The Kolmogorovbackwardequation KBE diffusion and its Adjoint of an operator adjoint sometimes known as the Kolmogorov forward equation diffusion are partial differential equation s PDE that arise in the theory of continuous time continuous state Markov process es. Both were published by Andrey Kolmogorov in 1931. Later it was realized that the forward equation was already known to physicists under the name Fokker&ndash Planck equation the KBE on the other hand was new. Informally, the Kolmogorov forward equation addresses the following problem. We have information about the state x of the system at time t namely a probability distribution math p t x math we want to know the probability distribution of the state at a later time math s t math . The adjective forward refers to the fact that math p t x math serves as the initial condition and the PDE is integrated forward in time. In the common case where the initial state is known exactly math p t x math is a Dirac delta function centered on the known initial state . The Kolmogorovbackwardequation on the other hand is useful when we ... is integrated backward in time, from s to t . Formulating the Kolmogorovbackwardequation Assume that the system state math x t math evolves according to the stochastic differential equation math dx t mu x t ,t ,dt sigma x t ,t ,dW t math then the Kolmogorovbackwardequation is, using Ito s lemma ... 1931 was developed before the Feynman Kac formula 1949 . Formulating the Kolmogorov forward equation With the same notation as before, the corresponding Kolmogorov forward equation is math frac partial ... math p x,s u s x math . This equation can also be derived from the Feynman Kac formula by noting ... x,s p x,s math for math s ge t math , with initial condition math p x,t p t x math . For more on this equation see Fokker&ndash Planck equation . nofootnotes date June 2011 References cite book author ... retrospettiva di Kolmogorov ... more details
See also Fokker Planck equation also known as Kolmogorov forward equationKolmogorovbackwardequation Examples of Markov chains Master equation physics References http www.kolmogorov.com The Legacy of Andrei Nikolaevich Kolmogorov Curriculum Vitae and Biography. Kolmogorov School. Ph.D. students and descendants of A.N. Kolmogorov. A.N. Kolmogorov works, books, papers, articles. Photographs and Portraits of A.N. Kolmogorov. mathworld urlname Chapman KolmogorovEquation title Chapman KolmogorovEquation Category Equations Category Markov processes af Chapman Kolmogorov vergelyking ca Llei de Chapman Kolmogorov de Chapman Kolmogorow Gleichung es Ley de Chapman Kolmog rov fr quation de Chapman Kolmogorov pl R wnania Chapmana Ko mogorowa ru uk ... Kolmogorovequation is math p i 1, ldots,i n 1 f 1, ldots,f n 1 int infty infty p i 1, ldots ... chain Markovian , the Chapman Kolmogorovequation is equivalent to an identity on transition densities ... ordering of the random variables&mdash the above equation applies equally to the marginalization ... i mid f j math is the transition probability between the times math i j math . So, the Chapman Kolmogorovequation takes the form math p i 3 i 1 f 3 mid f 1 int infty infty p i 3 i 2 f 3 mid f 2 p i 2 ..., the Chapman Kolmogorov equations can be expressed in terms of possibly infinite dimensional matrix ... more details
Kolmogorov s theorem is any of several different results by Andrey Kolmogorov In statistics Kolmogorov Smirnov test In probability theory Hahn Kolmogorov theorem Kolmogorov existence theorem Kolmogorov continuity theorem Kolmogorov Riesz compactness theorem Kolmogorov s three series theorem Kolmogorov s zero one law Chapman Kolmogorovequation s Kolmogorov inequalities Kolmogorov s inequality Kolmogorov s inequality for positive submartingales In functional analysis Landau Kolmogorov inequality disambig it Teorema di Kolmogorov pl Twierdzenie Ko mogorowa ... more details
context date January 2012 In probability theory , Kolmogorov equations , including Kolmogorov forward equations and Kolmogorovbackward equations , characterize random dynamic processes. Suppose we have ... ref William Feller makes reference to the equations for the jump process as Kolmogorov s equations . ref name f40 Willy Feller, On Boundaries and Lateral Conditions for the Kolmogorov Differential Equations, 1940, http www.jstor.org stable 1970064 ref He later gives the names forward equation and backwardequation to his more general version of the equations and uses the same names as nicknames ... and backward Fokker Planck equation . ref name f49 Feller, W. 1949 http projecteuclid.org DPubS?service ... and Kolmogorovbackward equations . ref name f57 William Feller, 1957. On Boundaries and Lateral Conditions ... Fokker Planck equation as Kolmogorov forward equation, a name that has persisted. References See ..., velocity which defines a new process y t related to x t . Then the Kolmogorov equations are a means ... ref Diffusion Processes vs. Jump Processes Writing in 1931, Andrei Kolmogorov started from the theory of discrete time Markov processes, which are described by the Chapman Kolmogorovequation , and sought to derive a theory of continuous time Markov processes by extending this equation. He found that there are two ... small time intervals will be also small ref name f49 . For each of these two kinds of processes, Kolmogorov derived a forward and a backward system of equations four in all . Kolmogorov equations the modern view In the context of a continuous time Markov process , the term refers to the Kolmogorov ... as master equation . In the context of diffusion equations these names refer to Fokker Planck equation forward equation and to the Kolmogorovbackward equations diffusion . History The equations are named after Andrei Kolmogorov s since they were highlighted in his 1931 foundational work. ref name k31 Andrei Kolmogorov, ber die analytischen Methoden in der Wahrscheinlichkeitsrechnung On Analytical ... more details
