Weasel date June 2010 A stochasticcontextfreegrammar SCFG also probabilistic contextfreegrammar , PCFG is a contextfreegrammar in which each production is augmented with a probability. The probability of a derivation parse is then the product of the probabilities of the productions used in that derivation thus some derivations are more consistent with the stochasticgrammar than others. SCFGs extend contextfree grammars in the same way that hidden Markov model s extend regular grammar s. SCFGs have application in areas as diverse as Natural language processing to the study of RNA molecules. SCFGs are a specialized form of weighted contextfreegrammar s. Techniques A variant of the CYK algorithm finds the Viterbi algorithm Viterbi parse of a sequence for a given SCFG. The Viterbi parse is the most likely derivation parse of the sequence by the given SCFG. The Inside and Outside algorithms ... Rfam Database DEFAULTSORT StochasticContextFreeGrammar Category Bioinformatics Category Formal ... of this base pairing can be represented in a contextfreegrammar the major exception being pseudoknot s . For example, consider the following grammar, where a,c,g,u represents nucleotides and S is the start ... processing Contextfree grammars were originally conceived in an attempt to model natural languages ... and thereby their performance. Citation needed date June 2010 RNA Contextfree grammars are adept at modeling ... of how consistent the sequence is with the given grammar. The Inside outside algorithm Inside ... this idea with SCFGs. Here is a tiny example of a 2 rule PCFG grammar. Each rule is preceded by a probability ... this grammar, we can now say that the number of NPs expected while deriving VPs is 0.7 x 1 0.3 x 2 ... of grammar including a complete conceptual lexicon in certain versions were hardwired from birth ... the grammar. One may construct a probabilistic grammar from a traditional formal syntax by assigning ... grammar Minimalist Grammars have been used to compute information theoretic entropy values which ... more details
A weighted contextfreegrammar WCFG is a contextfreegrammar where each production has a numeric weight associated with it. The weight of a parse tree in a WCFG is the weight of the rule used to produce the top node, plus the weights of its children. A special case of WCFGs are stochasticcontextfreegrammar s, where the weights are logarithm s of probability probabilities . An extended version of the CYK algorithm can be used to find the lightest least weight derivation of a string given some WCFG. comp sci theory stub Category Formal languages hr Te inska kontekstno neovisna gramatika ja ru ... more details
Synchronous contextfree grammars SynCFG or SCFG not to be confused with Stochasticcontextfreegrammarstochastic CFGs constitute a formal model of natural language syntax , developed in the area of statistical machine translation MT . The theory of SynCFGs borrows from syntax directed transduction and syntax based machine translation , modeling the reordering of clauses that occurs when translating a sentence by correspondences between phrase structure rules in the source and target languages. Performance of SCFG based MT systems has been found comparable with, or even better than, state of the art phrase based machine translation systems. ref name Chiang cite journal last1 Chiang first1 David year 2007 title Hierarchical phrase based translation journal Computational Linguistics journal Computational Linguistics volume 33 number 2 pages 201 228 ref Several algorithms exist to perform translation using SynCFGs. ref cite conference last1 Venugopal first1 Ashish last2 Zollmann first2 Andreas last3 Vogel first3 Stephan year 2007 title An efficient two pass approach to Synchronous CFG driven statistical MT booktitle Proc. NAACL HLT pages 500 507 ref Formalism Rules in a SynCFG are superficially similar to CFG rules, except that they specify the structure of two phrases at the same time one in the source language the language being translated and one in the target language. Numeric indices indicate correspondences between non terminals in both constituent trees. Chiang ref name Chiang gives the Chinese English example math X to math yu math X 1 math you math X 2 math , have math X 2 math with math X 1 math Software http cdec decoder.org cdec , MT decoding package that supports SynCFGs References references Category Formal languages Category Machine translation Category Natural language parsing Category Statistical natural language processing ... more details
