifecta box of 4 horses = 24 possible combinations = \\$24. What does a \\$2 exacta box cost? H = Total number of horses being boxed. A 'Key Box' bet includes all possible combinations of selected 'key' horse(s) when combined with other 'non-key' horses in a box bet. But the cost of the cover goes up because of the fabric and . \\$1 Trifecta Key Costs: To figure the cost of a Trifecta Key, use this simple equation: \\$ x Number of horses x number of horses minus one. Since Trifecta Part Wheels are largely played using \\$1 as the basic betting unit, and in the interest of displaying part wheels as clearly as possible, we'll feature only the costs of tickets using \\$1 in the chart that follows. How much does a \\$2 exacta box cost with 3 horses? Notes: Sportsbook will calculate box cost automatically.\n\nThis actually depends on the race and odds: There are no fixed numbers when it comes to how much does trifecta pay question. Starting from a base wager of \\$1, a trifecta box with three horses costs \\$6 because it covers six possible outcomes. \\$1 Trifecta box of 5 horses = 60 possible combinations = \\$60. This trifecta box costs \\$24 for 24 possible finishing combinations. The real contrast between the trifecta and the exacta become crystal-clear when you look at the payouts. This tri-folding truck bed cover is made of strong fabric that is made to look like leather. A \\$2 box of three horses would be (3 x 2 x 2) = \\$12. How much does a 3 horse box cost? C = Cost per Combination, usually \\$1. The chart does not cover all possible . A boxed trifecta will cost you more than a straight trifecta, as you will need to pay for every combination. A cardboard bike box is very popular, and most shipping companies have them for around \\$25.00. For Example, a \\$1 Trifecta Key Box: 1/2, 3, 4 This Key Box wager would cost \\$18. Second key: \\$1 trifecta, 5-6-7-8 with #4 (wins if #4 comes in second, while 5, 6, 7, and 8 account for first and third place in whatever sequence . A \\$2 box of four horses would be (4 x 3 x 2) = \\$24. \\$4 (two combinations) Exacta Box 1,2,3. a \\$2 Trifecta Key Box: 1/2,4,6,8 would cost \\$36; (the 1 is the\"KEY\" and must finish in the first three positions to have any chance of winning, and the other two trifecta positions must be filled by the 2,4,6 OR 8) Just so, how much does it cost to play a 10 cent superfecta box? Example: Let's say you select horse #8, #6, and #3 to finish in any order with a boxed trifecta bet.\n\nBelow is a chart showing how much a trifecta box bet costs, assuming a \\$1 base wager. Tip A \\$2 box of four horses would be (4 x 3 x 2) = \\$24. 43x11x32. Calculating the cost of trifectas where different selections are made for each place is more . A \\$2 box of three horses would be (3 x 2 x 2) = \\$12. For example, a \\$2 trifecta for the 2011 Kentucky Derby brought in \\$3,952.40 compared to a \\$2 exacta bringing in \\$329.80. How much does it . How much do Holmes fan parts cost? This depends on the odds of the horse combinations in relation to the total amount wagered in each of these pools. A \\$2 box of four horses would be (4 x 3 x 2) = \\$24. Quinella cost The cost of a quinella depends on how many selections are included to fill the first two places. Remember, of course, that \\$1 tickets always pay HALF as much as \\$2 ones! Example: To purchase a \\$1 Trifecta Box using four horses, tell the clerk: \"\\$1 Trifecta Box 11-2-3-4.\" The following examples are for a \\$1 Trifecta Box: For example, a \\$1 Trifecta Key 1 with 2,3,4,5 would be 1 x 4 x 3 = 12 possible combinations costing you \\$12. a \\$2 Exacta Key Box: 1/3,7,9,10 would cost \\$16 and is made up exacta box bets of 1 & 3; 1 & 7, 1 & 9 and 1 & 10. How much does it cost to overnight a small flat rate box? How much does a 4 horse quinella box cost? For example, here's how one would plug in a \\$2 trifecta box involving three horses: Next, select three horses you think could finish first, second, or third. This actually depends on the race and odds: There are no fixed numbers when it comes to how much does trifecta pay question. The gambler can put 2 trifecta keys in this particular instance: 1st key: \\$1 trifecta, #4 over 5-6-7-8 (ends up winning if #4 places first and 5, 6, 7, and 8 places second and third in any sequence). Starting from a base wager of \\$1, a trifecta box with three horses costs \\$6 because it covers six possible outcomes. . Overnight Domestic Shipping Up to 70 Pounds for \\$39.95 Ideal for consumers and small businesses selling merchandise online, the Postal Service's Express Mail Flat Rate Box takes the guess work out of shipping, providing overnight delivery up to 70 pounds almost anywhere in the . If 3 horses are selected, the quinella will cost \\$3, if 4 horses . Obviously, it pays to spend the extra \\$2 to take your chances with a serious win. It also has aluminium supports that make it easy to fold. The term 'key box' means that you are keying a horse(s) with other selections in a box bet.\n\nCommon alternatives are the four and five-horse trifectas which cost more, but gives punters a better chance of success. Let's look at how to calculate the costs of a Trifecta Bet. . Occasionally the . Tip a \\$2 Exacta Key Box: 1/3,7,9,10 would cost \\$16 and is made up exacta box bets of 1 & 3; 1 & 7, 1 & 9 and 1 & 10. a \\$1 Trifecta Key Box: 1,3 /5,7 would cost \\$12 and is made up of two trifecta bets that include a box; of 1 with 5,7 and 3 with 5,7 (the 1 AND 3 are \"KEYS\" and one of them must finish in 1 st, 2 nd, or 3rd to have any chance of winning, and the 5 and 7 must finish in the other 2 Trifecta spots.) Trifecta Box Payouts. Alternatively, bettors can calculate the cost for wagers of all prices with the following formula: (H) x (H1-1) x (H-2) x X. H = Number of horses. A 4 Horse Trifecta Box on Horses 6-1-8-3 means you are betting \\$1 that any combination horses 6, 1, 8 or 3 will finish first, second and third in any order. Many racetracks and online betting parlors offer a \\$1 minimum bet on the trifecta." ]
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https://www.shaalaa.com/question-bank-solutions/30-g-urea-m-60-g-mol-1-dissolved-846-g-water-calculate-vapour-pressure-water-this-solution-if-vapour-pressure-pure-water-298-k-23-8-mm-hg-vapour-pressure-liquid-solutions-vapour-pressure-solutions-solids-liquids_16751
[ "Share\n\n# 30 G of Urea (M = 60 G Mol−1) is Dissolved in 846 G of Water. Calculate the Vapour Pressure of Water for this Solution If Vapour Pressure of Pure Water at 298 K is 23·8 Mm Hg. - CBSE (Science) Class 12 - Chemistry\n\nConceptVapour Pressure of Liquid Solutions Vapour Pressure of Solutions of Solids in Liquids\n\n#### Question\n\n30 g of urea (M = 60 g mol−1) is dissolved in 846 g of water. Calculate the vapour pressure of water for this solution if vapour pressure of pure water at 298 K is 23·8 mm Hg.\n\n#### Solution\n\nIt is given that vapour pressure of water, p_1^0 = 23.8 mm of Hg\n\nWeight of water taken, w1 = 846 g\n\nWeight of urea taken, w2 = 30 g\n\nMolecular weight of water, M1 = 18 g mol−1\n\nMolecular weight of urea, M2 = 60 g mol−1\n\nNow, we have to calculate vapour pressure of water in the solution. We take vapour pressure as p1.\n\nNow, from Raoult’s law, we have:\n\n(p_1^0 - p_1)/p_1^0 = n_2/(n_1 - n_2)\n\n=> (p_1^0 - P_1)/p_1^0 = (w_2/M_2)/(w_1/M_1 - w_2/M_2)\n\n= (23.8 - p_1)/23.8 = (30/60)/(346/18 + 30/60)\n\n=> (23.8 - p_1)/23.8 = 0.0105\n\n=> p1 = 23.5501 mm of Hg\n\nHence, the vapour pressure of water in the given solution is 23.5501 mm of Hg and its relative lowering is 0.0105.\n\nIs there an error in this question or solution?\n\n#### Video TutorialsVIEW ALL \n\nSolution 30 G of Urea (M = 60 G Mol−1) is Dissolved in 846 G of Water. Calculate the Vapour Pressure of Water for this Solution If Vapour Pressure of Pure Water at 298 K is 23·8 Mm Hg. Concept: Vapour Pressure of Liquid Solutions - Vapour Pressure of Solutions of Solids in Liquids.\nS" ]
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https://pennstate.pure.elsevier.com/en/publications/dynamic-stability-of-passive-dynamic-walking-on-an-irregular-surf
[ "# Dynamic stability of passive dynamic walking on an irregular surface\n\nJimmy Li Shin Su, Jonathan B. Dingwell\n\nResearch output: Contribution to journalArticlepeer-review\n\n72 Scopus citations\n\n## Abstract\n\nFalls that occur during walking are a significant health problem. One of the greatest impediments to solve this problem is that there is no single obviously \"correct\" way to quantify walking stability. While many people use variability as a proxy for stability, measures of variability do not quantify how the locomotor system responds to perturbations. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and stability. We modified an irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. Because the model's global basin of attraction remained fixed, increasing the amplitude of the applied perturbations directly increased the risk of falling in the model. We generated ten simulations of 300 consecutive strides of walking at each of six perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the model could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., \"local\") perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the model. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating short-term and long-term local exponential rates of divergence for the model. As perturbation amplitudes increased, no changes were seen in orbital stability (r2 = 2.43%; p = 0.280) or long-term local instability (r2 = 1.0%; p = 0.441). These measures essentially reflected the fact that the model never actually \"fell\" during any of our simulations. Conversely, the variability of the walker's kinematics increased exponentially (r2 ≥ 99.6%; p < 0.001) and short-term local instability increased linearly ( r2 = 88.1%; p < 0.001). These measures thus predicted the increased risk of falling exhibited by the model. For all simulated conditions, the walker remained orbitally stable, while exhibiting substantial local instability. This was because very small initial perturbations diverged away from the limit cycle, while larger initial perturbations converged toward the limit cycle. These results provide insight into how these different proposed measures of walking stability are related to each other and to risk of falling.\n\nOriginal language English (US) 802-810 9 Journal of Biomechanical Engineering 129 6 https://doi.org/10.1115/1.2800760 Published - Dec 1 2007\n\n## All Science Journal Classification (ASJC) codes\n\n• Biomedical Engineering\n• Physiology (medical)" ]
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https://ifelse.info/questions/11983/malloc-and-wcscpy-heap-corruption-detected
[ "# Malloc and wcscpy: HEAP CORRUPTION DETECTED\n\n1\n\nI'm trying to create and use a pointer to a string and join it with another reserved string pointer with `malloc` , but I always get this error message:\n\nThis is the code:\n\n``````int wmain(int argc, WCHAR *argv[])\n{\nLPWSTR str1 = L\"Software\\WinSide\\\";\nLPWSTR str2 = (LPWSTR)malloc(wcslen(str1)+1);\nwcscpy(str2, str1);\n\nif (str2 == NULL)\n{\nwprintf(L\"Malloc error.\\n\");\n}\nelse\n{\nwprintf(L\"Result= %s\\n\", str2);\n}\n\nfree(str2);\n\nreturn 0;\n}\n``````\n\nIf I put a value in% co_of big% like 50, for example, it works fine. I know the problem is in memory allocation, but I do not understand why.\n\nCould you help me?\n\nEdit:\n\nIf I use the standard C data types, the program works, but I do not understand why. I add the code:\n\n``````int main(int argc, char * argv[])\n{\nchar * str1 = \"Software\\WinSide\\\";\nchar * str2 = (char *)malloc(strlen(str1)+1);\nstrcpy(str2, str1);\n\nif (str2 == NULL)\n{\nprintf(\"Malloc error.\\n\");\n}\nelse\n{\nprintf(\"Result= %s\\n\", str2);\n\n}\n\nfree(str2);\n\nreturn 0;\n}\n``````\n\nasked by Sergio Calderon 09.11.2016 в 22:38\nsource\n\n2\n\nWithout having experience in Windows, I see that in your code reserves 1 byte at the end of the chain, to store the end of it.\n\n``````LPWSTR str2 = (LPWSTR)malloc(wcslen(str1)+1);\nwcscpy(str2, str1);\n/*wcscat(str2, argv);*/\nDWORD size = wcslen(str1)+1;\n``````\n\nHowever, you use L-strings, with wide characters. I do not remember the exact size or the concrete type (wchar_t or similar), but I think that Window used 32-bit characters (4 bytes) for that type of strings.\n\nTry reserving 4 bytes, instead of one:\n\n``````malloc( wcslen( str1 ) + 4 );\n``````\n\nIf I remember the exact type, I will edit the answer.\n\npostdata: do not mix types. If you use wide strings, use wide characters; if you use normal strings `char *` (LPSTR in Windows?), then use normal characters (sizeof (char))\n\nEDITO\n\nIt's wchar_t; therefore, the correct thing would be\n\n``````LPWSTR str2 = (LPWSTR)malloc(wcslen(str1)+sizeof(wchar_t));\n``````\n\nIt's a common mistake to confuse bytes with characters .\n\n`malloc()` works with bytes .\n`char *str = \"hola\";` is an array of characters that, coincidentally, have a size of 1 byte. `wchar_t *str2 = L\"adios\";` is an array of characters that does not have to be 1 byte each.\n\nIf it were possible to use `sizeof` with memory blocks, we would have something like this:\n\n``````sizeof( malloc( 100 ) ) -> 100\nsizeof( \"hola\" ) -> 5 ( 4 caracteres de 1 byte, mas 1 caracter de terminador de la cadena.\nsizeof( L\"adios\" ) -> depende de la arquitectura, el sistema, etc. Como se vió en el problema, puede ser perfectamente de 48 bytes ( 5 caracteres * 4 bytes cada uno, + 1 caracter (otros 4 bytes) de terminador de la cadena.\n``````\n\nIn addition to the above, the functions that work with strings are prepared and specialized in the type of strings they use. Therefore, `strcpy()` adds 1 byte at the end, while `wcpcpy()` adds a width character (4 or more bytes) at the end.\n\nConclusion : do not assume sizes, use the `sizeof` (which is from the beginning of the language, for something will be), do not mix types, and use the appropriate functions for each one. p>" ]
[ null ]
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https://breakingdownfinance.com/finance-topics/finance-basics/return-calculation/?s=
[ "# Return calculation\n\nCalculating returns is a key aspect of investing. At the same time, we should keep in mind that returns are only half the equation. In addition to a security’s return, investors should always take into consideration the security’s risk as well. A good understanding of both is indispensable. In what follows, we will explain how to calculate and use holding period returns, annual percentage rates, and effective annual rates. Investors should be aware of the return on their investments and should be able to calculate returns themselves.\n\n## Holding period return\n\nHolding period returns (HPR) are the most basic and easiest to calculate returns. They are calculated by simply dividing the terminal value of an investment (Pt) by the initial investment value (P0) and subtracting 1. Obviously, the holding period return measures the percentage gain in wealth over the investment horizon.", null, "In case the investor received income, dividends, or interest over the investment horizon, the holding period return formula just expands by adding this income (denoted D) in the numerator.", null, "## Annual percentage rate\n\nUnfortunately, one disadvantage of holding period returns is that returns on assets with different investment horizons can’t be compared. To do this, we need to divide the holding period returns by their respective  investment horizon T.  The annual percentage rate (APR) we obtain measures the yearly return on each asset.", null, "## Effective annual rate\n\nUnfortunately, the annual percentage rate does not take interest compounding into account. Therefore, we need to adjust the HPR again. This slightly more complicated formula is shown below. The effective annual rate (EAR) measures the annual rate of return on an asset, taking into account any potential interest compounding. It is the most complicated way of calculating a security’s return, but probably also the most accurate.", null, "## Summary\n\nThe return on investment of a security can be calculated in different ways. and investors should be wary of the the advantages and disadvantagese of different methods. Misrepresentation of returns is a way of misleading uninformed investors. Holding period returns, annual percentage rates, and effective annual rates are among the most important ways of calculating returns.\n\n### Return calculation\n\nNeed to have more insights? Download our free excel file: return calculation." ]
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https://www.numbers.education/12749.html
[ "Is 12749 a prime number? What are the divisors of 12749?\n\n## Parity of 12 749\n\n12 749 is an odd number, because it is not evenly divisible by 2.\n\nFind out more:\n\n## Is 12 749 a perfect square number?\n\nA number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 12 749 is about 112.911.\n\nThus, the square root of 12 749 is not an integer, and therefore 12 749 is not a square number.\n\n## What is the square number of 12 749?\n\nThe square of a number (here 12 749) is the result of the product of this number (12 749) by itself (i.e., 12 749 × 12 749); the square of 12 749 is sometimes called \"raising 12 749 to the power 2\", or \"12 749 squared\".\n\nThe square of 12 749 is 162 537 001 because 12 749 × 12 749 = 12 7492 = 162 537 001.\n\nAs a consequence, 12 749 is the square root of 162 537 001.\n\n## Number of digits of 12 749\n\n12 749 is a number with 5 digits.\n\n## What are the multiples of 12 749?\n\nThe multiples of 12 749 are all integers evenly divisible by 12 749, that is all numbers such that the remainder of the division by 12 749 is zero. There are infinitely many multiples of 12 749. The smallest multiples of 12 749 are:\n\n## Numbers near 12 749\n\n### Nearest numbers from 12 749\n\nFind out whether some integer is a prime number" ]
[ null ]
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https://chemistry.stackexchange.com/questions/147863/how-to-find-enthalpy-of-solvation-for-gas-phase-cation-using-hesss-law
[ "# How to find enthalpy of solvation for gas phase cation using Hess's law?\n\nFind enthalpy of solvation $$\\Delta_\\mathrm{solv}H$$ using Hess's law, and show the expression that allows to calculate the enthalpy of solvation.\n\n$$\\ce{Ca^2+(g) -> Ca2+(aq)}$$\n\nI am not told which enthalpies of reaction to use. I don't need the exact value, but I do need to show the sum of each enthalpy. I managed to find the enthalpy of the following reactions:\n\n\\begin{align} \\ce{Ca(g) &-> Ca+(g) + e-} &\\quad \\Delta H &= \\pu{590 kJ mol-1} \\\\ \\ce{Ca+(g) &-> Ca^2+(g) + e-} &\\quad \\Delta H &= \\pu{1145 kJ mol-1} \\\\ \\ce{Ca(s) + 2 H+(aq) &-> Ca^2+(aq) + H2(g)} &\\quad \\Delta H &= \\pu{1925.9 kJ mol-1} \\\\ \\ce{Ca(s) &-> Ca(g)} &\\quad \\Delta H &= \\pu{178 kJ mol-1} \\end{align}\n\nI nearly have the reactions I need, but I am still needing\n\n$$\\ce{H2 -> 2 H+ + 2 e^-}$$\n\nI haven't been able to find the answer.\n\nP.S. I am aware of the enthalpy of formation of $$\\ce{H2}$$, but don't know how/if I can use it here.\n\n• By definition, the reaction $\\ce{H2 -> 2 H+}$ has an enthalpy of reaction equal to zero kJ/mol Mar 21, 2021 at 20:07\n\nOne approach to compute the enthalpy change for the reaction\n\n$$\\ce{H2(g)->2H+(aq) + 2e-}$$\n\nis to combine the bond dissociation enthalpy and hydrogen ionization energy (both refer to gas phase species) and the hydration enthalpy of the hydrogen ion:\n\n$$\\ce{H2(g)->2H(g)}~~~~~~~~{\\Delta H = \\pu{439 kJ/mol} }\\\\ \\ce{2H(g)->2H+(g) +2e-(g)}~~~~~~~~{\\Delta H = \\pu{262 kJ/mol} }\\\\ \\ce{2H+(g)->2H+(aq)}~~~~~~~~{\\Delta H = \\pu{-2260 kJ/mol} }$$\n\nIf you add up the enthalpies you obtain as the solvation enthalpy of $$\\ce{Ca^{2+}}$$ the value $$\\Delta_{\\text{solv}} H = -1546 \\pu{kJ/mol}$$ which is quite reasonable (see eg a table here)\n\nThe result is clearly very different from my earlier answer which I am still pondering:\n\nThe catch is that $$\\Delta H^\\circ=0$$ for this reaction. The reason is because $$\\Delta G^\\circ=0$$ for the reaction (by definition, see standard reduction potential) at all temperatures, and then, since\n\n$$\\Delta H = -T^2\\left( \\frac{\\partial (\\Delta G/T)}{\\partial T}\\right)_p$$ it follows that $$\\Delta H^\\circ=0$$. I suspect the problem with this approach is due to a missing term involving enthalpy of solvation of the electrons (or a similar term involving the electrons) but I haven't put my finger on it.\n\n• Hm, but is not the standard Delta G = 0 the trivial consequence of considering the same but the opposite half reactions ? The each half reaction has non zero but the opposite standard Delta G and Delta H. The above reaction would not have zero reaction enthalpy just because chemists decided SHE to have the reference potential. Mar 21, 2021 at 20:28\n• I would also like to ask, does that also apply to the change needed? I didn't add symbols, but the reaction I need for the hydrogen isn't in a single phase. To make it more accurate to what I need, it'd be this: $$\\ce{H2_{(g)}->2H^+_{(aq)} + 2e^-}$$ Mar 21, 2021 at 20:32\n• That's what I'm saying in my answer, you should just use $\\Delta H = 0$ for that reaction. @Poutnik what else would you suggest? Mar 21, 2021 at 20:55\n• @Buckthorn I say \"Why should be delta G and Delta H of that reaction accidentally zero ?“ It cannot be zero by convention. If we created convention 235U fission has zero enthalpy, it would not have any effect on real enthalpy of fission. That Delta G=0 is for reaction 2H+(aq) + 2e- + H2(g) -> H2(g) + 2 H+(aq) + 2e-. Similarly H2 formation enthalpy is zero, because it relates to another trivial reaction H2 -> H2. Mar 22, 2021 at 6:03\n• @BuckThorn By other words, evaluation of Delta G of redox reaction assumes having one of half-reactions from SHE. Evaluation H2(g)->2 H+(aq) + 2e- is evaluating 2 SHE electrodes together, for which Delta G = Delta G_forward + Delta G_backward = obviously 0, whatever value the single terms have. Mar 22, 2021 at 12:51" ]
[ null ]
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https://www.ictgames.com/mobilePage/doggyDivision/index.html
[ "", null, "# Doggy Division Dinners\n\n### A simple introduction to division in real-life situations\n\nLearning Objectives:\n• Y1: To solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.\n• Y2: To recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers\n• Y2: To solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.\nA simple introduction to division, (through sharing). The dogs are always hungry, there is no end to this game!\n\nThere are two types of division, 'Grouping' and 'Sharing'. Sharing is often used as a first introduction to division in real life situations. This game focusses on 'Sharing', e.g. 10 dog biscuits are shared between 2 dogs. How many biscuits do they get each?\n\nNB: If I were to solve 10 ÷ 2 via the 'Grouping' technique it would be... 'There are 10 dog biscuits. Dogs are allowed 5 biscuits each. How many dogs could you feed?'\n\n### Instructions:\n\nRead the Maths Sentence on the box of dog food, then share out the bones between all of the dogs.\n\nNB: In Year 2 children are expected to use their knowledge of multiplication facts for 2, 5 and 10. I could have focussed on having only 2, 5 or 10 dogs, but I wanted this to be more of an introduction to division rather than a place to use inverse multiplication facts. More able children in Year 2 will find this too simple.\n\nHave fun!\n\nBuild on the learning with\nthese games:", null, "Made using the", null, "and", null, "libraries." ]
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https://demo.formulasearchengine.com/wiki/Dimension_(vector_space)
[ "# Dimension (vector space)\n\nIn mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.Template:Efn\n\nFor every vector space there exists a basis,Template:Efn and all bases of a vector space have equal cardinality;Template:Efn as a result, the dimension of a vector space is uniquely defined. We say V is finite-dimensional if the dimension of V is finite.\n\nThe dimension of the vector space V over the field F can be written as dimF(V) or as [V : F], read \"dimension of V over F\". When F can be inferred from context, dim(V) is typically written.\n\n## Examples\n\nThe vector space R3 has\n\n$\\left\\{{\\begin{pmatrix}1\\\\0\\\\0\\end{pmatrix}},{\\begin{pmatrix}0\\\\1\\\\0\\end{pmatrix}},{\\begin{pmatrix}0\\\\0\\\\1\\end{pmatrix}}\\right\\}$", null, "as a basis, and therefore we have dimR(R3) = 3. More generally, dimR(Rn) = n, and even more generally, dimF(Fn) = n for any field F.\n\nThe complex numbers C are both a real and complex vector space; we have dimR(C) = 2 and dimC(C) = 1. So the dimension depends on the base field.\n\nThe only vector space with dimension 0 is {0}, the vector space consisting only of its zero element.\n\n## Facts\n\nIf W is a linear subspace of V, then dim(W) ≤ dim(V).\n\nTo show that two finite-dimensional vector spaces are equal, one often uses the following criterion: if V is a finite-dimensional vector space and W is a linear subspace of V with dim(W) = dim(V), then W = V.\n\nRn has the standard basis {e1, ..., en}, where ei is the i-th column of the corresponding identity matrix. Therefore Rn has dimension n.\n\nAny two vector spaces over F having the same dimension are isomorphic. Any bijective map between their bases can be uniquely extended to a bijective linear map between the vector spaces. If B is some set, a vector space with dimension |B| over F can be constructed as follows: take the set F(B) of all functions f : BF such that f(b) = 0 for all but finitely many b in B. These functions can be added and multiplied with elements of F, and we obtain the desired F-vector space.\n\nAn important result about dimensions is given by the rank–nullity theorem for linear maps.\n\nIf F/K is a field extension, then F is in particular a vector space over K. Furthermore, every F-vector space V is also a K-vector space. The dimensions are related by the formula\n\ndimK(V) = dimK(F) dimF(V).\n\nIn particular, every complex vector space of dimension n is a real vector space of dimension 2n.\n\nSome simple formulae relate the dimension of a vector space with the cardinality of the base field and the cardinality of the space itself. If V is a vector space over a field F then, denoting the dimension of V by dim V, we have:\n\nIf dim V is finite, then |V| = |F|dim V.\nIf dim V is infinite, then |V| = max(|F|, dim V).\n\n## Generalizations\n\nOne can see a vector space as a particular case of a matroid, and in the latter there is a well-defined notion of dimension. The length of a module and the rank of an abelian group both have several properties similar to the dimension of vector spaces.\n\nThe Krull dimension of a commutative ring, named after Wolfgang Krull (1899–1971), is defined to be the maximal number of strict inclusions in an increasing chain of prime ideals in the ring.\n\n### Trace\n\n{{#invoke:see also|seealso}} The dimension of a vector space may alternatively be characterized as the trace of the identity operator. For instance, $\\operatorname {tr} \\ \\operatorname {id} _{\\mathbf {R} ^{2}}=\\operatorname {tr} \\left({\\begin{smallmatrix}1&0\\\\0&1\\end{smallmatrix}}\\right)=1+1=2.$", null, "This appears to be a circular definition, but it allows useful generalizations.\n\nFirstly, it allows one to define a notion of dimension when one has a trace but no natural sense of basis. For example, one may have an algebra A with maps $\\eta \\colon K\\to A$", null, "(the inclusion of scalars, called the unit) and a map $\\epsilon \\colon A\\to K$", null, "(corresponding to trace, called the counit). The composition $\\epsilon \\circ \\eta \\colon K\\to K$", null, "is a scalar (being a linear operator on a 1-dimensional space) corresponds to \"trace of identity\", and gives a notion of dimension for an abstract algebra. In practice, in bialgebras one requires that this map be the identity, which can be obtained by normalizing the counit by dividing by dimension ($\\epsilon :=\\textstyle {\\frac {1}{n}}\\operatorname {tr}$", null, "), so in these cases the normalizing constant corresponds to dimension.\n\nAlternatively, one may be able to take the trace of operators on an infinite-dimensional space; in this case a (finite) trace is defined, even though no (finite) dimension exists, and gives a notion of \"dimension of the operator\". These fall under the rubric of \"trace class operators\" on a Hilbert space, or more generally nuclear operators on a Banach space.\n\nA subtler generalization is to consider the trace of a family of operators as a kind of \"twisted\" dimension. This occurs significantly in representation theory, where the character of a representation is the trace of the representation, hence a scalar-valued function on a group $\\chi \\colon G\\to K,$", null, "whose value on the identity $1\\in G$", null, "is the dimension of the representation, as a representation sends the identity in the group to the identity matrix: $\\chi (1_{G})=\\operatorname {tr} \\ I_{V}=\\dim V.$", null, "One can view the other values $\\chi (g)$", null, "of the character as \"twisted\" dimensions, and find analogs or generalizations of statements about dimensions to statements about characters or representations. A sophisticated example of this occurs in the theory of monstrous moonshine: the j-invariant is the graded dimension of an infinite-dimensional graded representation of the Monster group, and replacing the dimension with the character gives the McKay–Thompson series for each element of the Monster group." ]
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https://stats.hohoweiya.xyz/2022/10/31/JDAG/
[ "# Joint Bayesian Variable and DAG Selection\n\n##### Posted on Oct 31, 2022\n\njoint sparse estimation of regression coefficients and the covariance matrix for covariates in a high-dimensional regression model, where\n\n• the predictors are both relevant to a response variable of interest and functionally related to one another via a Gaussian directed acyclic graph (DAG) model\n• Gaussian DAG models introduce sparsity in the Cholesky factor of the inverse covariance matrix, and the sparsity pattern in turn corresponds to specific conditional independence assumptions on the underlying predictors\n\nThe paper considers a hierarchical model with spike and slab priors on the regression coefficients and a flexible and general class of DAG-Wishart distributions with multiple shape parameters on the Cholesky factors of the inverse covariance matrix.\n\nunder mild regularity assumptions, the paper establishes the joint selection consistency for both the variable and the underlying DAG of the covariates when the dimension of predictors is allowed to grow much larger than the sample size.\n\n## Literature Review\n\n### graph structure is known\n\n• Li and Li (2008, 2010): a graph-constrained regularization procedure and its theoretical properties to take into account the neighborhood information of the variables measured on a known graph.\n• Pan et al. (2010): a grouped penalty based on the $L_\\gamma$-norm that smooths the regression coefficients of the predictors over the available network\n• Li and Zhang (2010), Stingo and Vannucci (2010): incorporate a graph structure in the Markov random field (MRF) prior on indicators of variable selection\n• Stingo et al. (2011) and Peng et al. (2013): propose the selection of both pathways and genes within them based on prior knowledge on gene-gene-interactions or functional relationships.\n\n### underlying graph is unknown\n\n• Dobra (2009): estimate a network among relevant predictors by first performing a stochastic search in the regression setting to identify possible subsets of predictors, then applying a Bayesian model averaging method to estimate a dependency network\n• Liu et al. (2014): a Bayesian method for regularized regression, which provides inference on the inter-relationship between variables by explicitly modeling through a graph Laplacian matrix.\n• Peterson et al. (2016)\n• Chekouo et al. (2015) and Chekouo et al. (2016): relate two sets of covariate via a DAG to integrate multiple genomic platforms and select the most relevant features\n\nThe goal of the paper: investigate if joint selection consistency results could be established in the high-dimensional regression setting with network-structured predictors\n\nThe paper consider a hierarchical multivariate regression model with\n\n• DAG-Wishart priors on the covariance matrix for the predictors\n• spike and slab priors on regression coefficients\n• independent Bernoulli priors for each edge in the DAG\n• a MRF linking the variable indicators to the graph structure\n\nUnder high-dimensional settings, establish posterior ratio consistency.\n\n• the strong selection consistency implies that under the true model, the posterior probability of the true variable indicator and the true graph converges in probability to 1 as $n\\rightarrow \\infty$.\n\nA Gaussian DAG model over a given DAG $\\cal D$, denoted by $N_\\cD$, consists of all multivariate Gaussian distributions which obey the directed Markov property with respect to a DAG $\\cD$. In particular, if $x = (x_1,\\ldots,x_p)^T\\sim N_p(0,\\Sigma)$ and $N_p(0,\\Sigma)\\in N_\\cD$, then $x_i\\perp x_{i+1,\\ldots,p\\backslash pa_i(\\cD)}\\mid x_{pa_i(\\cD)}$ for each $i$.\n\nAny positive definite matrix $\\Omega$ can be uniquely decomposed as $\\Omega = LD^{-1}L^T$, where $L$ is a lower triangular matrix with unit diagonal entries, and $D$ is a diagonal matrix with positive diagonal entries.\n\nIf $\\Omega = LD^{-1}L^T$, then $N_p(0, \\Omega^{-1})\\in N_\\cD$ iff $L_{ij}=0$ whenever $i\\not\\in pa_j(\\cD)$.\n\nDAG-Wishart distributions form a conjugate family of priors for the Gaussian DAG model.\n\n• response $Y\\in\\IR^n \\sim N(X\\beta,\\sigma^2I_n)$\n• predictors $X=(X_1,\\ldots,X_n)^T\\in \\IR^{n\\times p}$, where $X_i\\sim N_p(0, (LD^{-1}L^T)^{-1})$ for $i=1,\\ldots,n$", null, "", null, "Published in categories Note" ]