developed the pivotal set of equations in the field, the Chapman Kolmogorovequation s. Image Kolm ... Borel Kolmogorov paradox Chapman Kolmogorovequation Sydney Chapman mathematician Chaitin Kolmogorov ...Infobox scientist name Andrey Kolmogorov image Kolmogorov m.jpg birth date birth date 1903 04 25 df y ... ref name frs cite doi 10.1098 rsbm.1991.0015 ref signature footnotes Andrey Nikolaevich Kolmogorov lang ... Early life Kolmogorov was born at Tambov in 1903. His unwed mother died in childbirth and he was raised ... movement. He disappeared and was presumed to have been killed in the Russian Civil War . Kolmogorov ... school gymnasium , graduating from it in 1920. In 1920, Kolmogorov began to study at the Moscow State University and the Chemistry Technological Institute. Kolmogorov gained a reputation for his wide ..., 2001 pp. 137&ndash 50. ref At the same time 1921&ndash 1922 , Kolmogorov derived and proved several ... Kolmogorov constructed a Fourier series that diverges almost everywhere , gaining international ... . In 1925 Kolmogorov graduated from Moscow State University , and began to study under the supervision .... Harvard University Press. p. 185. ISBN 978 0 674 03293 4. The police soon learned of Kolmogorov and Alexandrov .... When the police asked Kolmogorov and Alexandrov to join in attacking Luzin, they did so. ref ref cite ..., the so called Luzin affair . Kolmogorov together with Khinchin A. Khinchin became interested ... of classical formal logic can be formulated as those of intuitionistic logic. In 1929 Kolmogorov earned his Doctor of Philosophy degree, Ph.D. , at the Moscow State University . In 1930, Kolmogorov ... in 1931. Also in 1931, he became a professor at Moscow University. In 1933, Kolmogorov published ... expert in this field. In 1935, Kolmogorov became the first chairman of probability theory at the Moscow ... USSR Academy of Sciences . In a 1938 paper, Kolmogorov established the basic theorems for smoothing ... during the Cold War to come. ref Salsburg, p. 139. ref Around the same years 1936 Kolmogorov ... more details
Andrey KolmogorovKolmogorov microscales are the smallest scale ratio scale s in Turbulence turbulent flow . At the Kolmogorov scale viscosity dominates and the turbulent kinetic energy is dissipated into heat. They are defined ref Landahl, M.T. & E. Mollo Christensen. Turbulence and Random Processes in Fluid Mechanics. Cambridge, 2ed, 1992. ref by class wikitable Kolmogorov length scale math eta left frac nu 3 epsilon right 1 4 math Kolmogorov time scale math tau eta left frac nu epsilon right 1 2 math Kolmogorov velocity scale math u eta left nu epsilon right 1 4 math where math epsilon math is the average rate of dissipation of turbulence kinetic energy per unit mass, and math nu math is the kinematic viscosity of the fluid. In his 1941 theory, A. N. Kolmogorov introduced the idea that the smallest scales of turbulence are universal similar for every turbulent flow and that they depend only on math epsilon math and math nu math . The definitions of the Kolmogorov microscales can be obtained using this idea and dimensional analysis . It therefore is not a theory derived from first principles. Since the dimension of kinematic viscosity is length sup 2 sup time, and the dimension of the energy dissipation rate per unit mass is length sup 2 sup time sup 3 sup , the only combination that has the dimension of time is math tau eta nu epsilon 1 2 math which is the Kolmorogov time scale. Similarly, the Kolmogorov length scale is the only combination of math epsilon math and math nu math that has dimension of length. The Kolmogorov 1941 theory is a mean field theory since it assumes that the relevant dynamical parameter is the mean energy dissipation rate. In fluid turbulence , the energy ... microscale Integral length scale Batchelor scale References reflist 2 DEFAULTSORT Kolmogorov Microscales Category Turbulence de Mikroskala von Kolmogorow es Escala de Kolmog rov it Scala di Kolmogorov pt Escala de Kolmogorov ... more details
In mathematics, the Kolmogorov integral or Kolmogoroff integral is a general integral introduced by harvs txt last Kolmogoroff authorlink Andrey Kolmogorov year 1930 including the Lebesgue Stieltjes integral , the Burkill integral , and the Hellinger integral as special cases. References Citation last1 Kolmogoroff first1 A. authorlink Andrey Kolmogorov title Untersuchungen ber den Integralbegriff url http dx.doi.org 10.1007 BF01455714 publisher Springer Berlin Heidelberg doi 10.1007 BF01455714 year 1930 journal Mathematische Annalen issn 0025 5831 volume 103 issue 1 pages 654 696 eom id k k055720 first V. A. last Skvortsov integral Category Definitions of mathematical integration ... more details