Parsing expression grammarStochasticcontextfreegrammarContextfreegrammar generation algorithms ...In formal language theory , a contextfreegrammar CFG is a formal grammar in which every Production ... grammar to refer to contextfree grammars. In computer science , a popular notation for context ... such cases can be explained in an alternative way that doesn t assume overlap. A contextfreegrammar ... of the contextfreegrammar, but the basic recursive structure of sentences, the way in which ... s generative grammar framework, the syntax of natural language was described by a contextfree ... Generalized Phrase Structure Grammar Gazdar et al. 1985 , contextfree grammars were taken to be the mechanism ..., as a consequence, also featured a contextfreegrammar to describe the resulting Algol syntax. This became ... to grammar that the terms syntax and grammar are often identified with contextfreegrammar ... Rightarrow u 2 cdots Rightarrow u k Rightarrow v math Contextfree language The language of a grammar ... , such that math L , ,L G math . Proper CFGs A contextfreegrammar is said to be proper , if it has ... of a contextfreegrammar is parenthesis matching, which is representative of the general case. There are two ... in that grammar However, there is no contextfreegrammar for generating all sequences of two different ... while the original grammar did not. Algebraic expressions Here is a contextfreegrammar for syntactically ... examples Example 1 A contextfreegrammar for the language consisting of all strings over a,b ... rules for the terms and formulas of formal logic fit the definition of contextfreegrammar, except ... Kumar Ravindranath date 2003 08 22 title ContextFreeGrammar for Natural Language Constructs An implementation ... grammars such languages are called inherently ambiguous. Normal forms Every contextfreegrammar ... rule. Every contextfreegrammar with no production has an equivalent grammar in Chomsky ... for contextfree grammars e.g. the emptiness problem whether the grammar generates any terminal ... more details
Generalized ContextfreeGrammar GCFG is a grammar formalism that expands on contextfree grammars by adding potentially non contextfree composition functions to rewrite rules. ref name weir1988 Weir, David H. 1988. Characterizing mildly context sensitive grammar formalisms. Dissertation, U Penn. ref Head grammar and its weak equivalents is an instance of such a GCFG which is known to be especially adept at handling a wide variety of non CF properties of natural language. Description A GCFG consists of two components a set of composition functions that combine string tuples, and a set of rewrite rules. The composition functions all have the form math f langle x 1, ..., x m rangle, langle y 1, ..., y n rangle, ... gamma math , where math gamma math is either a single string tuple, or some use of a potentially different composition function which reduces to a string tuple. Rewrite rules look like math X to f Y, Z, ... math , where math Y math , math Z math , ... are string tuples or non terminal symbols. The rewrite semantics of GCFGs is fairly straight forward. An occurrence of a non terminal symbol is rewritten using rewrite rules as in a contextfreegrammar, eventually yielding just compositions composition functions applied to string tuples or other compositions . The composition ... A simple translation of a contextfreegrammar into a GCFG can be performed in the following fashion. Given the grammar in 1 , which generates the palindrome language math ww R w in a, b math , where ... Generalized ContextFreeGrammar Category Formal languages Category Grammar frameworks ... rangle, langle a rangle math math langle abbbba rangle math Linear Contextfree Rewriting Systems LCFRSs ... f x g x, y math or math f x, y g x math . A grammar in which all composition functions are both linear and regular is called a Linear Contextfree Rewriting System LCFRS , a subset of the GCFGs with strictly ... Tree adjoining grammar s. Head grammar is an example of an LCFRS that is strictly less powerful ... more details
In formal grammar theory, the deterministic contextfree grammars DCFGs are a proper subset of the contextfree grammars . The deterministic contextfree grammars are those a deterministic pushdown automaton can recognize. A DCFG is the finite set of rules defining the set of well formed expressions in some deterministic contextfree language . History In the 1960s, theoretic research in computer science on regular expressions and finite automata led to the discovery that contextfree grammars are equivalent to pushdown automata . These grammars were thought to capture the syntax of computer programming languages. The first computer programming languages were under development at the time see History of programming languages and writing compilers was difficult. But using contextfree grammars to help automate the parsing part of the compiler simplified the task. Deterministic contextfree grammars were particularly useful because they could be parsed sequentially, which was a requirement due to computer memory constraints. ref cite book editors A Salomaa & D Wood & S Yu title A Half Century of Automata Theory year 2001 publisher World Scientific Publishing Co. Pte. Ltd pages 38 39 ref Uses LALR parsers, which use a subset of DCFGs, have practical value as program code validators. Given the formal rules of a DCFG, these parsers efficiently ensure a program can be generated from those rules. In fact, this syntax validation is one of the operations a compiler performs. need to state the two restrictions for determinism, can t figure out how to express it simply Limitations Since DCFGs are a proper subset of CFGs, they are of less descriptive power than some CFGs. See also Deterministic parsing LR parser LL parser References references Formal languages and grammars Category Formal languages hr Deterministi ka kontekstno neovisna gramatika sr zh ... more details