[ null, "https://user-images.githubusercontent.com/13688320/198920310-5820766d-bd56-4f22-9719-19cc92e881f5.png", null, "https://user-images.githubusercontent.com/13688320/198920346-ef798edc-f92c-4bca-ba3f-1cec4f56d0ef.png", null ]
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https://www.tutorialspoint.com/draw-a-rectangular-shape-and-extract-objects-using-python-s-opencv
[ "# Draw a rectangular shape and extract objects using Python's OpenCV\n\nOpenCV is an Open Source Computer Vision Library in python. It provides numerous functions to perform various Image and video processing operations. The library uses the Numpy module to represent all the video frames and images as a ndarray type. It needs the numpy library, we need to make sure that the numpy module is also installed in our python interpreter.\n\nIn this article, we will see different ways to draw rectangular shapes and extract the object using python OpenCV.\n\n## Drawing a Rectangle\n\nTo draw the rectangular shape on an image, Python OpenCV module provides a method called cv2.rectangle(). This method will draw the rectangular shapes on an image. Following is the syntax –\n\ncv.rectangle(img, pt1, pt2, color[, thickness[, lineType[, shift]]]\t)\n\n\n### Parameters\n\n• img: The source image where to draw the rectangle.\n\n• pt1: A tuple with the x and y coordinates of one of the vertices of the rectangle (the top left corner of the rectangle)\n\n• pt2: A tuple with the x and y coordinates of the opposite vertex of the rectangle, regarding the previous one (the bottom right corner of the rectangle).\n\n• color: It specifies the color of the rectangle.\n\n• thickness: It is an optional parameter. It specifies the lines thickness of the rectangle. And the default thickness is 1.\n\nx1,y1----------|\n|\t\t |\n| \t\t |\n| ------------x2,y2\n\n\nTherefore the coordinates of pt1 pt2 will be (x1,y1) and (x2,y2) respectively.\n\n## Using pre-defined dimensions\n\nIn this approach we will draw the rectangular shape on an image using the predefined co-ordinates. Which means we will define the pt1, pt2 value manually.\n\n### Example\n\nIn this example, we will use the image co-ordinates to draw and extract the object from a rectangular shape.\n\nimport cv2\nimport numpy as np\n\n# Define the dimensions and position of the rectangle using two points\ntop_left = (80, 80)\nbottom_right = (500, 300)\n\n# defining the colour and thickness of the rectangle\nthickness = 2\ncolor = (0, 255, 0) # Green color\nshape = cv2.rectangle(img, top_left, bottom_right, color, thickness)\n\n# Extracting objects from the rectangular area\nrect_area = img[top_left:bottom_right, top_left:bottom_right]\n\n# Display the image with the drawn rectangle\ncv2.imshow(\"Image with Rectangle\", img)\n\n# Display the extracted rectangular area\ncv2.imshow(\"Rectangular Area\", rect_area)\n\ncv2.waitKey(0)\ncv2.destroyAllWindows()\n\n\n### Output", null, "### Cropped Image", null, "## Using mouse event flags\n\nTo draw the rectangular shapes on an image, here we will use the below mouse event −\n\n• cv2.EVENT_RBUTTONDOWN: indicates the right button is pressed.\n\n• cv2.EVENT_LBUTTONUP: indicates the left button is released\n\nAlso, we will use the setMouseCallback() function to set the mouse event handler for the specified window\n\n### The setMouseCallback() function\n\nThe function is used to specify which function has to be called for a specific window. In other words, the function creates a mouse event handler for the specified window.\n\n### Syntax\n\ncv2.setMouseCallback(winname, onMouse, userdata)\n\n\n### Parameters\n\n• Winname: Name of the specific window.\n\n• OnMouse: Callback function for mouse events.\n\n• Userdata: The optional parameter passed to the callback.\n\nThis approach can be executed using the command line interface. So here we will use the argparse module as it provides a convenient interface to handle the command line arguments.\n\nInitially, we will set a mouse callback function to a namedWindow() method to read the rectangular coordinates where the user draws. And by using the mouse click events we will identify the x and y coordinates and then will draw the rectangular shape using the cv2.rectangle() function.\n\nNote − To execute this code, we need to save the program file and input the image in the same location and then run the below command in the command prompt.\n\nPython program_file_name.py --image source_image_name.jpg\n\n\n### Example\n\nLet’s take an example to draw the rectangular shape to extract the object.\n\nimport cv2\nimport argparse\n\npoint = []\ncrop = False\n\ndef shape_selection(event, x, y, flags, param):\n# grab references to the global variables\nglobal point, crop\n\n# Record the starting(x, y) coordinates when the left mouse button was clicked\nif event == cv2.EVENT_LBUTTONDOWN:\npoint = [(x, y)]\n\n# check to see if the left mouse button was released\nelif event == cv2.EVENT_LBUTTONUP:\n# record the ending (x, y) coordinates\npoint.append((x, y))\n\n# draw a rectangle\ncv2.rectangle(image, point, point, (0, 255, 0), 2)\ncv2.imshow(\"image\", image)\n\n# construct the argument parser and parse the arguments\nap = argparse.ArgumentParser()\nap.add_argument(\"-i\", \"--image\", required = True, help =\"Images/Dog.jpg\")\nargs = vars(ap.parse_args())\n\nclone = image.copy()\ncv2.namedWindow(\"image\")\n# setting the mouse callback function\ncv2.setMouseCallback(\"image\", shape_selection)\n\n# keep looping until the 'q' key is pressed\nwhile True:\n# display the image and wait for a keypress\ncv2.imshow(\"image\", image)\nkey = cv2.waitKey(1) & 0xFF\n\n# press 'r' to reset window\nif key == ord(\"r\"):\nimage = clone.copy()\n\n# if the 'c' key is pressed, break from the loop\nelif key == ord(\"c\"):\nbreak\n\nif len(point) == 2:\ncrop_img = clone[point:point, point:point]\ncv2.imshow(\"crop_img\", crop_img)\ncv2.waitKey(0)\n\n# close all open windows\ncv2.destroyAllWindows()\n\n\nOpen the command prompt and execute the above program using the following command −\n\npython test.py --image image5.jpg\n\n\nThis will generate a window displaying the input image on which you can select the desired object as shown below –", null, "Note − After selecting the desired area of the image press the key C on your keyboard to crop.", null, "We have successfully drawn the rectangular shape and extracted that selected object from the image.\n\nUpdated on: 30-May-2023\n\n339 Views", null, "" ]
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https://nathalievialaneix.eu/doc/html/TP1_normalization.html
[ "This file illustrates the normalization and differential analysis of RNAseq data on a real life dataset. The data are provided by courtesy of the transcriptomic platform of IPS2 and the name of the genes were shuffled. Hence the results are not biologically interpretable. They are composed of three files, all included in the directory data:\n\n• D1-counts.txt contains the raw counts of the experiment (13 columns: the first one contains the gene names, the others correspond to 12 different samples);\n\n• D1-genesLength.txt contains information about gene lengths;\n\n• D1-targets.txt contains information about the sample and the experimental design.\n\nIn the rest of this file, we:\n\n1/ first import and describe the data;\n\n2/ then perform and compare different normalizations;\n\n3/ finally perform a differential analysis using different methods and models.\n\nWe advice that you use the file by reading the R code while trying to make sense of it. Then, you run it and analyze the results. The packages devtools, ggplot2, gridExtra, reshape2, mixOmics, RColorBrewer, DESeq, edgeR and VennDiagram are required to compile this file. Information about my system (including package and R versions) are provided at the end of this file, in Section “Session information”.\n\nlibrary(ggplot2)\nlibrary(gridExtra)\nlibrary(reshape2)\nlibrary(mixOmics)\nlibrary(RColorBrewer)\nlibrary(DESeq)\nlibrary(edgeR)\nlibrary(VennDiagram)\nlibrary(devtools)\n\n## Data description and importation\n\nThe data used in this practical session correspond to 12 samples of RNAseq obtained from microdissections on plants. Plants have four different genotypes: the wild type (“wt”“) plant and three types of mutants and are observed three times in the same conditions. for information Mutants 1 and 2 have a similar phenotype (more complicated leaves than the wild type) whereas mutant 3 has the opposite phenotype (simpler leaves than the wild type).\n\nThe datasets are included in the repository data located at the root of the material for this practical session. They can be loaded using:\n\nraw_counts <- read.table(\"../data/D1-counts.txt\", header = TRUE, row.names = 1)\nraw_counts <- as.matrix(raw_counts)\nstringsAsFactors = FALSE)\ngene_lengths <- scan(\"../data/D1-genesLength.txt\")\n\n### Raw counts\n\nThe dimensions of the raw count matrix are equal to:\n\ndim(raw_counts)\n## 50897 12\n\nwhich shows that the data contains 12 columns (samples) and 50897 rows (genes). And a quick look is obtained by:\n\nhead(raw_counts)\n## wt_1 wt_2 wt_3 mut1_1 mut1_2 mut1_3 mut2_1 mut2_2 mut2_3\n## Medtr0001s0010.1 0 0 0 1 0 1 0 0 0\n## Medtr0001s0070.1 0 0 0 0 0 0 0 0 0\n## Medtr0001s0100.1 0 0 0 0 0 0 0 0 0\n## Medtr0001s0120.1 0 0 0 0 0 0 0 0 0\n## Medtr0001s0160.1 0 0 0 0 0 0 0 0 0\n## Medtr0001s0190.1 0 0 0 0 0 0 0 0 0\n## mut3_1 mut3_2 mut3_3\n## Medtr0001s0010.1 0 1 0\n## Medtr0001s0070.1 0 0 0\n## Medtr0001s0100.1 0 0 0\n## Medtr0001s0120.1 0 0 0\n## Medtr0001s0160.1 0 0 0\n## Medtr0001s0190.1 0 0 0\n\nwhich shows that the row names are gene names and that the data are made of counts. Many of these counts are equal to 0. A basic exploratory analysis of the count data is provided in the next section.\n\n### Experimental design\n\nThe experimental design is described in the object design:\n\ndesign\n## labels group replicat\n## 1 wt_1 wt repbio1\n## 2 wt_2 wt repbio2\n## 3 wt_3 wt repbio3\n## 4 mut1_1 mut1 repbio1\n## 5 mut1_2 mut1 repbio2\n## 6 mut1_3 mut1 repbio3\n## 7 mut2_1 mut2 repbio1\n## 8 mut2_2 mut2 repbio2\n## 9 mut2_3 mut2 repbio3\n## 10 mut3_1 mut3 repbio1\n## 11 mut3_2 mut3 repbio2\n## 12 mut3_3 mut3 repbio3\n\nthat contains 3 columns: the first one labels is the sample name, the second one group is the group of the sample (wild type or one of three types of mutant) and the last one replicat is the biological replicate number.\n\n## Basic exploratory analysis of raw counts\n\nWe start the analysis by filtering out the genes for which no count has been found:\n\nraw_counts_wn <- raw_counts[rowSums(raw_counts) > 0, ]\ndim(raw_counts_wn)\n## 27916 12\n\nThe number of genes which have been filtered out is thus equal to 22981.\n\nIt is often useful, to visualize the count distribution, to compute “pseudo counts”, which are log-transformed counts:\n\npseudo_counts <- log2(raw_counts_wn + 1)\nhead(pseudo_counts)\n## wt_1 wt_2 wt_3 mut1_1 mut1_2 mut1_3\n## Medtr0001s0010.1 0.000000 0.000000 0.000000 1.000000 0.000000 1.000000\n## Medtr0001s0200.1 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000\n## Medtr0001s0260.1 6.357552 6.768184 6.643856 6.169925 6.507795 6.189825\n## Medtr0001s0360.1 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000\n## Medtr0001s0490.1 1.000000 2.000000 0.000000 0.000000 0.000000 0.000000\n## Medtr0002s0040.1 7.707359 6.918863 7.826548 2.584963 2.000000 4.643856\n## mut2_1 mut2_2 mut2_3 mut3_1 mut3_2 mut3_3\n## Medtr0001s0010.1 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000\n## Medtr0001s0200.1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000\n## Medtr0001s0260.1 6.209453 6.392317 6.672425 6.820179 6.554589 6.539159\n## Medtr0001s0360.1 0.000000 1.584963 0.000000 1.000000 0.000000 0.000000\n## Medtr0001s0490.1 0.000000 0.000000 1.584963 1.000000 0.000000 1.000000\n## Medtr0002s0040.1 6.643856 7.651052 8.044394 3.169925 3.459432 1.584963\ndf_raw <- melt(pseudo_counts, id = rownames(raw_counts_wn))\nnames(df_raw)[1:2]<- c(\"id\", \"sample\")\ndf_raw$method <- rep(\"Raw counts\", nrow(df_raw)) head(df_raw) ## id sample value method ## 1 Medtr0001s0010.1 wt_1 0.000000 Raw counts ## 2 Medtr0001s0200.1 wt_1 0.000000 Raw counts ## 3 Medtr0001s0260.1 wt_1 6.357552 Raw counts ## 4 Medtr0001s0360.1 wt_1 0.000000 Raw counts ## 5 Medtr0001s0490.1 wt_1 1.000000 Raw counts ## 6 Medtr0002s0040.1 wt_1 7.707359 Raw counts The object df_raw will be used later to compare the effect of different normalization on the count distribution in the different samples. ### Count distribution First, we provide an overview of the distribution of the first sample (without the genes that have been filtered out) by ploting the histograms of raw counts and pseudo counts: df <- data.frame(rcounts = raw_counts_wn[ ,1], prcounts = pseudo_counts[ ,1]) p <- ggplot(data=df, aes(x = rcounts, y = ..density..)) p <- p + geom_histogram(fill = \"lightblue\") p <- p + theme_bw() p <- p + ggtitle(paste0(\"count distribution '\", design$labels, \"'\"))\np <- p + xlab(\"counts\")\n\np2 <- ggplot(data=df, aes(x = prcounts, y = ..density..))\np2 <- p2 + geom_histogram(fill = \"lightblue\")\np2 <- p2 + theme_bw()\np2 <- p2 + ggtitle(paste0(\"count distribution - '\", design$labels, \"'\")) p2 <- p2 + xlab(expression(log(counts + 1))) grid.arrange(p, p2, ncol = 2)", null, "This figure shows that the count distribution is highly skewed with a large proportion of genes with a count equal to 0 and a few number of genes with an extreme count (more that $$2^{15}$$). ### Relation between mean and variance Another important feature of RNAseq data is the fact that they are overdispersed. This means that the variance of the count of a given gene over different biological samples within a given condition is larger than the average count for the same gene. This feature is illustrated by plotting the graphics of the mean vs variance for condition “wt” for all genes with an average count smaller than 5000 (otherwise the chart can not be read easily): df <- data.frame(mean = apply(raw_counts_wn[ ,design$group == \"wt\"], 1, mean),\nvar = apply(raw_counts_wn[ ,design$group == \"wt\"], 1, var)) df <- df[df$mean <= 5000, ]\np <- ggplot(data=df, aes(x = mean, y = var))\np <- p + geom_point(colour = \"orange\")\np <- p + theme_bw()\np <- p + geom_abline(aes(intercept=0, slope=1))\np <- p + ggtitle(\"Variance versus mean in counts\") + ylab(\"variance\")\nprint(p)", null, "In this figure, the black line is the “y=x” diagonal. It is easy to see that, for most genes, the variance is much larger than the mean.\n\n### PCA\n\nFinally, a PCA is performed to identify the main sources of variability in the dataset. Pseudo-counts are used to perform this PCA.\n\nresPCA <- pca(t(pseudo_counts), ncomp = 12)\nplot(resPCA)", null, "The first component explains more variance than the other components which almost all equally reproduce variance. The projection of the samples on the first two PCs is obtained with:\n\nplotIndiv(resPCA, group = design$group, col.per.group = brewer.pal(4, \"Dark2\"))", null, "This figure shows that mutants 1 and 3 are well separated from the other wild type but that wild type is not well separated from mutant 2. ## Normalization This section performs different normalization approaches for RNAseq data. These normalization are performed using either DESeq (RLE) or edgeR (TC, RPKM, UQ, TMM). The final count distribution is compared to the raw count distribution in the last part of this section. ### DESeq To perform the normalization with DESeq, an object of type CountDataSet has to be created: dge <- newCountDataSet(raw_counts_wn, conditions = design$group)\ndge\n## CountDataSet (storageMode: environment)\n## assayData: 27916 features, 12 samples\n## element names: counts\n## protocolData: none\n## phenoData\n## sampleNames: wt_1 wt_2 ... mut3_3 (12 total)\n## varLabels: sizeFactor condition\n## featureData: none\n## experimentData: use 'experimentData(object)'\n## Annotation:\n\nIn this object, the attribute sizeFactor is at first missing:\n\nsizeFactors(dge)\n## wt_1 wt_2 wt_3 mut1_1 mut1_2 mut1_3 mut2_1 mut2_2 mut2_3 mut3_1\n## NA NA NA NA NA NA NA NA NA NA\n## mut3_2 mut3_3\n## NA NA\n\nThe function estimateSizeFactors() allows to estimate the size factors. The dge object is unchanged but the attribute sizeFactor is now given:\n\ndge <- estimateSizeFactors(dge)\nsizeFactors(dge)\n## wt_1 wt_2 wt_3 mut1_1 mut1_2 mut1_3 mut2_1\n## 0.9753728 1.1491346 1.0187414 0.9167701 1.0326086 1.1436435 0.9664323\n## mut2_2 mut2_3 mut3_1 mut3_2 mut3_3\n## 0.9570126 0.9826726 1.1355102 0.9271699 0.9202688\n\nNormalized counts can be obtained using the function counts with the option normalized = TRUE. The calculation of the normalized counts is performed with the formula $$\\tilde{K}_{gj} = \\frac{K_{gj}}{s_j}$$. The following command lines compare the result of the counts function with this calculation:\n\ndeseq_normcount <- counts(dge, normalized = TRUE)\ntest_normcount <- sweep(raw_counts_wn, 2, sizeFactors(dge), \"/\")\nsum(test_normcount != deseq_normcount)\n## 0\n\nFinally, pseudo counts are computed and stored in a data frame for further comparison.\n\npseudo_deseq <- log2(deseq_normcount + 1)\ndf_deseq <- melt(pseudo_deseq, id = rownames(raw_counts_wn))\nnames(df_deseq)[1:2]<- c(\"id\", \"sample\")\ndf_deseq$method <- rep(\"DESeq (RLE)\", nrow(df_raw)) ### edgeR In this section, the package edgeR is perform to compare the other normalization approaches. To do so, a DGEList object has to be created from the count data: dge2 <- DGEList(raw_counts_wn) dge2 ## An object of class \"DGEList\" ##$counts\n## wt_1 wt_2 wt_3 mut1_1 mut1_2 mut1_3 mut2_1 mut2_2 mut2_3\n## Medtr0001s0010.1 0 0 0 1 0 1 0 0 0\n## Medtr0001s0200.1 0 1 0 0 0 0 0 0 0\n## Medtr0001s0260.1 81 108 99 71 90 72 73 83 101\n## Medtr0001s0360.1 0 0 1 0 0 0 0 2 0\n## Medtr0001s0490.1 1 3 0 0 0 0 0 0 2\n## mut3_1 mut3_2 mut3_3\n## Medtr0001s0010.1 0 1 0\n## Medtr0001s0200.1 0 0 0\n## Medtr0001s0260.1 112 93 92\n## Medtr0001s0360.1 1 0 0\n## Medtr0001s0490.1 1 0 1\n## 27911 more rows ...\n##\n## $samples ## group lib.size norm.factors ## wt_1 1 5932414 1 ## wt_2 1 7129204 1 ## wt_3 1 6223759 1 ## mut1_1 1 5577595 1 ## mut1_2 1 6272344 1 ## 7 more rows ... The library sizes and the normalization factors for all samples are obtained by: dge2$samples\n## group lib.size norm.factors\n## wt_1 1 5932414 1\n## wt_2 1 7129204 1\n## wt_3 1 6223759 1\n## mut1_1 1 5577595 1\n## mut1_2 1 6272344 1\n## mut1_3 1 6634542 1\n## mut2_1 1 5897356 1\n## mut2_2 1 5785184 1\n## mut2_3 1 5767730 1\n## mut3_1 1 7106881 1\n## mut3_2 1 5872052 1\n## mut3_3 1 6035692 1\n\n#### Total count\n\nNormalization by Total Count (TC) is obtained directly by the function cpm. Pseudo-counts ($$\\log_2$$ transformed counts) are computed and stored in a data frame for later use.\n\npseudo_TC <- log2(cpm(dge2) + 1)\n\ndf_TC <- melt(pseudo_TC, id = rownames(raw_counts_wn))\nnames(df_TC)[1:2] <- c (\"id\", \"sample\")\n\n#### Upper quartile\n\nUpper quartile normalization is obtained with the function calcNormFactors. This function changes the variable norm.factors in the DGEList object and thus also the way the functions cpm and rpkm are computing counts: now, a normalized library size, equal to the original library size multiplied by the normalization factor, is used to compute normalized counts: $$\\tilde{K}_{gj} = \\frac{K_{gj}}{\\mbox{modified LS}}*10^6$$. The normalization factors are computed using:\n\ndge2 <- calcNormFactors(dge2, method = \"upperquartile\")\ndge2$samples ## group lib.size norm.factors ## wt_1 1 5932414 1.0047308 ## wt_2 1 7129204 0.9810476 ## wt_3 1 6223759 1.0130558 ## mut1_1 1 5577595 1.0068753 ## mut1_2 1 6272344 0.9942229 ## mut1_3 1 6634542 1.0593861 ## mut2_1 1 5897356 0.9873347 ## mut2_2 1 5785184 1.0124342 ## mut2_3 1 5767730 1.0453656 ## mut3_1 1 7106881 0.9792811 ## mut3_2 1 5872052 0.9857220 ## mut3_3 1 6035692 0.9361638 The previous formula is compared to the result of the function cpm in the following command lines: test_normcount <- sweep(dge2$counts, 2,\ndge2$samples$lib.size*dge2$samples$norm.factors / 10^6,\n\"/\")\nrange(as.vector(test_normcount - cpm(dge2)))\n## -1.818989e-12 0.000000e+00\n\nwhich shows no difference. Finally, pseudo counts are obtained and stored in a data frame:\n\npseudo_UQ <- log2(cpm(dge2) + 1)\n\ndf_UQ <- melt(pseudo_UQ, id = rownames(raw_counts_wn))\nnames(df_UQ)[1:2] <- c (\"id\", \"sample\")\ndf_UQ$method <- rep(\"UQ\", nrow(df_UQ)) #### TMM TMM normalization works similarly as UQ and updates the value of the variable norm.factors: dge2 <- calcNormFactors(dge2, method = \"TMM\") dge2$samples\n## group lib.size norm.factors\n## wt_1 1 5932414 1.0082044\n## wt_2 1 7129204 0.9850930\n## wt_3 1 6223759 1.0047944\n## mut1_1 1 5577595 1.0064979\n## mut1_2 1 6272344 1.0094894\n## mut1_3 1 6634542 1.0593265\n## mut2_1 1 5897356 0.9977013\n## mut2_2 1 5785184 1.0096719\n## mut2_3 1 5767730 1.0387295\n## mut3_1 1 7106881 0.9791254\n## mut3_2 1 5872052 0.9637238\n## mut3_3 1 6035692 0.9429276\n\nNormalized pseudo counts are obtained with the function cpm and stored in a data frame:\n\npseudo_TMM <- log2(cpm(dge2) + 1)\n\ndf_TMM <- melt(pseudo_TMM, id = rownames(raw_counts_wn))\nnames(df_TMM)[1:2] <- c (\"id\", \"sample\")\ndf_TMM$method <- rep(\"TMM\", nrow(df_TMM)) ### Comparison This last section shows the comparison between all normalization methods (and original raw data) for this data set. First, the distributions of all samples and all normalization methods are compared with boxplots and density plots: df_allnorm <- rbind(df_raw, df_deseq, df_TC, df_RPKM, df_UQ, df_TMM) df_allnorm$method <- factor(df_allnorm\\$method,\nlevels = c(\"Raw counts\", \"DESeq (RLE)\", \"TC\",\n\"RPKM\", \"TMM\", \"UQ\"))\n\np <- ggplot(data=df_allnorm, aes(x=sample, y=value, fill=method))\np <- p + geom_boxplot()\np <- p + theme_bw()\np <- p + ggtitle(\"Boxplots of normalized pseudo counts\\n\nfor all samples by normalization methods\")\np <- p + facet_grid(. ~ method)\np <- p + ylab(expression(log ~ (normalized ~ count + 1))) + xlab(\"\")\np <- p + theme(title = element_text(size=10), axis.text.x = element_blank(),\naxis.ticks.x = element_blank())\nprint(p)" ]
[ null, 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null, 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", null, 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", null, 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", 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http://www.worldlibrary.in/articles/eng/Teleparallelism
[ "", null, "#jsDisabledContent { display:none; } My Account | Register | Help", null, "Flag as Inappropriate", null, "This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate?          Excessive Violence          Sexual Content          Political / Social Email this Article Email Address:\n\n# Teleparallelism\n\nArticle Id: WHEBN0000903686\nReproduction Date:\n\n Title: Teleparallelism", null, "Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:\n\n### Teleparallelism\n\nTeleparallelism (also called teleparallel gravity), was an attempt by Einstein to base a unified theory of electromagnetism and gravity on the mathematical structure of distant parallelism, also referred to as absolute or teleparallelism. In this theory, a spacetime is characterized by a curvature-free linear connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field.\n\n## Contents\n\n• Teleparallel spacetimes 1\n• New teleparallel gravity theory 2\n• Møller Tetrad Theory of Gravitation 2.1\n• New translation teleparallel gauge theory of gravity 3\n• Non-gravitational contexts 4\n• References 6\n• Books 7\n\n## Teleparallel spacetimes\n\nThe crucial new idea, for Einstein, was the introduction of a tetrad field, i.e., a set \\{\\mathrm X_1, \\dots,\\mathrm X_4\\} of four vector fields defined on all of M\\, such that for every p\\in M\\, the set \\{\\mathrm X_1(p), \\dots,\\mathrm X_4(p)\\} is a basis of T_pM\\,, where T_pM\\, denotes the fiber over p\\, of the tangent vector bundle TM\\,. Hence, the four-dimensional spacetime manifold M\\, must be a parallelizable manifold. The tetrad field was introduced to allow the distant comparison of the direction of tangent vectors at different points of the manifold, hence the name distant parallelism. His attempt failed because there was no Schwarzschild solution in his simplified field equation.\n\nIn fact, one can define the connection of the parallelization (also called Weitzenböck connection) \\{\\mathrm X_{i}\\} to be the linear connection \\nabla\\, on M\\, such that \n\n\\nabla_{v}(f^{i}\\mathrm X_{i})=(vf^{i})\\mathrm X_{i}(p)\\,,\n\nwhere v\\in T_pM\\, and f^{i}\\, are (global) functions on M\\,; thus f^{i}X_{i}\\, is a global vector field on M\\,. In other words, the coefficients of Weitzenböck connection \\nabla\\, with respect to \\{X_{i}\\} are all identically zero, implicitly defined by:\n\n\\nabla_{\\mathrm{X}_i} \\mathrm{X}_j = 0 \\, ,\n\nhence W^k{}_{ij}=\\omega^k(\\nabla_{\\mathrm{X}_i} \\mathrm{X}_j)\\equiv0 \\, , for the connection coefficients (also called Weitzenböck coefficients) —in this global basis. Here \\omega^k\\, is the dual global basis (or co-frame) defined by \\omega^i(\\mathrm{X}_j)=\\delta^i_j\\,.\n\nThis is what usually happens in Rn, in any affine space or Lie group (for example the 'curved' sphere S3 but 'Weitzenböck flat' manifold).\n\nUsing the transformation law of a connection, or equivalently the \\nabla properties, we have the following result.\n\nProposition. In a natural basis, associated with local coordinates (U, x^{\\mu}), i.e., in the holonomic frame \\partial_{\\mu}, the (local) connection coefficients of the Weitzenböck connection are given by:\n\n\\Gamma^{\\beta}{}_{\\mu\\nu}= h^{\\beta}_{i} \\partial_{\\nu}h^{i}_{\\mu}\\,,\n\nwhere \\mathrm X_{i} = h^{\\mu}_{i}\\partial_{\\mu}\\quad {i,\\mu} = 1,2, \\dots n are the local expressions of a global object, that is, the given tetrad.\n\nWeitzenböck connection has vanishing curvature, but —in general— non-vanishing torsion.\n\nGiven the frame field \\{X_{i}\\}, one can also define a metric by conceiving of the frame field as an orthonormal vector field. One would then obtain a pseudo-Riemannian metric tensor field g\\, of signature (3,1) by\n\ng(X_{i},X_{j})=\\eta_{ij}\\,,\n\nwhere\n\n\\eta_{ij}={\\mathrm {diag}}(-1,-1,-1,1)\\,.\n\nThe corresponding underlying spacetime is called, in this case, a Weitzenböck spacetime.\n\nIt is worth noting to see that these 'parallel vector fields' give rise to the metric tensor as a by-product.\n\n## New teleparallel gravity theory\n\nNew teleparallel gravity theory (or new general relativity) is a theory of gravitation on Weitzenböck space-time, and attributes gravitation to the torsion tensor formed of the parallel vector fields.\n\nIn the New teleparallel gravity theory the fundamental assumptions are as follows: (A) Underlying space-time is the Weitzenböck space-time, which has a quadruplet of parallel vector fields as the fundamental structure. These parallel vector fields give rise to the metric tensor as a by-product. All physical laws are expressed by equations that are covariant or form invariant under the group of general coordinate transformations. (B) The equivalence principle is valid only in classical physics. (C) Gravitational field equations are derivable from the action principle. (D) The field equations are partial differential equations in the field variables of not higher than the second order.\n\nIn 1961 Møller revived Einstein’s idea, and Pellegrini and Plebanski found a Lagrangian formulation for absolute parallelism.\n\n### Møller Tetrad Theory of Gravitation\n\nIn 1961, Møller showed that a tetrad description of gravitational fields allows a more rational treatment of the energy-momentum complex than in a theory based on the metric tensor alone. The advantage of using tetrads as gravitational variables was connected with the fact that this allowed to construct expressions for the energy-momentum complex which had more satisfactory transformation properties than in a purely metric formulation.\n\n## New translation teleparallel gauge theory of gravity\n\nIn 1967, quite independently, Hayashi and Nakano revived Einstein’s idea, and Pellegrini—Plebanski started to formulate the gauge theory of the space-time translation group. Hayashi pointed out the connection between the gauge theory of space-time translation group and absolute parallelism. The first fiber bundle formulation was provided by Cho. This model was later studied by Schweizer et al., Nitsch and Hehl, Meyer, and more recent advances can be found in Aldrovandi and Pereira, Gronwald, Itin, Maluf and da Rocha-Neto, Muench, Obukhov and Pereira, and Schucking and Surowitz.\n\nNowadays, people study teleparallelism purely as a theory of gravity without trying to unify it with electromagnetism. In this theory, the gravitational field turns out to be fully represented by the translational gauge potential B^a{\\!}_\\mu, as it should be for a gauge theory for the translation group.\n\nIf this choice is made, then there is no longer any Lorentz gauge symmetry because the internal Minkowski space fiber—over each point of the spacetime manifold—belongs to a fiber bundle with the abelian R4 as structure group. However, a translational gauge symmetry may be introduced thus: Instead of seeing tetrads as fundamental, we introduce a fundamental R4 translational gauge symmetry instead (which acts upon the internal Minkowski space fibers affinely so that this fiber is once again made local) with a connection B and a \"coordinate field\" x taking on values in the Minkowski space fiber.\n\nMore precisely, let \\pi\\colon{\\mathcal M}\\to M be the Minkowski fiber bundle over the spacetime manifold M. For each point p\\in M, the fiber {\\mathcal M}_p is an affine space. In a fiber chart (V,\\psi)\\,, coordinates are usually denoted by \\psi = (x^\\mu,x^a)\\,, where x^{\\mu}\\, are coordinates on spacetime manifold M, and xa are coordinates in the fiber {\\mathcal M}_p\\,.\n\nUsing the abstract index notation, let abc, ... refer to {\\mathcal M}_p and μν, ... refer to the tangent bundle TM. In any particular gauge, the value of xa at the point p is given by the section\n\nx^\\mu \\to (x^\\mu,x^a = \\xi^a(p)).\nD_\\mu \\xi^a \\equiv (d \\xi^a)_\\mu + B^a{\\!}_\\mu = \\partial_\\mu \\xi^a + B^a{\\!}_\\mu\n\nis defined with respect to the connection form B, a 1-form assuming values in the Lie algebra of the translational abelian group R4. Here, d is the exterior derivative of the ath component of x, which is a scalar field (so this isn't a pure abstract index notation). Under a gauge transformation by the translation field αa,\n\nx^a\\rightarrow x^a+\\alpha^a\n\nand\n\nB^a{\\!}_\\mu\\rightarrow B^a{\\!}_\\mu - \\partial_{\\mu}\\alpha^a\n\nand so, the covariant derivative of x^a=\\xi^a(p) is gauge invariant. This is identified with the translational (co-)tetrad\n\nh^a{\\!}_\\mu = \\partial_{\\mu}\\xi^a + B^a{\\!}_\\mu\n\nwhich is a one-form which takes on values in the Lie algebra of the translational abelian group R4, whence is gauge invariant. But what does this mean? x^a=\\xi^a(p) is a local section of the (pure translational) affine internal bundle {\\mathcal M} \\to M, another important structure in addition to the translational gauge field B^a{\\!}_\\mu. Geometrically, this field determines the “origin” of the affine spaces; it is known as Cartan’s “radius vector”. In the gauge-theoretic framework, the 1-form\n\nh^a = h^a{\\!}_\\mu dx^{\\mu} = (\\partial_{\\mu}\\xi^a + B^a{\\!}_\\mu)dx^{\\mu}\n\narises as the nonlinear translational gauge field with \\xi^a interpreted as the Goldstone field describing the spontaneous breaking of the translational symmetry.\n\nA crude analogy: Think of {\\mathcal M}_p as the computer screen and the internal displacement as the position of the mouse pointer. Think of a curved mousepad as spacetime and the position of the mouse as the position. Keeping the orientation of the mouse fixed, if we move the mouse about the curved mousepad, the position of the mouse pointer (internal displacement) also changes and this change is path dependent; i.e., it doesn't only depend upon the initial and final position of the mouse. The change in the internal displacement as we move the mouse about a closed path on the mousepad is the torsion.\n\nAnother crude analogy: Think of a crystal with line defects (edge dislocations and screw dislocations but not disclinations). The parallel transport of a point of {\\mathcal M} along a path is given by counting the number of (up/down, forward/backwards and left/right) crystal bonds transversed. The Burgers vector corresponds to the torsion. Disinclinations correspond to curvature, which is why they are left out.\n\nThe torsion, i.e., the translational field strength of Teleparallel Gravity (or the translational \"curvature\"),\n\nT^a{\\!}_{\\mu\\nu} \\equiv (DB^a)_{\\mu\\nu} = D_\\mu B^a{\\!}_\\nu - D_\\nu B^a{\\!}_\\mu,\n\nis gauge invariant.\n\nOf course, we can always choose the gauge where xa is zero everywhere (a problem though; {\\mathcal M}_p is an affine space and also a fiber and so, we have to define the \"origin\" on a point by point basis, but this can always be done arbitrarily) and this leads us back to the theory where the tetrad is fundamental.\n\nTeleparallelism refers to any theory of gravitation based upon this framework. There is a particular choice of the action which makes it exactly equivalent to general relativity, but there are also other choices of the action which aren't equivalent to GR. In some of these theories, there is no equivalence between inertial and gravitational masses.\n\nUnlike GR, gravity is not due to the curvature of spacetime. It is due to the torsion.\n\n## Non-gravitational contexts\n\nThere exists a close analogy of geometry of spacetime with the structure of defects in crystal. Dislocations are represented by torsion, disclinations by curvature. These defects are not independent of each other. A dislocation is equivalent to a disclination-antidisclination pair, a disclination is equivalent to a string of dislocations. This is the basic reason why Einstein's theory based purely on curvature can be rewritten as a teleparallel theory based only on torsion. There exists, moreover, infinitely many ways of rewriting Einstein's theory, depending on how much of the curvature one wants to reexpress in terms of torsion, the teleparallel theory being merely one specific version of these.\n\nA further application of teleparallelism occurs in quantum field theory, namely, two-dimensional non-linear sigma models with target space on simple geometric manifolds, whose renormalization behavior is controlled by a Ricci flow, which includes torsion. This torsion modifies the Ricci tensor and hence leads to an infrared fixed point for the coupling, on account of teleparallelism (\"geometrostasis\")." ]