one source date April 2012 Infobox football biography image playername Boris Kolmogorov fullname Boris Olegovich Kolmogorov dateofbirth birth date and age 1990 01 12 df yes cityofbirth countryofbirth height height m 1.80 position Midfielder currentclub clubnumber years1 2011 clubs1 FC Sibiryak Bratsk caps1 1 goals1 0 pcupdate 16 59, 21 April 2012 UTC ntupdate Boris Olegovich Kolmogorov lang ru born January 12, 1990 is a Russia n association football football midfielder , who last played for FC Sibiryak Bratsk . He made his debut in the Russian Second Division for FC Sibiryak Bratsk on September 28, 2011 in a game against FC Metallurg Kuzbass Novokuznetsk . ref cite web publisher Russian Football Union url http www.rfspro.ru cgi bin player script2.cgi?par1 116472 title Career Summary date 21 April 2012 ref References Reflist External links http news.sportbox.ru Vidy sporta Futbol stats man 1218099992 Career summary by sportbox.ru DEFAULTSORT Kolmogorov, Boris Category 1990 births Category Living people Category Russian footballers Russia footy midfielder 1990s stub ... more details
In probability theory , Kolmogorov s criterion , named after Andrey Kolmogorov , is a theorem in Markov process es concerning stationary Markov chain s i.e. ones with stationary transition probabilities, also called Markov chain Variations time homogeneous Markov chains . The theorem states that such a chain is time reversibility reversible if and only if its transition probabilities or rates for a continuous chain satisfy math p j 1 j 2 p j 2 j 3 cdots p j n 1 j n p j n j 1 p j 1 j n p j n j n 1 cdots p j 3 j 2 p j 2 j 1 math for all finite sequences of states math j 1, j 2, ldots, j n in S . math Here p sub ij sub are elements of the transition matrix P and S is the state space of the chain. Explanation File Kolmogorov criterion.png Consider this figure depicting a section of a CTMC with states i, j, k and l and the corresponding transition rates. Here Kolmogorov s criterion implies that the product of rates when traversing through any closed loop must be equal. For example, from i j k l i, the rate product is math q ij q jk q kl q li math . On the other hand, the rate through i l k j i, the product rate is math q il q lk q kj q ji math . The criterion says that the CTMC is Reversible Markov process reversible if and only if it satisfies the above equality. Notes references See also Kolmogorov s generalized criterion Category Markov processes ... more details
a subfield of computer science , the Kolmogorov complexity of an object, such as a piece of text ... Russian mathematician Andrey Kolmogorov . Kolmogorov complexity is also known as descriptive complexity ... of decision problems by their expressibility as logical formulae. ref Kolmogorov Gregory Chaitin ... of the Mandelbrot set and the coordinates of the corners of the image. Thus, the Kolmogorov ... language is discussed below. It can be shown that the Kolmogorov complexity of any string cannot be more than a few bytes larger than the length of the string itself. Strings whose Kolmogorov complexity is small relative to the string s size are not considered to be complex. The notion of Kolmogorov ... theorem and halting problem Turing s halting problem . Definition To define Kolmogorov complexity, we ... is the Kolmogorov complexity of s , written K s . Symbolically, math K s d s . quad math We now consider ... theory is the area of computer science that studies Kolmogorov complexity and other complexity measures on strings or other data structure s . The concept and theory of Kolmogorov Complexity is based ... 254 month June year 1964 ref Andrey Kolmogorov later multiple discovery independently published this theorem ... 1966, revised in December 1968 and cites both Solomonoff s and Kolmogorov s papers. ref cite journal .... Kolmogorov used this theorem to define several functions of strings complexity, randomness, and information. When Kolmogorov became aware of Solomonoff s work, he acknowledged Solomonoff s priority ref cite journal last1 Kolmogorov first1 A. title Logical basis for information theory and probability ..., was to associate this type of complexity with Kolmogorov, who was concerned with randomness of a sequence ... of Kolmogorov complexity or algorithmic information. The most widely used one is based on self delimiting program s and is mainly due to Leonid Levin 1974 . An axiomatic approach to Kolmogorov complexity ... by Andrey Kolmogorov Burgin 1982 . Some consider that naming the concept Kolmogorov complexity ... more details
that can be placed on a topological space. The Kolmogorov quotient Topological indistinguishability ... the Kolmogorov quotient of X , which we will denote KQ X . Of course, if X was T sub 0 sub to begin with, then KQ X and X are natural category theory natural ly homeomorphic . Categorically, Kolmogorov spaces are a reflective subcategory of topological spaces, and the Kolmogorov quotient is the reflector. Topological spaces X and Y are Kolmogorov equivalent when their Kolmogorov quotients are homeomorphic ... and Y are Kolmogorov equivalent, then X has such a property if and only if Y does. On the other hand ... 0 sub space with the same structures and properties by taking the Kolmogorov quotient. The example of L ... with this topology. When we form the Kolmogorov quotient, the actual L sup 2 sup R , these structures ... mechanics generally want to study. Note that the notation L sup 2 sup R usually denotes the Kolmogorov ... if and only if the Kolmogorov quotient KQ X is Hausdorff. This is a sensible, albeit less ... be added or removed arbitrarily using the concept of Kolmogorov quotient. External links http www.mathematik.tu ... Properties of topological spaces ar ca Espai de Kolmogorov de Kolmogoroff Raum es Espacio de Kolmog rov ko T0 it Spazio T0 nl Kolmogorov ruimte pl Przestrze T0 pt Espa o de Kolmogorov ... more details