A stochasticgrammar statistical grammar is a grammar framework with a probabilistic notion of grammaticality Stochasticcontextfreegrammar Statistical parsing Data oriented parsing Hidden Markov model Estimation theory Statistical natural language processing uses stochastic , probabilistic and statistical methods, especially to resolve difficulties that arise because longer sentences are highly ambiguous when processed with realistic grammars, yielding thousands or millions of possible analyses. Methods for disambiguation often involve the use of corpus linguistics corpora and Markov model s. A probabilistic model consists of a non probabilistic model plus some numerical quantities it is not true that probabilistic models are inherently simpler or less structural than non probabilistic models. ref John Goldsmith. 2002. Probabilistic Models of Grammar Phonology as Information Minimization. Phonological Studies 5 21&ndash 46. ref The technology for statistical NLP comes mainly from machine learning and data mining , both of which are fields of artificial intelligence that involve learning from data. See also Colorless green ideas sleep furiously Computational linguistics Refimprove date March 2011 More footnotes date March 2011 References references Further reading Christopher D. Manning, Hinrich Sch tze Foundations of Statistical Natural Language Processing , MIT Press 1999 , ISBN 978 0262133609. Stefan Wermter, Ellen Riloff, Gabriele Scheler eds. Connectionist, Statistical and Symbolic Approaches to Learning for Natural Language Processing , Springer 1996 , ISBN 978 3540609254. Category Grammar frameworks Category Statistical natural language processing Category Probabilistic models ling stub nl Stochastische grammatica ... more details
Contextfree may refer to Concepts contextfreegrammar deterministic contextfreegrammarstochasticcontextfreegrammar weighted contextfreegrammarcontextfree language Software ContextFree , a computer language for contextfree grammars disambig ... more details
be replaced with or not. This is different from a contextfreegrammar where the context of a nonterminal is not taken into consideration. Indeed, every production of a contextfreegrammar is of the form ... are feasible, such as tree adjoining grammar s, combinatory categorial grammar s, coupled contextfree language s, and linear contextfree rewriting system s. The languages generated by these formalisms properly lie between the contextfree and context sensitive languages. See also Chomsky hierarchy ...A context sensitive grammar CSG is a formal grammar in which the left hand sides and right hand sides of any production rule s may be surrounded by a context of terminal symbol terminal and nonterminal symbol s. Context sensitive grammars are more general than contextfreegrammar s but still orderly enough to be parsing parsed by a linear bounded automaton . The concept of context sensitive grammar ... upon the context. A formal language that can be described by a context sensitive grammar is called a context sensitive language . Formal definition A formal grammar G N , , P , S this is the same ... add that for any production rule of the form u v of a context sensitive grammar, it shall be true that u ... are a proper superset of the contextfree languages, rather than having to make the weaker statement that all contextfree grammars with no productions are also context sensitive grammars. The name ... contextfree language math a n b n c n n ge 1 math math S rightarrow aSBC math math S rightarrow aBC ... the non contextfree copy language, math C x x x in a,b math math S rightarrow Ca CbS aA bB math ... B rightarrow b math Normal forms Every context sensitive grammar which does not generate the empty ... whether a certain string s belongs to the language of a certain context sensitive grammar G , is PSPACE complete . There are even some context sensitive grammars whose fixed grammar recognition ... by is context sensitive if all rules in P are of the form A where A N i.e., A is a single ... more details
The following problems are Undecidable language undecidable for arbitrary contextfreegrammar s A and B ... of contextfree languages The reverse of a contextfree language is contextfree, but the complement need not be. Every regular language is contextfree because it can be described by a regular grammar . The intersection of a contextfree language and a regular language is always contextfree ...In formal language theory , a contextfree language is a formal language language generated by some contextfreegrammar . The set of all contextfree languages is identical to the set of languages accepted by pushdown automaton pushdown automata . Examples An archetypical contextfree language is math ... symbol and math x math means pop action. center Contextfree languages have many applications in programming ... by contextfree grammars. Closure properties Contextfree languages are closure mathematics closed under the following operations. That is, if L and P are contextfree languages, the following languages are contextfree as well the union set