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https://kr.mathworks.com/matlabcentral/answers/1446199-image-analysis-measure-the-radius-of-a-bending-filament-as-a-function-of-arc-length
[ "# Image analysis. Measure the radius of a bending filament as a function of arc length\n\n조회 수: 24(최근 30일)\nbernardo palacios muniz 2021년 9월 3일\n답변: darova 2021년 9월 6일\nI need help measuring the radius of the filament on the image bellow.", null, "So far my approach is to binarize the image and fill holes, which results in the next image BW", null, "What I am trying to do next is to find the centerline and measure the radius normal to that center line. However this is where I fail. To find the centerline I first tried using bwskel, but the results where unsatisfactory.\nI followed the suggested approach by ̌Image Analyst to find the centerline of the filament on his answer to this very related question https://nl.mathworks.com/matlabcentral/answers/508300-how-to-find-the-centreline-of-two-curves?s_tid=mwa_osa_a . Howerve for me, the radius is changing so the minimum distance approach is not working great.\n%Find the 2 edges and label them\nBWE=edge(BW);\nBWE=bwlabel(BWE);\n%obtain the points for each edge\n[row,col]=find(BWE==1);\nedge1=[col,row];\n[row,col]=find(BWE==2);\nedge2=[col,row];\nx1=edge1(:,1);\ny1=edge1(:,2);\nx2=edge2(:,1);\ny2=edge2(:,2);\n%find the closest point on edge 1 for each point of edge 2\n[D,idx]=pdist2(edge1,edge2,\"euclidean\",\"Smallest\",1);\nedge1_closest=edge1(idx,:);\n%plot the edges and the minimum distance between them over the original image\nimshow(I)\nhold on\nplot(edge1(:,1),edge1(:,2),'*b')\nplot(edge2(:,1),edge2(:,2),'*r')\nfor c=1:size(edge1,1)\nplot([edge1_closest(c,1);edge2(c,1)],[edge1_closest(c,2);edge2(c,2)],'g')\nend\nhold off\nThe result is", null, "If I close in yu can see that the center of the green lines do not represent the centerline :(", null, "And this is where I stand. Any hep to obtain a better centerline or to find a way to measure the radius as a function of the arc length is very much apreaciated\nThank you all for your help,\nBernardo\n\n댓글을 달려면 로그인하십시오.\n\n### 답변(1개)\n\ndarova 2021년 9월 6일\nSee this example. Red lines are normals from first edge/curve. I'd use polyxpoly to calculate intersections between normals and the right(second) edge\nBW1 = im2bw(BW,0.65);\n[col1,col2] = deal(zeros(size(BW1,1),1));\nfor i = 1:size(BW1,1) % read each row of the image\ncol1(i) = find(~BW1(i,:),1,'first'); % find first black pixel (left edge)\ncol2(i) = find(~BW1(i,:),1,'last'); % find last black pixel (right edge\nend\n% take only n-th element and interpolate curves (to smooth)\nx1 = col1;\ny1 = 1:numel(col1);\nii = 1:20:numel(col1);\nx1 = spline(y1(ii),x1(ii),y1); % interpolation (taking each 20th element)\nx2 = col2;\ny2 = 1:numel(col2);\nii = 1:20:numel(col2);\nx2 = spline(y2(ii),x2(ii),y2);\n% find tangent\ndx1 = diff(x1);\ndy1 = diff(y1);\ndx2 = diff(x2);\ndy2 = diff(y2);\nii = 1:50:numel(x1);\nimshow(BW1)\nline(x1,y1)\nline([x1(ii); x1(ii)+dy1(ii)*100], [y1(ii); y1(ii)-dx1(ii)*100],'color','r')\nline(x2,y2)", null, "댓글을 달려면 로그인하십시오.\n\n### 범주\n\nFind more on Object Analysis in Help Center and File Exchange\n\nR2020a\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!" ]
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https://www.digglicious.com/types-of-essays/are-the-three-mean-mode-and-median-same/
[ "## Are the three mean mode and median same?\n\nThe mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set. Created by Sal Khan.\n\n## What does tri mean in statistics?\n\nA trimean is a number that represents the general tendency of a set of numbers or data set. Like the mean, median, and mode, it is a measure of central tendency. It is defined to be the weighted average of the median and upper and lower quartiles. As a formula: Trimean = (Q1 + 2Q2 + Q3)/4.\n\nWhat is the difference between median and mean and mode?\n\nThe arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list. This is what is most often meant by an average. The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.\n\n### What are the three measures of central tendency?\n\nThere are three main measures of central tendency: the mode, the median and the mean. Each of these measures describes a different indication of the typical or central value in the distribution.\n\n### Is mode the highest number?\n\nMode: The most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.\n\nHow is tri mean calculated?\n\nThe trimean is an estimate of central tendency, and is calculated as a weighted average of the median and the two quartiles of a set of values. The formula for trimean is (quartile1 + median * 2 + quartile3) / 4.\n\n## How do you find Winsorized mean?\n\nThe winsorized mean is achieved by replacing the smallest and largest data points, then summing all the data points and dividing the sum by the total number of data points.\n\n## What technique is better to go with mean vs median VS mode?\n\nWhen data is normally distributed, the mean is widely preferred. When data distribution is skewed, median is the best representative. When there is a nominal distribution of data, the mode is preferred.\n\nWhat is mean median and mode explain with example?\n\nExample: The median of 4, 1, and 7 is 4 because when the numbers are put in order (1 , 4, 7) , the number 4 is in the middle. Mode: The most frequent number—that is, the number that occurs the highest number of times." ]
[ null ]
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https://www.mathsphy.com/topic/11th-ncert:-145-videos/sets
[ "# mathsphy Maths NO MORE scary\n\nS No. Topic Video\n1 What are sets, How to read them and write them, Epsilon, Roaster or Tabular Format and Set Builder Format.\n2 Exemplar 1.3 Question # 2: Write the following sets in the roaster form:\n3 Exemplar 1.3 Question # 9: Write the following set, containing all the elements satisfying the given conditions.\n4 NCERT Ex. 1.1 Question 4: Write the following sets in the set-builder form\n5 NCERT Ex. 1.1 Question 4: Write the following sets in the set-builder form\n6 NCERT Ex. 1.1 Question 5: List all the elements of the following sets\n7 \"NCERT Ex. 1.3 Question 3: Which of the following statements are incorrect and why? \"\n8 NCERT Ex. 1.4 Question 1: Find the union of each of the following pairs of sets\n9 \"In a school there are 20 teachers who teach maths or physics. Of these, 12 teach maths and 4 teach both physics and maths. How many teach physics. \"\n10 \"NCERT Ex. 1.6 Question 5: If X and Y are two sets such that X has 40 elements, X union Y has 60 elements and X intersection Y has 10 elements, how many elements does Y have? \"\nTopic/Video\n\n1 What are sets, How to read them and write them, Epsilon, Roaster or Tabular Format and Set Builder Format.\n\n2 Exemplar 1.3 Question # 2: Write the following sets in the roaster form:\n\n3 Exemplar 1.3 Question # 9: Write the following set, containing all the elements satisfying the given conditions.\n\n4 NCERT Ex. 1.1 Question 4: Write the following sets in the set-builder form\n\n5 NCERT Ex. 1.1 Question 4: Write the following sets in the set-builder form\n\n6 NCERT Ex. 1.1 Question 5: List all the elements of the following sets\n\n7 \"NCERT Ex. 1.3 Question 3: Which of the following statements are incorrect and why? \"\n\n8 NCERT Ex. 1.4 Question 1: Find the union of each of the following pairs of sets\n\n9 \"In a school there are 20 teachers who teach maths or physics. Of these, 12 teach maths and 4 teach both physics and maths. How many teach physics. \"\n\n10 \"NCERT Ex. 1.6 Question 5: If X and Y are two sets such that X has 40 elements, X union Y has 60 elements and X intersection Y has 10 elements, how many elements does Y have? \"" ]
[ null ]
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https://codegolf.stackexchange.com/questions/170229/gold-collector-koth
[ "# Gold Collector KoTH\n\nNote: The survey for community favorite will be released soon\n\nIn this KoTH, the aim is to be the last bot alive. Coins will be placed in random areas, and your bot must get the coins first. If a bot runs into another bot, the bot with more coins wins, and the other bot dies. More details below.\n\n## Coin types\n\nThere will be 2 types of coins: gold and silver. Gold adds 5 coins to the bot's strength, and silver adds 2. Once a coin is collected, another coin is placed at another spot on the board. At any given time, there is one gold coin and four silver coins in the arena.\n\n## Bot collisions\n\nIn the event of two bots trying to occupy the same space, the one with more coins will stay, and the one with less will...not. The winning bot will gain 85% of opponents coins (Rounded up). If they are tied, both die. If three or more try to occupy the same space, the most powerful wins, and gets 85% of all the other bot's coins. In the event that the most powerful bot is a tie, all of the bots die who tried to enter the space.\n\n## Arena\n\nThe arena's side length is calculated with 4 + botCount. When placing bots in the beginning of the game, random places are chosen. The system ensures that no bots start in the same space, or next to each other. Coins generate randomly, excluding a 3 by 3 square centered on each bot. If a bot is found outside of the arena, it dies instantly. The arena starts at (0,0), or Northwest, in the upper left corner, and the location of a bot is always an integer.\n\nYour bot should be a function, in any object oriented language that has arrays, integers, strings, and functions. Note that all submissions will be converted to Javascript, to make things simple. To store information between moves, use botNotes.storeData(key, value) and botNotes.getData(key, value). You may not store or access data any way, other than that which is provided through the parameters and botNotes. You should create a function that, when called, returns a string north, east, south, west, or none. There will be 3 arguments for the function:\n\n• An object with four integers (locationX, locationY, coins, arenaLength), your current location, your coins, and the length of the arena\n\n• A multidimensional array with the X and Y coordinates of other bots, and their coin count, ex-[[0,5,4],[4,7,1],[7,4,12]]\n\n• An array with the coin locations listed (Gold is always first)\n\nThis is a king of the hill challenge, Standard Loopholes prohibited. Your function will be run several thousand times, each time allowed one \"Move\". Note that if the game exceeds 20,000 moves, the bot with the most coins wins. This will be done 8,000 times, to remove randomness.\n\nPrizes:\n\nFirst Place: 100-point bounty\n\nWinners:\n\nFirst Place: TBTPTGCBCBA\nSecond Place: Big King Little Hill\nThird Place: Potentially Victorious\nFourth Place: Polite Near-Sighted Drunk Bot\nFifth Place: Safety Coin\n\n• \"Note that all submissions will be converted to Javascript, to make things simple.\" How is this supposed to work? Do you make the conversion? – Laikoni Aug 8 '18 at 14:20\n• There's nothing wrong with a koth only allowing a single language, especially one as widely spread as JavaScript. Rather than ambiguously \"converting\" answers to JavaScript (presumably yourself and by hand) you should simply limit the challenge to JS only. We've had plenty of Java-only and Python-only koths in the past, after all. – Skidsdev Aug 8 '18 at 14:23\n• A version of this where you control acceleration instead of position would be pretty cool. – akozi Aug 8 '18 at 19:21\n• To everyone: There are waaaay too many comments already. Do not leave useless comments such as \"+1, nice bot\", and please delete your comments if it's redundant. We are not a typical Q&A site, but nobody likes reading hundreds of commands. – user202729 Aug 9 '18 at 5:16\n• (To my own question): According to N.P. in chat, it is the latter: all the bots move, then all the conflicts get resolved, then all the coin pickups occur, then all the new coins are placed. – BradC Aug 9 '18 at 20:59\n\n## BaitBot - JavaScript Node.JS\n\nWhy bother chasing or running if you can never catch? Instead, BaitBot finds the nearest coin and waits for a weaker bot to also approach it. When they're both adjacent, baitBot goes for the coin assuming the weaker bot will as well. If baitBot is waiting and a stronger bot approaches, he just grabs the coin and skedaddles. Try Me!\n\nfunction baitBot(me, others, coins) {\nlet directions = ['none','east','south','west','north']\nfunction distanceTo(a) {\nreturn (Math.abs(a - me.locationX) + Math.abs(a - me.locationY))\n}\nfunction distanceBetween(a, b){\nreturn (Math.abs(a - b) + Math.abs(a - b))\n}\n//0 = no, 1,2,3,4 = ESWN\nif(distanceTo(a) == 1) {\nif(a > me.locationX){ return 1}\nelse if(a < me.locationX) {return 3}\nelse if(a > me.locationY) {return 2}\nelse{ return 4}\n}\nelse {return 0}\n}\nfunction edibility(a) {\nreturn me.coins - a\n}\n\n//Find nearest coin and get next to it\nlet closestCoin = coins.sort((a,b) => distanceTo(a) - distanceTo(b))\nif(distanceTo(closestCoin) > 1) {\nif(closestCoin > me.locationX){ return 'east'}\nelse if(closestCoin < me.locationX){ return 'west'}\nelse if(closestCoin < me.locationY){ return 'north'}\nelse if(closestCoin > me.locationY){ return 'south'}\n}\n\n//If we're next to a coin and there's a threat close, just grab it\nlet nearestThreat = others.filter(a => edibility(a) < 0).sort((a,b) => distanceBetween(a, closestCoin) - distanceBetween(b, closestCoin))\nif(nearestThreat && distanceBetween(nearestThreat, closestCoin) <= 2) {\n}\n\n//Otherwise, wait until there's a target also next to the coin. If none are close, just take it\nlet targets = others.filter(a => edibility(a) > 0 && distanceBetween(closestCoin, a) <= 3)\ntargets.sort((a,b) => distanceBetween(a, closestCoin) - distanceBetween(b, closestCoin))\nif(targets.length > 0 && distanceBetween(targets, closestCoin) > 1){\nreturn directions\n}\n\n}\n\n• Ha, that's a neat idea, I like it. – sundar - Remember Monica Aug 8 '18 at 21:37\n• This approach is pretty cool...no, very cool – Redwolf Programs Aug 9 '18 at 0:45\n• BaitBot needs nearestThreat && distanceTo(nearestThreat) rather than just distanceTo(nearestThreat). It fails when there is no threat. – Redwolf Programs Aug 10 '18 at 13:55\n• Yes, nearestThreat is undefined if all other bots have more points than yours. – Night2 Aug 10 '18 at 17:35\n• Well, I get notices like Bot Bait Bot tired of this world, and jumped off its edge in my event log – Redwolf Programs Aug 13 '18 at 15:17\n\n# Big King Little Hill | JavaScript\n\nfunction BigKingLittleHill(me, enemies, coins) {\n\n// Is a move safe to execute?\nfunction isItSafe(x){\nlet loc = [x + me.locationX,x + me.locationY];\nreturn loc >= 0 && loc < me.arenaLength\n&& loc >= 0 && loc < me.arenaLength\n&& enemies\n.filter(enemy => me.coins <= enemy)\n.filter(enemy => getDist(enemy,loc) == 1).length === 0;\n}\n\n// Dumb conversion of relative coord to direction string\nfunction coordToString(coord){\nif (coord == 0 && coord == 0) return 'none';\nif (Math.abs(coord) > Math.abs(coord))\nreturn coord < 0 ? 'west' : 'east';\nreturn coord < 0 ? 'north' : 'south';\n}\n\n// Calculate a square's zone of control\nfunction getZOC(x) {\nlet n = 0;\nfor(let i = 0; i < me.arenaLength;i++){\nfor(let j = 0; j < me.arenaLength;j++){\nif (doesAControlB(x, [i,j])) n++;\n}\n}\nreturn n;\n}\n\nfunction doesAControlB(a, b) {\nreturn getEnemyDist(b) > getDist(a, b);\n}\n\n// Distance to nearest enemy\nfunction getEnemyDist(x) {\nreturn enemies.filter(enemy => enemy >= me.coins/50).map(enemy => getWeightedDist(enemy, x)).reduce((accumulator, current) => Math.min(accumulator, current));\n}\n\n// Weights distance by whether enemy is weaker or stronger\nfunction getWeightedDist(enemy, pos) {\nreturn getDist(enemy, pos) + (enemy < me.coins ? 1 : 0);\n}\n\nfunction getDist(a, b){\nreturn (Math.abs(a - b) + Math.abs(a - b))\n}\n\n//check whether there are coins in our Zone of Control, if yes move towards the closest one\nlet loc = [me.locationX,me.locationY];\nlet sortedCoins = coins.sort((a,b) => getDist(loc,a) - getDist(loc,b));\nfor (let coin of sortedCoins) {\nif (doesAControlB(loc,coin)){\nreturn coordToString([coin - loc,coin - loc]);\n}\n}\n\n//sort moves by how they increase our Zone of Control\nnorthZOC = [[0,-1], getZOC([loc,loc-1])];\nsouthZOC = [[0,1], getZOC([loc,loc+1])];\nwestZOC = [[-1,0], getZOC([loc-1,loc])];\neastZOC = [[1,0], getZOC([loc+1,loc])];\nnoneZOC = [[0,0], getZOC([loc,loc])];\nlet moves = [northZOC,southZOC,westZOC,eastZOC,noneZOC].sort((a,b) => b - a);\n\n//check whether these moves are safe and make the highest priority safe move\nfor (let move of moves) {\nif (isItSafe(move)) {\nreturn coordToString(move);\n}\n}\n//no moves are safe (uh oh!), return the highest priority\nreturn coordToString(moves)\n}\n\n\nTry it online!\n\nBig King Little Hill makes decisions based on “zones of control”. It will only pursue coins that are in its zone of control meaning it can reach the coin before any other bot can. When there are no coins in its zone of control it instead moves to maximize the size of its zone of control. Big King Little Hill calculates the zone of control of each of its 5 possible moves and favors the moves that maximize the size of its zone of control. In this way, Big King Little Hill eventually reaches a local maximum (little hill) of control and waits for a coin to be generated within its zone. Additionally, Big King Little Hill rejects any move that could result in its death unless there are no alternatives.\n\nBig King Little Hill is a pessimist (it prefers the term realist) because it does not bother to contest any coin it isn't assured to get. It is also a pacifist in that it does not pursue weaker bots in any sense (although it might step on one if they get in the way). Lastly, Big King Little Hill is a coward that will not jeopardize its own life for any reward unless it absolutely has to.\n\n• Welcome to PPCG! That's a very good bot =D – Luis felipe De jesus Munoz Aug 10 '18 at 20:55\n• This is what I was thinking for a bot. Good job. – Jo. Aug 11 '18 at 18:48\n\n# First Gen Learning Algorithm | JavaScript (Node.js)\n\nfunction run() {\nreturn ['north','east','south','west'][(Math.random()*4)|0];\n}\n\n\nTry it online!\n\nHave you ever seen those timelapses of learning algorithms learning to play a game? They often move almost randomly in the first few generations...\n\n• LOL...It might still work! – Redwolf Programs Aug 8 '18 at 16:10\n• Most learning algorithms work literally random for the first few iterations, not just almost randomly. – fəˈnɛtɪk Aug 8 '18 at 16:56\n• Guess what? This bot got almost 0.22 coins per round on average! – Redwolf Programs Aug 16 '18 at 22:44\n\n# Potentially Victorious | JavaScript\n\nPreferred color for this bot is #1600a6.\n\nfunction (me, others, coins)\n{\nlet huntingTimer = botNotes.getData(\"huntingTimer\");\nlet huntedIndex = botNotes.getData(\"huntedIndex\");\nif(!huntingTimer)\nhuntingTimer = 0;\nelse if(huntingTimer >0)\nhuntingTimer--;\nelse if(huntingTimer == -1)\nhuntingTimer = Math.ceil(20*(1+Math.log2(me.coins/25)));\nelse\nhuntingTimer++;\n\nfunction distanceFromMe(X, Y) { return Math.abs(me.locationX - X) + Math.abs(me.locationY - Y); }\n\nfunction U(x, y)\n{\nfunction distance(X, Y) { return Math.abs(X-x) + Math.abs(Y-y); }\nfunction gravitation(k, X, Y) { return - k / ( distance(X, Y) + .2 ); }\nfunction exponential(k, q, X, Y) { return - 5*k * Math.exp(- q * distance(X,Y)); }\n\n// No going away from the arena.\nif(!((0 <= x) && (x < me.arenaLength) && (0 <= y) && (y < me.arenaLength)))\n{\nreturn Infinity;\n}\n\nlet reachability = [1, 1, 1, 1, 1];\nlet distances = coins.map(c => distanceFromMe(c, c));\nfor(let i = 0; i < others.length; i++)\n{\nfor(let coin = 0; coin < 5; coin++)\nreachability[coin] += (Math.abs(others[i] - coins[coin]) + Math.abs(others[i] - coins[coin])) < distances[coin];\n}\n\nlet potential = gravitation(40, coins, coins) / (reachability); // Gold\n\n// Silver\nfor(let i = 1; i < 5; i++)\n{\npotential += gravitation(10, coins[i], coins[i]) / (reachability[i]);\n}\n\nothers.sort((a, b) => b - a);\n\n// Other bots\nfor(let i = 0; i < others.length; i++)\n{\nif(\n((Math.abs(me.locationX - others[i]) + Math.abs(me.locationY - others[i])) < 3) &&\n(huntingTimer == 0) &&\n(me.coins > 25) &&\n(me.coins < (others*.9)) &&\n(others[i] < me.coins-5) && (others[i] >= 10)\n)\n{\nhuntingTimer = -10;\nhuntedIndex = i;\n}\n\nif((huntingTimer < 0) && (huntedIndex == i))\npotential += exponential(30, 1, others[i], others[i]);\n\nif(others[i] >= me.coins)\n{\n// Otherwise, they could eat us, and we will avoid them.\npotential += exponential(-1400, 3, others[i], others[i]);\n}\n}\n\nreturn potential;\n}\n\n// All possible squares we can move to, with their names.\nlet movements = [\n[ \"north\", U(me.locationX, me.locationY - 1)],\n[ \"south\", U(me.locationX, me.locationY + 1)],\n[ \"east\", U(me.locationX + 1, me.locationY)],\n[ \"west\", U(me.locationX - 1, me.locationY)],\n[ \"none\", U(me.locationX, me.locationY)]\n];\n\nbotNotes.storeData(\"huntingTimer\", huntingTimer);\nbotNotes.storeData(\"huntedIndex\", huntedIndex);\n\n// Sort them according to the potential U and go wherever the potential is lowest.\nmovements.sort((a, b) => a - b);\nreturn movements;\n}\n\n\n(Apologies for sloppy formatting, the 4 spaces indentation for this site doesn't go well with my custom of using tabs.)\n\n## Rough explanation\n\nI hereby resign at the attempt to update the explanation of the formulae. The coefficients are constantly changing and it's kinda hard to keep the explanation up to date. So I will just explain the general principle.\n\nEach coin and each bot generates a force field with some potential. I just add the potentials from everything together and the bot then goes wherever the potential is the lowest. (Obviously this idea is stolen from physics.)\n\nI use two kinds of potentials. First one is a pseudo-gravitational one (which acts at any range), with $$U = - \\frac{k}{r + \\frac 1 5} \\cdot \\frac{1}{1 + n}.$$ The k is a \"strength\" of the field, and, with this choice of sign, the potential is attractive. The r here (and everywhere else) is the distance in the taxicab metric, r = |x₁ - x₂| + |y₁ - y₂|.\n\nI use k = 40 for gold coins and k = 10 for silver coins. n is the number of bots who are nearer to the particular coin than we are. Otherwise, we absolutely ignore the other bots (if we get in the way of a stronger bot, we run away, but that's it). I value gold coins for more than they are worth because otherwise the bots that go primarily after the gold all the time beat me.\n\nThe second potential is an exponentially decaying one (which effectively acts only at very small distances). This is generated by the other, mainly the more powerful, bots.\n\nThese produce a field with $$U = -5 \\times 1400 e^{-3r}.$$ This force is prohibitively strong at range 0-1, but decays to almost nothing at the larger distances. (Distance + 1 means cutting the force in 1/20.)\n\nWe generally don't attack the other bots intentionally (of course if they get in our way and we step on them, it's their fault), but there is a possibility to do that. If some harsh conditions are fulfilled, we may enter the hunting mode, being focused on a single bot. To enter the hunting mode:\n\n1. We must have at least 25 coins. (We need to get some coins first.)\n2. They must have at most (our coins - 5) coins, and at least 10 coins. (We don't want to be hunting someone who grabs one coin and is suddenly more powerful, and we don't want to be pursuing zero-coin bots either.)\n3. We must lag behind the currently leading bot by at least 1/10 of his coins. (You need to be lucky to hunt something, so there is no need to give away a good position just for trying our luck.)\n4. We must not be on a hunting cooldown (see below).\n\nIf all these are satisfied, the hunting mode is activated. For the next 10 rounds, the hunted bot only emits the potential $$U = -150 e^{-r}.$$ After these 10 rounds elapse, we enter the hunting cooldown, during which we may not enter hunting mode again. (That is to prevent us from endlessly and fruitlessly chasing one bot while all other happily grab coins.) The hunting cooldown is 20 rounds when we have 25 coins, and increases by 20 coins per each doubling of that. (In other words, the cooldown is 20(1 + log2(c / 25)).) (We use that because in the endgame, all the huntable bots are most likely dead, and so any hunt will be most likely in vain. Because of that, we want to limit the wasted time. But sometimes, a lucky late-game eating can change everything, so we keep the possibility.)\n\nFinally, the whole arena is placed into an infinite potential well which prevents the bot from escaping.\n\n• I think this bot probably beats out my weighted movement too. – fəˈnɛtɪk Aug 8 '18 at 18:18\n• @fəˈnɛtɪk — So do I :—). I think that this one can handle the other bots quite a bit better. (Also it's not \"blinded\" by a coin at an adjacent square.) But I definitely gave you +1 because I'm a huge fan of this idea. – Ramillies Aug 8 '18 at 18:25\n• Could you apply the principle of least action to this? – Beta Decay Aug 8 '18 at 19:05\n• @BetaDecay: Not quite I'm afraid, calculus doesn't respond well to discrete problems like this. Even in the continuous case it wouldn't be trivial (because of fixed magnitude of velocity), but it could be doable after some polar coordinates magic I guess. – Ramillies Aug 8 '18 at 19:10\n• This is cool. I'm not sure risk is monotonically related to distance though, it seems like a threat 2 spaces away is more likely to kill you than one adjacent, since in the latter case one of you needs to stay stationary for a collision to occur. – Cain Aug 8 '18 at 21:45\n\n# The Bot That Plays The Game Cautiously But Can Be Aggressive | JavaScript\n\nPreferred color: #F24100\n\nNote: Although this bot has taken 1st place, it is due to teaming up with \"Feudal Noble\" at the end and eating him for more coins. Otherwise this bot would have been 3rd. If you are interested in bots that are more powerful individually, checkout Potentially Victorious and Big King Little Hill.\n\nfunction (me, monsters, coins) {\nvar i, monstersCount = monsters.length, phaseSize = Math.round((me.arenaLength - 4) / 4),\ncenter = (me.arenaLength - 1) / 2, centerSize = me.arenaLength / 4,\ncenterMin = center - centerSize, centerMax = center + centerSize, centerMonsters = 0, centerMonstersAvg = null,\nend = 2e4, apocalypse = end - ((me.arenaLength * 2) + 20), mode = null;\n\nvar getDistance = function (x1, y1, x2, y2) {\nreturn (Math.abs(x1 - x2) + Math.abs(y1 - y2)) + 1;\n};\n\nvar isAtCenter = function (x, y) {\nreturn (x > centerMin && x < centerMax && y > centerMin && y < centerMax);\n};\n\nvar round = botNotes.getData('round');\nif (round === null || !round) round = 0;\nround++;\nbotNotes.storeData('round', round);\n\nvar isApocalypse = (round >= apocalypse && round <= end);\nif (isApocalypse) {\nmode = botNotes.getData('mode');\nif (mode === null || !mode) mode = 1;\n}\n\nfor (i = 0; i < monstersCount; i++) if (isAtCenter(monsters[i], monsters[i])) centerMonsters++;\n\nvar lc = botNotes.getData('lc');\nif (lc === null || !lc) lc = [];\nif (lc.length >= 20) lc.shift();\nlc.push(centerMonsters);\nbotNotes.storeData('lc', lc);\n\nif (lc.length >= 20) {\ncenterMonstersAvg = 0;\nfor (i = 0; i < lc.length; i++) centerMonstersAvg += lc[i];\ncenterMonstersAvg = centerMonstersAvg / lc.length;\n}\n\nvar getScore = function (x, y) {\nvar score = 0, i, chaseFactor = 0.75, coinFactor = 1;\n\nif (monstersCount < phaseSize) {\nchaseFactor = 0;\ncoinFactor = 0.25;\n} else if (monstersCount < phaseSize * 2) {\nchaseFactor = 0;\ncoinFactor = 0.5;\n} else if (monstersCount < phaseSize * 3) {\nchaseFactor = 0.5;\ncoinFactor = 0.75;\n}\n\nif (isApocalypse) {\nif (mode === 1) {\nvar centerDistance = getDistance(x, y, center, center);\nif (centerDistance <= 3) {\nmode = 2;\n} else {\nscore += 5000 / (centerDistance / 10);\n}\n}\nif (mode === 2) chaseFactor = 1000;\n}\n\nfor (i = 0; i < monstersCount; i++) {\nvar monsterCoins = monsters[i], monsterDistance = getDistance(x, y, monsters[i], monsters[i]);\nif (me.coins > monsterCoins && monsterDistance <= 3) {\nscore += (Math.min(5, monsterCoins) * chaseFactor) / monsterDistance;\n} else if (me.coins <= monsterCoins && monsterDistance <= 3) {\nscore -= (monsterDistance === 3 ? 50 : 10000);\n}\n}\n\nfor (i = 0; i < coins.length; i++) {\nvar coinDistance = getDistance(x, y, coins[i], coins[i]),\ncoinDistanceCenter = getDistance(center, center, coins[i], coins[i]),\ncoinValue = (i === 0 ? 250 : 100), coinCloserMonsters = 0;\n\nfor (var j = 0; j < monstersCount; j++) {\nvar coinMonsterDistance = getDistance(monsters[j], monsters[j], coins[i], coins[i]);\nmonsterCoins = monsters[j];\n\nif (\n(coinMonsterDistance < coinDistance && monsterCoins >= me.coins / 2) ||\n(coinMonsterDistance <= coinDistance && monsterCoins >= me.coins)\n) {\ncoinCloserMonsters++;\n}\n}\n\nvar coinMonsterFactor = (100 - ((100 / monstersCount) * coinCloserMonsters)) / 100;\nif (coinMonsterFactor < 1) coinMonsterFactor *= coinFactor;\nif (coinMonsterFactor >= 1) coinMonsterFactor *= 15;\nscore += ((coinValue * coinMonsterFactor) / coinDistance) + (centerMonstersAvg === null || centerMonstersAvg > 1.75 ? -1 * (50 / coinDistanceCenter) : 200 / coinDistanceCenter);\n}\n\nreturn score + Math.random();\n};\n\nvar possibleMoves = [{x: 0, y: 0, c: 'none'}];\nif (me.locationX > 0) possibleMoves.push({x: -1, y: 0, c: 'west'});\nif (me.locationY > 0) possibleMoves.push({x: -0, y: -1, c: 'north'});\nif (me.locationX < me.arenaLength - 1) possibleMoves.push({x: 1, y: 0, c: 'east'});\nif (me.locationY < me.arenaLength - 1) possibleMoves.push({x: 0, y: 1, c: 'south'});\n\nvar topCommand, topScore = null;\nfor (i = 0; i < possibleMoves.length; i++) {\nvar score = getScore(me.locationX + possibleMoves[i].x, me.locationY + possibleMoves[i].y);\nif (topScore === null || score > topScore) {\ntopScore = score;\ntopCommand = possibleMoves[i].c;\n}\n}\n\nif (isApocalypse) botNotes.storeData('mode', mode);\n\n}\n\n\nThis bot (aka \"TBTPTGCBCBA\") tries to make the best decision possible by generating a score for each possible move and selects the move with higher score for each turn.\n\nThe scoring system has many details which are evolved since the start of the challenge. They can be described generally like this:\n\n• The closer the coins are to a possible move, the more score that move gets. If a coin has no other possible contestants, the score goes even higher. If a coin has other possible contestants, the score goes lower.\n• If another bot is close to a possible move and has less coins, depending on the phase of the game, it could mean more score for that move. So it is casual for \"TBTPTGCBCBA\" to eat a few of other bots in each game.\n• If another bot is close to a possible move with equal or more points, that move gets enough negative score to make sure death is avoided. Of course there could be some cases that all possible moves are bad and death can't be avoided, but that is very rare.\n• There is a mechanism to keep track of number of bots in middle of the board for last 20 turns. If average is low enough, all moves towards coins in the middle get more score and if the average is high, then all moves towards coins in the middle get lower score. This mechanism allows to avoid conflicts with \"Feudal Noble\". Since the \"Feudal Noble\" is always in the middle (unless it is being chased), the average number of bots in the middle goes up and \"TBTPTGCBCBA\" understands to avoid middle if there is a better option outside of middle area. If \"Feudal Noble\" dies, the average goes down and \"TBTPTGCBCBA\" understands that it can use the middle.\n• There are some factors that dynamically change based on the phase of the game (detected from number of bots alive), these factors affect the scoring in each of above items.\n• This bot has a special ability. Over time it grows tired of the selfishness of \"Feudal Noble\" and the oppression of peasants. At the right moment, it will rise to end the unpleasant Feudalism system. A successful attempt not only helps poor peasants, but also provides a higher win chance due to the coins taken from the \"Feudal Noble\".