In probability theory , Kolmogorov s inequality is a so called maximal inequality mathematics inequality that gives a bound on the probability that the partial sum s of a Finite set finite collection of independent random variables exceed some specified bound. The inequality is named after the Russia n mathematician Andrey Kolmogorov . Citation needed date May 2007 Statement of the inequality Let X sub 1 sub , ..., X sub n sub R be Statistical independence independent random variable s defined on a common probability space , F , Pr , with expected value E X sub k sub 0 and variance Var X sub k sub < for k 1, ..., n . Then, for each > 0, math Pr left max 1 leq k leq n S k geq lambda right leq frac 1 lambda 2 operatorname Var S n equiv frac 1 lambda 2 sum k 1 n operatorname Var X k , math where S sub k sub X sub 1 sub ... X sub k sub . Proof The following argument is due to Kareem Amin and employs discrete martingale s. As argued in the discussion of Doob s martingale inequality , the sequence math S 1, S 2, dots, S n math is a martingale. Without loss of generality , we can assume that math S 0 0 math and math S i geq 0 math for all math i math . Define math Z i i 0 n math as follows. Let math Z 0 0 math , and math Z i 1 left begin array ll S i 1 & text if displaystyle max 1 leq j leq i S j lambda Z i & text otherwise end array right. math for all math i math . Then math Z i i 0 n math is a also a martingale. Since math S i S i 1 math is independent and mean zero, math begin align sum i 1 n text E S i S i 1 2 & sum i 1 n text E S i 2 2 S i S i 1 S i 1 ... s inequality Doob s martingale inequality Etemadi s inequality Landau Kolmogorov inequality Markov ... xviii 509 PlanetMath attribution id 3687 title Kolmogorov s inequality Category Probability theory ... de Kolmogorow Ungleichung fr In galit de Kolmogorov km pl Nier wno Ko mogorowa ... more details
Backward induction is the process of reasoning backwards in time, from the end of a problem or situation, to determine a sequence of optimal actions. It proceeds by first considering the last time a decision might be made and choosing what to do in any situation at that time. Using this information, one can then determine what to do at the second to last time of decision. This process continues backwards until one has determined the best action for every possible situation i.e. for every possible information set at every point in time. In the mathematical optimization mathematics optimization method of dynamic programming , backward induction is one of the main methods for solving the Bellman equation . ref Jerome Adda and Russell Cooper, Dynamic Economics Quantitative Methods and Applications ... Economics and Finance , Section 7.3.1, page 164. MIT Press, 2002. ref In game theory , backward ... of automated planning and scheduling and automated theorem proving , the method is called backward search or backward chaining . In chess it is called retrograde analysis . Backward induction has ... Morgenstern suggested solving zero sum , two person games by backward induction in their Theory of Games ... Mathematics of Chess , webpage by John MacQuarrie. ref An example of decision making by backward ... to contexts like shopping, job search, and marriage. An example of backward induction in game theory ... Nash equilibria which are not subgame perfect. See also centipede game . Backward induction and economic ... equilibrium can be eliminated by backward induction. A paradox of backward induction The unexpected hanging paradox is a paradox related to backward induction. Suppose a prisoner is told that she will be hanged ... next week. To her surprise, she is hanged on Wednesday. Here the prisoner reasons by backward induction ... assumes it is possible to surprise someone who is performing backward induction. The mathematical theory of backward induction does not make this assumption, so the paradox does not call into question ... more details
In a data transmission circuit a backward channel is the channel that passes data in a direction opposite to that of its associated forward channel . The backward channel is usually used for transmission of request, supervisory, acknowledgement data networks acknowledgement , or error control signals. The direction of flow of these signals is opposite to that in which user information is being transferred. The backward channel Bandwidth computing bandwidth is usually less than that of the primary channel, that is, the forward user information channel communications channel . For example, Asymmetric Digital Subscriber Line ADSL s upstream channel, considered a backward channel for some types of analysis, typically has a bandwidth less than one fourth of the downstream channel. In data transmission , it is a secondary channel in which the direction of transmission is constrained to be opposite to that of the primary, i.e. , the forward user information channel. The direction of transmission in the backward channel is restricted by the control interchange circuit that controls the direction of transmission in the primary channel . See also Return channel Source Partly from Federal Standard 1037C and from MIL STD 188 Category Telecommunications terms telecomm stub ... more details