theory union math L cup P math of L and P the reversal of L ... of L the language math vu uv in L math Contextfree languages are not closed under complement complexity ... difference . However, if L is a contextfree language and D is a regular language then both their intersection math L cap D math and their difference math L setminus D math are contextfree languages. Nonclosure under intersection and complement The contextfree languages are not closed under ... B a m b n c n mid m,n geq 0 math , which are both contextfree. Their intersection is math A cap B a n b n c n mid n geq 0 math , which can be shown to be non contextfree by the pumping lemma for contextfree languages . Contextfree languages are also not closed under complementation, as for any ... of a contextfree language and a regular language is contextfree, so if math B math were a regular ... problems are decidable for arbitrary contextfree languages is math L A emptyset math ... more details
. The deterministic contextfree languages are exactly those recognized by some LR grammar ref ...A deterministic contextfree language is a formal language which is defined by a deterministic contextfreegrammar . ref cite book last John Hopcroft Hopcroft first John coauthors Jeffrey Ullman title Introduction to automata theory, languages, and computation year 1979 publisher Addison Wesley page 233 ref The set of deterministic contextfree languages is called DCFL ref CZoo Class DCFL D dcfl ref and is identical to the set of languages accepted by a deterministic pushdown automaton . The set of deterministic contextfree languages are a proper subset of the set of contextfree language s that possess an unambiguous contextfreegrammar . For example, the language of even length palindrome s on the alphabet of 0 and 1 has the simple, unambiguous grammar S 0S0 1S1 , but it cannot be parser parsed by a deterministic push down automaton. ref cite book last John Hopcroft Hopcroft first John coauthors Rajeev Motwani & Jeffrey Ullman title Introduction to automata theory, languages, and computation 2nd edition year 2001 publisher Addison Wesley pages 249 253 ref The languages of this class have practical importance in computer science. The complexity of the program and execution of a deterministic pushdown automaton is vastly less than that of a nondeterministic one. In the naive implementation, it must make copies of the stack every time a nondeterministic step occurs. The best known algorithm to test membership in any contextfree language is CYK algorithm Extensions Valiant s algorithm , taking O n sup 2.378 sup time, whereas membership in a deterministic contextfree language can be tested in O n time, ref cite book last Harrison first Michael A. title Introduction to Formal ... contextfree languages can be recognized by a deterministic Turing machine in polynomial ... pushdown language s Greibach s theorem proves that it is undecidable whether a given contextfree ... more details
Multiple issues unreferenced February 2011 incomplete February 2011 The Mirfield FreeGrammar and Sixth Form is a secondary school in the town of Mirfield, West Yorkshire. The school has pretty good grades. Uncategorized date January 2011 Yorkshire school stub ... more details
Primarysources date March 2008 Infobox UK school name Newport FreeGrammar School image size latitude 51.990558 longitude 0.213817 dms dms motto Suffer and Serve motto pl established 1588 approx closed c approx type Comprehensive school Comprehensive religion president head label Headteacher head Sean O Hagan r head label r head chair label chair founder founder pl specialist Language College Language specialist pl y street Bury Water Lane city Newport, Essex Newport county Essex country England flagicon England postcode CB11 3TR LEA Essex ofsted yes urn 115352 staff enrollment approx. 1034 gender mixed sex education Mixed lower age 11 upper age 18 houses houses color box green Frankland color box silver Caius br color box gold Saxie color box red Banstead br color box purple Morden color box royalblue Trappes colours publication free label 1 free 1 free label 2 free 2 free label 3 free 3 website http www.nfgs.essex.sch.uk website name Newport FreeGrammar School , in Newport, Essex Newport , Essex , England was founded in 1588. ref cite web url http www.nfgs.essex.sch.uk tradition.html title Tradition to Technology accessdate 2007 01 11 publisher Newport FreeGrammar School archiveurl http web.archive.org web 20061009140720 http www.nfgs.essex.sch.uk tradition.html Bot retrieved archive archivedate 2006 10 09 ref The school is a mixed sex education mixed comprehensive school with a sixth form . It previously existed in different forms including a boarding school and a grammar school . The Headteacher is Sean O Hagan and the Deputy headteachers are Kay Turner, Matt Gibson and Mike ... the school as good , Grade 2 on a four point scale. They said blockquote Newport FreeGrammar is a good ...&providerCategoryID 8192&fileName school 115 s5 115352 20060424.pdf Newport FreeGrammar School Inspection ... www.nfgs.essex.sch.uk apps nfgssite title Newport ... the positive choice publisher Newport FreeGrammar School accessdate 2007 01 11 archiveurl http web.archive.org web 20061009135255 http www.nfgs.essex.sch.uk ... more details