\n• It seems a lot more...intelligent than the others – Redwolf Programs Aug 8 '18 at 16:15\n• I like the monsters part of the params – Redwolf Programs Aug 10 '18 at 22:25\n\n# Safety coin | JavaScript\n\nSafetyCoin=(myself,others,coins)=>{\nx=myself.locationX;\ny=myself.locationY;\npower=myself.coins;\narenaSize=myself.arenaLength;\ndist=0;\noptimalCoin=7;\noptimalDist=11*arenaSize;\nfor(i=0;i<coins.length;i++){\nenemyDist=3*arenaSize;\ndist=Math.abs(x-coins[i])+Math.abs(y-coins[i])\nfor(j=0;j<others.length;j++){\nif(i==0){\nif(others[j]+5>=power){\nenemyDist=Math.min(enemyDist,Math.abs(others[j]-coins[i])+Math.abs(others[j]-coins[i]))\n}\n}\nelse{\nif(others[j]+2>=power){\nenemyDist=Math.min(enemyDist,Math.abs(others[j]-coins[i])+Math.abs(others[j]-coins[i]))\n}\n}\n\n}\nif(enemyDist>dist){\nif(i==0){\nif(dist/5<optimalDist){\noptimalDist=dist/5;\noptimalCoin=i;\n}\n}\nelse{\nif(dist/2<optimalDist){\noptimalDist=dist/2;\noptimalCoin=i;\n}\n}\n}\n}\nif(optimalCoin==7){\nsafeDir=15;\nif(x==0){safeDir-=8;}\nif(x==arenaSize-1){safeDir-=2;}\nif(y==0){safeDir-=1;}\nif(y==arenaSize-1){safeDir-=4;}\nfor(i=0;i<others.length;i++){\nif(others[i]>=power){\nif(Math.abs(x-others[i])+Math.abs(y-others[i])==2){\nif(x-others[i]>0){safeDir-=8;}\nif(x-others[i]<0){safeDir-=2;}\nif(y-others[i]>0){safeDir-=1;}\nif(y-others[i]<0){safeDir-=4;}\n}\n}\n}\ndirections=[\"north\",\"east\",\"south\",\"west\"];\nif(safeDir!=0){\ntmp=\"\";\ntmp+=\"0\".repeat(Math.max(Math.sqrt(arenaSize)/2|0,y-(arenaSize/2|0)));\ntmp+=\"2\".repeat(Math.max(Math.sqrt(arenaSize)/2|0,(arenaSize/2|0)-y));\ntmp+=\"1\".repeat(Math.max(Math.sqrt(arenaSize)/2|0,(arenaSize/2|0)-x));\ntmp+=\"3\".repeat(Math.max(Math.sqrt(arenaSize)/2|0,x-(arenaSize/2|0)));\nrnd=tmp[Math.random()*tmp.length|0];\nwhile(!(2**rnd&safeDir)){rnd=tmp[Math.random()*tmp.length|0];}\nreturn directions[rnd];\n}\nreturn \"none\";//the only safe move is not to play :P\n}\ndistX=coins[optimalCoin]-x;\ndistY=coins[optimalCoin]-y;\nif(Math.abs(distX)>Math.abs(distY)){\nif(distX>0){return \"east\";}\nelse{return \"west\";}\n}\nelse{\nif(distY>0){return \"south\";}\nelse{return \"north\";}\n}\n}\n\n\nThis bot heads straight towards a weighted valued coin (value/distance) which it can not die from reaching at the same time or after another bot. If there is no valid coin with this property it sits where it is the bot now moves in a random safe direction(safety means that if a bot moves towards it, safety coin cannot collide. This allows the bot to swap places with another bot if immediately next to it), weighted towards the center of the arena.\n\n• Huh, this may actually win. Although, there are a lot of bots – Redwolf Programs Aug 8 '18 at 18:00\n• This method will have more problems the more unevenly the enemy bots with higher or equal value are placed. – fəˈnɛtɪk Aug 8 '18 at 18:01\n• Well, they'll probably all be making a beeline to the coin nearest to them/gold coin. – Redwolf Programs Aug 8 '18 at 18:03\n• It will only do well if it manages to get some coins right at the start. – fəˈnɛtɪk Aug 8 '18 at 18:06\n• And that is mostly luck, since the place where coins generate is randomly decided – Redwolf Programs Aug 8 '18 at 18:13\n\n# The AntiCapitalist | Javascript\n\nHas no incentive to go after coins, but tries to place himself exactly between the two richest bots with the same amount of money, in the hope they will hunt him and eventually catch him at the same time, taking two capitalists with him when he dies. Does not actively resist getting coins, so he might become a more juicy target.\n\nfunction antiCapitalist(me, capitalists, coins){\n\nfunction acquireTargets(capitalists){\ncapitalists.sort((a, b) => a < b);\nlet previousCapitalist;\nfor(let i in capitalists){\nlet capitalist = capitalists[i];\n\nif(capitalist === 0){\nreturn false;\n}\nif(previousCapitalist && capitalist === previousCapitalist){\nreturn [previousCapitalist, capitalist];\n}\n\npreviousCapitalist = capitalist;\n}\n\nreturn false;\n}\n\nfunction move(){\nconst targets = acquireTargets(capitalists);\nif(!targets){\nreturn 'none';\n}\n\nconst coordinates = [Math.floor((targets + targets) / 2), Math.floor((targets + targets) / 2)];\nif(me.locationX !== coordinates){\nreturn me.locationX < coordinates ? 'east' : 'west';\n}\nelse if(me.locationX !== coordinates){\nreturn me.locationY < coordinates ? 'south' : 'north';\n}\nelse {\nreturn 'none';\n}\n}\n\nreturn move();\n}\n\n\n# The GUT, JavaScript\n\nfunction gut(me, others, coins) {\n// Prepare values for the calculation\nvar x = me.locationX;\nvar y = me.locationY;\nvar cMe = me.coins+1;\nvar arenaLen = me.arenaLength;\n\nvar objects = [];\n\nfor (var i = 0; i < others.length; i++) {\nobjects.push([others[i],others[i],others[i]/cMe]);\n}\n\nfor (var j = 0; j < coins.length; j++) {\nvar coinVal = 0;\n\nif (j == 0) {\n// Gold has a higher coin value\ncoinVal = -10;\n} else {\n// Silver has a lower coin value\ncoinVal = -5;\n}\n\nobjects.push([coins[j],coins[j],coinVal/cMe]);\n}\n\n// Perform the calculation\n// x acceleration\nvar x_acceleration = 0;\n\nfor (var k=0; k < objects.length; k++) {\nvar kval = objects[k];\nvar xval = objects[k];\n\nx_acceleration += 200*kval/cMe*(x-xval)*Math.exp(Math.pow(kval,2)-50*Math.pow(x-xval,2));\n}\n\n// y acceleration\nvar y_acceleration = 0;\n\nfor (var l=0; l < objects.length; l++) {\nvar kval = objects[l];\nvar yval = objects[l];\n\ny_acceleration += 200*kval/cMe*(y-yval)*Math.exp(Math.pow(kval,2)-50*Math.pow(y-yval,2));\n}\n\n// Compare the values\nif (Math.abs(y_acceleration)>Math.abs(x_acceleration)) {\nif (y_acceleration < 0) {\n// Don't fall off the edge\nif (y>0) {\nreturn \"north\";\n} else {\nreturn \"none\";\n}\n} else {\nif (y<arenaLen-1) {\nreturn \"south\";\n} else {\nreturn \"none\";\n}\n}\n} else if (Math.abs(y_acceleration)<Math.abs(x_acceleration)) {\nif (x_acceleration < 0) {\nif (x>0) {\nreturn \"west\";\n} else {\nreturn \"none\";\n}\n} else {\nif (x<arenaLen-1) {\nreturn \"east\";\n} else {\nreturn \"none\";\n}\n}\n} else {\nreturn \"none\";\n}\n}\n\n\nWith Potentially Victorious we've got two fields: the bot field and the coin field. However, nature isn't that complicated. It's time to unify the two fields to produce the Grand Unified Theory.\n\nFirstly, we need to work out what the potential of the field is. Assuming our own bot doesn't influence the field in any way, we can write this as:\n\n$$V = \\sum_\\limits{n} k_n\\left(e^{k_n^2-100(x-x_n)^2}+e^{k_n^2-100(y-y_n)^2}\\right)$$\n\nWhere $k_n$ is the \"relative property\" of the object and $(x_n, y_n)$ are the coordinates of each object.\n\nThe relative property of the object is calculated like so:\n\n$$k = \\frac{c_{\\text{object}}}{c_{\\text{me}}}$$\n\nWhere $c$ is the coin value. (The coin value is positive for bots and negative for coins). And $c_{\\text{me}} = c_{\\text{self}} + 1$ where $c_{\\text{self}}$ is my own coin value (with 1 correction to prevent a division by zero).\n\nLet's just call this correction part of Modified Betanian Dynamics (MOBD).\n\nWe can also find the kinetic energy as:\n\n$$T = \\frac{1}{2}c_{\\text{me}}(\\dot{x}^2 + \\dot{y}^2)$$\n\nWe can now calculate the action:\n\n\\begin{align}\\text{Action} &= \\int^b_a (T-V)dt\\\\&=\\int^b_a \\left(\\frac{1}{2}c_{\\text{me}}(\\dot{x}^2 + \\dot{y}^2) - \\sum_\\limits{n} k_n\\left(e^{k_n^2-100(x-x_n)^2}+e^{k_n^2-100(y-y_n)^2}\\right)\\right) dt\\end{align}\n\nAnd so the Lagrangian of our bot in the coin-bot field is:\n\n$$\\mathcal{L} = \\frac{1}{2}c_{\\text{me}}(\\dot{x}^2 + \\dot{y}^2) - \\sum_\\limits{n} k_n\\left(e^{k_n^2-100(x-x_n)^2}+e^{k_n^2-100(y-y_n)^2}\\right)$$\n\nWe now need to solve the Euler-Lagrange equations:\n\n$$\\frac{d}{dt} \\frac{\\partial \\mathcal{L}}{\\partial \\dot{x}} = \\frac{\\partial \\mathcal{L}}{\\partial x}$$\n\nand:\n\n$$\\frac{d}{dt} \\frac{\\partial \\mathcal{L}}{\\partial \\dot{y}} = \\frac{\\partial \\mathcal{L}}{\\partial y}$$\n\nSo:\n\n$$\\frac{d}{dt} \\frac{\\partial \\mathcal{L}}{\\partial \\dot{x}} = \\frac{d}{dt} \\left[c_{\\text{me}}\\dot{x}\\right] = c_{\\text{me}}\\ddot{x}$$\n\n$$\\frac{\\partial \\mathcal{L}}{\\partial x} = \\sum\\limits_n 200 k_n \\left(x - x_n\\right) e^{k_n^2 - 100(x-x_n)^2}$$\n\n$$\\Rightarrow \\ddot{x} = \\sum\\limits_n \\frac{200k_n}{c_{\\text{me}}} \\left(x - x_n\\right) e^{k_n^2 - 100(x-x_n)^2}$$\n\nAnd also:\n\n$$\\frac{d}{dt} \\frac{\\partial \\mathcal{L}}{\\partial \\dot{y}} = \\frac{d}{dt} \\left[c_{\\text{me}}\\dot{y}\\right] = c_{\\text{me}}\\ddot{y}$$\n\n$$\\frac{\\partial \\mathcal{L}}{\\partial y} = \\sum\\limits_n 200 k_n \\left(y - y_n\\right) e^{k_n^2 - 100(y-y_n)^2}$$\n\n$$\\Rightarrow \\ddot{y} = \\sum\\limits_n \\frac{200k_n}{c_{\\text{me}}} \\left(y - y_n\\right) e^{k_n^2 - 100(y-y_n)^2}$$\n\nNow we don't need to go any further: we just look at the direction of the overall acceleration:\n\n$$\\text{output} = \\begin{cases}\\text{north} &\\text{if }\\ddot{y}<0 \\text{ and } |\\ddot{y}|>|\\ddot{x}| \\\\ & \\\\ \\text{south} &\\text{if }\\ddot{y}>0 \\text{ and } |\\ddot{y}|>|\\ddot{x}| \\\\ & \\\\ \\text{west} &\\text{if }\\ddot{x}<0 \\text{ and } |\\ddot{x}|>|\\ddot{y}| \\\\ & \\\\ \\text{east} &\\text{if }\\ddot{x}>0 \\text{ and } |\\ddot{x}|>|\\ddot{y}| \\\\ & \\\\ \\text{none} &\\text{if }|\\ddot{y}|=|\\ddot{x}|\\end{cases}$$\n\nAnd just like that, we've unified the coins and the bots. Where's my Nobel Prize?\n\n• Your Nobel Prize was lost in the mail, but we could give you an Emmy Award instead – Redwolf Programs Aug 9 '18 at 12:47\n• Looks like physics starts getting popular in this challenge. :—D. And of course I'm very curious about how well it will do. – Ramillies Aug 9 '18 at 13:27\n• (By the way, you could have saved the hassle with Euler-Lagrange equations, because they reduce to the well-known fact that F = c_me a = - grad U :—).) – Ramillies Aug 9 '18 at 13:34\n• @Ramillies Meh, it was more fun doing it this way :D – Beta Decay Aug 9 '18 at 13:48\n• Are you sure that you want to be using the k = coins of something else / your coins? You start with no coins... and with NaN everywhere, you're not too likely to get any. – Ramillies Aug 10 '18 at 14:38\n\n# Goldilocks, JavaScript (Node.js)\n\nfunction goldilocks(me, others, coins) {\nlet target = coins; // Gold\nlet x = target - me.locationX;\nlet y = target - me.locationY;\n\nmymove = 'none'\nif (Math.abs(x) <= Math.abs(y) && x != 0)\nmymove = x < 0 ? 'west' : 'east'\nelse if (y != 0)\nmymove = y < 0 ? 'north' : 'south'\n\nreturn mymove\n}\n\n\nTry it online!\n\nJust locks on to the gold coin's location and moves towards it every time. (Thanks to @Mayube's 'B33-L1N3' bot for the original code this used, though barely any of it remains.)\n\n• This is a pretty nice, simple bot. I like it. – Redwolf Programs Aug 8 '18 at 16:09\n• By the way, I'm using this bot as a test for my controller (: – Redwolf Programs Aug 8 '18 at 19:44\n\n# Third Gen Learning Algorithm | JavaScript (Node.js)\n\nfunction run(me) {\noptions = [];\nif (me.locationX > 0) options.push('west');\nif (me.locationY > 0) options.push('north');\nif (me.locationX < me.arenaLength) options.push('east');\nif (me.locationY < me.arenaLength) options.push('south');\n\nreturn options[Math.floor(Math.random() * options.length)];\n}\n\n\nTry it online!\n\nAfter a few generations of learning, this bot has learned that leaving the arena = bad\n\n• Oh, good. I've heard this is called \"Natural Selection\" – Redwolf Programs Aug 8 '18 at 16:16\n• Where is the second gen – Luis felipe De jesus Munoz Aug 8 '18 at 17:15\n• @LuisfelipeDejesusMunoz He left the arena. – Jo. Aug 9 '18 at 0:13\n• This is a good bot for debugging the controller – Redwolf Programs Aug 9 '18 at 13:50\n• Oh, by the way, the arena starts at 0, so it should be arenaLength - 1. This killed your bot a fair few times to many – Redwolf Programs Aug 9 '18 at 13:52\n\n# B33-L1N3 | JavaScript (Node.js)\n\nfunction(me, others, coins) {\n// Do nothing if there aren't any coins\nif (coins.length == 0) return 'none';\n// Sort by distance using Pythagoras' Theorem\ncoins = coins.sort((a, b) => (a ** 2 + a ** 2) - (b ** 2 + b ** 2));\n// Closest coin\nlet target = coins;\nlet x = target;\nlet y = target;\n\n// Util function for movement\nfunction move(pos, type) {\nlet moveTypes = { X: ['east', 'west'], Y: ['south', 'north'] };\nif (pos > me['location'+type]) return moveTypes[type];\nelse return moveTypes[type];\n}\n\n// Move the shortest distance first\nif (x < y && x != me.locationX) return move(x, 'X');\nelse if (y != me.locationY) return move(y, 'Y');\n}\n\n\nTry it online!\n\nMakes a beeline for the closest coin\n\n• Oh, I thought B33-L1N3 was some sort of model number – Redwolf Programs Aug 8 '18 at 16:16\n• +1 for the name – Cain Aug 8 '18 at 21:47\n• let coins = ... Uncaught SyntaxError: Identifier 'coins' has already been declared – Night2 Aug 10 '18 at 17:20\n• Delete the let – Redwolf Programs Aug 10 '18 at 18:24\n\n# Livin' on the Edge, JavaScript\n\nfunction LivinOnTheEdge (myself, others, coins) {\nx = myself.locationX;\ny = myself.locationY;\nxymax = myself.arenaLength - 1;\nif (x < xymax && y == 0) {\nreturn 'east';\n} else if (y < xymax && x == xymax) {\nreturn 'south';\n} else if (x > 0 && y == xymax) {\nreturn 'west';\n} else {\nreturn 'north';\n}\n}\n\n\nThis one heard the edge of the arena is a dangerous place to be. Knowing no fear, it tirelessly circles the board clockwise, only inches away from the certain death that awaits behind the border, hoping no other bot will dare to move so closely to the edge's vicinity.\n\n• This wouldn't end well if another bot were created that had 1 more coin, and patrolled the border in the opposite direction (: – Redwolf Programs Aug 8 '18 at 23:07\n• I would make a border control joke, but I'm leaving that one up to @BetaDecay – Redwolf Programs Aug 9 '18 at 0:53\n\n# Damacy, JavaScript (Node.js)\n\nfunction damacy(me, others, coin) {\nlet xdist = t => Math.abs(t - me.locationX)\nlet ydist = t => Math.abs(t - me.locationY)\nfunction distanceCompare(a, b, aWt, bWt) {\naWt = aWt || 1\nbWt = bWt || 1\nreturn (xdist(a) + ydist(a)) / aWt - (xdist(b) + ydist(b)) / bWt\n}\nfunction hasThreat(loc) {\nlet threat = others.filter(b => b == loc && b == loc && b >= me.coins)\nreturn (threat.length > 0)\n}\nfunction inArena(loc) { // probably unnecessary for this bot\nreturn loc >= 0 && loc >= 0 && loc < me.arenaLength && loc < me.arenaLength\n}\nfunction sortedCoins() {\ncoinsWithValues = coin.map((coords, i) => coords.concat((i == 0) ? 5 : 2))\ncoinsWithValues.sort((a, b) => distanceCompare(a, b, a, b))\nreturn coinsWithValues.map(c => c.slice(0, 2))\n}\nothersPrev = botNotes.getData('kata_others_pos')\nbotNotes.storeData('kata_others_pos', others)\nif (othersPrev) {\n\nfor(let i = 0; i < others.length; i++) {\nlet bot = others[i]\n\nlet matchingBots = othersPrev.filter(function (b) {\nlet diff = Math.abs(b - bot) + Math.abs(b - bot)\nif (diff >= 2)\nreturn false // bot can't have jumped\nreturn [0, 2, 5].includes(bot - b)\n})\n\nif (matchingBots.length > 0) {\nlet botPrev = matchingBots.shift()\n// remove matched bot so it doesn't get matched again later\nothersPrev = othersPrev.filter(b => b != botPrev || b != botPrev)\nbot = Math.min(Math.max(bot + bot - botPrev, 0), me.arenaLength-1)\nbot = Math.min(Math.max(bot + bot - botPrev, 0), me.arenaLength-1)\n}\n}\n}\n\nlet eatables = others.filter(b => b < me.coins && b > 0)\nlet targets\nif (eatables.length > 0) {\ntargets = eatables.sort(distanceCompare)\n}\nelse {\ntargets = sortedCoins()\n}\n\nlet done, newLoc, dir\nwhile (!done && targets.length > 0) {\nt = targets.shift()\nif ((xdist(t) <= ydist(t) || ydist(t) == 0) && xdist(t) != 0) {\nlet xmove = Math.sign(t - me.locationX)\ndir = xmove < 0 ? 'west' : 'east'\nnewLoc = [me.locationX + xmove, me.locationY]\nif (!hasThreat(newLoc) && inArena(newLoc))\ndone = 1\n}\n\nif (!done) {\nlet ymove = Math.sign(t - me.locationY)\ndir = ['north', 'none', 'south'][ymove + 1]\nnewLoc = [me.locationX, me.locationY + ymove]\nif (!hasThreat(newLoc) && inArena(newLoc))\ndone = 1\n}\n}\n\nif (!done)\ndir = 'none'\n\nreturn dir\n}\n\n\n\nTry it online!\n\nOne last katamari-based bot for today, this time with a little bit of memory. Thanks to @BetaDecay for the name suggestion - definitely a more fun name than my simplePredictorKatamari.\n\nTries to figure out how bots have moved in the last turn, and based on that, predicts where they'll try to move at the end of this turn (assuming they continue to move in the same direction).\n\n(Thanks to @fəˈnɛtɪk, for noticing that I was calling the wrong function name in botNotes, and to @OMᗺ for noticing a bug in the base code.)\n\n• This is probably the only one right now that can catch others outside of just being lucky. – Cain Aug 8 '18 at 22:56\n• Isn't botnotes supposed to be \"storedata\" not setdata? – fəˈnɛtɪk Aug 9 '18 at 1:26\n• @fəˈnɛtɪk See, already needs a bugfix! :) Thanks, corrected now. – sundar - Remember Monica Aug 9 '18 at 7:59\n• You should replace aWt = 1 in the params with aWt, and put aWt = aWt || 1 underneath (Same with bWt). This prevents errors. – Redwolf Programs Aug 10 '18 at 14:57\n\n# Proton | JavaScript\n\nProton=(myself,others,coins)=>{\nx=myself.locationX;\ny=myself.locationY;\npower=myself.coins;\narenaSize=myself.arenaLength;\nforceX=0;\nforceY=0;\nprevState=botNotes.getData(\"proton_velocity\");\nif(prevState){\nvelocity=prevState;\ndirection=prevState;\n}\nelse{\nvelocity=0;\ndirection=0;\n}\nfor(i=0;i<coins.length;i++){\nif(Math.abs(x-coins[i])+Math.abs(y-coins[i])==1){\nvelocity=0;\ndirection=0;\nbotNotes.storeData(\"proton_velocity\",[velocity,direction]);\nif(x-coins[i]==1){return \"west\";}\nif(coins[i]-x==1){return \"east\";}\nif(y-coins[i]==1){return \"north\";}\nif(coins[i]-y==1){return \"south\";}\n}\nelse{\ndist=Math.sqrt(Math.pow(x-coins[i],2)+Math.pow(y-coins[i],2));\nif(i==0){\nforceX+=(x-coins[i])*5/Math.pow(dist,3);\nforceY+=(y-coins[i])*5/Math.pow(dist,3);\n}\nelse{\nforceX+=(x-coins[i])*2/Math.pow(dist,3);\nforceY+=(y-coins[i])*2/Math.pow(dist,3);\n}\n}\n}\nfor(i=0;i<others.length;i++){\nif(Math.abs(x-others[i])+Math.abs(y-others[i])==1&&power>others[i]){\nvelocity=0;\ndirection=0;\nbotNotes.storeData(\"proton_velocity\",[velocity,direction]);\nif(x-others[i]==1){return \"west\";}\nif(others[i]-x==1){return \"east\";}\nif(y-others[i]==1){return \"north\";}\nif(others[i]-y==1){return \"south\";}\n}\nelse{\ndist=Math.sqrt(Math.pow(x-others[i],2)+Math.pow(y-others[i],2));\nforceX+=(x-others[i])*others[i]/Math.pow(dist,3);\nforceY+=(y-others[i])*others[i]/Math.pow(dist,3);\n}\n}\nvX=velocity*Math.cos(direction)+10*forceX/Math.max(1,power);\nvY=velocity*Math.sin(direction)+10*forceY/Math.max(1,power);\nvelocity=Math.sqrt(vX*vX+vY*vY);\nif(velocity==0){return \"none\"}\nretval=\"none\";\nif(Math.abs(vX)>Math.abs(vY)){\nif(vX>0){\nif(x<arenaSize-1){retval=\"east\";}\nelse{vX=-vX;retval=\"west\";}\n}\nelse{\nif(x>0){retval=\"west\";}\nelse{vX=-vX;retval=\"east\";}\n}\n}\nelse{\nif(vY>0){\nif(y<arenaSize-1){retval=\"south\";}\nelse{vY=-vY;retval=\"north\";}\n}\nelse{\nif(y>0){retval=\"north\";}\nelse{vY=-vY;retval=\"south\";}\n}\n}\ndirection=Math.atan2(-vY,vX);\nbotNotes.storeData(\"proton_velocity\",[velocity,direction]);\nreturn retval;\n}\n\n\nAll coins (including those held by other bots) emit a repulsive force towards Protonbot. Based on this force, it builds up velocity and bounces off of walls (turns around immediately upon hitting a boundary). If it ends up next to a bot or coin it can consume, the Strong nuclear force takes over and it moves to consume it, dropping all velocity when it does so.\n\n• Hmm, nuclear physics applied to treasure hunting? This beats Science Channel any day! – Redwolf Programs Aug 9 '18 at 2:41\n• You need to replace sin with Math.sin, cos with Math.cos, and so on – Redwolf Programs Aug 10 '18 at 15:23\n\n## Not so Blindly | JavaScript (Node.js)\n\nImportant Note: This approach is not entirely mine and has been answered in a similar question. Make sure to vote that answer as well.\n\nHaev you ever heard about A* pathfinding algorithm? here it is. It creates the best path from one point to the less valuable coin (as everyone is going for the most valuable, no one is going for the less) and tries to not collide with any other user.\n\nExpects parameters as follow:\n\nAI({locationX: 3, locationY: 1, arenaLength: [5,5]}, [[2,1],[2,2], ...],[[1,2],[3,1], ...])\n\n\nMaybe I do one that goes hunting other bots\n\nfunction AI(me, others, coins){\nvar h = (a,b) => Math.abs(a -b) + Math.abs(a -b)\nvar s = JSON.stringify;\nvar p = JSON.parse;\nvar walls = others.slice(0,2).map(s);\nvar start = [me.locationX, me.locationY];\nvar goal = coins.pop();\nvar is_closed = {};\nis_closed[s(start)] = 0;\nvar open = [s(start)];\nvar came_from = {};\nvar gs = {};\ngs[s(start)] = 0;\nvar fs = {};\nfs[s(start)] = h(start, goal);\nvar cur;\nwhile (open.length) {\nvar best;\nvar bestf = Infinity;\nfor (var i = 0; i < open.length; ++i) {\nif (fs[open[i]] < bestf) {\nbestf = fs[open[i]];\nbest = i;\n}\n}\ncur = p(open.splice(best, 1));\nis_closed[s(cur)] = 1;\nif (s(cur) == s(goal)) break;\nfor (var d of [[0, 1], [0, -1], [1, 0], [-1, 0]]) {\nvar next = [cur + d, cur + d];\nif (next < 0 || next >= me.arenaLength ||\nnext < 0 || next >= me.arenaLength) {\ncontinue;\n}\nif (is_closed[s(next)]) continue;\nif (open.indexOf(s(next)) == -1) open.push(s(next));\nvar is_wall = walls.indexOf(s(next)) > -1;\nvar g = gs[s(cur)] + 1 + 10000 * is_wall;\nif (gs[s(next)] != undefined && g > gs[s(next)]) continue;\ncame_from[s(next)] = cur;\ngs[s(next)] = g;\nfs[s(next)] = g + h(next, goal);\n}\n}\nvar path = [cur];\nwhile (came_from[s(cur)] != undefined) {\ncur = came_from[s(cur)];\npath.push(cur);\n}\nvar c = path[path.length - 1];\nvar n = path[path.length - 2];\nif(n){\nif (n < c) {\nreturn \"west\";\n} else if (n > c) {\nreturn \"east\";\n} else if (n < c) {\nreturn \"north\";\n} else {\nreturn \"south\";\n}\n}else{\nreturn \"none\";\n}\n}\n\n• Wow...a pathfinding algorithm already? It's only been 3 hours! – Redwolf Programs Aug 8 '18 at 17:55\n• My algorithms go for whichever coins are safest to go to. – fəˈnɛtɪk Aug 8 '18 at 17:59\n\n# Coward | Python 2\n\nimport random\n\ndef move(me, others, coins):\ntarget = (me.locationX, me.locationY)\n\n# Identify the dangerous opponents.\nthreats = [i for i, value in enumerate(others) if value >= me.coins]\n\n# If no one scary is nearby, find a nearby coin.\nsafe = True\nfor x, y in self.coins:\ndistance = abs(me.locationX - x) + abs(me.locationY - y)\nsafe = True\nfor i in threats:\nif abs(others[i] - x) + abs(others[i] - y) <= distance:\nsafe = False\nbreak\n\nif safe:\ntarget = (x, y)\nbreak\n\n# Otherwise, just try not to die.\nif not safe:\ncertain = []\npossible = []\nfor x, y in [\n(me.locationX, me.locationY),\n(me.locationX + 1, me.locationY),\n(me.locationX - 1, me.locationY),\n(me.locationX, me.locationY + 1),\n(me.locationX, me.locationY - 1),\n]:\n# Don't jump off the board.\nif x < 0 or y < 0 or x == me.arenaLength or y == me.arenaLength:\ncontinue\n\n# Check if we can get away safely.\nfor i in threats:\nif abs(others[i] - x) + abs(others[i] - y) <= 1:\nbreak\nelse:\ncertain.append((x, y))\n\n# Check if we can take a spot someone is leaving.\nfor i in threats:\nif others[i] = x and others[i] == y:\nfor i in threats:\nif abs(others[i] - x) + abs(others[i] - y) == 1:\nbreak\nelse:\npossible.append((x, y))\n\nif certain:\ntarget = random.choice(certain)\nelif possible:\ntarget = random.choice(possible)\n# Otherwise, we're doomed, so stay still and pray.\n\ndirections = []\nx, y = target\nif x < me.locationX:\ndirections.append('west')\nif x > me.locationX:\ndirections.append('east')\nif y < me.locationY:\ndirections.append('north')\nif y > me.locationY:\ndirections.append('south')\nif not directions:\ndirections.append('none')\n\nreturn random.choice(directions)\n\n\nAvoid bots with more money if at all possible. Otherwise, grab money that's lying around.\n\n• This is the most basic bot that has a chance at winning – Redwolf Programs Aug 9 '18 at 0:51\n\n# Wild Goose Chase Bot, Javascript\n\nA bot that's really good at dodging other bots, but very bad at getting coins.\n\nAlgorithm:\n\n1. If there are no adjacent bots, return none\n2. Otherwise:\n1. Return none with a random chance 1/500 chance (this is intended to prevent stalemates).\n2. Determine which spaces are safe to move to (ie inside the arena and not occupied by another bot)\n3. Return one at random\n\nCode:\n\nfunction wildGooseChase(me, others, coins){\nx = me.locationX;\ny = me.locationY;\n\ndirs = {};\ndirs[(x+1)+\" \"+y] = \"east\";\ndirs[(x-1)+\" \"+y] = \"west\";\ndirs[x+\" \"+(y+1)] = \"south\";\ndirs[x+\" \"+(y-1)] = \"north\";\n\nmov = {};\nmov[\"east\"] = [x+1,y];\nmov[\"west\"] = [x-1,y];\nmov[\"north\"] = [x,y-1];\nmov[\"south\"] = [x,y+1];\n\npossibleDirs = [\"east\",\"west\",\"north\",\"south\"];\n\nfor (i = 0; i < others.length; i++){\nif (others[i]+\" \"+others[i] in dirs){\npossibleDirs.splice(possibleDirs.indexOf(dirs[others[i]+\" \"+others[i]]),1);\n}\n}\n\nif (possibleDirs.length == 4 || Math.floor(Math.random() * 500) == 0){\nreturn \"none\"\n}\n\nfor (i = 0; i < possibleDirs.length; i++){\nif (mov[possibleDirs[i]] == me.arenaLength || mov[possibleDirs[i]] < 0\n|| mov[possibleDirs[i]] == me.arenaLength || mov[possibleDirs[i]] < 0){\nvar index = possibleDirs.indexOf(possibleDirs[i]);\nif (index != -1) {\npossibleDirs.splice(index, 1);\ni--;\n}\n}\n}\n\nif (possibleDirs.length == 0){\nreturn \"none\";\n}\n\nreturn possibleDirs[Math.floor(Math.random() * possibleDirs.length)];\n}\n\n\nTry it Online!\n\nNote to Redwolf Programs:\n\nThis bot has the potential to cause very long rounds. I have taken some liberties to prevent stalemates, but have not tested if they are actually effective. If this bot becomes a problem during testing, please feel free to disqualify it.\n\n• Thanks for the note. An expert evader has an okay chance if it happens to collect enough coins while being chased – Redwolf Programs Aug 10 '18 at 0:50\n• I like this. It's almost like bait for the hunting robots – Beta Decay Aug 12 '18 at 10:58\n\n# KatamariWithValues, JavaScript (Node.js),\n\nfunction katamariWithValues(me, others, coin) {\nlet xdist = t => Math.abs(t - me.locationX)\nlet ydist = t => Math.abs(t - me.locationY)\nfunction distanceCompare(a, b, aWt = 1, bWt = 1) {\nreturn (xdist(a) + ydist(a)) / aWt - (xdist(b) + ydist(b)) / bWt\n}\nfunction hasThreat(loc) {\nlet threat = others.filter(b => b == loc && b == loc && b >= me.coins)\nreturn (threat.length > 0)\n}\nfunction inArena(loc) { // probably unnecessary for this bot\nreturn loc >= 0 && loc >= 0 && loc < me.arenaLength && loc < me.arenaLength\n}\nfunction sortedCoins() {\ncoinsWithValues = coin.map((coords, i) => coords.concat((i == 0) ? 5 : 2))\ncoinsWithValues.sort((a, b) => distanceCompare(a, b, a, b))\nreturn coinsWithValues.map(c => c.slice(0, 2))\n}\n\nlet eatables = others.filter(b => b < me.coins && b > 0)\nlet targets\nif (eatables.length > 0) {\ntargets = eatables.sort(distanceCompare)\n}\nelse {\ntargets = sortedCoins()\n}\n\nlet done, newLoc, dir\nwhile (!done && targets.length > 0) {\nt = targets.shift()\nif ((xdist(t) <= ydist(t) || ydist(t) == 0) && xdist(t) != 0) {\nlet xmove = Math.sign(t - me.locationX)\ndir = xmove < 0 ? 'west' : 'east'\nnewLoc = [me.locationX + xmove, me.locationY]\nif (!hasThreat(newLoc) && inArena(newLoc))\ndone = 1\n}\n\nif (!done) {\nlet ymove = Math.sign(t - me.locationY)\ndir = ['north', 'none', 'south'][ymove + 1]\nnewLoc = [me.locationX, me.locationY + ymove]\nif (!hasThreat(newLoc) && inArena(newLoc))\ndone = 1\n}\n}\n\nif (!done)\ndir = 'none'\n\nreturn dir\n}\n\n\n\nTry it online!\n\n(Thanks to @OMᗺ for pointing out a bug in the original code this was based on.)\n\nTries to grow by \"eating\" bots with less coins than itself. If that's not possible (no such bot exists), then seeks out the nearest coin.\n\nThis version has small tweaks to (a) give higher preference to gold coins than to silver coins - with the risk that seeking a more distant gold coin may end up costing the bot's life or lead to chasing after fool's gold (b) skip bots with 0 coins - no need to waste time chasing after those.\n\n# Polite Near-Sighted Drunk Bot | JavaScript\n\nfunction politeNearSightedDrunkBot(me, others, coins) {\nlet directions = ['none','east','south','west','north']\nlet drunkennessCoefficient = .2\nlet nearSightedness = me.arenaLength - others.length + 2\n//drawCircle(me.locationX, me.locationY, nearSightedness*squareSize)\n\nfunction randomInt(a) {\nreturn Math.floor(Math.random() * a);\n}\nfunction getRandomDirection() {\nreturn ['east', 'west', 'north', 'south'][randomInt(4)]\n}\n\nfunction distanceTo(a) {\nreturn (Math.abs(a - me.locationX) + Math.abs(a - me.locationY))\n}\nfunction distanceBetween(a, b){\nreturn (Math.abs(a - b) + Math.abs(a - b))\n}\nfunction isTargetSafe(a) {\nfor (let i = 0; i < others.length; i++) {\nif (others[i] >= me.coins && distanceBetween(a, others[i]) <= distanceTo(a)) {\nreturn false //unnecessary loop, but I don't want to split out into a function\n}\n}\nreturn true\n}\nfunction amISafe() {\nfor (let i = 0; i < others.length; i++) {\nif (others[i] >= me.coins && distanceTo(others[i]) == 1) {\nif (!num) {\nconsole.log('politeNearSightedDrunkBot: Woops!')\n} else if (num == 1) {\nconsole.log('politeNearSightedDrunkBot: \\'Scuse me...')\n} else if (num == 2) {\nconsole.log('politeNearSightedDrunkBot: D\\'ye mind?')\n} else if (num == 3) {\nconsole.log('politeNearSightedDrunkBot: Bugger off!')\n}*/\nreturn false\n}\n}\nreturn true\n}\nfunction getSafeDirections() {\nlet candidates = {'none': true, 'east': true, 'south': true, 'west': true, 'north': true}\nif (me.locationY == 0) {\ncandidates['north'] = false\n} else if (me.locationY == me.arenaLength - 1) {\ncandidates['south'] = false\n}\nif (me.locationX == 0) {\ncandidates['west'] = false\n} else if (me.locationX == me.arenaLength - 1) {\ncandidates['east'] = false\n}\nif (!amISafe()) {\ncandidates['none'] = false\n}/* else {\n}*/\nif (candidates['north'] && !isTargetSafe([me.locationX, me.locationY-1])) {\ncandidates['north'] = false\n}\nif (candidates['south'] && !isTargetSafe([me.locationX, me.locationY+1])) {\ncandidates['south'] = false\n}\nif (candidates['west'] && !isTargetSafe([me.locationX-1, me.locationY])) {\ncandidates['west'] = false\n}\nif (candidates['east'] && !isTargetSafe([me.locationX+1, me.locationY])) {\ncandidates['east'] = false\n}\nif (candidates['none']) {\n}\nreturn candidates\n}\nfunction getSafeCoins() {\nlet safestCoins = []\nlet coinSizes = [5, 2, 2, 2, 2]\nfor (let i = 0; i < coins.length; i++) {\nlet distanceToThisCoin = distanceTo(coins[i])\nif (distanceToThisCoin < nearSightedness && isTargetSafe(coins[i])) {\nsafestCoins.push([coins[i], coins[i], coinSizes[i], distanceToThisCoin])\n//alert('Coin at (' + coins[i] + ', ' + coins[i] + ') is safe!')\n}\n}\nif (safestCoins.length == 0) {\n}\nreturn safestCoins\n}\n\nlet candidates = {'east': 0, 'south': 0, 'west': 0, 'north': 0}\nfor (let i = 0; i < targets.length; i++) {\nif (targets[i] < me.locationX) {\ncandidates['west'] = candidates['west'] + targets[i]/targets[i]\n} else if (targets[i] > me.locationX) {\ncandidates['east'] = candidates['east'] + targets[i]/targets[i]\n}\nif (targets[i] > me.locationY) {\ncandidates['south'] = candidates['south'] + targets[i]/targets[i]\n} else if (targets[i] < me.locationY) {\ncandidates['north'] = candidates['north'] + targets[i]/targets[i]\n}\n}\nfor (let key in candidates) {\n//alert(key + ': ' + candidates[key])\n}\nreturn candidates\n}\n\nlet targetCoins = getSafeCoins()\nlet safeDirections = getSafeDirections()\nlet chosenDir = null\nif (targetCoins.length > 0) {\n//alert('Coins found! Exactly ' + targetCoins.length)\nlet bestOptionWeight = 0\nlet choices = []\nfor (let key in safeDirections) {\nif (safeDirections[key] && key != 'none') {\nif (weightedDirections[key] == bestOptionWeight) {\nchoices.push(key)\n} else if (weightedDirections[key] > bestOptionWeight) {\nchoices = [key]\nbestOptionWeight = weightedDirections[key]\n}\n}\n}\nif (choices.length > 0) {\n//alert('Picking from choices, ' + choices.length + ' options and best weight is ' + bestOptionWeight)\nchosenDir = choices[randomInt(choices.length)]\n} else {\n}\n} else {\nlet lastDir = botNotes.getData('direction') || 'none'\nif (safeDirections[lastDir] && Math.random() >= drunkennessCoefficient) {\nchosenDir = lastDir\n}\n}\n\nif (!chosenDir) {\nlet choices = []\nfor (key in safeDirections) {\nif (safeDirections[key]) {\nchoices.push(key)\n}\n}\nif (choices.length > 0) {\nchosenDir = choices[randomInt(choices.length)]\n} else {\nchosenDir = getRandomDirection()\n}\n}\n\nbotNotes.storeData('direction', chosenDir)\nreturn chosenDir\n}\n\n\nStaggers around picking up nearby coins, but randomly switches directions every so often. Does what he can to avoid bumping into anyone, but he gets... belligerent... when aggravated. Tends to sober up as the competition goes on.\n\nMay need some debugging, when the controller is fully done I'll work on it.\n\n• Hmm, it raises the bar, then gets drunk at it – Redwolf Programs Aug 9 '18 at 21:51\n\n# Weighted Motion | JavaScript\n\nWeightedMotion=(myself,others,coins)=>{\nx=myself.locationX;\ny=myself.locationY;\npower=myself.coins;\narenaSize=myself.arenaLength;\ndirX=0;\ndirY=0;\nfor(i=0;i<coins.length;i++){\nif(i==0){\ndirX+=5/(x-coins[i]);\ndirY+=5/(y-coins[i]);\n}\nelse{\ndirX+=2/(x-coins[i]);\ndirY+=2/(y-coins[i]);\n}\n}\nfor(i=0; i<others.length;i++){\ndirX+=(power-others[i])/(2*(x-others[i]));\ndirY+=(power-others[i])/(2*(y-others[i]));\n}\nif(Math.abs(dirX)>Math.abs(dirY)){\nif(dirX>0){\nif(x>0){return \"west\";}\nelse{\nif(dirY>0){if(y>0)return \"north\";}\nelse if(dirY<0){if(y<arenaSize-1)return \"south\";}\n}\n}\nelse if(x<arenaSize-1){return \"east\";}\nelse{\nif(dirY>0){if(y>0)return \"north\";}\nelse if(dirY<0){if(y<arenaSize-1)return \"south\";}\n}\n}\nelse{\nif(dirY>0){\nif(y>0){return \"north\";}\nelse{\nif(dirX>0){if(x>0)return \"west\";}\nelse if(dirX<0){if(x<arenaSize-1)return \"east\";}\n}\n}\nelse if(y<arenaSize-1){return \"south\";}\nelse{\nif(dirX>0){if(x>0)return \"west\";}\nelse if(dirX<0){if(x<arenaSize-1){return \"east\";}\n}\n}\nreturn \"none\";\n}\n\n\nMoves in the direction it has assigned the highest value while avoiding running off the edge of the board.