Image Backward diode.svg right frame The schematic symbol for the backward diode, ref cite book title Newnes Dictionary of Electronics author Stanley William Amos, Roger S. Amos publisher Newnes year 1999 isbn 0750643315 url http books.google.com books?id c4qHqtC9JkgC&pg PA22&dq backward diode symbol&lr &as brr 3&ei cMKbR8nHI5u8swOzqYGrCg&sig IsGtLx01PJY K5YnLAwFO Z9hXU ref annotated to show which side is P type and which is N current flows most easily from N to P, backward relative to the arrow. In semiconductor device s, a backward diode is a variation on a Zener diode or tunnel diode having a better conduction for small reverse biases for example 0.1 to 0.6 V than for forward bias voltages. The reverse current in such a diode is by tunneling, which is also known as the Zener effect. ref cite book title A First Course in Electronics author Anwar A. Khan and Kanchan K. Dey publisher Prentice Hall of India year 2006 isbn 8120327764 url http books.google.com books?id MgAXj7xKnNgC&pg PA111&dq backward diode tunnel zener&lr &as brr 3&ei MrebR j3IInUsgOjgqWiCg&sig wr0axvXDkxMUNsyKP9XEk3OkE5M PPA111,M1 ref ref name Kakani cite book title Electronics Theory and Applications author S.L. Kakani ...&pg PA50&dq backward diode tunnel zener effect&lr &as brr 3&ei JcCbR5b K5rUswPL9PWqCg&sig KqttpNGPIenUehLSAGqIXDo2aik ...&pg PA284&dq backward diode tunneling&lr &as brr 3&ei WcGbR72DL4qKsgOy6vCiCg&sig dP6h5WEmFU7IMPE1N9d9J1ywOjE PPA283,M1 ref Current voltage characteristics of backward diode The forward I V characteristic ... relatively constant independent of current when it is connected in reverse bias. The backward ... to the reverse current of a conventional diode. Applications of backward diodes Detector Since ... signal characteristic, the backward diode can be used as a detector up to 40 GHz. Rectifier A backward diode can be used for rectifying weak signals with peak amplitudes of 0.1 to 0.7 V. Switch Backward ... Backward Diode pl Dioda wsteczna ru ... more details
Multiple issues unreferenced December 2009 howto August 2009 Backward design is a method of designing curriculum by setting goals before choosing activities or content to teach. The idea is to teach towards those goals, which ensures that the content taught remains focused and organized, promoting a better understanding for students. Backward Design is a term coined by Grant Wiggins in his book, Understanding by Design 1999, 1st ed. . The concept of Backward Design was based upon a concept first utilized by contractors to the Department of the Navy in the late 1970 s. It was enhanced and refined by Landmark Education in 1991. Retitled Structure for Fulfillment, it became the cornerstone of their leadership training program, the Team Management and Leadership Program. Backward design challenges the traditional methods of curriculum planning. In traditional curriculum planning, one sits down and write down the list of content that will be taught. Citation needed date August 2009 In backward design, one starts with goals, then Educational assessment assessments and finally lesson plan s. A metaphor used by proponents of backward design is a roadmap with backward design, one chooses the destination first and then follows the map to go directly there. With traditional curriculum planning, one just hits the road hoping to reach the final destination if it is even defined . Steps of backward design Established goals First the educator chooses the goals of the curriculum or the unit to be taught. This is divided in five sections The established goals usually national or local standards ... will be able to... Assessment The second part of curriculum planning with backward design is finding an assessment. This is usually the most difficult part for traditional educator s switching to backward ... that it does not fit the goals set out by the team. In backward design, educators approach ... is assessed properly. References reflist DEFAULTSORT Backward Design Category Education related ... more details
Citations missing date November 2008 Backward running , also known as backwards running , running backwards , reverse running , retro running , or retro locomotion is the act of running in reverse, so ... and Marcha reversiva . Backward running is a less natural motion, but can be accomplished with some speed with practice. It is better to start out backward walking also called retropedaling , which is relatively ... that someone learn how to drop into a backward wikt roll roll before attempting it, to deal with any ... running, than when running level ground, so it can be done more instinctively. This applies to backward ... or in the way of his or her path. Unlike forward running, it is also much more difficult to brace a backward ... or stopping falls. Physical benefits The combination of normal running forward running and backward ... down, raises front of foot more as a prime mover than a shock absorber. When running backward ... power. While downhill backward running is essentially the reverse of uphill running, and uphill backward ... lifters perform both for set times. With all forms there is an obvious backward lean relative to normal ... advantages to backward running are a reduction in fear related to the movement, a form of exercise ... could lead to adaptations in them. Backward running adds another dimension to running, and when complemented ... July 2011 http www.reverserunning.com London Backward Running Championships , Crystal Palace, South London Sunday 14th August 2011 http www.reverserunning.com 2nd UK Backward Running Championships , Heaton ... 