Cleanup date July 2009 The pumping lemma for contextfree languages , also known as the Yehoshua Bar Hillel Bar Hillel lemma , is a lemma mathematics lemma that gives a property shared by all contextfree language s. Formal statement If a language L is contextfree, then there exists some integer p 1 ... integer n 0. Informal statement and explanation The pumping lemma for contextfree languages called just the pumping lemma from now on describes a property that all contextfree languages are guaranteed ... p , where p is a constant called the pumping length that varies between contextfree languages. Say ... its name. Note that finite language s which are regular and hence contextfree obey the pumping lemma ... language is non contextfree by showing that for each p , we can find some string s of length at least ... for contextfree languages can be used to show that certain languages are not contextfree. For example, we can show that language math L lbrace a ib ic i i 0 rbrace math is not contextfree by using the pumping lemma in a proof by contradiction . First, assume that math L math is contextfree. By the pumping ... the definition of math L math . Therefore, our initial assumption that math L math is contextfree must be false. While the pumping lemma is often a useful tool to prove that a given language is not contextfree, it does not give a complete characterization of the contextfree languages. If a language does not satisfy the condition given by the pumping lemma, we have established that it is not contextfree. On the other hand, there are languages that are not contextfree, but still satisfy ... 94728 X Section 1.4 Nonregular Languages, pp. 77&ndash 83. Section 2.3 Non contextfree Languages, pp. 115&ndash 119. DEFAULTSORT Pumping Lemma For ContextFree Languages Category Formal languages ... s lemma , but also these techniques do not give a complete characterization of the contextfree languages. See also Pumping lemma for regular languages Formal languages References cite journal ... more details
refimprove date June 2007 Cleanup date September 2010 Wiktionarypar stochasticStochastic from the Greek language Greek for aim or guess means random . A stochastic process is one whose behavior ... which is analyzable in terms of probability deserves the name of stochastic process . Mathematical theory The use of the term stochastic to mean based on the theory of probability has been traced back ... , specifically in probability theory , the field of stochastic process es has been a major area of research. A stochastic matrix is a matrix mathematics matrix that has non negative real number real entries that sum to one in each row. Artificial intelligence In artificial intelligence , stochastic programs work by using probabilistic methods to solve problems, as in simulated annealing , stochastic neural network s, stochastic optimization , and genetic algorithms . A problem itself may be stochastic ... An example of a stochastic process in the natural world is pressure in a gas as modeled by the Wiener ... of molecules will exhibit stochastic characteristics, such as filling the container, exerting equal ... and experimentation generally considered forms of stochastic simulation can be arguably traced back ... of random numbers which had been previously used for statistical sampling. Biology Stochastic resonance In biological systems, introducing stochastic noise has been found to help improve the signal ... also lend themselves to stochastic analysis. Gene expression , for example, is a stochastic process ... polymerase to a promoter resulting from Brownian motion . Medicine Stochastic effect, or chance effect ... of an effect increases with dose. Cancer is a stochastic effect. Stochastic theory of hematopoiesis Geomorphology meander Stochastic theory of meander formation Creativity Simonton 2003, Psych Bulletin argues that creativity in science of scientists is a constrained stochastic behaviour such that new theories in all sciences are, at least in part, the product of a stochastic process . Statistics ... more details
ConTeXt is free software the program code i.e. anything not under the code doc code subtree is distributed ... center 500px ConTeXt document See also Portal Free software LaTeX TeX References Reflist 2 External ..., split, etc. . DEFAULTSORT Context Category Page description languages Category Free TeX software de ...Distinguish ConTEXT Infobox software name ConTeXt logo Image ConTeXt Unofficial Logo.svg The Unofficial ConTeXt logo contextgarden.net logo 200px author Mainly Hans Hagen and http www.pragma ade.com Pragma ... of ConTeXt at contextgarden ref ref http foundry.supelec.fr frs ?group id 14 List of releases of ConTeXt ref ref http foundry.supelec.fr gf project contextrev frs ConTeXt files in Supelec ref operating ... Share Alike 3.0 ref http www.pragma ade.com general manuals mreadme.pdf Readme First license of ConTeXt code and documentation ref website http wiki.contextgarden.net contextgarden ConTeXt is a general ... and automated capabilities of ConTeXt are extensive, including interfaces for handling