\n\nValue is calculated as such:\n\n• Coin = power of coin / distance to coin\n• Bot = Difference in power of bots / 2 * distance to bot\n• Well, this looks like a pretty awesome bot. Be sure to check the directions, since it would be a real loss if your bot was a master at running away from coins (: – Redwolf Programs Aug 8 '18 at 17:17\n• Well, still. I've got to be nice, right? – Redwolf Programs Aug 8 '18 at 17:32\n• Well, post it! It'll make up for the smaller, faster bots that also exist at the moment in large quantities. – Redwolf Programs Aug 8 '18 at 17:37\n• for(i=0;i<6;i++){ there are only 5 coins in total, 1 gold and 4 silver. Your loop is running 6 times from 0 to 5. – Night2 Aug 10 '18 at 17:22\n\n## Blindy | JavaScript (Node.js)\n\nThis definitely wont win but at least participate. First try at KoH challenge. It sorts the coins and goes to the closest one. He doesn't look for players so he doesn't care if he collide with other.\n\nfunction(myself, others, coins){\nmx = myself.locationX\nmy = myself.locationY\nl=\"west\"\nr=\"east\"\nu=\"north\"\nd=\"south\"\nn=\"none\"\n\nif(coins.length == 0)\nreturn n\n\nvar closestCoin = coins.sort(a=>Math.sqrt(Math.pow(mx-a,2) + Math.pow(my-a,2))).pop()\ncx = closestCoin\ncy = closestCoin\n\nreturn mx>cx?l:mx<cx?r:my>cy?u:my<cy?d:n\n}\n\n• Hmm, it might work since other bots will be seeking the gold primarily, potentially leaving you to get the silver without any fighting – Redwolf Programs Aug 8 '18 at 16:13\n\n# Feudal Noble | JavaScript\n\nPreferred color: #268299\n\nfunction (noble, peasants, coins) {\nvar center = (noble.arenaLength - 1) / 2, centerSize = noble.arenaLength / 4, peasantsCount = peasants.length,\ncenterMin = center - centerSize, centerMax = center + centerSize, apocalypse = 2e4 - ((noble.arenaLength * 2) + 20), inDanger = false;\n\nvar round = botNotes.getData('round');\nif (round === null || !round) round = 0;\nround++;\nbotNotes.storeData('round', round);\n\nvar getDistance = function (x1, y1, x2, y2) {\nreturn (Math.abs(x1 - x2) + Math.abs(y1 - y2)) + 1;\n};\n\nvar isAtCenter = function (x, y) {\nreturn (x > centerMin && x < centerMax && y > centerMin && y < centerMax);\n};\n\nvar getScore = function (x, y) {\nvar score = 0, i, centerFactor = 10;\n\nfor (i = 0; i < peasantsCount; i++) {\nvar peasantCoins = peasants[i], peasantDistance = getDistance(x, y, peasants[i], peasants[i]);\n\nif (noble.coins > peasantCoins && isAtCenter(x, y)) {\nscore += Math.min(100, peasantCoins) / peasantDistance;\n} else if (noble.coins <= peasantCoins && peasantDistance <= 3) {\nscore -= (peasantDistance === 3 ? 50 : 2000);\ninDanger = true;\n}\n}\n\nfor (i = 0; i < coins.length; i++) {\nif (isAtCenter(coins[i], coins[i])) {\nvar coinDistance = getDistance(x, y, coins[i], coins[i]),\ncoinValue = (i === 0 ? 500 : 200),\ncoinCloserPeasants = 1;\n\nfor (var j = 0; j < peasantsCount; j++) {\nvar coinPeasantDistance = getDistance(peasants[j], peasants[j], coins[i], coins[i]);\nif (coinPeasantDistance <= coinDistance && peasants[j] >= noble.coins) coinCloserPeasants++;\n}\n\nscore += (coinValue / coinCloserPeasants) / (coinDistance / 3);\n}\n}\n\nif (round >= apocalypse) centerFactor = 1000;\nscore -= getDistance(x, y, center, center) * centerFactor;\n\nreturn score;\n};\n\nvar possibleMoves = [{x: 0, y: 0, c: 'none'}];\nif (noble.locationX > 0) possibleMoves.push({x: -1, y: 0, c: 'west'});\nif (noble.locationY > 0) possibleMoves.push({x: -0, y: -1, c: 'north'});\nif (noble.locationX < noble.arenaLength - 1) possibleMoves.push({x: 1, y: 0, c: 'east'});\nif (noble.locationY < noble.arenaLength - 1) possibleMoves.push({x: 0, y: 1, c: 'south'});\n\nvar topCommand, topScore = null;\nfor (var i = 0; i < possibleMoves.length; i++) {\nvar score = getScore(noble.locationX + possibleMoves[i].x, noble.locationY + possibleMoves[i].y);\nif (topScore === null || score > topScore) {\ntopScore = score;\ntopCommand = possibleMoves[i].c;\n}\n}\n\nif (round >= apocalypse) {\nvar dg = botNotes.getData('dg');\nif (dg === null || !dg) dg = [];\nif (dg.length >= 20) dg.shift();\ndg.push(inDanger);\nbotNotes.storeData('dg', dg);\nif (dg.length >= 20) {\nvar itsTime = true;\nfor (i = 0; i < dg.length; i++) if (!dg[i]) itsTime = false;\nif (itsTime) return 'none';\n}\n}\n\n}\n\n\nThis feudal noble stays at the center of the field and claims it as his own palace. Collects anything at the center for himself, but anything in farms far away should be brought to him by peasants. Of course if an angry powerful peasant appears at the palace, noble might run away to save his life, but he comes back as soon as it is safe!\n\nAs the time goes on, peasants get stronger and stronger. Professional fighters and powerful heros start to rise from the peasantry. Power of the noble keeps decaying. He tries to keep his wealth and his Feudalism system together as long as he can. But finally a time comes that he should accept his faith, he should accept that people don't want Feudalism anymore. That is the day that feudal noble gives up everything, doesn't run from powerful peasants anymore and gets killed by one of them.\n\n# Quantum Gnat Bot | JavaScript\n\nfunction quantumGnatBot(me, others, coins) {\nlet quantumCoefficient = .2\nlet turn = botNotes.getData('turn')\nbotNotes.storeData('turn', turn+1)\nbotNotes.storeData('test', [2, 5, 7])\nbotNotes.getData('test')\nlet dG = {'none': [0, 0, -2, -2], 'east': [1, 0, me.arenaLength-1, -2], 'south': [0, 1, -2, me.arenaLength-1], 'west': [-1, 0, 0, -2], 'north': [0, -1, -2, 0]}\n\nfunction randomInt(a) {\nreturn Math.floor(Math.random() * a);\n}\nfunction getRandomDirection() {\nreturn ['east', 'west', 'north', 'south'][randomInt(4)]\n}\nfunction distanceBetween(a, b){\nreturn (Math.abs(a - b) + Math.abs(a - b))\n}\nfunction isTargetSafe(a) {\nfor (let i = 0; i < others.length; i++) {\nif (others[i] >= me.coins && distanceBetween(a, others[i]) <= 1) {\nreturn false\n}\n}\nreturn true\n}\nfunction isEnemySquare(a) {\nfor (let i = 0; i < others.length; i++) {\nif (distanceBetween(a, others[i]) == 0) {\nreturn true\n}\n}\nreturn false\n}\nfunction getSafeDirections() {\nlet candidates = {'none': true, 'east': true, 'south': true, 'west': true, 'north': true}\nfor (let key in dG) {\nif (me.locationX == dG[key] || me.locationY == dG[key] || !isTargetSafe([me.locationX+dG[key], me.locationY+dG[key]])) {\ncandidates[key] = false\n}\n}\n//alert('Safe: ' + candidates['north'] + ', ' + candidates['east'] + ', ' + candidates['south'] + ', ' + candidates['west'])\nreturn candidates\n}\nfunction getThreatDirections() {\nlet candidates = {'none': false, 'east': false, 'south': false, 'west': false, 'north': false}\nfor (let key in dG) {\nif (isEnemySquare([me.locationX+dG[key], me.locationY+dG[key]])) {\ncandidates[key] = true\n}\n}\nreturn candidates\n}\nfunction getTargetDirections() {\nlet targetBot = null\nlet candidates = {'none': false, 'east': false, 'south': false, 'west': false, 'north': false}\nfor (let i = 0; i < others.length; i++) {\nif (distanceBetween([me.locationX, me.locationY], others[i]) > 2 && (!targetBot || targetBot < others[i])) {\ntargetBot = others[i]\n}\n}\nif (targetBot < me.locationX) {\ncandidates['west'] = true\n} else if (targetBot > me.locationX) {\ncandidates['east'] = true\n}\nif (targetBot > me.locationY) {\ncandidates['south'] = true\n} else if (targetBot < me.locationY) {\ncandidates['north'] = true\n}\n//alert('Chasing ' + targetBot + ', ' + targetBot + ' (' + targetBot + ')')\n//alert('Path: ' + candidates['north'] + ', ' + candidates['east'] + ', ' + candidates['south'] + ', ' + candidates['west'])\nreturn candidates\n}\n\nlet safeDirections = getSafeDirections()\nlet threatDirections = getThreatDirections()\nlet targetDirections = getTargetDirections()\nlet chosenDir = null\nlet choices = []\nfor (key in safeDirections) {\nif (safeDirections[key] && targetDirections[key]) {\nchoices.push(key)\n}\n}\nif (choices.length == 0) {\nfor (key in safeDirections) {\nif (safeDirections[key]) {\nchoices.push(key)\n}\n}\n}\nfor (key in threatDirections) {\nif (threatDirections[key] && Math.random() < quantumCoefficient) {\nchoices.push(key)\n}\n}\nif (choices.length > 0) {\nchosenDir = choices[randomInt(choices.length)]\n} else {\n//alert('No options? Guess we spin the wheel.')\nchosenDir = getRandomDirection()\n}\n\nreturn chosenDir\n}\n\n\nThis annoying bot tries to buzz around the strongest bot without getting swatted and has a slight chance of phasing through those who try to hunt it. It has a tendency to draw the two most powerful bots into close proximity... ;)\n\n• If he can't find a suitable target in getTargetDirections(), then interesting things start to happen. (Such as breaking down everything due to undefined has no property 0 error.) – Ramillies Aug 11 '18 at 10:40\n\n# Retired ICE Agent, JavaScript\n\nPreferred colour: indianred\n\nfunction(me, others, coins) {\nme.arenaLength = me.arenaLength - 1;\n// Calculate the average coin value of bots\nvar avg = 2;\n\nfor (var i = 0; i < others.length; i++) {\navg += others[i];\n}\n\navg /= others.length;\n\n// Find nearest coins\nvar min = [];\nvar min_distance = 100000\nfor (var j = 0; j < coins.length; j++) {\nvar distance = Math.sqrt(Math.pow(me.locationX - coins[j],2) + Math.pow(me.locationY - coins[j],2));\nif (distance < min_distance) {\nmin_distance = distance;\nmin = coins[j];\n}\n}\n\nif (me.coins <= avg || min_distance < 5) {\n// If own coinage is lower than the average or a coin is very close, find some coins\n\n// Move straight to the nearest coin\nif (me.locationY != min) {\nif (me.locationY - min > 0) {\nreturn \"north\";\n} else {\nreturn \"south\";\n}\n} else {\nif (me.locationX - min > 0) {\nreturn \"west\";\n} else {\nreturn \"east\";\n}\n}\n} else {\n// You have enough money to eat most bots\n// Find the weakest bot\nvar weakling = [];\nvar weakling_money = 1000000;\n\nfor (var k = 0; k < others.length; k++) {\nif (others[k] < weakling_money) {\nweakling_money = others[k];\nweakling = others[k];\n}\n}\n\n// Move to the weakest bot\nif (me.locationY != weakling) {\nif (me.locationY - weakling > 0) {\nreturn \"north\";\n} else {\nreturn \"south\";\n}\n} else {\nif (me.locationX - weakling > 0) {\nreturn \"west\";\n} else {\nreturn \"east\";\n}\n}\n}\n}\n\n\nNow retired, this ICE agent is bitter about humanity. As a result, Retired ICE now targets the weakest bot, while keeping its coin value above the average (as per ICE policy).\n\nPreferred colour: #62bda4\n\nimport Data.List\n\nf x y c _ bs _\n| [bx,by,_]:_ <- sortByDist x y \\$ filter ((c>).last) bs = toDir (bx-x,by-y)\nf x y _ _ _ cs\n| [cx,cy,_]:_ <- sortByDist x y cs = toDir (cx-x,cy-y)\nf _ _ _ _ _ _ = \"none\"\n\nsortByDist x y = sortOn (\\[bx,by,_]-> abs (bx-x) + abs (by-y))\n\ntoDir (dx,dy)\n| dx > 0 = \"east\"\n| dx < 0 = \"west\"\n| dy > 0 = \"south\"\n| dy < 0 = \"north\"\n| otherwise = \"none\"\n\n\nPretty simple strategy, picks the first decision from:\n\n• if there are bots with less coins: pick closest and move towards it\n• if there are coins: pick closest and move towards it\n• default: stay\n\nThe bot only tries to catch other bots or coins without caring about potentially stronger bots that might try to catch it.\n\n* I don't really know JavaScript but I did the thing with google (might be inaccurate): Try it online!\n\n• I wonder how he is going to translate haskell into js – Luis felipe De jesus Munoz Aug 8 '18 at 15:16\n• @LuisfelipeDejesusMunoz: Yeah me too. But luckily, it's not very sophisticated code. – ბიმო Aug 8 '18 at 15:19\n• @LuisfelipeDejesusMunoz Just use Node.JS and process.open (or child_process.spawn, or similar) with some parsing. – user202729 Aug 8 '18 at 15:20\n• @LuisfelipeDejesusMunoz: I tried to translate it and added a link, but I don't feel very confident writing JavaScript, so it might be buggy. – ბიმო Aug 8 '18 at 15:48\n• @LuisfelipeDejesusMunoz It would be one thing if this was a 10,000 line AI learning program, but I think I can manage this (: – Redwolf Programs Aug 8 '18 at 16:14\n\n# Coin Magnet | JavaScript\n\nCoinMagnet=(myself,others,coins)=>{\nx=myself.locationX;\ny=myself.locationY;\npower=myself.coins;\narenaSize=myself.arenaLength;\ndirX=0;\ndirY=0;\nfor(i=0;i<coins.length;i++){\nif(i==0){\ndirX+=(coins[i]-x)*3\ndirY+=(coins[i]-y)*3\n}\ndirX+=(coins[i]-x)*2\ndirY+=(coins[i]-y)*2\n}\nfor(i=0;i<others.length;i++){\ndirX+=Math.ceil(0.85*others[i])*(others[i]-x)\ndirX+=Math.ceil(0.85*others[i])*(others[i]-y)\n}\nif(Math.abs(dirX)>Math.abs(dirY)){\nif(dirX>0){return \"east\";}\nelse{return \"west\";}\n}\nelse if(dirY!=0){\nif(dirY>0){return \"south\";}\nelse{return \"north\";}\n}\nreturn \"none\";\n}\n\n\nThis bot is rather dumb, it heads in the direction of the most acquirable coins. This includes coins that it can not get because other bots have higher power than itself.\n\n# ICE Agent | Javascript\n\nfunction(me, others, coins) {\nme.arenaLength = me.arenaLength - 1;\n// Calculate the average coin value of bots\nvar avg = 2;\n\nfor (var i = 0; i < others.length; i++) {\navg += others[i];\n}\n\navg /= others.length;\n\n// Find nearest coins\nvar min = [];\nvar min_distance = 100000\nfor (var j = 0; j < coins.length; j++) {\nvar distance = Math.sqrt(Math.pow(me.locationX - coins[j],2) + Math.pow(me.locationY - coins[j],2));\nif (distance < min_distance) {\nmin_distance = distance;\nmin = coins[j];\n}\n}\n\nif (me.coins <= avg || min_distance < 5) {\n// If own coinage is lower than the average or a coin is very close, find some coins\n\n// Move straight to the nearest coin\nif (me.locationY != min) {\nif (me.locationY - min > 0) {\nreturn \"north\";\n} else {\nreturn \"south\";\n}\n} else {\nif (me.locationX - min > 0) {\nreturn \"west\";\n} else {\nreturn \"east\";\n}\n}\n} else {\n// You have enough money to eat most bots\n// Check if already on border\nif (me.locationX == 0 || me.locationX == me.arenaLength || me.locationY == 0 || me.locationY == me.arenaLength) {\n// Move anticlockwise around the border\nif (me.locationX == 0 && me.locationY != 0 && me.locationY != me.arenaLength) {\nreturn \"south\";\n}\nif (me.locationX == 0 && me.locationY == 0) {\nreturn \"south\";\n}\n\nif (me.locationY == me.arenaLength && me.locationX != 0 && me.locationX != me.arenaLength) {\nreturn \"east\";\n}\nif (me.locationX == 0 && me.locationY == me.arenaLength) {\nreturn \"east\";\n}\n\nif (me.locationX == me.arenaLength && me.locationY != 0 && me.locationY != me.arenaLength) {\nreturn \"north\";\n}\nif (me.locationX == me.arenaLength && me.locationY == me.arenaLength) {\nreturn \"north\";\n}\n\nif (me.locationY == 0 && me.locationX != 0 && me.locationX != me.arenaLength) {\nreturn \"west\";\n}\nif (me.locationX == me.arenaLength && me.locationY == 0) {\nreturn \"west\";\n}\n} else {\n// Find the nearest border and move to it\nif (me.locationX <= me.arenaLength - me.locationX) {\n// Move to left border\nreturn \"west\";\n} else {\n// Move to right border\nreturn \"east\";\n}\n}\n}\n}\n\n\nWhat's the point of a border if isn't being patrolled? ICE moves anticlockwise around the border, picking up any bots which stray into its path.\n\nBefore it can do that, it needs to be able to eat other bots first. For that reason ICE, keeps its coins above the average of all of the bots.\n\nGuaranteed to steal kids from their parents™\n\n• This would be more funny if it weren't so relevant – Don Thousand Aug 13 '18 at 2:05\n\n# X Marks The Spot | JavaScript\n\nfunction(me, others, coins){\nif (me.locationY != 0) {\n// If not on X axis\nif (others.every(other => other==me.locationY-1)) {\n// If any in my way\nif (!others.every(other => other==me.locationX-1)) {\nif (me.locationX != 0) {\n// If no one to my left and not on edge of board\nreturn \"west\"\n} else {\nreturn \"none\"\n}\n} else if (!others.some(other => other==me.locationX+1)) {\nif (me.locationX != me.arenaLength-1) {\n// If no one to my right and not on edge of board\nreturn \"east\"\n} else {\nreturn \"none\"\n}\n} else {\n// I'm surrounded\nreturn \"none\"\n}\n} else {\n// No one in my way\nreturn \"north\"\n}\n} else {\n// If on the x axis\nif (!others.some(other => Math.abs(other-me.locationX)==1 && other == me.locationY)) {\n// If no one next to me\nmove = [\"east\",\"west\"][Math.floor(Math.random()*2)]\n\n// Prevent from falling off the board\nif (move == \"east\" && me.locationX == me.arenaLength-1) {\nreturn \"west\"\n} else if (move == \"west\" && me.locationX == 0) {\nreturn \"east\"\n} else {\nreturn move\n}\n} else {\n// I'm surrounded\nreturn \"none\"\n}\n}\n}\n\n\nX marks the spot, so all the gold must be on the x axis, right? My bot makes a beeline for the y=0 line then stays there, moving about randomly.\n\n• Huh, an interesting method indeed – Redwolf Programs Aug 8 '18 at 16:15\n• – user202729 Aug 8 '18 at 16:21\n• Given that The arena starts at (0,0) in the upper left corner, are you sure you want to move south to get to y=0? – AdmBorkBork Aug 8 '18 at 16:45\n• @AdmBorkBork Thanks, that could've been bad – Beta Decay Aug 8 '18 at 16:50\n\n# Firebird\n\n function(me,others,coins) {\nvar x = me.locationX;\nvar y = me.locationY;\nvar safe = [true, true, true, true];\nvar threats = [];\nvar targets = [];\nvar opps = [];\n\nvar meTo = (loc) => (Math.abs(x - loc) + Math.abs(y - loc));\nvar inSquare = (loc, r) => (Math.abs(loc - x) <= r && Math.abs(loc - y) <= r);\nvar distance = (from, loc) => (Math.abs(from - loc) + Math.abs(from - loc));\nvar attackRange = (from, check, r) => {\nfor (var i = 0; i < check.length; i++) {\nif (distance(check[i], from) == (r || 1)) {\nreturn true;\n}\n}\nreturn false;\n};\nvar dirStr = (dir) => (['north','east','south','west'][dir]);\n\nvar i, n, o, p;\nfor (i = 0; i < others.length; i++) {\no = others[i];\nif (o >= me.coins) {\nthreats.push(o);\n} else {\ntargets.push([o, o, Math.floor(o * 0.55)]);\n}\n}\nfor (i = 1; i < 5; i++) {\ntargets.push([coins[i], coins[i], 2]);\n}\ntargets.push([coins, coins, 5]);\nif (y === 0 || attackRange([x, y - 1], threats)) {\nsafe = false;\n}\nif (x == me.arenaLength - 1 || attackRange([x + 1, y], threats)) {\nsafe = false;\n}\nif (y == me.arenaLength - 1 || attackRange([x, y + 1], threats)) {\nsafe = false;\n}\nif (x === 0 || attackRange([x - 1, y], threats)) {\nsafe = false;\n}\nif (safe.includes(false)) {\nif (!(safe) && safe) {\nopps.push(2);\n}\nif (!(safe) && safe) {\nopps.push(3);\n}\nif (!(safe) && safe) {\nopps.push(0);\n}\nif (!(safe) && safe) {\nopps.push(1);\n}\n} else {\ntargets.sort((a,b)=>(meTo(a) - meTo(b)));\no = targets;\nif (o == x) {\nif (o < y) {\nreturn 'north';\n} else {\nreturn 'south';\n}\n} else if (o == y) {\nif (o < x) {\nreturn 'west';\n} else {\nreturn 'east';\n}\n} else if (Math.abs(o - x) < Math.abs(o - y)) {\nif (o < y) {\nreturn 'north';\n} else {\nreturn 'south';\n}\n} else if (Math.abs(o - x) > Math.abs(o - y)) {\nif (o < x) {\nreturn 'west';\n} else {\nreturn 'east';\n}\n}\n}\nconsole.log(safe[opps]);\nvar lx, ly;\nfor (i = 0; i < opps.length; i++) {\nif (opps[i] === 0) {\nlx = x;\nly = y - 1;\n}\nif (opps[i] == 1) {\nlx = x + 1;\nly = y;\n}\nif (opps[i] == 2) {\nlx = x;\nly = y + 1;\n}\nif (opps[i] == 3) {\nlx = x - 1;\nly = y;\n}\nif (attackRange([lx, ly], targets, 0)) {\nreturn dirStr(opps[i]);\n}\n}\nreturn dirStr(opps);\n}\n\n\nCompletely revamped to be more deadly than before (:\n\n• My absolute loser of a bot – Redwolf Programs Aug 10 '18 at 22:09\n• It's not targeting them, it's avoiding them – Redwolf Programs Aug 10 '18 at 22:24\n• Oh sorry, I misunderstood – Beta Decay Aug 10 '18 at 22:35\n\n# A-Path-y | JavaScript\n\nPreferred color for this bot is #0077b3.\n\n run: function (me, others, coins)\n{\nvar X_INDEX = 0;\nvar Y_INDEX = 1;\nvar COIN_INDEX = 2;\n\nvar GOLD_POINTS = 5;\nvar SILVER_POINTS = 2;\n\nvar NORTH = 0;\nvar SOUTH = 1;\nvar WEST = 2;\nvar EAST = 3;\nvar IDLE = 4;\nvar MOVE_COMMANDS_COUNT = IDLE+1;\n\nvar MAP_TYPE_BLANK = 0;\nvar MAP_TYPE_BOT = 1;\nvar MAP_TYPE_GOLD_COIN = 2;\nvar MAP_TYPE_SILVER_COIN = 3;\n\nvar MIDGAME_THRESHOLD = 25;\n\nvar PATH_FINDING_MAX_STEPS = 10000;\nvar offsets = [[0,-1],[1,0],[0,1],[-1,0]];\n\nfunction randInt(min,max)\n{\nreturn Math.floor(Math.random() * ((max - min) + 1)) + min;\n}\n\n/**\n* Find a path using a*, returns the direction to take from the starting position coupled with a metric describing the cost of the path\n*/\nfunction pathFind(startX,startY,targetX,targetY,map,mapSize)\n{\nvar i;\nvar j;\n\n// shuffleIndecies to make path selection slightly random\nvar indecies = [0,1,2,3];\nvar shuffleIndecies = new Array(4);\nfor (j=0;j<4;j++)\n{\nvar randomIndex = randInt(0,3-j);\nshuffleIndecies[j] = indecies[randomIndex];\nindecies[randomIndex] = indecies;\nvar lastElementIndex = 4-j-1;\nindecies = indecies[lastElementIndex];\n}\n\n// A*\nif (!(startX===targetX && startY===targetY))\n{\n\nvar tileX = new Array(PATH_FINDING_MAX_STEPS);\nvar tileY = new Array(PATH_FINDING_MAX_STEPS);\nvar fscore = new Array(PATH_FINDING_MAX_STEPS);\nvar gscore = new Array(PATH_FINDING_MAX_STEPS);\nvar openList = new Array(PATH_FINDING_MAX_STEPS);\nvar tileParent = new Array(PATH_FINDING_MAX_STEPS);\nvar tileIsClosed = new Array(mapSize);\n\nfor (i = 0;i<PATH_FINDING_MAX_STEPS;i++)\n{\ntileX[i]=0;\ntileY[i]=0;\nfscore[i]=0;\ngscore[i]=0;\nopenList[i]=0;\ntileParent[i]=0;\n}\n\nfor (i = 0;i<mapSize;i++)\n{\nvar newArray = new Array(mapSize);\ntileIsClosed[i] = newArray;\nfor (j = 0;j<mapSize;j++)\n{\ntileIsClosed[i][j] = 0;\n}\n}\n\nvar currentIndex = -1;\n\nvar openListSize=1;\nvar tileId=1;\n\ntileX=targetX;\ntileY=targetY;\nfscore=1;\ngscore=map[targetX][targetY].negativeWeight;\n\ndo\n{\nvar currentBestIndex=-1;\nvar currentBestScore=2147483647;\n// Look for the lowest F cost square on the open list\nfor (var ii=0;ii<openListSize;ii++)\n{\nif (fscore[openList[ii]]<currentBestScore)\n{\ncurrentBestScore=fscore[openList[ii]];\ncurrentBestIndex=ii;\n}\n}\nif (currentBestIndex===-1)\n{\nbreak;\n}\ncurrentIndex=openList[currentBestIndex];\nvar currentTileX=tileX[currentIndex];\nvar currentTileY=tileY[currentIndex];\n\n// found path\nif (startX===currentTileX && startY===currentTileY)\n{\nbreak;\n}\n\n// if not in closed list\nif (tileIsClosed[currentTileX][currentTileY]===0)\n{\n// Switch it to the closed list.\ntileIsClosed[currentTileX][currentTileY]=1;\n// remove from openlist\nopenList[currentBestIndex]=openList[--openListSize];\n\n// add neighbours to the open list if necessary\nfor (j=0;j<4;j++)\n{\ni = shuffleIndecies[j];\n\nvar surroundingCurrentTileX=currentTileX+offsets[i];\nvar surroundingCurrentTileY=currentTileY+offsets[i];\nif (surroundingCurrentTileX>=0 && surroundingCurrentTileX<mapSize &&\nsurroundingCurrentTileY>=0 && surroundingCurrentTileY<mapSize )\n{\ntileX[tileId]=surroundingCurrentTileX;\ntileY[tileId]=surroundingCurrentTileY;\n\nvar surroundingCurrentGscore=gscore[currentIndex] + map[surroundingCurrentTileX][surroundingCurrentTileY].negativeWeight;\ngscore[tileId]=surroundingCurrentGscore;\nfscore[tileId]=surroundingCurrentGscore+Math.abs( surroundingCurrentTileX-startX)+Math.abs( surroundingCurrentTileY-startY);\ntileParent[tileId]=currentIndex;\nopenList[openListSize++]=tileId++;\n}\n}\n}\nelse\n{\n// remove from openlist\nopenList[currentBestIndex]=openList[--openListSize];\n}\n} while(true);\n\nif (tileX[tileParent[currentIndex]]<startX) return {moveDirection:WEST, pathLength:currentIndex, pathScore:gscore[currentIndex]+currentIndex/4};\nelse if (tileX[tileParent[currentIndex]]>startX) return {moveDirection:EAST, pathLength:currentIndex, pathScore:gscore[currentIndex]+currentIndex/4};\nelse if (tileY[tileParent[currentIndex]]<startY) return {moveDirection:NORTH, pathLength:currentIndex, pathScore:gscore[currentIndex]+currentIndex/4};\nelse if (tileY[tileParent[currentIndex]]>startY) return {moveDirection:SOUTH, pathLength:currentIndex, pathScore:gscore[currentIndex]+currentIndex/4};\n}\nconsole.log(\"Path finding failed\");\nreturn {moveDirection:IDLE, pathLength:0, pathScore:2147483647};\n}\n\nfunction process(info,bots,coins)\n{\nvar i;\nvar j;\nvar k;\nvar x;\nvar y;\n\n// initialise map\nvar mapSize = info.arenaLength;\nvar map = new Array(mapSize);\nfor (i = 0;i < info.arenaLength;i++)\n{\nvar newArray = new Array(info.arenaLength);\nmap[i] = newArray;\nfor (j = 0;j < mapSize;j++)\n{\nmap[i][j] = {type:MAP_TYPE_BLANK, coins: 0 , negativeWeight:i===0||i===mapSize-1||j===0||j===mapSize-1?3:1};\n}\n}\n\n// populate map with bots\nfor (i = 0 ; i<bots.length;i++)\n{\nmap[bots[i][X_INDEX]][bots[i][Y_INDEX]].type = MAP_TYPE_BOT;\nmap[bots[i][X_INDEX]][bots[i][Y_INDEX]].coins = bots[i][COIN_INDEX];\n\nfor (j=-1;j<2;j++)\n{\nx = bots[i][X_INDEX] + j;\nif (x>=0 && x < mapSize)\n{\nfor(k=-1;k<2;k++)\n{\nif (Math.abs((k+j)%2) === 1)\n{\ny = bots[i][Y_INDEX] + k;\nif (y>=0 && y< mapSize )\n{\n// are we adjacent the bot or potentially will be?\nif (Math.abs(info.locationX-x)<=1 && Math.abs(info.locationY-y)<=1)\n{\n// make the cell significantly less attractive when the bot is stronger than us, or\n// make the cell slightly more attactive when the bot is weaker than us, or\n// not change if the bot has no coins\nmap[x][y].negativeWeight+= bots[i][COIN_INDEX] >= info.coins?100000:(bots[i][COIN_INDEX]===0?0:-1);\n}\n// another bot is not a direct threat/target\nelse\n{\n// make the cell moderately less attractive when the bot is stronger than us, or\n// make the cell slightly more attactive when the bot is weaker than us, or\n// not change if the bot has no coins\nmap[x][y].negativeWeight+= bots[i][COIN_INDEX] >= info.coins?3:(bots[i][COIN_INDEX]===0?0:-1);\n}\n}\n}\n}\n}\n}\n}\n\n// populate map with coins\nfor (i = 0 ; i<coins.length;i++)\n{\nmap[coins[i][X_INDEX]][coins[i][Y_INDEX]].type = i === 0?MAP_TYPE_GOLD_COIN:MAP_TYPE_SILVER_COIN;\nmap[coins[i][X_INDEX]][coins[i][Y_INDEX]].coins = i === 0?GOLD_POINTS:SILVER_POINTS;\n\n// check to see whether bots are adjacent to the coin\nfor (j=-1;j<2;j++)\n{\nx = coins[i][X_INDEX] + j;\nif (x>=0 && x < mapSize)\n{\nfor(k=-1;k<2;k++)\n{\nif ((k+j)%2 === 1)\n{\ny = coins[i][Y_INDEX] + k;\nif (y>=0 && y< mapSize )\n{\nif (map[x][y].type === MAP_TYPE_BOT)\n{\n// this coin looks like a trap as a stronger bot is adjacent to it\nif (map[x][y].coins >= info.coins)\n{\nmap[coins[i][X_INDEX]][coins[i][Y_INDEX]].negativeWeight+=100000;\n}\nelse\n{\n// are we adjacent the coin? we might be able to kill another bot if it trys to get the coin\nif (Math.abs(info.locationX-coins[i][X_INDEX])<=1 && Math.abs(info.locationY-coins[i][Y_INDEX])<=1)\n{\nmap[coins[i][X_INDEX]][coins[i][Y_INDEX]].negativeWeight+=-20;\n}\n// another bot is likely to get this coin... make it less attractive\nelse\n{\nmap[coins[i][X_INDEX]][coins[i][Y_INDEX]].negativeWeight=+100;\n}\n}\n}\n}\n}\n}\n}\n}\n\n// add the coin attractiveness, more for gold coins\nmap[coins[i][X_INDEX]][coins[i][Y_INDEX]].negativeWeight += i === 0?-20:-10;\n}\n\nvar pathBest = {moveDirection:IDLE, pathLength: 2147483647, pathScore: 2147483647};\n\nif (info.coins > MIDGAME_THRESHOLD)\n{\nvar viableCoinCount =0;\nvar viableCoins = new Array(5);\n\n// find coins that are reachable before any other bot\nouter1:\nfor (j = 0 ; j<coins.length;j++)\n{\nvar contention = 0;\n\nvar myDistanceToCoin = Math.abs(info.locationX-coins[j][X_INDEX]) + Math.abs(info.locationY-coins[j][Y_INDEX]);\n\nfor (i = 0 ; i<bots.length;i++)\n{\nvar dist = Math.abs(bots[i][X_INDEX]-coins[j][X_INDEX]) + Math.abs(bots[i][Y_INDEX]-coins[j][Y_INDEX]);\nif (dist < myDistanceToCoin)\n{\ncontinue outer1;\n}\n}\nviableCoins[viableCoinCount++] = j;\n}\n\n// no coins are reachable before another bot so find the cell that is furthest away from any bot and head there\nif (viableCoinCount ===0)\n{\nvar mostIsolatedCellX = mapSize/2;\nvar mostIsolatedCellY = mapSize/2;\nvar mostIsolatedCellMinBotDistance = 0;\n\nfor (x=5;x<mapSize-5;x++)\n{\nfor (y=5;y<mapSize-5;y++)\n{\nif (x!= info.locationX && y!=info.locationY)\n{\n\n// ignore coin attractiveness\nmap[x][y].negativeWeight = map[x][y].negativeWeight<-4?map[x][y].negativeWeight:1;\n\nvar currentCellMinBotDistance = 2147483647;\n\nfor (i = 0 ; i<bots.length;i++)\n{\nvar dist = Math.abs(bots[i][X_INDEX]-x) + Math.abs(bots[i][Y_INDEX]-y) + Math.abs(info.locationX-x) + Math.abs(info.locationY-y);\nif (dist < currentCellMinBotDistance )\n{\n{\ncurrentCellMinBotDistance = dist;\nif (currentCellMinBotDistance>mostIsolatedCellMinBotDistance)\n{\nmostIsolatedCellMinBotDistance = currentCellMinBotDistance;\nmostIsolatedCellX=x;\nmostIsolatedCellY=y;\n}\n}\n}\n}\n}\n}\n}\n\n// attempt to find path to most isolated cell\npathBest = pathFind(info.locationX, info.locationY, mostIsolatedCellX,mostIsolatedCellY, map, mapSize);\n}\n\n// attempt to find paths to each viable coin, keeping the best result\nfor (i = 0 ; i<viableCoinCount;i++)\n{\nvar path = pathFind(info.locationX, info.locationY, coins[viableCoins[i]][X_INDEX],coins[viableCoins[i]][Y_INDEX], map, mapSize);\nif (path.pathScore < pathBest.pathScore)\n{\npathBest = path;\n}\n}\n}\nelse\n{\n// attempt to find paths to each coin, keeping the best result\nfor (i = 0 ; i<coins.length;i++)\n{\nvar path = pathFind(info.locationX, info.locationY, coins[i][X_INDEX],coins[i][Y_INDEX], map, mapSize);\nif (path.pathScore < pathBest.pathScore)\n{\npathBest = path;\n}\n}\n}\n\nvar move = IDLE;\nif (pathBest.pathLength === 2147483647)\n{\nouter:\nfor (i=0;i<MOVE_COMMANDS_COUNT;i++)\n{\nswitch (i)\n{\ncase NORTH:\nif (info.locationY-1 < 0)\n{\ncontinue;\n}\nmove = i;\nbreak outer;\ncase SOUTH:\nif (info.locationY+1 === info.arenaLength)\n{\ncontinue;\n}\nmove = i;\nbreak outer;\ncase WEST:\nif (info.locationX-1 < 0)\n{\ncontinue;\n}\nmove = i;\nbreak outer;\ncase EAST:\nif (info.locationX+1 === info.arenaLength)\n{\ncontinue;\n}\nmove = i;\nbreak outer;\ncase IDLE:\nmove = i;\nbreak;\ndefault:\n}\n}\n}\nelse\n{\nmove = pathBest.moveDirection;\n}\n\nswitch (move)\n{\ncase NORTH:\nreturn \"north\";\ncase SOUTH:\nreturn \"south\";\ncase EAST:\nreturn \"east\";\ncase WEST:\nreturn \"west\";\ndefault:\nreturn \"none\";\n}\n}\nreturn process(me, others, coins);\n}\n\n\nThis bot uses path finding coupled with a map of cell desirabilities to avoid bots that could kill us, go for coins that are close, not traps and are least risky.\n\nIt does not seem to be a contender for the winning place, but it does hold its own and will be alive at the end of the match if it survives the initial melee.\n\nBot now has mid-to-late game strategy that ignores coins it cannot reach before other bots and if cannot go to any coin then moves to the closest cell that is furthest away from all other bots that are stronger than itself.\n\nIt now has a chance of winning.\n\nNote sorry for the crappy code, I have automatically converted it from Java\n\n• Be sure to get any bugs and/or updates out of the way soon, 18 hours to due date! – Redwolf Programs Aug 14 '18 at 17:55\n• @RedwolfPrograms Have you observed a bug? if so please let me know so I can correct. Thanks – Moogie Aug 14 '18 at 22:42\n• No, but you never know. Just be sure to double check, since I've seen many bots lose due to one wrong number, or wrong function, or mistype more times than I can count – Redwolf Programs Aug 14 '18 at 22:44" ]
[ null ]
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https://ssconlineexam.com/onlinetest/SSC-CGL-Tier-1/Quantitative-Aptitude/QA-Test-13
[ "# SSC CGL Tier 1 :: Quantitative Aptitude QA Test 13", null, "ssc Online for Discuss\n\n## Home SSC CGL Tier 1 / Quantitative Aptitude QA Test 13 Questions and Answers\n\n1 . A tank can be f ill ed by t wo pipes in 20 minutes and 30 minutes respectively. When the tank was empty, the two pipes were opened. After some time, the first pipe was stopped and the tank was filled in 18 minutes. After how much time of the start was the first pipe stopped ?\n5 minutes\n8 minutes\n10 minutes\n12 minutes", null, "View Answer", null, "Discuss in Forum\n2 . A hare sees a dog 100 metres away from her and scuds off in the opposite direction at a speed of 12 km per hr. A minute later the dog perceives her and chases her at a speed of 16 km per hr. At what distance from the spot dog will overtake the hare when the hare took flight ?\n900 metre\n950 metre\n1000 metre\n1100 metre", null, "View Answer", null, "Discuss in Forum\n3 . A train met with an accident 3 hours after starting, which detains it for one hour, after which it proceeds at 75% of its original speed. It arrives at the destination 4 hours late. Had the accident taken place 150 km further along the railway line, the train would have arrived only 3$1\\over2$ 2 hours late. Find the length of the trip and the original speed of the train\n1100 km and 100 kmph\n1200 km and 100 kmph\n1200 km and 90 kmph\n1600 km and 90 kmph", null, "View Answer", null, "Discuss in Forum\n4 . A motorboat in still water travels at a speed of 36 kmph. It goes 56 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be –\n2 hours 25 minutes\n3 hours\n1 hour 24 minutes\n2 hours 21 minutes", null, "View Answer", null, "Discuss in Forum\n5 .", null, "a\nb\nc\nd", null, "View Answer", null, "Discuss in Forum\n6 .", null, "32\n8\n1\n0", null, "View Answer", null, "Discuss in Forum\n7 . the value of $1\\over20$+$1\\over30$+$1\\over42$+$1\\over56$+$1\\over72$+$1\\over90$ is ---\nA.$31\\over10$\nB.$3\\over5$\nC.$3\\over20$\nD.$7\\over20$\na\nb\nc\nd", null, "View Answer", null, "Discuss in Forum\n8 . (x+$1\\over x$)(x-$1\\over x$)($x^2$ + $1\\over x^2$ -1)($x^2$ + $1\\over x^2$ +1) is equal to --\n\nA.$x^6$ + $1\\over x^6$\nB.$x^8$ + $1\\over x^8$\nC.$x^8$ - $1\\over x^8$\nD.$x^6$ - $1\\over x^6$\na\nb\nc\nd", null, "View Answer", null, "Discuss in Forum\n9 . The value of the expression\n\n$(a-b)^2\\over (b-c)(c-a)$+ $(b-c)^2\\over (b-c)(c-a)$+ $(c-a)^2\\over (b-c)(c-a)$ is --\n0\n3\n$1\\over2$\n2", null, "View Answer", null, "Discuss in Forum\n10 . If a+ b+ c= 2s, then $(s-a)^2+(s-b)^2+(s-c)^2+(s-d)^2+d^2\\over a^2+b^2+c^2$ is equal to –\n\n$a^2+b^2+c^2$\n0\n1\n2", null, "View Answer", null, "Discuss in Forum", null, "ssc Recruitment", null, "ssc Upcoming Exams Notifications", null, "Latest Govt Jobs" ]
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https://arxiv.org/abs/1903.08611v1