22 08 2010 1st UK Backward Running Championships, Manchester Winner was Garret Doherty of Eire Film ... Level and Incline Running References reflist External links http www.pyroenergen.com articles backward running.htm Backward Running and Walking in Japan http darkwing.uoregon.edu btbates backward ... http www.reverserunning.com Reverse Running http www.reverserunning.com Backward Running UK and UK Backward Running Championships http www.retrorunning.org Germany and World Championship http ... more details
Refimprove date March 2011 Backward chaining or backward reasoning is an inference method that can be described in lay terms as working backward from the goal s . It is used in automated theorem prover s, proof assistant s and other artificial intelligence applications, but it has also been observed in primates. In game theory , its application to simpler subgame s in order to find a solution to the game is called backward induction . In chess, it is called retrograde analysis , and it is used to generate tablebases for chess endgame s for computer chess . Backward chaining is implemented in logic programming by SLD resolution . Both rules are based on the modus ponens inference rule. It is one of the two most commonly used methods of reasoning with inference rule s and logical implications the other is forward chaining . Backward chaining systems usually employ a depth first search strategy, e.g. Prolog . ref name CheinMugnier2009 cite book author1 Michel Chein author2 Marie Laure Mugnier ... 297 ref How it works Backward chaining starts with a list of Objective goal goal s or a hypothesis ... using backward chaining would search the inference rules until it finds one which has a consequent ... four rules Image Backward Chaining Frog Color Example.png upright 0.56 thumb alt An Example of Backward Chaining. An Example of Backward Chaining. If X croaks and eats flies Then X is a frog If X ... , in contrast to data driven data driven forward chaining forward chaining inference. The backward ... Machine and ECLiPSe support backward chaining within their inference engines. ref name Programming Languages See also Backward induction Forward chaining Opportunistic reasoning Working backward from the goal References references ref name Norwig Definition Definition of backward chaining ... that support backward chaining Harvnb Russell Norvig 2009 p 339 ref references Other sources ... . External links http www.j paine.org students lectures lect3 node12.html Backward chaining example ... more details
chess notation Chess diagram tright pd pd pl Black s c6 pawn is a typical example of a backward pawn. In chess , a backward pawn is a pawn chess pawn that is behind the pawns of the same color on the adjacent Chess terminology File files and that cannot be advanced without loss of material, usually the backward pawn itself. In the diagrammed position, the Black pawn on the c6 square is backward. Backward pawns are usually a positional disadvantage, since they are hard to defend. Also, the opponent can place a piece, usually a knight, on the Chess terminology Hole hole in front of the pawn without any risk of a pawn driving it away. The backward pawn also prevents the black rook chess rooks and queen chess queen on the eighth rank from attacking the piece placed on the hole. If the backward pawn is on a half open file , as in this case, the disadvantage is much larger, as it can be more easily attacked by an opponent s rook or queen on the c file. Pieces can become weak when they are devoted to protecting a backward pawn because they are obligated to defend the pawn and cannot be developed for other uses. Chess diagram tright rd bd qd kd bd rd pd pd pd pd pd nd pd nd nl pd pl nl pl pl pl pl pl pl rl bl ql kl bl rl after Black has played 6...d6 Modern opening theory features several openings in which one of the players deliberately takes on a backward pawn in exchange for some other advantage such as the initiative or better Chess terminology Develop development . An excellent example is the Sicilian Defence Sveshnikov Variation 4...Nf6 5.Nc3 e5 Sveshnikov Variation of the Sicilian Defence . After the moves 1.e4 c5 2.Nf3 Nc6 3.d4 cxd4 4.Nxd4 Nf6 or 4...e5 ? 5.Nb5 d6 the Kalashnikov Variation 5.Nc3 e5 ? 6.Ndb5 d6 Diagram above , Black has a backward pawn on d6, but White now has to endure a displacement of his knights and an undermining of his center after 7.Bg5 a6 8.Na3 b5 9.Bxf6 gxf6 10.Nd5 dodging the threatened pawn fork of the knights 10...f5 or 10...Bg7 11.c3 facilitating ... more details