microtypography ... it easy to create new layouts and styles without learning the low level TeX macro language. ConTeXt .... ConTeXt from the ground up is a typography and typesetting system meant to provide users easy and consistent ... at the same time, ConTeXt s unified design avoids the package clashes that can happen with LaTeX. ref http www.tex.ac.uk cgi bin texfaq2html?label context FAQ of the UK TeX Archive ref ref name whatiscontextwiki http wiki.contextgarden.net What is ConTeXt What is ConTeXt page at contextgarden ref ConTeXt ... As its native drawing engine, ConTeXt integrates a superset of MetaPost called MetaFun ref name whatiscontextwiki ... and ornaments. Metafun can also be used with stand alone MetaPost. ConTeXt also supports the use of other ... generic pgf pgfmanual.pdf PGF TikZ official manual. Version 2.0 . Section 9.1.3 Using the ConTeXt Format . p. 88 ref and PSTricks. ref name list modules http wiki.contextgarden.net Modules List of ConTeXt modules at contextgarden ref ConTeXt also provides a Macro computer science macro package for typesetting ... more details
Wiktionary Wikipedia Books ContextContext may refer to Context language use , the relevant constraints of the communicative situation that influence language use, language variation, and discourse Archaeological context , an event in time which has been preserved in the archaeological record Operational context , a temporarily defined environment of cooperation Computing Context computing , the virtual environment required to suspend a running software program Context menu , a menu in a graphical user interface that appears upon user interaction ConTeXt , a macro package for the TeX typesetting system ConTEXT , a text editor for Microsoft Windows Other Opaque context Trama mycology context or flesh , the mass of non hymenial tissues that composes the mass of a fungal fruiting body See also lookfrom intitle Contextual disambiguation Contextualization disambiguation Locality disambiguation State disambiguation disambig de Kontext es Contexto fr Contexte nl Context simple Context sk Kontext ... more details
Infobox Software name ConTEXT logo Image ConTEXT Logo.png screenshot Image ConTEXT 0.98.3.png 250px caption ConTEXT v0.98.6 developer ConTEXT Project released ? frequently updated yes Release version update? Don t edit this page, just click on the version number programming language Delphi programming language Delphi operating system Microsoft Windows language english german genre Text editor license New BSD License website http www.contexteditor.org www.contexteditor.org distinguish ConTeXtConTEXT is a text editor for Microsoft Windows that can open and edit very large files, while requiring only modest amounts of RAM and hard drive space to run. It has built in Syntax highlighting syntax highlighters for C programming language C C , Delphi programming language Delphi Pascal programming language Pascal , FORTRAN , 80x86 assembler, Java programming language Java , JavaScript , Visual Basic , Perl Common Gateway Interface CGI , HTML , SQL , Python programming language Python , PHP , Tcl Tk , and its own syntax highlighter definition language. Other features are code templates and the ability to work with several document windows using the Multiple Document Interface . ConTEXT can integrate ... are supported for searching and replacing. ConTEXT is available in many languages. On 7 September 2007 the creator of ConTEXT announced he wanted to sell the project including the full source, copyrights, website and domain. ref http www.contexteditor.org ConTEXT Freeware Text Editor Home Bot generated title ref In December 2007 it was announced that the complete project was bought and ConTEXT Project was set up as a company. In March 2009 the decision was made to make ConTEXT open source ... www.contexteditor.org Freeware Text Editor http www.contexteditor.org downloads ConTEXT Downloads Windows software stub Category Windows text editors Category Windows only freeware fr ConTEXT it ConTEXT hu ConTEXT nl ConTEXT pl ConTEXT fi ConTEXT ... more details
Stochastic computing is a collection of techniques that represent continuous values by streams of random ... the similarity in their names, stochastic computing is distinct from the study of randomized algorithm ... to compute math p times q math . Stochastic computing performs this operation using probability instead ... operations evaluation of math a i land b i math on random bits. More generally speaking, stochastic ... of reconstruction, devices that perform these operations are sometimes called stochastic averaging processors. In modern terms, stochastic computing can be viewed as an interpretion of calculations in probabilistic ... stochastic computer 1969.png thumb alt A photograph of the RASCEL stochastic computer. The RASCEL stochastic computer, circa 1969 Stochastic computing was first described in a very rough form by a classic ... W. last2 Afuso first2 C. last3 Esch first3 J. title Stochastic computing elements and systems journal ... B. title Stochastic Computing journal AFIPS SJCC year 1967 volume 30 pages 149 156 ref By the late 1960s, attention turned to the design of special purpose