[ "math.ST\n\n# Title:Autocovariance Varieties of Moving Average Random Fields\n\nAbstract: We study the autocovariance functions of moving average random fields over the integer lattice $\\mathbb{Z}^d$ from an algebraic perspective. These autocovariances are parametrized polynomially by the moving average coefficients, hence tracing out algebraic varieties. We derive dimension and degree of these varieties and we use their algebraic properties to obtain statistical consequences such as identifiability of model parameters. We connect the problem of parameter estimation to the algebraic invariants known as euclidean distance degree and maximum likelihood degree. Throughout, we illustrate the results with concrete examples. In our computations we use tools from commutative algebra and numerical algebraic geometry.\n Comments: 20 pages, 5 tables, 2 figures Subjects: Statistics Theory (math.ST); Algebraic Geometry (math.AG) MSC classes: 60G60, 62M10, 62F10, 14Q15, 13P25 Cite as: arXiv:1903.08611 [math.ST] (or arXiv:1903.08611v1 [math.ST] for this version)\n\n## Submission history\n\nFrom: Carlos Améndola [view email]\n[v1] Wed, 20 Mar 2019 16:53:30 UTC (262 KB)" ]
[ null ]
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https://www.hindawi.com/journals/mpe/2014/853821/
[ "Special Issue\n\n## Sensor/Actuator Networks and Networked Control Systems\n\nView this Special Issue\n\nResearch Article | Open Access\n\nVolume 2014 |Article ID 853821 | https://doi.org/10.1155/2014/853821\n\nKun Zhao, Kegang Pan, Bangning Zhang, \"Cooperative Transmission in Mobile Wireless Sensor Networks with Multiple Carrier Frequency Offsets: A Double-Differential Approach\", Mathematical Problems in Engineering, vol. 2014, Article ID 853821, 13 pages, 2014. https://doi.org/10.1155/2014/853821\n\n# Cooperative Transmission in Mobile Wireless Sensor Networks with Multiple Carrier Frequency Offsets: A Double-Differential Approach\n\nAccepted10 Mar 2014\nPublished03 Apr 2014\n\n#### Abstract\n\nAs a result of the rapidly increasing mobility of sensor nodes, mobile wireless sensor networks (MWSNs) would be subject to multiple carrier frequency offsets (MCFOs), which result in time-varying channels and drastically degrade the network performance. To enhance the performance of such MWSNs, we propose a relay selection (RS) based double-differential (DD) cooperative transmission scheme, termed RSDDCT, in which the best relay sensor node is selected to forward the source sensor node’s signals to the destination sensor node with the detect-and-forward (DetF) protocol. Assuming a Rayleigh fading environment, first, exact closed-form expressions for the outage probability and average bit error rate (BER) of the RSDDCT scheme are derived. Then, simple and informative asymptotic outage probability and average BER expressions at the large signal-to-noise ratio (SNR) regime are presented, which reveal that the RSDDCT scheme can achieve full diversity. Furthermore, the optimum power allocation strategy in terms of minimizing the average BER is investigated, and simple analytical solutions are obtained. Simulation results demonstrate that the proposed RSDDCT scheme can achieve excellent performance over fading channels in the presence of unknown random MCFOs. It is also shown that the proposed optimum power allocation strategy offers substantial average BER performance improvement over the equal power allocation strategy.\n\n#### 1. Introduction\n\nIn recent years, with the rapid advances in microelectromechanical systems (MEMS) and wireless communication technologies, wireless sensor networks (WSNs) have gained an increasing research attention for their various military and civil applications, including intrusion detection, automated data collection, healthcare, and environmental monitoring [1, 2]. A WSN is usually composed of a large amount of low-cost and low-power sensor nodes, which are statically deployed in a certain region of interest. However, in many application scenarios, for example, wildlife protection and object tracking, due to the dynamic changes of events and environment, a purely static WSN could face severe problems, such as limited coverage and channel capacity, unfair energy usage, and increasing multiple missions . To handle these problems, a new class of WSNs, namely, mobile wireless sensor networks (MWSNs), has been proposed by introducing mobility to some or all the sensor nodes, and it is shown that the MWSNs outperform the static WSNs in terms of longer network lifetime, more channel capacity, enhanced coverage and targeting, and so on [3, 4]. Many researchers have been dedicated to exploring the aforementioned advantages of MWSNs, and great progress has been made . However, there are still numerous key technical issues that need further research, among which how to realize reliable communications between the mobile sensor nodes over fading channels stands out as critical consideration.\n\nCooperative communications have been demonstrated as a promising technology to improve the spectral efficiency and reliability of wireless communication systems by forming a virtual antenna array among cooperating nodes [11, 12]. The numerous sensor nodes and the resource-constrained nature make WSNs one of the most important application fields for cooperative communications, and a variety of cooperative schemes have been proposed to improve the performance of different kinds of WSNs. These cooperative schemes generally focus on two aspects. On one hand, a number of literatures investigated the cooperative multiple-input and multiple-output (MIMO) transmission technique for WSNs, where the sensor nodes cooperate with each other to form a virtual MIMO channel. The contribution first proposed a cooperative MIMO transmission scheme with Alamouti coding for WSNs, and, based on the similar virtual MIMO, various cooperative schemes employing space-time block codes (STBC) were proposed and analyzed in . On the other hand, many other researchers endeavored to design excellent selective cooperative relaying schemes. In , by combining relay selection with power control, a selective single-relay cooperative scheme was proposed, which can minimize the energy consumption and extend the network’s lifetime. A simple geographic-based relay selective cooperative relaying protocol was proposed in , where the best relay can be efficiently determined by using the geographical information among nodes. The authors in proposed an adaptive relay selection based cooperative scheme for a cluster-based WSN, which can guarantee the quality of service (QoS) without the needs of prior knowledge of the wireless network model and centralized control.\n\nWhile all these aforementioned cooperative schemes can significantly improve the performance of WSNs, the key limitation of them is that they all assume full channel state information (CSI) and perfect synchronization can be achieved. However, in actual WSNs, especially MWSNs, where the channels between the sensor nodes undergo different kinds of fading, it is challenging even impossible to obtain perfect CSI. Moreover, as the sensor nodes are evolving towards high mobility, for example, more and more sensors are deployed on ground vehicles and unmanned aerial vehicles [21, 22], the perfect synchronization assumption is also not justifiable in MWSNs, where each distributed sensor node is equipped with its local oscillator and the presence of multiple carrier frequency offsets (MCFOs) can be caused by: (i) simultaneous transmissions from spatially separated sensor nodes equipped with different oscillators and (ii) Doppler shifts introduced by the relative motions between the transmit and receive sensor nodes. In such cases, the channels in MWSNs are time-varying; therefore, all these existing cooperative schemes originally developed for static WSNs inevitably suffer drastic performance degradation or even break down.\n\nIn order to reduce the burden of channel estimation, noncoherent and differential cooperative transmission schemes have been proposed in [23, 24]. The works in [25, 26] extended the differential modulation to multirelay cooperative networks and showed that full diversity could be achieved. In [27, 28] the authors proposed a differential modulation (DM) and relay selection (RS) based scheme for a detect-and-forward (DetF) cooperative network (DM-RS-DetF) [27, 28], and it was revealed that the DM-RS-DetF network could also achieve full diversity order. However, these schemes still assume that no CFOs exist in the networks, which make them not applicable to the MWSNs with MCFOs.\n\nThe approaches for dealing with CFOs in communication systems can be generally classified into two main categories; the first one focuses on estimating and compensating the CFOs by designing excellent estimators, while the second one resorts to developing novel techniques which are robust to the CFOs. Recently, in an effort to eliminate the impact of the MCFOs, a number of MCFOs estimators have been proposed for both amplify-and-forward (AF) and decode-and-forward (DecF) cooperative networks . Nevertheless, as observed in these literatures, the estimators as well as the transceivers are generally quite computationally complex and the overheads consumed by the parameters estimation are always significant, which limit their deployment on resource-constrained sensor nodes. Moreover, it is also a challenge task to reliably feedforward/feedback the CSI or MCFOs estimates to different sensor nodes. On the other hand, imperfect MCFOs estimates and compensation still degrade the network performance. Hence, given all these reasons, it may be more practical to address the MCFOs by developing robust transmission techniques rather than by designing estimators to estimate and compensate the MCFOs in actual MWSNs.\n\nIn this paper, we consider a MWSN over Rayleigh fading channels, where all the wireless links among the sensor nodes are perturbed by different random MCFOs. This is a practical scenario which has scarcely appeared in the literature. Instead of devising complicated CFO estimator, we propose to address the MCFOs in the MWSN employing double-differential (DD) modulation technique, which was originally proposed by Okunev . The major advantage of the DD modulation is its bypass of the CFO and channel estimation, and it has turned out to be a powerful technique to cope with unknown CFOs in a number of cooperative systems . The AF and DecF based DD cooperative systems were introduced and analyzed in and , respectively. The authors in proposed a selective DecF protocol, which could compensate the signal-to-noise ratio (SNR) loss in a single-relay DD cooperative system. To further improve the channel utilization, a low complexity piecewise linear (PL) decoder for the DecF based DD cooperative system was designed in , and it was shown that the proposed PL decoder could achieve full spatial diversity, while, in , the authors investigated the AF based DD multirelay networks and presented an effective relay selection strategy to improve the system performance.\n\nMotivated by the excellent performance of these schemes, we herein focus on the DetF relaying protocol and develop a robust relay selection (RS) based double-differential cooperative transmission scheme (RSDDCT) to enhance the performance of the MWSN under consideration. In our scheme, a simple and effective Max-Min relay selection strategy is applied to reduce the energy consumption of the network, through which only the best relay sensor is selected to forward the source sensor’s double-differential modulated signals to the destination sensor with the DetF protocol. For simplicity, we show MWSN with the proposed RSDDCT scheme RSDDCT-DetF network in the remainder of this paper. To facilitate the performance characterization, we present a comprehensive performance analysis for the RSDDCT-DetF network. In this light, we derive exact closed-form expressions for the outage probability and average bit error rate (BER), along with their asymptotic expressions in the high SNR regime. Simulation results show that the RSDDCT-DetF network can achieve excellent performance over fading channels in the presence of random MCFOs. While the contributions have significantly improved our knowledge on the DD cooperative systems, the most important differences between our work and them are as follows. In , the authors only focused on single-relay scenarios, whereas WSNs are generally modeled as multirelay networks; moreover, all the analytical results were limited to the error probability and only lower or upper bounds but no exact expressions were derived; In , only AF multirelay systems were considered, and the proposed relay selection strategy is not applicable to regenerative networks; in addition, there was no analytical result on the system performance. To the best of the authors’ knowledge, there is no previous work on regenerative multirelay cooperative networks with DD modulation. The main contributions of the paper can be summarized as follows.(i)We propose addressing the MCFOs in MWSNs employing DD modulation technique, which is practical but has not been reported in the literature. More specifically, we develop a robust relay selection based double-differential cooperative transmission scheme, termed RSDDCT, to enhance the performance of MWSNs with MCFOs.(ii)Assuming a Rayleigh fading environment, we derive exact closed-form expressions for the outage probability and average BER of the RSDDCT-DetF network at arbitrary SNRs, which provide a fast and efficient means to evaluate the performance of the MWSNs employing the proposed scheme.(iii)In order to gain further insights into the impact of system parameters, such as fading parameters and number of relay sensors, we look into the high SNR regime and present simple and informative high SNR approximations for the outage probability and average BER, which reveal that the MWSN with the proposed scheme can achieve full diversity order.(iv)Based on the derived analytical expressions, we formulate an interesting optimization problem which seeks to minimize the average BER. In particular, we consider power allocation among the source sensor and the relay sensors under a total transmit power constraint, and simple closed-form solutions are derived. Comparisons based on simulations demonstrate that a significant performance improvement is achieved using the optimum power allocation compared to the equal power allocation, which provide an effective method to improve the MWSN’s performance under a fixed power budget.\n\nThe rest of the paper is organized as follows. Section 2 introduces the DD modulation and the system model of the RSDDCT-DetF network. In Section 3, we derive closed-form expressions for the outage probability and average BER of the RSDDCT-DetF network. The asymptotic system behaviors and the power allocation strategy are provided in Sections 4 and 5, respectively. Finally, Section 6 presents our numerical results, and Section 7 concludes the paper.\n\n#### 2. System Model\n\n##### 2.1. Double-Differential Modulation\n\nWe suppose that double-differential binary phase shift keying (DDBPSK) modulation is utilized in the network. Let denote the unitary symbols belonging to the BPSK constellation to be transmitted in the th symbol interval. As shown in Figure 1(a), in a DD modulation based system, the double-differential modulated signals are obtained from in the following way: where and is the number of the symbols to be sent within a frame.\n\nConsider a fading channel with random CFO; the received signals can be expressed as where is the transmit power, is the channel fading coefficient, is the unknown normalized random CFO in radians, and is the additive white Gaussian noise (AWGN), with representing a complex Gaussian random variable with mean and variance .\n\nThe optimal decoder for DDBPSK signals is the maximum likelihood decoder (MLD), which is given by where . It is noted from (3) that the MLD for DD signals can be regarded as a differential detector for the equivalent single-differential signals , which is clearly depicted in Figure 1(b). Thus, the BER performance of DD signals can be characterized by , which is given by where . It is shown that the instantaneous SNR of can be approximated as where . Based on the SNR approximation, the BER performance of the DDBPSK modulation can be evaluated as \n\n##### 2.2. RSDDCT-DetF Mobile Wireless Sensor Networks\n\nConsider a MWSN as shown in Figure 2(a), where a source sensor node () communicates with a destination sensor node () with the assistance of a number of potential relay sensor nodes (). We suppose that the channel coefficients (between and ), (between and ), and (between and ) are all flat Rayleigh fading coefficients. In addition, , , and are mutually independent and nonidentical. It is assumed that all the links are perturbed by independent random CFOs (, , and ) and the fading coefficients keep constant within one frame and independently change from one frame to another, which are modeled as , , and . We also assume here that all the AWGN terms of all links have zero mean and equal two-sided spectral density (). The transmit powers of the source sensor and each relay sensor are and , respectively, where denotes the total transmit power of the network and is the power allocation factor. In this respect, the MWSN under consideration can be further described by a more informative block model, which is presented in Figure 2(b).\n\nSuppose that each transmission frame is of length , where is the number of the data symbols transmitted from each sensor node within a frame. During the first phase, broadcasts a stream of signal sequence of length to all the relay sensors and ; the received symbols at the th relay sensor and can be expressed as where and are the random CFOs; and denote the AWGN at the th relay and , respectively. In this paper, we assume that all the CFOs follow uniform distribution and remain constant over at least three consecutive symbol intervals. However, it should be pointed out that, in general, there is no restriction over the probability distribution of the CFOs and they could have any probability distribution.\n\nIn the second phase, only the relay sensor with the best link is selected to forward the remodulated signals to . Assuming that relay sensor is selected, the received symbols at can be written as where denotes the CFO of the second-link, represents the remodulated symbols at , and is the AWGN of the selected link.\n\nTo take into account the detection errors at the relay sensors, we apply the one-hop equivalent link model developed in . As shown in Figure 2(b), the equivalent one-hop links are denoted by , , and the SNR of each equivalent link can be approximated as where and are the instantaneous SNR of the and links, respectively, with denoting the average SNR. It is worth pointing out that the same bounding technique has been widely adopted in the performance analysis of various relay systems; see [25, 27, 28] and references therein. In addition, it has been demonstrated that this lower bound is in general very tight for a wide range of SNR.\n\nBased on the equivalent links, the best relay sensor is selected according to the Max-Min criterion given by where the instantaneous SNR of the worst one of the two-hop relay link is maximized. To perform relay selection at the relay sensors, the source sensor and destination sensor should send request-to-send (RTS) and clear-to-send (CTS) packets before each transmission, respectively. Based on the RTS and CTS packets, each relay sensor first estimates the amplitudes of the channels from the source and destination sensors to calculate , and the equivalent SNR ; then a backoff timer is set to be inversely proportional to ; therefore, the best relay sensor with the largest equivalent SNR has the smallest backoff time and consequently occupies the channel to forward its signals to the destination sensor, and all other relay sensors keep silent in this transmission interval.\n\nIn order to efficiently combine the two received signals, we propose a new linear combiner to process the DD signals, where the two branches are combined as in which the weights of the two branches are chosen to maximize the output SNR of and and denote the equivalent SNR and second-hop SNR of the selected link, respectively. After combination, the total output SNR can be rewritten as where is the instantaneous SNR of the direct link.\n\nAccording to (3), the combined signals can be rewritten as where and , and the detection of the transmitted symbols is performed as\n\n#### 3. Performance Analysis\n\nIn this section, we present a comprehensive performance analysis for the RSDDCT-DetF network described in the previous section. Specifically, we derive exact closed-form expressions for two important performance metrics, that is, outage probability and average BER.\n\n##### 3.1. Preliminaries\n\nBefore delving into the detailed analysis, we first present the statistical behaviors of and , which will be frequently invoked in the subsequent derivations.\n\nAs all the channels undergo Rayleigh fading, the PDFs and CDFs of , , and can be written as where , , and . Using (16) as a starting point, we can derive the statistic properties of as the following lemma.\n\nLemma 1. The PDF and CDF of are given by where and denotes the binomial coefficient.\n\nProof. As is the smaller one between and , we can write its CDF as where . Setting derivative of (19) with respect to , the PDF of can be derived as\nNote that (10) suggests that is essentially the largest order statistic of ; hence, by utilizing [41, Equation ], we can obtain the CDF in (18); then differentiating it with respect to and with the help of the binomial theorem, the PDF (17) can be derived.\n\n##### 3.2. Outage Probability\n\nThe outage probability is defined as the probability that the end-to-end SNR drops below a certain threshold . With the help of (12), the outage probability can be rewritten as\n\nA closed-form outage probability of the network can be derived as the following theorem.\n\nTheorem 2. The outage probability of the RSDDCT-DetF network is given by where and are the average SNR of the direct and equivalent links, respectively.\n\nProof. By utilizing the law of total probability, the outage probability (21) can be calculated as ; substitute (15) and (17) into (21); and, with the help of the binomial theorem, Theorem 2 can be derived.\n\n##### 3.3. Average Bit Error Rate\n\nWe now turn our attention to the average BER performance of the network. According to [42, Equation ], the conditional BER of the differential BPSK modulation with -channel diversity reception is given by where is the instantaneous total SNR at the receiver and is defined as\n\nWith the help of (5) and (12), the conditional BER of the RSDDCT-DetF network with DDBPSK can be approximated by the conditional BER of the 2-channel reception DBPSK, which arrives at where denotes the total instantaneous SNR of the equivalent single-differential signals.\n\nTheorem 3. The closed-form average BER of the RSDDCT-DetF network with DDBPSK modulation is given by\n\nProof. Due to the independence of and , the average BER can be obtained by averaging (25) with respect to and , respectively, as follows:\nWe first calculate the first part as where the second equality is derived by using [43, Equation ] and is the Gamma function. On the other hand, substituting (15) and (17), with the help of [43, Equation ], the second part of   can be simplified into\nTo this end, Theorem 3 is obtained by combining (28) and (29).\n\nNote that Theorems 2 and 3 present accurate expressions for the outage probability and average BER of a network with arbitrary number of relay sensors, and the formulas (22) and (26) only involve standard functions which can be directly calculated, thereby providing fast and efficient means to evaluate the system performance.\n\n#### 4. Asymptotic Behaviors Analysis\n\nAlthough the expressions for the outage probability and average BER derived in Theorems 2 and 3 enable numerical evaluation of the system performance and may not be computationally intensive, they do not offer physical insights into the impact of the system parameters, for example, fading parameters and number of relay sensors. To circumvent this, we now focus on the high SNR regime to analyze the asymptotic behaviors of the outage probability and average BER.\n\n##### 4.1. Asymptotic Outage Probability\n\nCorollary 4. The asymptotic outage probability of the RSDDCT-DetF network in the high SNR regime is given by where , with .\n\nProof. Making use of the Maclaurin series expansion of the exponential function, and can be approximated in the high SNR region as where the high-order terms are ignored. Substituting (31) into (22), the outage probability can be rewritten as where we have utilized the identity to derive the second equality. Substituting and in (32), we can rewrite the outage probability as where . Note that the second term in (33) can be ignored when is large enough, which yields Corollary 4.\n\n##### 4.2. Asymptotic Average Bit Error Rate\n\nCorollary 5. The asymptotic average BER of the RSDDCT-DetF network with DDBPSK modulation at high SNRs is given by where , is the number of relay sensors, and denotes the average SNR.\n\nProof. It is obvious that the first part of can be approximated at sufficiently high SNRs as\nTo obtain the asymptotic expression of , we first denote the sum term of (29) by , as\nLetting , after some manipulations, we have where the second equality is derived in a way similar to [27, Equation ]. By using [43, Equation ] to calculate the sum term, (37) can be approximated at high SNRs as\nRecall that ; we then have ; thus the second part of can be approximated as\nAdding (35) to (39), we can rewrite the average BER as\nSubstituting and in (40), the asymptotic average BER can be expressed as\nTo this end, Corollary 5 is proved.\n\nCorollaries 4 and 5 demonstrate that a RSDDCT-DetF network with relay sensors can achieve a full diversity order of at sufficiently high SNRs. The above expressions (30) and (34) also reveal straightforwardly the impact of the model parameters on the system performance. More specifically, we can see that, by increasing and the sensor nodes’ power, the outage probability and average BER will reduce. In addition, we can also observe that the diversity of the MWSN is determined by the number of relay sensors. We will show through numerical evaluation in Section 6 that both the asymptotic outage probability (30) and the average BER (34) tightly correlate with their exact analytical counterparts in the high SNR regime; thus we can precisely predict the system performance through Corollaries 4 and 5 at sufficiently high SNRs.\n\n#### 5. Optimum Power Allocation\n\nThe optimum power allocation for improving the system performance (e.g., minimizing the outage probability or error probability) has been a very hot research area [24, 26, 34]. As MSNs are generally power-limited systems, it may be of particular importance to investigate the optimum power allocation for MSNs. With this observation in mind, in this section, we address the power allocation issue for the RSDDCT-DetF sensor network under consideration to improve its average BER performance.\n\nHaving the closed-form average BER (26), we are about to investigate the power allocation among the source sensor and the relay sensors to minimize the average BER under a total transmit power . The optimization problem of the power allocation can be formulated as\n\nHowever, it is generally difficult to directly manipulate the exact average BER expression (26), and the optimum solution can only be derived through exhaustive search. In order to obtain a simple closed-form solution, we choose to look into the high SNR regime and determine the optimum power allocation scheme by use of the asymptotic average BER expression. Note that, given a fading scenario, in (34) is a constant which only depends on the average SNR and the number of relay sensors; therefore, based on the asymptotic average BER expression, the optimization problem of the power allocation can be rewritten as\n\nNote that (43) is an equation with only one variable, namely, ; thus, by differentiating the objective function in (43) with respect to and setting the derivative equal to zero, we can derive the optimum power allocation factor as follows.\n\nCase A. For the scenario , the optimum power allocation factor is\n\nCase B. For the scenario , the optimum power allocation factor is where .\n\nWe observe from (44) and (45) that the equal power allocation always cannot provide the best average BER performance and the optimum power allocation is dependent on the channel variances, that is, , and the number of relay sensors. More specifically, in the case , the optimum power factor is larger than 1/2 and when , the equal power allocation yields the best average BER performance. It can be easily shown that, for the scenario , the best power allocation factor is smaller than , and when , we further have , which indicates that more power should be allocated to the relay sensors. On the other hand, when it comes to the scenario , the optimum power factor is larger than 1/2, which suggests that more transmit power should be allocated to the source sensor.\n\n#### 6. Numerical Results\n\nIn this section, the theoretical results derived in the previous sections are validated by a set of Monte Carlo simulations, where we consider slow Rayleigh fading channels with random CFOs, and the transmission length is set to 100. Throughout our simulations, we suppose that all the CFOs are mutually independent and uniformly distributed over , where denotes the maximum normalized CFO. Without special explanation, the transmit power is always equally split between the source sensor and the relay sensors, that is, . Note that the SNR refers to the average SNR in the following discussions.\n\nWe first examine the outage performance of the RSDDCT-DetF network. Figures 3 and 4 demonstrate the simulated outage probabilities along with the accurate outage probabilities in (22) and their corresponding asymptotic approximations in (30). In our simulations, the predetermined SNR threshold is dB, and the maximum CFO is . In Figure 3, we consider three possible numbers of the relay sensors, namely, , respectively, and the fading gains are equal, that is, . In Figure 4, is fixed to 3, and four different fading scenarios are investigated. As can be seen from the two figures, the accurate analytical curves match well with the simulation results across the entire SNR range in all the scenarios. Moreover, the proposed asymptotic outage probabilities yield excellent tightness at high SNRs. Likewise, the analytical outage probability expressions can very efficiently predict the exact outage probability. Another observation is that the achieved diversity order is dependent on the number of relay sensors, and it increases when more relay sensors are used. Specifically, about 5dB performance improvement can be observed at an outage probability of as increases from 1 to 2. In addition, we can obtain a performance gain of about 4dB at the same outage probability by increasing from 2 to 4.\n\nIn Figures 5 and 6, we proceed to illustrate the average BER performance of the RSDDCT-DetF network. We have performed the simulations in the same scenarios as these of Figures 3 and 4. In the two figures, the simulated average BER curves are plotted along with the analytical average BER given in (26). Also, the results pertaining to the asymptotic expression for the average BER given by (34) are included in the figures. Note that, for the sake of completeness, the simulated average BER curve of the noncooperative or direct transmission system () is also plotted to serve as a benchmark. It is worth noting that, to fairly compare the performances, we assume that the total transmit powers are equal; in other words, the transmit power of in the case is twice that of the other systems. As observed, the analytical expression is in great match with the simulated results, even in the low SNR region in each scenario. In addition, for all the cases, the asymptotic BERs and their other two corresponding curves overlap at high SNRs, which indicate the correctness of our theoretical analysis. In Figure 5, it is clear that each cooperative network outperforms the noncooperative network when SNR exceeds a certain threshold. We can also observe from the two graphs that the achievable diversity order of the network depends on the number of relay sensors, and it is increasing with the number of the potential relay sensors. To be specific, we can observe about 3.5dB performance improvement at an average BER of when the number of relay sensors increases from 1 to 2. And an additional 2.7dB gain is obtained at the same average BER when increases from 2 to 4.\n\nFigure 7 compares the average BER performance of the RSDDCT-DetF network and the DM-RS-DetF network with DBPSK modulation, where five different random CFOs are considered, that is, . The number of relay sensors is and the channel variances are . As the RSDDCT-DetF network almost has the same performance under different CFOs, we only plot its one average BER curve. We observe that there is a performance gap of about 3.8dB between the RSDDCT-DetF network and the single-differential network in the absence of CFOs (). It is also shown that when random CFOs are involved, the DM-RS-DetF network suffers severe performance degradation while the DD network can achieve excellent performance. For example, when, the performance gap shrinks to 2.2dB. Furthermore, we can observe two collapses from the average BER curves of the DM-RS-DetF network in the cases and 0.5.