is said to be backward or downward compatible if it can work with input generated by an older device. ref cite web url http www.yourdictionary.com computer backward compatible title backward compatible ..., read, view or play older standards or formats, then the product is said to be backward compatible ... standard. For example, the introduction of FM stereo transmission allowed backward compatibility ... from a new transmitter. In programming languages, backward compatibility refers to the ability of a compiler ..., if previous versions N 1, N 2, etc. were also backward compatible, which is often the case ..., the latest one that was not backward compatible. However, in practice, features are often deprecated and support is dropped in a later release, which is yet thought of as backward compatible. In other contexts, a product or a technology is said to be backward compatible when it is able ... said to be backward compatible with its predecessor if every message or file that is valid under ... Backward compatibility is a relationship between two components, rather than being an attribute of just one of them. More generally, a new component is said to be backward compatible if it provides all of the functionality of the old component. Citation needed date March 2009 Backward compatibility ... spoken of as backward compatibility but is instead just compatible &mdash a consistent interface ... of a program that creates document files, a new version of that program v2 is said to be backward ... save files that can be read by the older version, it is not backward compatible with the older version ... backward compatibility. Bugwards Compatible If a newer system is attempting to achieve integration ... The NTSC color broadcast system was engineered by RCA to be backward compatible with black and white ... standard . Numerous video game consoles are backward compatible and are able to play the games created for predecessor consoles The Atari 7800 is backward compatible with almost all Atari 2600 games ... more details
about equations in mathematics the chemistry term chemical equation Image First Equation Ever.png thumb ... of Witte by Robert Recorde 1557 . An equation is a mathematics mathematical Proposition ... . ref cite web url http dictionary.reference.com browse equation title Equation work Dictionary.com ..., a , b , c , d , . The process of expressing the unknowns in terms of the knowns is called Equation solving solving the equation . In an equation with a single unknown, a value of that unknown for which the equation is true is called a solution or root of the equation. In a set simultaneous equations ... and quantities involved. Important types include An algebraic equation is an equation involving ... . A linear equation is an algebraic equation of degree one. A Polynomial Polynomial equations polynomial equation is an equation in which a polynomial is set equal to another polynomial. A transcendental equation is an equation involving a transcendental function of one of its variables. A functional equation is an equation in which the unknowns are Function mathematics functions rather than simple quantities. A differential equation is an equation involving derivative s. An integral equation is an equation involving integral s. A Diophantine equation is an equation where the unknowns are required to be integer s. A quadratic equation Identities One use of equations is in mathematical identity ..., they can be equation solving solved to find the values that satisfy the equality. For example, consider the following. math x 2 x 0 ,. math The equation is true only for two values of x , the solutions of the equation. In this case, the solutions are math x 0 math and math x 1 math . Many mathematicians ref name Nahin reserve the term equation exclusively for the second type, to signify an equality ..., math x 1 2 x 2 2x 1 , math is an identity, while math x 1 2 2x 2 x 1 , math is an equation with solutions math x 0 math and math x 1 math . Whether a statement is meant to be an identity or an equation ... more details
Infobox Film name The Dark Backward image TheDarkBackward.jpg caption The Dark Backward theatrical poster director Adam Rifkin producer Brad Wyman br Cassian Elwes writer Adam Rifkin starring Judd Nelson br Bill Paxton br Wayne Newton br Lara Flynn Boyle br James Caan actor James Caan br Rob Lowe music Marc David Decker cinematography Joey Forsyte editing Peter Schink distributor David Whitten Greycat Films released July 26, 1991 runtime 101 min. country United States language English language English The Dark Backward is a 1991 Satire satirical comedy film directed and written by Adam Rifkin . Plot summary Marty Malt Judd Nelson is an unhappy garbage man who moonlights as an atrociously unfunny standup comic . He lives in a dark, grimy, garbage strewn urban netherworld, where a company named ... Box office The Dark Backward performed extremely poorly during its limited run, making only 28,654. ref cite news title The Dark Backward work Box Office Mojo pages language publisher date url http www.boxofficemojo.com ... Tomatoes based on 11 reviews 5 positive, 6 negative . ref http www.rottentomatoes.com m dark backward The Dark Backward Rotten Tomatoes profile ref Janet Maslin of the New York Times criticized the film ... Review The Dark Backward A Garbage Man With Aspirations New York Times Review The Dark Backward ... m dark backward reviews Dark Backward reviews Rotten Tomatoes reviews ref Not all reviews were negative ... it as Odd and twisted, The Dark Backward has plenty to thrill admirers of ugliness and enough food for thought to interest the rest of us too. ref http www.rottentomatoes.com m dark backward reviews Dark Backward reviews Rotten Tomatoes reviews ref References reflist External links imdb title id 0101660 title The Dark Backward amg movie id dark backward special edition 99353 title The Dark Backward Adam Rifkin DEFAULTSORT Dark Backward, The Category 1991 films Category American films Category ... Category Independent films Category Satirical films Category 1990s comedy films pt The Dark Backward ... more details