hardware to perform stochastic computation. A host ref cite book last1 Mars first1 P. last2 Poppelbaum first2 W. title Stochastic and deterministic ... array of stochastic computing element logic year 1969 location University of Illinois, Urbana, Illinois ref is pictured in this article. Despite the intense interest in the 1960s and 1970s, stochastic ... below. The first and last International Symposium on Stochastic Computing ref cite conference title Proceedings of the first International Symposium on Stochastic Computing and its Applications location ... few years. Although stochastic computing declined as a general method of computing, it has shown ... learning and control. ref cite conference booktitle Advances in Information Systems Science title Stochastic ... IEEE, NAPA title A stochastic neural architecture that exploits dynamically reconfigurable FPGAs last van Daalen, M. R. et al year 1993 ref More recently, interest has turned towards stochastic ... more details
Refimprove date December 2009 Stochastic cooling is a form of particle beam cooling . It is used in some particle accelerator s and storage ring s to control the Beam emittance emittance of the particle beam s in the machine. This process uses the Signal electrical engineering electrical signals that the individual charged particle s generate in a feedback loop to reduce the tendency of individual particles to move away from the other particles in the beam. It is accurate to think of this as thermodynamic cooling, or the reduction of entropy , in much the same way that a refrigerator or an air conditioner cools its contents. The technique was invented and applied at the Intersecting Storage Rings , ref name overview Citation arxiv physics 0308044 title Stochastic Cooling Overview author John Marriner arxiv physics.acc ph 0308044 doi 10.1016 j.nima.2004.06.025 date 2003 08 11 journal Nuclear Instruments and Methods A volume 532 issue 1 2 pages 11 18 ref and later the Super Proton Synchrotron , at CERN in Geneva, Switzerland by Simon van der Meer , ref http www.nytimes.com 2011 03 12 science ... continues to use stochastic cooling in its antiproton source. The accumulated antiprotons are used ... and the D0 experiment . Stochastic cooling in the Tevatron at Fermilab was attempted, but was not fully ... needs to be edited for clarity by a stochastic cooling expert. Stochastic cooling uses the electrical ... that is required. Stochastic cooling is used to reduce the transverse momentum spread within a bunch ... by this damping. The key to stochastic cooling is to address individual particles within each ... motion can only be increased by simple devices see for example Free electron laser . To achieve ... directional coupler s, that integrate measurement and steering adjustment in this context often ... stochastic in the title stems from the fact that usually only some of the particles can unambiguously ... and stochasitic cooling applied. See also Electron cooling References reflist DEFAULTSORT Stochastic ... more details
In probability theory , stochastic drift is the change of the average value of a stochastic process stochastic random process . A related term is the drift rate which is the rate at which the average changes. This is in contrast to the random fluctuations about this average value. For example, the process which counts the number of heads in a series of math n math coin toss es has a drift rate of 1 2 per toss. Stochastic drifts in population studies Longitudinal studies of secular events are frequently conceptualized as consisting of a trend component fitted by a polynomial , a cyclical component often fitted by an analysis based on autocorrelation s or on a Fourier series , and a random component stochastic drift to be removed. In the course of the time series analysis , identification of cyclical and stochastic drift components is often attempted by alternating autocorrelation analysis and differencing of the trend. Autocorrelation analysis helps to identify the correct phase of the fitted model while the successive differencing transforms the stochastic drift component into white noise . Stochastic drift can also occur in population genetics where it is known as Genetic drift . A finite population of randomly reproducing organisms would experience changes from generation to generation in the frequencies of the different genotypes. This may lead to the fixation of one of the genotypes ... can also neutralize the effect of deterministic natural selection on the population. Stochastic ... variable. In this case the stochastic drift can be removed from the data by regressing math y t math ... where math u t math is a zero long run mean stationary random variable here c is a non stochastic ... no drift. In the context of monetary policy , one policy question is whether a central bank ... any stochastic change to the price level permanently affects the expected values of the price level ... analysis Category Stochastic processes Category Economics Category Finance ... more details