\n\nFigure 8 elaborates on the optimum power allocation factors for the RSDDCT-DetF network with three relay sensors. We consider three different fading scenarios: (A) all the channel gains are equal; that is, refers to the scenarios where all the relay sensors are located at halfway between the source sensor and the destination sensor; (B) , refers to the scenarios where the relay sensors are closer to the source sensor; and (C) , refers to the scenarios where all the relay sensors are much closer to the destination sensor. Note that, in the graph, we set dB, and the analytical average BER curves calculated from (34) are plotted against the power allocation factor , which increases from 0.01 to 0.99 by a step 0.01. In addition, the optimum power allocation factors obtained from (44) and (45) are also presented. We observe that the numerically derived optimum power factors yield the minimum average BER in all cases. Specifically, in Scenario A, the best power allocation factor is , and, for Scenario B, the best choice of powers is and , while, in Scenario C, the best power allocation factor changes to . This is consistent with our analysis in Section 5.\n\nFinally, we study the benefits of power allocation. Figure 9 shows the average BER performance of the RSDDCT-DetF network with optimum power allocation (OPA) in contrast to that with equal power allocation (EPA). The three scenarios outlined in Figure 8 are investigated. Note that each of the graphs depicts two optimized average BER curves: TOPA, which refers to the average BER of the network with theoretical optimum power allocation (TOPA) given by (44) and (45) and SOPA, which represents the average BER of the network with simulated optimum power allocation (SOPA) derived through exhaustive search. It is clear that in all the three scenarios our derived TOPA and the exhaustively searched SOPA almost yield the same performance. From Figure 9(a), we observe that the OPA outperforms the EPA by about 0.7dB at an average BER of in Scenario A. However, when it comes to Scenario B, where the relay sensors are closer to the source sensor node, the OPA has a marginal performance gain against the EPA. The reason is that in this scenario the remodulated signals at the relay sensors are as good as those at the source sensor node; therefore, the EPA scheme almost yields the same performance as the OPA, while, for Scenario C, it is observed in Figure 9(b) that the OPA is about 1.5dB superior to the EPA at the same average BER. It is because that using EPA in this scenario leads to low quality of the received signals at the relay sensors, thereby causing high detection errors at the destination sensor. While, with the OPA, more power is allocated to the source sensor, it consequently reduces the detection errors at the relay sensors, which leads to an improvement to the quality of the combined signals at the destination sensor, hence yielding a better average BER performance.\n\n#### 7. Conclusion\n\nIn this paper, we have proposed and analyzed a robust relay selection based double-differential cooperative transmission (RSDDCT) scheme for MWSNs over Rayleigh fading channels, where all the links are perturbed by random MCFOs. In particular, we have derived closed-form expressions for the outage probability and average BER performance of a RSDDCT-DetF network at arbitrary SNRs. Moreover, simplified asymptotic outage probability and average BER expressions in the high SNR regime are deduced, which indicate that a RSDDCT-DetF network consisting of a source sensor, relay sensors, and a destination sensor can achieve a full diversity order of at sufficiently high SNRs. We have shown that in the RSDDCT-DetF networks, the destination sensors are able to detect their data without any knowledge of the channel fading coefficients or MCFOs. It is revealed that the RSDDCT-DetF network is inferior to its single-differential counterpart in the absence of MCFOs; however, the RSDDCT-DetF network performs well over fading channels with random MCFOs, where the single-differential networks fail to work. We have also investigated the power allocation optimization problem to improve the average BER performance based on the derived analytical expressions. Monte Carlo simulations show that our optimum power allocation strategy provides considerable average BER performance enhancement as compared to the equal power allocation strategy.\n\n#### Conflict of Interests\n\nThe authors declare that there is no conflict of interests regarding the publication of this paper.\n\n1. I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “A survey on sensor networks,” IEEE Communications Magazine, vol. 40, no. 8, pp. 102–114, 2002. View at: Publisher Site | Google Scholar\n2. J. Yick, B. Mukherjee, and D. Ghosal, “Wireless sensor network survey,” Computer Networks, vol. 52, no. 12, pp. 2292–2330, 2008. View at: Publisher Site | Google Scholar\n3. J. Rezazadeh, M. Moradi, and A. S. Ismail, “Mobile wireless sensor networks overview,” International Journal of Computer Communications and Networks, vol. 2, no. 1, pp. 17–22, 2012. View at: Google Scholar\n4. S. A. Munir, B. Ren, W. Jiao, B. Wang, D. Xie, and J. Ma, “Mobile wireless sensor network: architecture and enabling technologies for ubiquitous computing,” in Proceedings of International Conference on Advanced Information Networking and Applications Workshops, pp. 113–120, Niagara Falls, Canada, May 2007. View at: Publisher Site | Google Scholar\n5. X. Huang, H. Zhai, and Y. Fang, “Robust cooperative routing protocol in mobile wireless sensor networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 12, pp. 5278–5285, 2008. View at: Publisher Site | Google Scholar\n6. Y.-C. Wang and Y.-C. Tseng, “Distributed deployment schemes for mobile wireless sensor networks to ensure multilevel coverage,” IEEE Transactions on Parallel and Distributed Systems, vol. 19, no. 9, pp. 1280–1294, 2008. View at: Publisher Site | Google Scholar\n7. S. A. B. Awwad, C. K. Ng, N. K. Noordin, and M. F. A. Rasid, “Cluster based routing protocol for mobile nodes in wireless sensor network,” in Proceedings of of the International Symposium on Collaborative Technologies and Systems (CTS '09), pp. 233–241, Baltimore, Md, USA, May 2009. View at: Publisher Site | Google Scholar\n8. N. Meghanathan, “Impact of the Gauss-Markov mobility model on network connectivity, lifetime and hop count of routes for mobile Ad hoc networks,” Journal of Networks, vol. 5, no. 5, pp. 509–516, 2010. View at: Publisher Site | Google Scholar\n9. J. Rezazadeh, M. Moradi, and A. S. Ismail, “Efficient localization via middle-node cooperation in wireless sensor networks,” in Proceedings of International Conference on Electrical, Control, and Computer Engineering (INECCE '11), pp. 410–415, Pahang, Malaysia, June 2011. View at: Publisher Site | Google Scholar\n10. L. Karim and N. Nasser, “Reliable location-aware routing protocol for mobile wireless sensor network,” IET Communications, vol. 6, no. 14, pp. 2149–2158, 2012. View at: Google Scholar\n11. A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity-part I: system description,” IEEE Transactions on Communications, vol. 51, no. 11, pp. 1927–1938, 2003. View at: Publisher Site | Google Scholar\n12. A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity-part II: implementation aspects and performance analysis,” IEEE Transactions on Communications, vol. 51, no. 11, pp. 1939–1948, 2003. View at: Publisher Site | Google Scholar\n13. S. Cui, A. J. Goldsmith, and A. Bahai, “Energy-efficiency of MIMO and cooperative MIMO techniques in sensor networks,” IEEE Journal on Selected Areas in Communications, vol. 22, no. 6, pp. 1089–1098, 2004. View at: Publisher Site | Google Scholar\n14. A. D. Coso, U. Spagnolini, and C. Ibars, “Cooperative distributed MIMO channels in wireless sensor networks,” IEEE Journal on Selected Areas in Communications, vol. 25, no. 2, pp. 402–414, 2007. View at: Publisher Site | Google Scholar\n15. Z. Zhou, S. Zhou, J.-H. Cui, and S. Cui, “Energy-efficient cooperative communication in a clustered wireless sensor network,” IEEE Transactions on Vehicular Technology, vol. 57, no. 6, pp. 3618–3628, 2008. View at: Publisher Site | Google Scholar\n16. Z. Rafique, B. C. Seet, and A. Al-Anbuky, “Performance analysis of cooperative virtual MIMO systems for wireless sensor networks,” Sensors, vol. 13, no. 5, pp. 7033–7052, 2013. View at: Google Scholar\n17. S. Cho, J.-W. Choi, and C. You, “Adaptive multi-node multiple input and multiple output (MIMO) transmission for mobile wireless multimedia sensor networks,” Sensors, vol. 13, no. 10, pp. 13382–13401, 2013. View at: Google Scholar\n18. Z. Zhou, S. Zhou, J.-H. Cui, and S. Cui, “Energy-efficient cooperative communication based on power control and selective single-relay in wireless sensor networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 8, pp. 3066–3079, 2008. View at: Publisher Site | Google Scholar\n19. C.-L. Wang and S.-J. Syue, “An efficient relay selection protocol for cooperative wireless sensor networks,” in Proceedings of of the IEEE Wireless Communications and Networking Conference (WCNC '09), pp. 1–5, Budapest, Hungary, April 2009. View at: Publisher Site | Google Scholar\n20. X. Liang, I. Balasingham, and V. C. M. Leung, “Cooperative communications with relay selection for QoS provisioning in wireless sensor networks,” in Proceedings of IEEE Global Communications Conference (GLOBECOM '09), pp. 1–8, Honolulu, Hawaii, USA, December 2009. View at: Publisher Site | Google Scholar\n21. I. Joe and M. Shin, “An energy-efficient mobile cluster-based approach for vehicular wireless sensor networks,” in Proceedings of the 6th International Conference on Networked Computing (INC '10), pp. 1–5, Gyeongju, Korea, May 2010. View at: Google Scholar\n22. M. Quaritsch, K. Kruggl, D. Wischounig-Strucl, S. Bhattacharya, M. Shah, and B. Rinner, “Networked UAVs as aerial sensor network for disaster management applications,” Elektrotechnik und Informationstechnik, vol. 127, no. 3, pp. 56–63, 2010. View at: Publisher Site | Google Scholar\n23. D. Chen and J. N. Laneman, “Modulation and demodulation for cooperative diversity in wireless systems,” IEEE Transactions on Wireless Communications, vol. 5, no. 7, pp. 1785–1794, 2006. View at: Publisher Site | Google Scholar\n24. Q. Zhao and H. Li, “Differential modulation for cooperative wireless systems,” IEEE Transactions on Signal Processing, vol. 55, no. 5, pp. 2273–2283, 2007. View at: Publisher Site | Google Scholar | MathSciNet\n25. T. Wang, A. Cano, G. B. Giannakis, and J. N. Laneman, “High-performance cooperative demodulation with decode-and-forward relays,” IEEE Transactions on Communications, vol. 55, no. 7, pp. 1427–1438, 2007. View at: Publisher Site | Google Scholar\n26. T. Himsoon, W. P. Siriwongpairat, W. Su, and K. J. R. Liu, “Differential modulations for multinode cooperative communications,” IEEE Transactions on Signal Processing, vol. 56, no. 7, pp. 2941–2956, 2008. View at: Publisher Site | Google Scholar | MathSciNet\n27. J. Yuan, Y. Li, and L. Chu, “Differential modulation and relay selection with detect-and-forward cooperative relaying,” IEEE Transactions on Vehicular Technology, vol. 59, no. 1, pp. 261–268, 2010. View at: Publisher Site | Google Scholar\n28. Y. Gao, J. Ge, and C. Han, “Performance analysis of differential modulation and relay selection with detect-and-forward cooperative relaying,” IEEE Communications Letters, vol. 15, no. 3, pp. 323–325, 2011. View at: Publisher Site | Google Scholar\n29. H. Mehrpouyan and S. Blostein, “Synchronization in cooperative networks: estimation of multiple carrier frequency offsets,” in Proceedings of IEEE International Conference on Communications (ICC '10), pp. 1–6, Cape Town, South Africa, May 2010. View at: Google Scholar\n30. H. Mehrpouyan and S. D. Blostein, “Bounds and algorithms for multiple frequency offset estimation in cooperative networks,” IEEE Transactions on Wireless Communications, vol. 10, no. 4, pp. 1300–1311, 2011. View at: Publisher Site | Google Scholar\n31. A. A. Nasir, H. Mehrpouyan, S. D. Blostein, S. Durrani, and R. A. Kennedy, “Timing and carrier synchronization with channel estimation in multi-relay cooperative networks,” IEEE Transactions on Signal Processing, vol. 60, no. 2, pp. 793–811, 2012. View at: Publisher Site | Google Scholar | MathSciNet\n32. A. A. Nasir, H. Mehrpouyan, S. D. Blostein, S. Durrani, and R. A. Kennedy, “Estimation of synchronization parameters in AF cooperative networks,” in Proceedings of the IEEE International Conference on Communications (ICC '12), pp. 3713–3717, Ottawa, Canada, June 2012. View at: Google Scholar\n33. Y. B. Okunev, Theory of Phase-Difference Modulation, Moscow, Russia, 1979.\n34. M. R. Bhatnagar, A. Hjørungnes, and L. Song, “Cooperative communications over flat fading channels with carrier offsets: a double-differential modulation approach,” EURASIP Journal on Advances in Signal Processing, no. 15, pp. 1–11, 20082008. View at: Google Scholar\n35. M. R. Bhatnagar, A. Hjørungnes, L. Song, and R. Bose, “Double-differential decode-and-forward cooperative communications over Nakagami-m channels with carrier offsets,” in Proceedings of the IEEE Sarnoff Symposium, pp. 1–5, Princeton, NJ, USA, April 2008. View at: Publisher Site | Google Scholar\n36. N. Yi, Y. Ma, and R. Tafazolli, “Doubly differential communication assisted with cooperative relay,” in Proceedings of the IEEE Vehicular Technology Conference (VTC Spring '08), pp. 644–647, Singapore, May 2008. View at: Publisher Site | Google Scholar\n37. M. R. Bhatnagar and O. Tirkkonen, “PL decoding in double differential modulation based decode-and-forward cooperative system,” IEEE Communications Letters, vol. 17, no. 5, pp. 860–863, 2013. View at: Google Scholar\n38. C. Kim, S. Heo, Y. Bae, and J. Lee, “Relay selection for amplify-and-forward systems with differential and double-differential modulation,” in Proceedings of the IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS '11), pp. 1–4, Seoul, Korea, August 2011. View at: Publisher Site | Google Scholar\n39. P. Stoica, J. Liu, and J. Li, “Maximum-likelihood double differential detection clarified,” IEEE Transactions on Information Theory, vol. 50, no. 3, pp. 572–576, 2004. View at: Publisher Site | Google Scholar | MathSciNet\n40. M. K. Simon and M.-S. Alouini, Digital Communications Over Fading Channels, John Wiley & Sons, Hoboken, NJ, USA, 2nd edition, 2005.\n41. H. A. David and H. N. Nagaraja, Order Statistics, John Wiley & Sons, Hoboken, NJ, USA, 3rd edition, 2003. View at: Publisher Site | MathSciNet\n42. J. G. Proakis, Digital Communications, McGraw-Hill, New York, NY, USA, 4th edition, 2001.\n43. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Elsevier/Academic Press, San Diego, Calif, USA, 7th edition, 2007. View at: MathSciNet" ]
[ null ]
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https://nebraska.pure.elsevier.com/en/publications/tree-based-construction-of-ldpc-codes-having-good-pseudocodeword-
[ "# Tree-based construction of LDPC codes having good pseudocodeword weights\n\nChristine A. Kelley, Deepak Sridhara, Joachim Rosenthal\n\nResearch output: Contribution to journalArticle\n\n5 Citations (Scopus)\n\n### Abstract\n\nWe present a tree-based construction of low-density parity-check (LDPC) codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree. Methods are presented for degrees d=ps and d=ps + 1, for p a prime. One class corresponds to the well-known finite-geometry and finite generalized quadrangle LDPC codes; the other codes presented are new. We also present some bounds on pseudocodeword weight for p-ary LDPC codes. Treating these codes as p-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite-geometry LDPC codes where p > 2.\n\nOriginal language English (US) 1460-1478 19 IEEE Transactions on Information Theory 53 4 https://doi.org/10.1109/TIT.2007.892774 Published - Apr 1 2007\n\n### Fingerprint\n\nmathematics\nIterative decoding\nGeometry\n\n### Keywords\n\n• Iterative decoding\n• Low-density parity-check (LDPC) codes\n• Min-sum iterative decoding\n• P-ary pseudoweight\n• Pseudocodewords\n\n### ASJC Scopus subject areas\n\n• Information Systems\n• Computer Science Applications\n• Library and Information Sciences\n\n### Cite this\n\nTree-based construction of LDPC codes having good pseudocodeword weights. / Kelley, Christine A.; Sridhara, Deepak; Rosenthal, Joachim.\n\nIn: IEEE Transactions on Information Theory, Vol. 53, No. 4, 01.04.2007, p. 1460-1478.\n\nResearch output: Contribution to journalArticle\n\nKelley, Christine A. ; Sridhara, Deepak ; Rosenthal, Joachim. / Tree-based construction of LDPC codes having good pseudocodeword weights. In: IEEE Transactions on Information Theory. 2007 ; Vol. 53, No. 4. pp. 1460-1478.\n@article{c7e5edf32deb4e2a8bc9ae7fdf43f841,\ntitle = \"Tree-based construction of LDPC codes having good pseudocodeword weights\",\nabstract = \"We present a tree-based construction of low-density parity-check (LDPC) codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree. Methods are presented for degrees d=ps and d=ps + 1, for p a prime. One class corresponds to the well-known finite-geometry and finite generalized quadrangle LDPC codes; the other codes presented are new. We also present some bounds on pseudocodeword weight for p-ary LDPC codes. Treating these codes as p-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite-geometry LDPC codes where p > 2.\",\nkeywords = \"Iterative decoding, Low-density parity-check (LDPC) codes, Min-sum iterative decoding, P-ary pseudoweight, Pseudocodewords\",\nauthor = \"Kelley, {Christine A.} and Deepak Sridhara and Joachim Rosenthal\",\nyear = \"2007\",\nmonth = \"4\",\nday = \"1\",\ndoi = \"10.1109/TIT.2007.892774\",\nlanguage = \"English (US)\",\nvolume = \"53\",\npages = \"1460--1478\",\njournal = \"IEEE Transactions on Information Theory\",\nissn = \"0018-9448\",\npublisher = \"Institute of Electrical and Electronics Engineers Inc.\",\nnumber = \"4\",\n\n}\n\nTY - JOUR\n\nT1 - Tree-based construction of LDPC codes having good pseudocodeword weights\n\nAU - Kelley, Christine A.\n\nAU - Sridhara, Deepak\n\nAU - Rosenthal, Joachim\n\nPY - 2007/4/1\n\nY1 - 2007/4/1\n\nN2 - We present a tree-based construction of low-density parity-check (LDPC) codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree. Methods are presented for degrees d=ps and d=ps + 1, for p a prime. One class corresponds to the well-known finite-geometry and finite generalized quadrangle LDPC codes; the other codes presented are new. We also present some bounds on pseudocodeword weight for p-ary LDPC codes. Treating these codes as p-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite-geometry LDPC codes where p > 2.\n\nAB - We present a tree-based construction of low-density parity-check (LDPC) codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree. Methods are presented for degrees d=ps and d=ps + 1, for p a prime. One class corresponds to the well-known finite-geometry and finite generalized quadrangle LDPC codes; the other codes presented are new. We also present some bounds on pseudocodeword weight for p-ary LDPC codes. Treating these codes as p-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite-geometry LDPC codes where p > 2.\n\nKW - Iterative decoding\n\nKW - Low-density parity-check (LDPC) codes\n\nKW - Min-sum iterative decoding\n\nKW - P-ary pseudoweight\n\nKW - Pseudocodewords\n\nUR - http://www.scopus.com/inward/record.url?scp=34147129057&partnerID=8YFLogxK\n\nUR - http://www.scopus.com/inward/citedby.url?scp=34147129057&partnerID=8YFLogxK\n\nU2 - 10.1109/TIT.2007.892774\n\nDO - 10.1109/TIT.2007.892774\n\nM3 - Article\n\nAN - SCOPUS:34147129057\n\nVL - 53\n\nSP - 1460\n\nEP - 1478\n\nJO - IEEE Transactions on Information Theory\n\nJF - IEEE Transactions on Information Theory\n\nSN - 0018-9448\n\nIS - 4\n\nER -" ]
[ null ]
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https://unapologetic.wordpress.com/2011/08/05/
[ "# The Unapologetic Mathematician\n\n## Chains\n\nWe can integrate on the standard cube, and on singular cubes in arbitrary manifolds. What if it’s not very easy to describe a region as the image of a singular cube? This is where chains come in.\n\nSo a chain is actually pretty simple; it’s just a formal linear combination of singular", null, "$k$-cubes. That is, for each", null, "$k$ we build the free abelian group", null, "$C_k(M)$ generated by the singular", null, "$k$-cubes in", null, "$M$.\n\nIf we have a formal sum", null, "$c=a_1c_1+\\dots+a_lc_l$ — the", null, "$c_i$ are all singular", null, "$k$-cubes and the", null, "$a_i$ are all integers — then we define integrals over the chain by linearity:", null, "$\\displaystyle\\int\\limits_c\\omega=a_1\\int\\limits_{c_1}\\omega+\\dots+a_l\\int\\limits_{c_l}\\omega$\n\nAnd that’s all there is to it; just cover the", null, "$k$-dimensional region you’re interested in with singular", null, "$k$-cubes. If there are some overlaps, those areas will get counted twice, so you’ll have to cover them with their own singular", null, "$k$-cubes with negative multipliers to cancel them out. Take all the integrals — by translating each one back to the standard", null, "$k$-cube — and add (or subtract) them up to get the result!\n\nAugust 5, 2011" ]
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https://socratic.org/questions/why-is-the-theory-of-plate-tectonics-not-a-law
[ "# Why is the theory of plate tectonics not a law?\n\nJan 20, 2017\n\nPlate tectonics explains the evidence of volcanos, earth quakes and mountain building.\n\n#### Explanation:\n\nA law usually gives a precise prediction of what will happen. Newtons law of gravitation gives a precise mathematical formula for calculating the force of attraction between two masses. But Newton's law is not a theory of gravitation because it does not explain why this force of attraction exists.\n\nThe theory of plate tectonics does not give a precise prediction of the rate or direction of plate movements. The plate movements first proposed under the theory of continental drift hypothesis rapid and sudden massive movements of the continents in the past. The plate movements observed today are very slow but the theory does not specify how fast the plates may have moved in the past or may move in the future. So the theory of plate tectonics can not function as a law.\n\nA theory explains why and how something happens. Einstein's general theory of relativity provides an explanation of why two masses create a force of attraction. Good theories make good predictions. Einsteins theory precisely predicted the bending of light in a solar eclipse due to the gravitational force bending space.\nEinstein's theory is accepted because it explains accurately what is observed and predicts what will happen ( Einstein's theory not only explains why it makes precise prediction so some say it should now be called a law as well as a theory)\n\nPlate Tectonics explains the mid Atlantic Ridge, The great rift valley of Africa, the subduction zones, earthquakes, the location of volcanos, and Mountain ranges. Plate Tectonic explained the earth movements much better than the early geosyncline theories.\n\nBecause Plate Tectonics explains things it is a theory, Because it does not provide a means of calculation precisely when and where the plates will move it is not a law." ]
[ null ]
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http://mizar.uwb.edu.pl/version/current/html/proofs/fin_topo/31
[ "let FT be non empty filled RelStr ; :: thesis: for A being Subset of FT holds A c= A ^b\nlet A be Subset of FT; :: thesis: A c= A ^b\nlet x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in A or x in A ^b )\nassume A1: x in A ; :: thesis: x in A ^b\nthen reconsider y = x as Element of FT ;\ny in U_FT y by Def4;\nthen U_FT y meets A by ;\nhence x in A ^b ; :: thesis: verum" ]
[ null ]
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https://perl.mines-albi.fr/perl5.6.1/site_perl/5.6.1/Graphics/Simple/PDLPlot.html
[ "Graphics::Simple::PDLPlot -- Plot PDL data using Graphics::Simple\n\n# NAME\n\nGraphics::Simple::PDLPlot -- Plot PDL data using Graphics::Simple\n\n# DESCRIPTION\n\nFunctions:\n\n``` line \\$pdl_y;\nline \\$pdl_x, \\$pdl_y;```\n\nMethods:\n\n` \\$g = Graphics::Simple::PDLPlot::Graph->new();`\n``` \\$g->line(\\$pdl_x, \\$pdl_y);\n\\$g->points(\\$pdl_x, \\$pdl_y);\n\\$g->x_axis(1.0,2.0);\n\\$g->y_axis(0.1,1000,LOG);\n\\$g->plot(\\$win);```\n\n# BUGS\n\nThis module is in the wrong place - it should be in the PDL distribution and will be in the future.\n\nWildly inefficient - there must be more synergy between this module and the `Graphics::Simple` implementations for vectorization.\n\n# AUTHOR\n\n`Copyright(C)` Tuomas J. Lukka 1999. All rights reserved. This software may be distributed under the same conditions as Perl itself.\n\n Graphics::Simple::PDLPlot -- Plot PDL data using Graphics::Simple" ]
[ null ]
{"ft_lang_label":"__label__en","ft_lang_prob":0.7114964,"math_prob":0.897994,"size":777,"snap":"2023-40-2023-50","text_gpt3_token_len":229,"char_repetition_ratio":0.1862872,"word_repetition_ratio":0.11702128,"special_character_ratio":0.2857143,"punctuation_ratio":0.29651162,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9824241,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-08T22:50:47Z\",\"WARC-Record-ID\":\"<urn:uuid:a3bc0208-3c87-43b1-8dbb-91ff1ff50ee0>\",\"Content-Length\":\"2402\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:245e1e4f-5f41-413c-8ef8-d066551fce9e>\",\"WARC-Concurrent-To\":\"<urn:uuid:e1c0c330-7485-462b-ba52-c53628d7d168>\",\"WARC-IP-Address\":\"194.167.201.52\",\"WARC-Target-URI\":\"https://perl.mines-albi.fr/perl5.6.1/site_perl/5.6.1/Graphics/Simple/PDLPlot.html\",\"WARC-Payload-Digest\":\"sha1:5CTULQ72QDPGYNSAHKXOYXIZZRI3J5BD\",\"WARC-Block-Digest\":\"sha1:FZCEEUD4A5TSP66TUJAS74D6CM7W6LRT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100779.51_warc_CC-MAIN-20231208212357-20231209002357-00617.warc.gz\"}"}
https://m.everything2.com/title/watt
[ "display | more...\n\nThe term \"watt\" is derived from English inventor James Watt. It is a unit of power, used to measure radiant flux. The watt is a derived SI unit, meaning it is defined in terms of two more base SI units. In terms of base units, one watt can be expressed as:\n\n`W = m2·kg·s-3`\n\nA simpler definition, in terms of a non-base unit, would be:\n\n`W = J/s`\n\nBasically what this means is that one watt is the amount of work done by applying one joule of energy per second. Alternately, you could also say that the watt is the power produced by one ampere of current across a potential difference of one volt in an electric circuit.\n\nConversions:\n\n1 W = 1 J/s =\n\n```0.000947817144 Btu/s\n0.0568690286 Btu/min\n3.41214172 Btu/hour\n0.0000341214172 therms/hour\n0.238845897 calories/s\n14.3307538 calories/min\n0.000238845897 kilocalories/s (Calories/s)\n0.0143307538 kilocalories/min\n0.859845228 kilocalories/hour\n0.00134048257 horsepower (electric)\n0.00135962162 horsepower (metric)\n0.06 kilojoules/min\n0.0036 megajoules/hour\n0.101971621 kgf·m/s*\n0.737562149 foot·lbf/s**```\n\n* kgf·m is kilogram-force meter\n** foot·lbf is foot pound-force\n\nConversions courtesy of: http://www.ex.ac.uk/cimt/dictunit/ccpower.htm\n\nWatt (?), n. [From the distinguished mechanician and scientist, James Watt.] Physics\n\nA unit of power or activity equal to 107 C.G.S. units of power, or to work done at the rate of one joule a second. An English horse power is approximately equal to 746 watts.\n\nLog in or register to write something here or to contact authors." ]
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{"ft_lang_label":"__label__en","ft_lang_prob":0.8360135,"math_prob":0.8171507,"size":1173,"snap":"2020-24-2020-29","text_gpt3_token_len":357,"char_repetition_ratio":0.10778443,"word_repetition_ratio":0.0,"special_character_ratio":0.35038364,"punctuation_ratio":0.14,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97002375,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-05T14:44:55Z\",\"WARC-Record-ID\":\"<urn:uuid:fa77e463-f4f0-4d2a-8a32-844d925016be>\",\"Content-Length\":\"22773\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:63b2d8db-c26f-4e86-ad37-6c85b6fe827f>\",\"WARC-Concurrent-To\":\"<urn:uuid:dc850b94-2170-4dc4-84e2-c8b4a5d1989c>\",\"WARC-IP-Address\":\"50.112.81.62\",\"WARC-Target-URI\":\"https://m.everything2.com/title/watt\",\"WARC-Payload-Digest\":\"sha1:XMBNGLH3RGSEZNYMSDSM3L4YXE3SW76Z\",\"WARC-Block-Digest\":\"sha1:W5EVNUGORFVY2FLDFDREXQ2B6YUA2WRV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655887360.60_warc_CC-MAIN-20200705121829-20200705151829-00495.warc.gz\"}"}
https://www.hindawi.com/journals/jam/2012/635909/
[ "/ / Article\n\nResearch Article | Open Access\n\nVolume 2012 |Article ID 635909 | https://doi.org/10.1155/2012/635909\n\nPing Wang, Fangguo Zhang, \"An Efficient Collision Detection Method for Computing Discrete Logarithms with Pollard's Rho\", Journal of Applied Mathematics, vol. 2012, Article ID 635909, 15 pages, 2012. https://doi.org/10.1155/2012/635909\n\n# An Efficient Collision Detection Method for Computing Discrete Logarithms with Pollard's Rho\n\nRevised15 Nov 2011\nAccepted21 Nov 2011\nPublished16 Jan 2012\n\n#### Abstract\n\nPollard's rho method and its parallelized variant are at present known as the best generic algorithms for computing discrete logarithms. However, when we compute discrete logarithms in cyclic groups of large orders using Pollard's rho method, collision detection is always a high time and space consumer. In this paper, we present a new efficient collision detection algorithm for Pollard's rho method. The new algorithm is more efficient than the previous distinguished point method and can be easily adapted to other applications. However, the new algorithm does not work with the parallelized rho method, but it can be parallelized with Pollard's lambda method. Besides the theoretical analysis, we also compare the performances of the new algorithm with the distinguished point method in experiments with elliptic curve groups. The experiments show that the new algorithm can reduce the expected number of iterations before reaching a match from 1.309 to 1.295 under the same space requirements for the single rho method.\n\n#### 1. Introduction\n\nOne of the most important assumptions in modern cryptography is the hardness of the discrete logarithm problem (DLP). Many popular cryptosystems base their security on DLP. Such cryptosystems are, for example, the Diffie-Hellman key agreement protocol , the ElGamal signature and encryption schemes , the US Government Digital Signature Algorithm (DSA) , and the Schnorr signature scheme . Originally, they worked with multiplicative groups of finite prime fields. Once elliptic curve cryptosystems were proposed by Koblitz and Miller , analogous practical systems based on the DLP in groups of points of elliptic curves over finite fields were designed . Recall the following two definitions.\n\nDefinition 1.1 (discrete logarithm problem, DLP). Let be a cyclic group of prime order , and let be generator of . Given , determine the integer such that .\n\nDefinition 1.2 (elliptic curve discrete logarithm problem, ECDLP). Let be an elliptic curve defined over finite field . Let be a point of prime order , and let be the subgroup of generated by . Given , determine the integer such that .\n\nFor DLP on a multiplicative subgroup of prime order of finite field , the index calculus method determines the size of , which is a subexponential time algorithm, while the size of is set by Pollard's rho method .\n\nFurthermore, for ECDLP, Pollard's rho method and its modifications by Gallant et al. and Wiener and Zuccherato are to date known as the most efficient general algorithms. van Oorschot and Wiener showed that the modified Pollard's rho method can be parallelized with linear speedup.\n\nPollard's rho method is a randomized algorithm for computing discrete logarithms. Generally, an iteration function is used to define a pseudorandom sequence by for , with some initial value . The sequence represents a walk in the group . The basic assumption is that the walk behaves as a random walk. Because the order of the group is finite, the sequence will ultimately reach an element that has occurred before. This is called a collision or a match. The advantage of this method is that the space requirements are small if one uses a clever method of detecting a collision. The problem of efficient collision detection of a pseudo-random walk in Pollard's rho method is the central topic of this paper.\n\nThere are several collision detection algorithms for a random walk in the group . These algorithms in general do not exploit the group structure of . As a result, the algorithms discussed in this paper in fact apply to any set on which an iterated function is used to make random walks, and their utilization goes beyond discrete logarithm computation.\n\nA simple approach to detecting a collision with Pollard's rho method is to use Floyd's cycle-finding algorithm , which shows that it suffices to compare and for all to find a collision. Floyd's algorithm uses only a small constant amount of storage, but needs roughly three times more work than is necessary. Brent improved this approach by using an auxiliary variable. Nivasch designed an algorithm for detecting periodicity in sequences using a single pointer and a small stack. This stack algorithm halts at a uniformly random point in the second loop through the sequence's cycle.\n\nIn finding DES collisions [14, 15], Quisquater and Delescaille took a different approach based on storing distinguished points, an idea noted earlier by Rivest to reduce the search time in Hellman time-memory tradeoff . A distinguished point is one that has some easily checked property such as having a fixed number of leading zero bits. During the pseudo-random walk, points that satisfy the distinguishing property are stored. Collision can be detected when a distinguished point is encountered a second time. This technique can be efficiently applied to find collisions among multiple processors .