Infobox book See Wikipedia WikiProject Novels or Wikipedia WikiProject Books name Looking Backward 2000 ... Backward 2000 1887 author Edward Bellamy illustrator cover artist country United States language English ... vii, 470 pp isbn NA preceded by followed by Equality book Equality Looking Backward 2000 1887 is a utopia ... published in 1887 in literature 1887 . According to Erich Fromm , Looking Backward is one of the most remarkable books ever published in America . ref name qlfjpt Edward Bellamy, Looking Backward ... Backward , p. vi. ref In the United States alone, over 162 Bellamy Clubs sprang up to discuss and propagate the book s ideas. ref cite book last Bellamy first Edward title Looking backward 2000 ... or the economy in detail, commentators frequently compare Looking Backward with actual economic ... Backward shares relationships and resemblances with several earlier works most notably the anonymous ... Bellamy s Looking Backward , Yellow Springs, Ohio, privately printed, 1944. ref Critic R. L. Shurter has gone as far as to argue that Looking Backward is actually a fictionalized version of The Co ... 1900 , New York, AMS Press, 1975 p. 177. ref Reaction and sequels main List of sequels to Looking Backward ... touched upon in Looking Backward . The success of Looking Backward provoked a spate of sequels, parodies ... A partial list includes Looking Further Forward An Answer to Looking Backward by Edward Bellamy 1890 , by Richard C. Michaelis Looking Backward and What I Saw 1890 , by W. W. Satterlee Looking Further Backward 1890 , by Arthur Dudley Vinton Speaking of Ellen 1890 , by Linn Boyd Porter Looking Beyond ... Looking Within The Misleading Tendencies of Looking Backward Made Manifest 1893 , by J. W. Roberts Young West A Sequel to Edward Bellamy s Celebrated Novel Looking Backward 1894 , by Solomon Schindler ... by the subtitle of Geissler s 1891 Looking Beyond , which is A Sequel to Looking Backward by Edward ... of Biesterfeld, p.301f. ref Later responses Looking Backward was rewritten in 1974 by American ... more details
context date January 2008 Backward inhibition is a theory of sequential task control that asserts switching between tasks requires the just completed task to be suppressed to allow a new task to be completed. Support from the theory comes from research which has observed larger response times when returning to a task after an intermediate task than when completing three, or more, different tasks in a row. For example, for tasks A, B, and C the response times for the third task will be slower in the case of an A B A sequence than a C B A sequence. In a series of experiments it was shown that this inhibitory process is not the result of priming Mayr & Keele, 2000 . References Mayr, U., & Keele, S. W. 2000 . Changing internal constraints on action The role of backward inhibition. Journal of Experimental Psychology General, 129, 4 26. Category Experimental psychology cognitive psych stub ar ... more details
Backward masking has several meanings The original meaning of the term, in psychoacoustics , refers to temporal masking of quiet sounds that occur moments before a louder sound. A similar meaning, in use in cognitive psychology , refers to a phenomenon wherein presenting one visual Stimulus physiology stimulus a mask or masking stimulus immediately after another brief 50 ms target visual stimulus leads to a failure to consciously perceive the first stimulus. ref name scholarpedia Breitmeyer, B.G. and Ogmen, H. 2007 http www.scholarpedia.org article Visual masking Visual masking , Scholarpedia, 2 7 3330. ref A similar phenomenon can occur when a masking stimulus precedes a target stimulus rather than following it this is known as forward masking . ref name scholarpedia While not consciously perceived, the masked stimulus can nevertheless still have an effect on cognitive processes such as Context language use context interpretation. It has been shown that visually masked stimuli can elicit motor responses in simple reaction time tasks e.g., Response Priming independent of their conscious visibility. ref Vorberg, D., Mattler, U., Heinecke, A., Schmidt, T., & Schwarzbach, J. Different time courses for visual perception and action priming. In Proceedings of the National Academy of Sciences USA , Nr. 100, 2003, p. 6275 6280. ref It is a widespread belief that masked stimuli can be used for psychological manipulation see subliminal messages , psychorama . However, the empirical evidence for subliminal stimuli subliminal persuasion is limited. In popular music, backward masking incorrectly refers to backmasking , or hiding messages in sound recordings that are audible when played backward. References reflist disambig ... more details
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