\n\nIn this paper, we describe a new efficient collision detection algorithm for computing discrete logarithm with Pollard's rho method. It is a probabilistic algorithm and more efficient than the previous methods. With this algorithm, we can significantly reduce the space requirements and provide a better time-space trade-off approach. We also compare their performances in experiments with elliptic curve groups, and our experimental results confirmed the theoretical analysis.\n\nThe remainder of this paper is organized as follows. In Section 2, we recall Pollard's rho method for discrete logarithm computation and discuss several previous methods for collision detection. We describe and analyze the new algorithm in Section 3 and discuss its applications in Section 4. We present our experiments in Section 5 and conclude the paper in Section 6.\n\n#### 2. Preliminary\n\nIn this section, we describe Pollard's rho method for discrete logarithm computation and then discuss several collision detection algorithms and their performances.\n\n##### 2.1. Pollard's Rho Method\n\nPollard proposed an elegant algorithm for the discrete logarithms based on a Monte Carlo idea and called it the rho method. The rho method works by first defining a sequence of elements that will be periodically recurrent, then looking for a match in the sequence. The match will lead to a solution of the discrete logarithm problem with high probability. The two key ideas involved are the iteration function for generating the sequence and the cycle-finding algorithm for detecting a match.\n\nIf is any finite set and is a mapping and the sequence in is defined by the rule: this sequence is ultimately periodic. Hence, there exist unique integers and such that are all distinct, but for all . A pair of two elements of the sequence is called a match if where, . For the expected values of and , we have the following theorem.\n\nTheorem 2.1 (see ). Under the assumption that an iteration function behaves like a truly random mapping and the initial value is a randomly chosen group element, the expected values for and are . The expected number of evaluations before a match appears is .\n\nNow we explain how the rho method for computing discrete logarithms works. Let be a cyclic group of prime order , and let be generator of and . The discrete logarithm problem is to compute satisfying . Pollard defined the iteration function as follows:\n\nLet the initial value . In each iteration of , the function uses one of three rules depending on the value of . The group is partitioned into three subsets , , of roughly equal size. Each has the form . The sequence (and similarly for ) can be computed as follows:\n\nAs soon as we have a match , we have the equation .\n\nSince , this gives Now, if , we get that . Due to the method of Pohlig and Hellman , in practice applications the group order is prime, so that it is very unlikely that if is large.\n\nTheorem 2.1 makes the assumption of true randomness. However, it has been shown empirically that this assumption does not hold exactly for Pollard's iteration function . The actual performance is worse than the expected value given in Theorem 2.1.\n\nTeske proposed better iteration functions by applying more arbitrary multipliers. Assume that we are using partitions (multipliers). We generate random numbers, Then we precompute multipliers , where , for . Define a hash function, Then the iteration function defined as The indices are update by\n\nThe difference in performance between Pollard's original walk and Teske’s -adding walk has been studied in [19, 20]. We summarize the results as follows. In prime order subgroups of , the value of for Pollard's original walk and Teske's -adding walk is and , while in groups of points of elliptic curves over finite fields, the value is and , respectively.\n\n##### 2.2. Previous Methods for Collision Detection\n\nTo find the collision in the pseudo-random walk, it always needs much storage. In order to minimize the storage requirements, a collision detection algorithm can be applied with a small penalty in the running time.\n\nFloyd's Cycle-Finding Algorithm\nIn Pollard's paper, Floyd's algorithm is applied. To find , the algorithm calculates until . For each iteration, we compute and , which means that this algorithm requires negligible storage. Floyd's algorithm is based on the following idea.\n\nTheorem 2.2 (see ). For a periodic sequence , there exists an such that and the smallest such lies in the range .\n\nThe best running time requires iterations and the worst takes iterations. Under the assumption that behaves like a truly random mapping, the expected number of iterations before reaching a match is . The key point for this algorithm is that we need three group operations and one comparison for each iteration, which makes it inefficient.\n\nBrent's Algorithm\nBrent proposed an algorithm which is generally 25% faster than Floyd's method. It uses an auxiliary variable, say , which at each stage of the algorithm holds , where . is compared with for each iteration and is updated by when for . The correctness of this algorithm depends on the following fact.\n\nTheorem 2.3 (see ). For a periodic sequence , there exists an such that and . The smallest such is .\n\nUnder the assumption that is a random mapping, with Brent's algorithm the first match is expected to occur after iterations . The algorithm needs one group operation and one comparison for each iteration, which makes it 25%–30% faster than Floyd's algorithm. Variations of Brent's algorithm requiring slightly more storage and comparisons but less iterations can be found in [21, 22].\n\nStack Algorithm\nIn 2004, Nivasch proposed an interesting algorithm that uses logarithmic storage space and can be adapted with tradeoff for storage space versus speed. This algorithm requires that a total ordering < be defined on the set , and it works as follows. Keep a stack of pairs , where, at all times, both the 's and the 's in the stack form strictly increasing sequences. The stack is initially empty. At each step , pop from the stack all entries , where . If a match is found with an element in the stack, the algorithm terminates successfully. Otherwise, push on top of the stack and continue. The stack algorithm depends on the following fact.\n\nTheorem 2.4 (see ). The stack algorithm always halts on the smallest value of the sequence's cycle, at some time in .\n\nUnder the assumption that is a random mapping, the expected number of iterations before finding a match is . The algorithm needs a little bit more than one group operation and one comparison for each iteration. Under the same assumption, Nivasch proves also that the expected size of the stack is ln . Therefore, the algorithm only requires a logarithmic amount of memory.\n\nDistinguished Point\nThe idea of the distinguished point method is to search for a match not among all terms of the sequence, but only among a small subset of terms that satisfy a certain distinguishing property. It works as follows. One defines a set , a subset of , that consists of all group elements that satisfy a certain distinguishing property. During the pseudo-random walk, points that satisfy the distinguishing property are stored. Collision can be detected when a distinguished point is encountered a second time.\nCurrently, the distinguished point method is the most efficient algorithm to detect collisions in pseudo-random walk when is large. A popular way of defining is to fix an integer and to define that if and only if the least significant bits in the representation of as a binary string are zero. To break ECC2K-130, it defines the distinguishing property as the Hamming weight of normal-basis representation of -coordinate of the point less than or equal to 34. Notice that this kind of definitions allows a fast check for the distinguishing property to hold, and the size of can be easily monitored as well. Obviously, we have the following theorem.\n\nTheorem 2.5 (see ). Let be the proportion of points in which satisfy the distinguishing property, that is, . Under the assumption that is a random mapping and is a uniform distribution in , the expected number of iterations before finding a match is .\n\n#### 3. The New Algorithm\n\nWe are motivated by the fact that, in distinguished point method, the distinguished points may be not uniformly distributed in the pseudo-random walk, also the points in subset may be not uniformly distributed in , which always results in more iteration requirements. We are trying to design an algorithm which leads to a uniform distribution and also to provide a better way for time-space tradeoff rather than distinguishing property.\n\n##### 3.1. The Basic Algorithm\n\nTo find a collision in pseudo-random walk, which is produced by the iteration function , assuming is a random mapping on , our basic algorithm works as follows. We fix an integer and use an auxiliary variable, say , which at each iterations keep the minimum value of successive values produced by the iteration function . Once getting the minimum value from successive values, we check whether this value has occurred before in the stored sequence, if so, we find the match and we are done. Otherwise, store this value to the sequence. Then continue to compute the next new values and repeat the previous procedures. Choose the integer properly, we will find the match among the newly generated minimum value and stored minimum values.\n\nMore precisely, to find a collision in pseudo-random sequence , which is produced by the iteration function , we have Algorithm 1.\n\n Input: Initial value 𝑌 0 , iteration function 𝐹 ∶ 𝐺 → 𝐺 , fixed integer 𝑁 Output: 𝑚 and 𝑛 , such that 𝑌 𝑚 = 𝑌 𝑛 (1) 𝑤 ← 𝑌 0 , 𝑚 ← 0 , 𝑛 ← 0 (2) for 𝑖 = 1 to ⌈ | 𝐺 | / 𝑁 ⌉   do (3)  for 𝑗 = ( 𝑖 − 1 ) 𝑁 + 1 to 𝑖 𝑁 − 1   do (4)    𝑌 𝑗 ← 𝐹 ( 𝑌 𝑗 − 1 ) (5)   if 𝑌 𝑗 < 𝑤 then (6)     𝑤 ← 𝑌 𝑗 , 𝑛 ← 𝑗 (7)   else if 𝑌 𝑗 = 𝑤   then (8)     𝑚 ← 𝑗 (9)    return   𝑚 , 𝑛 (10)    end if (11)   end for (12) (13)   for 𝑘 = 1 to 𝑖 − 1   do (14)     if 𝑢 𝑘 = 𝑤   then (15)      𝑚 ← 𝑣 𝑘 (16)     return   𝑚 , 𝑛 (17)     end if (18)    end for (19)    𝑢 𝑖 ← 𝑤 , 𝑣 𝑖 ← 𝑛 (20)    𝑤 ← 𝐹 ( 𝑌 𝑖 𝑁 − 1 ) , 𝑛 ← 𝑖 𝑁 (21) end for\n\nIt is obvious that the algorithm can be considered as two parts. In the first part, that is from step (3) to step (11), we seek the minimum value from successive values in the pseudo-random walk. The operation is very simple; if the current value is smaller than , then just update with the current value and continue the next iteration. Notice that steps (7), (8), and (9) can be omitted, since it is unlikely that there is a match within iterations. Even if it happened, the algorithm ensures that we can find a match within the next iterations. As a result, there is only one group operation and one comparison in the first part, which consist the main operations of the algorithm.\n\nIn the second part, that is from step (13) to step (19), once we get a minimum value , we check whether has appeared before in the previous stored values , which is empty at the beginning. If this is the case, the algorithm will return the corresponding indices and we are done. Otherwise, save the value to the sequence of the minimum values, and the second part is finished, continue the next iterations. It is clear that the second part can be speeded up by using a hash table. And, more important, the second part can be independent to the first part, which means the stored sequence of minimum values can be off line; that is, the first part is response for generating minimum values along the random walk, while the second part searches the collision among stored minimum values independently.\n\n##### 3.2. Analysis\n\nFor further analysis of the algorithm, we assume that the iteration function behaves like a truly random mapping. According to Theorem 2.1, the expected number of iterations before reaching a match is . Let us look at some simple cases for the new algorithm. For , which means we store all the values in the sequence before reaching a match, and the match can be found once it appears. For , we need to store half of the values in the sequence before reaching a match, and always the match can be found once it appears. Obviously, the bigger the integer , the less values we need to store. As a result, with the integer increasing, there is a probability that we cannot detect the collision immediately when it happens. So, the new algorithm is a probabilistic algorithm. However, with high probability, the algorithm will halt close to the beginning of the second loop. More precisely, we have the following theorem.\n\nTheorem 3.1. Under the assumption that an iteration function behaves like a truly random mapping and the initial value is a randomly chosen group element, for Algorithm 1, the expected number of iterations before finding a match is with probability , where .\n\nProof. Let be the set that consists of the th successive values generated by iteration function ; that is, For finite group , the sequence produced by is eventually period; that is, for any fixed and , there exist certain integers and , such that and also\nTo prove the theorem, we divide it into two cases, that is, and . For , let and be the minimum values of and , then that is, the probability of successfully detecting the collision within the first two intersection sets is .\nFor each of , we notice that, for two (intersected) sets and , let and be the minimum values of and , respectively, we have Therefore, we have Under the assumption that the iteration function is a random mapping, according to Theorem 2.1, the expected number of evaluations before a match appears is . Combining the above two cases, using Algorithm 1, the expected number of iterations before reaching a match among minimum values is with probability , where .\n\nRemark 3.2. According to the above theorem, we need to store terms to find the match with the probability , where can be ; that is, by setting parameter , we can balance the expected number of iterations and the expected space requirements. Therefore, Algorithm 1 is a time-space trade-off algorithm.\n\nRemark 3.3. Algorithm 1 is a probabilistic algorithm. There is a probability that we cannot detect the collision immediately when it happens. However, with high probability, the algorithm will halt close to the beginning of the second loop. For example, the probability of successfully detecting the collision is 0.90 with .\n\nNotice that, compared to the distinguished point method, the new algorithm has two advantages. First, the distinguished point method depends on the assumption that the distinguished points are uniformly distributed in the pseudo-random walk, and also the points in subset are uniformly distributed in . However, in practice this may not be the case, which generally results in more iterations requirement, while, for the new algorithm, each stored minimum value represents successive values and the performance of the new algorithm independent of such assumption. Because the distinguished point method is currently the most efficient algorithm, we compare the actual performances of the new algorithm with the distinguished point method under the same expected storage requirement in experiments with elliptic curve groups in Section 5.\n\nSecond, using distinguished point method, it is possible for a random walk to fall into a loop which contains no distinguished point . Then, the processor cannot find new distinguished point any more on the path. Left undetected, the processor would cease to contribute to the collision search. In this case, we can restart the random walk by choosing a different initial point. However, those points calculated by previous walk do not help for the collision search, while the new algorithm can avoid such problem, because it can always find the collision among minimum values whenever it falls into a loop.\n\n#### 4. Applications\n\nThe new algorithm can be combined with other algorithms, such as Pollard's lambda method, and can be adapted to a wide range of problems which can be reduced to finding collisions, such as in Pollard's rho method for factorization and in studying the behavior of random number generators . In this section, we will address some of these issues.\n\n##### 4.1. Pollard's Lambda Method\n\nIt is clear that the new algorithm can be applied to Pollard's lambda method (also called the kangaroo method). The lambda method computes a discrete logarithm in an arbitrary cyclic group, given that the value is known to lie in a certain interval, that is, , where but unknown.\n\nGenerally, we have two kangaroos, one tame and one wild. Their positions are represented by group elements, the tame kangaroo with starting point and the wild kangaroo with starting point , and they travel in the cyclic group . In terms of the exponents of , starts at the middle of the interval , while starts at . Since we do not know , we do not know the exact location of the wild kangaroo, and that is why it is called wild. The two kangaroos produce two different pseudo-random walks with the same walking rules. It is obvious that, at all times, the point of tame kangaroo has the form and the point of wild kangaroo has the form for some known integers and . The purpose is to provoke a collision between the tame and the wild kangaroos, from which we can deduce the wild kangaroo's starting point, that is, .\n\nSimilar to the case of Pollard's rho method, the new algorithm can be applied in this case to efficiently detect the collision. The advantage of the new algorithm is that we can achieve uniform distributions of minimum values in the pseudo-random walks both for the tame kangaroos and the wild kangaroos. The different performances of the new algorithm and distinguished point method in this case can refer to the case of Pollard's rho method.\n\n##### 4.2. Parallelization\n\nAs we have mentioned above, during the random walk, finding the minimum value from iterations and comparing the minimum value to all previously stored values can be separated. This feature makes the new algorithm suit for distributed computation.\n\nHowever, Pollard's rho method is inherently serial in nature; one must wait for the current iteration of the function to complete before the next can begin. Each value in the sequence totally depends on the previous value and the iteration rules. In discussing the rho method for factorization, Brent considered running many processors in parallel each producing an independent sequence and noted that “Unfortunately, parallel implementation of the “rho” method does not give linear speedup” . Analogous comments apply to the rho method for computing logarithms and the generalized rho method for collision search. Notice that here each parallel processor is producing its own sequence of points independently of the others and each particular processor does not increase the probability of success of any other processor. For the corresponding picture, with high probability, each processor draws a different “rho” that never intersect with each other. There is a little chance that different processors may intersect with each other.\n\nvan Oorschot and Wiener showed that the expected speedup of the direct parallelization of Pollard's rho method, using processors, is only a factor of . This is a very inefficient use of parallelization. They provided a modified version of Pollard's rho method and claimed that it can be linearly parallelized with the distinguished point method; that is, the expected running time of the modified version, using processors, is roughly group operations.\n\nIn the modified version, to perform a parallel collision search each processor proceeds as follows. Select a random starting point , and produce the trail of points , for , until a distinguished point is reached based on some easily testable distinguished property. Store distinguished point, and start producing a new trail from a new random starting point. Unfortunately, the new algorithm is not efficient for the parallelized modified version of Pollard's rho method. The key point is that there is a probability that the new algorithm fails to detect the collision while it actually happened, which cannot be efficiently solved like the serial version.\n\nHowever, for Pollard's lambda method, the new algorithm can be efficiently parallelized with linear speedup. We present here a modified version of parallelized Pollard's lambda method from . Assume we have processors with even. Then, instead of one tame and one wild kangaroo, we work with two herds of kangaroos, one herd of tame kangaroos and one herd of wild kangaroos, with one kangaroo on each processor. Each kangaroo starts from a different point, stores a minimum value every iterations, just like the serial version. A center server collects all the minimums, and tries to find a collision between the tame kangaroo minimums and the wild kangaroo minimums By choosing a reasonable integer , the new algorithm provides an optimal time-space trade-off method for collision detection.\n\n#### 5. Experiments\n\nWe implemented Pollard's rho method with elliptic curve groups over prime fields using SAGE , which is an open source computer algebra software. Obviously, such experiments can also be done for DLP on a multiplicative subgroup of finite field . We compared the different performances between distinguished point method and the new algorithm. In this section, we describe these experiments and analyse the results.\n\nFor our experiments, we briefly introduce the elliptic curve groups over prime fields and the notation we use in the following. Let be a prime, and let denote the field of integers modulo . Let such that . Then the elliptic curve over is defined through the equation The set of all solutions of this equation, together with the element called the “point at infinity,” forms a finite abelian group which we denote by . Usually, this group is written additively. Let be a point of prime order , and let denote the subgroup of generated by . Given , determine the integer such that .\n\nFor the iteration function, we use Teske's -adding walk and set ; that is, we divide the group into 20 subsets: . Define the iteration function as follows: where and randomly chosen from and can be precomputed for . This means it only needs one group operation for each iteration.\n\nLet be any point of ; we define the partition of into subsets as follows. First we compute a rational approximation of the golden ratio , with a precision of decimal places. Let where is the nonnegative fraction part of . Then let This method is originally from Knuth's multiplicative hash function and suggested by Teske . From the theory of multiplicative hash functions, we know that, among all numbers between 0 and 1, choosing as a rational approximation of with a sufficiently large precision leads to the most uniformly distributed hash values, even for nonrandom inputs.\n\nThe purpose of our experiments is to evaluate the expected numbers of steps until a match is found with different collision detection methods, that is, distinguished point method and the new algorithm, under the same expected space requirement. Generally, we randomly choose a big prime number , where is in certain range. Then we randomly choose the parameters and , where , which determine the unique elliptic curve over . We will check whether the order of group has large prime factor in certain range. If not, repeat the above procedures until we get a prime order subgroup of . Then we set the generator of and choose a random point of . When using Pollard's rho method to compute this discrete logarithm, we count the number of steps we performed until a match is found with different collision detection methods on the same case. Then we determine the ratio of the number of steps and . We repeat it a couple of times with the same but several randomly chosen ’s. Furthermore, for practical reasons, we do the above procedures with a couple of groups, where the group order is between 231 and 236. We have Algorithm 2.\n\n Input: Iteration function 𝐹 ∶ 𝐺 → 𝐺 Output: The average ratio √ ( n u m b e r o f s t e p s ) / 𝑛 ∶ 𝑅 𝑖 1 and 𝑅 𝑖 2 for distinguished point method and the new algorithm, respectively (1) for 𝑖 = 3 1 to 36  do (2)  for 𝑗 = 1 to 20  do (3)   repeat (4)    Choose a random prime number 𝑞 ∈ [ 2 𝑖 + 1 , 2 𝑖 + 3 ] (5)    Choose two random numbers 𝑎 , 𝑏 ∈ 𝔽 q, where 4 𝑎 3 + 2 7 𝑏 2 ≠ 0 (6)    𝑛 ← the largest prime factor of # 𝐸 𝑎 , 𝑏 (7)   until 2 𝑖 ≤ 𝑛 ≤ 2 𝑖 + 1 (8)   Choose a random point 𝑊 ∈ 𝐸 𝑎 , 𝑏 , where the order of 𝑊 equal to # 𝐸 𝑎 , 𝑏 (9)    𝑃 ← ( # 𝐸 𝑎 , 𝑏 / 𝑛 ) ∗ 𝑊 (the generator of 𝐺 ) (10)   for 𝑙 = 1 to 3 2 0 0 / 2 𝑖 − 3 1   do (11)    Choose a random number 𝑐 ∈ [ 0 , 𝑛 − 1 ] , 𝑄 ← 𝑐 ∗ 𝑃 (12)    Choose a random point in 𝐺 be the initial point 𝑌 0 (13)     𝑘 ← 1 (14)    repeat (15)      𝑌 𝑘 ← 𝐹 ( 𝑌 𝑘 − 1 ) (16)     Check whether the Hamming weight of 𝑌 𝑘 less than certain value (17)     Check whether the 𝑥 -coordinate of 𝑌 𝑘 is a minimum value (18)     if there is a match among distinguished points  then (19)       𝑘 1 ← 𝑘 (20)     end if (21)     if there is a match among minimum values  then (22)       𝑘 2 ← 𝑘 (23)     end if (24)    until  Both of two methods have found the match (25)     𝑅 𝑙 1 ← 𝑘 1 / √ 𝑛 for distinguished point method (26)     𝑅 𝑙 2 ← 𝑘 2 / √ 𝑛 for the new algorithm (27)    end for (28)    𝑅 𝑗 1 ∑ 𝑅 ← ( 𝑙 1 ) / 3 2 0 0 / 2 𝑖 − 3 1 for distinguished point method (29)    𝑅 𝑗 2 ∑ 𝑅 ← ( 𝑙 2 ) / 3 2 0 0 / 2 𝑖 − 3 1 for the new algorithm (30)  end for (31)   𝑅 𝑖 1 ∑ 𝑅 ← ( 𝑗 1 ) / 2 0 for distinguished point method (32)  𝑅 𝑖 2 ∑ 𝑅 ← ( 𝑗 2 ) / 2 0 for the new algorithm (33) end for\n\nMore precisely, for each , we generate 20 elliptic curves, where each of them has a subgroup of prime order , such that . Then for, each group , we generate 100 to 3200 DLPs with the same generator but randomly generated . The number of elliptic curves and instances of DLPs computed is given in Table 1. For each DLP, we use Teske's -adding walk for iteration function and find the match using distinguished point method and the new algorithm simultaneously. Once reaching a match, we compute the ratio as (the number of steps until match is found)/. Then we compute the average ratio of all DLPs over the same elliptic curve. Finally, we count the average ratio of all DLPs with the same , where and .\n\n Bits No. of elliptic curves No. of DLPs per curve 31 20 3200 32 20 1600 33 20 800 34 20 400 35 20 200 36 20 100\n\nNow, let us explain the parameters for distinguishing property and the new algorithm in more detail. In our experiments, we compute the average ratio of under the same space requirement. To do this, generally we first define the distinguishing property and then compute the expected storage requirements. With the same storage requirements, we can deduce the parameter for the new algorithm.\n\nFor example, if , which means , the order of is a 36-bit prime number. According to , we are expected to take iterations before reaching a match. We define the distinguishing property as the Hamming weight of normal-basis representation of -coordinate of the point less than or equal to 9. Each point has probability almost exactly of being a distinguished point, that is, ; that is, to find a collision it is expected to compute distinguished points. To keep the same storage requirements, we set for the new algorithm.\n\nThe experimental results are given in Table 2. It shows that on average using the new algorithm for collision detection can reduce the number of iterations until a match is found from to under the same space requirements for the single rho method.\n\n Bits No. of DLPs Ratio for distinguished point Ratio for the new algorithm 31 64000 1.309 1.295 32 32000 1.309 1.295 33 16000 1.310 1.296 34 8000 1.310 1.297 35 4000 1.309 1.295 36 2000 1.310 1.294 Average 126000 1.309 1.295\n\nUnder the same expected storage requirements, the main reason for the different performances of the distinguished point method and the new algorithm is that the distinguished points may be not uniformly distributed in the pseudo-random walk, also the points in subset may be not uniformly distributed in , which always results in more iterations requirement. while, for the new algorithm, each stored minimum value represents successive values, which leads to an equal-interval distribution.\n\n#### 6. Conclusion\n\nIn this paper, we proposed an optimal time-space trade-off method for collision detection in the pseudo-random walk when computing discrete logarithms with Pollard's rho method. We discussed the new algorithm both in theoretical analysis and in practical experiments. By comparison to other methods, it shows that the new algorithm is more efficient than previous methods. Unfortunately, the only practical application of the new idea is with the parallelized lambda method and it does not work with the parallelized rho method. As a further work, we would like to explore the performances of the new algorithm in other applications.\n\n#### Acknowledgments\n\nThis work is partially supported by the National Natural Science Foundation of China (no. 61070168). The authors would like to thank the reviewers for their helpful comments and suggestions.\n\n1. W. Diffie and M. Hellman, “New directions in cryptography,” IEEE Transactions on Information Theory, vol. 22, no. 6, pp. 644–654, 1976. View at: Google Scholar | Zentralblatt MATH\n2. T. ElGamal, “A public key cryptosystem and a signature scheme based on discrete logarithms,” IEEE Transactions on Information Theory, vol. 31, no. 4, pp. 469–472, 1985.\n3. FIPS 186-2, “Digital signature standard,” Tech. Rep. 186-2, Federal Information Processing Standards Publication, 2000. View at: Google Scholar\n4. C. P. Schnorr, “Efficient signature generation by smart cards,” Journal of Cryptology, vol. 4, no. 3, pp. 161–174, 1991. View at: Publisher Site | Google Scholar\n5. N. Koblitz, “Elliptic curve cryptosystems,” Mathematics of Computation, vol. 48, no. 177, pp. 203–209, 1987.\n6. V. Miller, “Use of elliptic curves in cryptography,” in Advances in Cryptology: Proceedings of Crypto'85, vol. 218 of LNCS, pp. 417–426, Springer, New York, NY, USA, 1986. View at: Google Scholar\n7. A. Menezes, P. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, Fla, USA, 1996.\n8. J. M. Pollard, “Monte Carlo methods for index computation mod p,” Mathematics of Computation, vol. 32, no. 143, pp. 918–924, 1978. View at: Google Scholar | Zentralblatt MATH\n9. R. Gallant, R. Lambert, and S. Vanstone, “Improving the parallelized Pollard lambda search on anomalous binary curves,” Mathematics of Computation, vol. 69, no. 232, pp. 1699–1705, 2000.\n10. M. Wiener and R. Zuccherato, “Faster attacks on elliptic curve cryptosystems,” in Selected Areas in Cryptography'98, vol. 1556 of LNCS, pp. 190–200, Springer, Berlin, Germany, 1998.\n11. P. van Oorschot and M. Wiener, “Parallel collision search with cryptanalytic applications,” Journal of Cryptology, vol. 12, no. 1, pp. 1–28, 1999.\n12. R. P. Brent, “An improved Monte Carlo factorization algorithm,” BIT, vol. 20, no. 2, pp. 176–184, 1980.\n13. G. Nivasch, “Cycle detection using a stack,” Information Processing Letters, vol. 90, no. 3, pp. 135–140, 2004.\n14. J. J. Quisquater and J. P. Delescaille, “How easy is collision search? Application to DES,” in Proceedings of the Advances in Cryptology—Eurocrypt, vol. 434 of Lecture Notes in Computer Science, pp. 429–434, Springer, New York, NY, USA, 1989. View at: Google Scholar\n15. J. J. Quisquater and J. P. Delescaille, “How easy is collision search. New results and applications to DES,” in Proceedings of the Advances in Cryptology—Crypto, vol. 435 of Lecture Notes in Computer Science, pp. 408–413, Springer, New York, NY, USA, 1989. View at: Google Scholar\n16. M. E. Hellman, “A cryptanalytic time-memory trade-off,” IEEE Transactions on Information Theory, vol. 26, no. 4, pp. 401–406, 1980.\n17. B. Harris, “Probability distributions related to random mappings,” Annals of Mathematical Statistics, vol. 31, pp. 1045–1062, 1960.\n18. S. C. Pohlig and M. E. Hellman, “An improved algorithm for computing logarithms over GF(p) and its cryptographic significance,” IEEE-Transactions on Information Theory, vol. 24, no. 1, pp. 106–110, 1978. View at: Google Scholar | Zentralblatt MATH\n19. E. Teske, “Speeding up Pollard's rho method for computing discrete logarithms,” in Algorithmic Number Theory Symposium (ANTS IV), vol. 1423 of LNCS, pp. 541–553, Springer, New York, NY, USA, 1998.\n20. S. Bai and R. P. Brent, “On the efficiency of Pollard’s rho method for discrete logarithms,” in CATS 2008, J. Harland and P. Manyem, Eds., pp. 125–131, Australian Computer Society, 2008. View at: Google Scholar\n21. C.-P. Schnorr and H. W. Lenstra Jr., “A Monte Carlo factoring algorithm with linear storage,” Mathematics of Computation, vol. 43, no. 167, pp. 289–311, 1984.\n22. E. Teske, “A space efficient algorithm for group structure computation,” Mathematics of Computation, vol. 67, no. 224, pp. 1637–1663, 1998.\n23. D. V. Bailey, L. Batina, D. J. Bernstein et al., “Breaking ECC2K-130,” Tech. Rep. 2009/541, Cryptology ePrint Archive, 2009. View at: Google Scholar\n24. J. M. Pollard, “A Monte Carlo method for factorization,” BIT, vol. 15, no. 3, pp. 331–335, 1975. View at: Google Scholar | Zentralblatt MATH\n25. D. E. Knuth, The Art of Computer Programming, vol. 2, Addison-Wesley, Reading, Mass, USA, 3rd edition, 1997.\n26. R. P. Brent, “Parallel algorithms for integer factorisation,” in Number Theory and Cryptography, J. H. Loxton, Ed., vol. 154 of London Mathematical Society Lecture Note Series, pp. 26–37, Cambridge University, Cambridge, UK, 1990. View at: Google Scholar | Zentralblatt MATH\n27. “SAGE: an open source mathematics software,” http://www.sagemath.org/. View at: Google Scholar\n28. D. E. Knuth, The Art of Computer Programming, vol. 3, Addison-Wesley, Reading, Mass, USA, 2nd edition, 1981.\n29. E. Teske, “On random walks for Pollard's rho method,” Mathematics of Computation, vol. 70, no. 234, pp. 809–825, 2001." ]
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