No footnotes date November 2010 In probability theory , a stochastic process , or sometimes random process ..., for solutions of an ordinary differential equation , in a stochastic or random process there is some ... time discrete time , a stochastic process amounts to a sequence mathematics sequence of random variables known as a time series for example, see Markov chain . Another basic type of a stochastic process ... arguments are drawn from a range of continuously changing values. One approach to stochastic processes ... to the codomain of the function . Although the random values of a stochastic process at different ... they exhibit complicated statistical correlations. Familiar examples of processes modeled as stochastic ... Definition Given a probability space math Omega, mathcal F , P math , a stochastic process ... T time . That is, a stochastic process F is a collection math F t t in T math where each math F t math is an X valued random variable. A modification G of the process F is a stochastic process on the same ... Let F be an X valued stochastic process. For every finite subset math T subseteq T math ... can be used to define a stochastic process see Kolmogorov extension in the next section . Construction ... blown stochastic process, is not a requirement. Such a condition only holds, for example, if the stochastic ... class but not in general for all stochastic processes. When this condition is expressed ... Kolmogorov equation . The Kolmogorov extension theorem guarantees the existence of a stochastic process ... extension makes it possible to construct stochastic processes with fairly arbitrary finite dimensional .... One solution to this problem is to require that the stochastic process be separable . In other ... special case is math T mathbb R math . Stochastic processes may be defined in higher dimensions ... a multidimensional index set. Indeed a multivariate random variable can itself be viewed as a stochastic process with index set T 1, ..., n . Examples The paradigm of continuous stochastic process ... more details
stochastics Stochastic programming is a framework for modeling Optimization mathematics optimization ... mathematics optimal in some sense. Stochastic programming mathematical model models are similar ... Alexander last2 Dentcheva first2 Darinka last3 Ruszczy ski first3 Andrzej title Lectures on stochastic ... in response to each random outcome. Stochastic programming has applications in a broad range of areas ... eds. . Applications of Stochastic Programming . MPS SIAM Book Series on Optimization 5, 2005. ref ref Applications of stochastic programming are described at the following website, http stoprog.org Stochastic Programming Community . ref Biological Applications Stochastic dynamic programming ... than two staged. Economic Applications Stochastic dynamic programming is a useful tool in understanding ..., S., Reynaud, A and K. Knapp. 2002. Using Polynomial Approximations to Solve Stochastic Dynamic ... solver for stochastic programming problems See also Portal Computer science Stochastic optimization Dynamic programming References Reflist John R. Birge and Fran ois V. Louveaux. Introduction to Stochastic ... first2 Stein W. title Stochastic programming series Wiley Interscience Series in Systems and Optimization ... 95158 7 url http stoprog.org index.html?introductions.html id MR 1315300 G. Ch. Pflug Optimization of Stochastic ... Prekopa. Stochastic Programming. Kluwer Academic Publishers, Dordrecht, 1995. Andrzej Ruszczynski and Alexander Shapiro eds. . Stochastic Programming . Handbooks in Operations Research and Management ... Darinka last3 Ruszczy ski first3 Andrzej title Lectures on stochastic programming Modeling and theory ... id MR 2562798 Stein W. Wallace and William T. Ziemba eds. . Applications of Stochastic Programming . MPS SIAM Book Series on Optimization 5, 2005. External links http stoprog.org Stochastic Programming Community Home Page . DEFAULTSORT Stochastic Programming Category Stochastic optimization Category Stochastic algorithms Category Mathematical optimization Category Operations research ru ... more details
Stochastic calculus is a branch of mathematics that operates on stochastic process es. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly. The best known stochastic process to which stochastic calculus is applied is the Wiener process named in honor of Norbert Wiener , which is used for modeling Brownian motion as described by Albert Einstein and other physical diffusion processes in space of particles subject to random forces. Since the 1970s, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates. The main flavours of stochastic calculus are the It calculus and its variational relative the Malliavin calculus . For technical reasons the It integral is the most useful for general classes of processes but the related Stratonovich integral is frequently useful in problem formulation particularly in engineering disciplines. The Stratonovich integral can readily be expressed in terms of the It integral. The main benefit of the Stratonovich integral is that it obeys the usual chain rule and does therefore not require It s lemma . This enables problems to be expressed in a co ordinate system invariant form, which is invaluable when developing stochastic calculus on manifolds other than R sup n sup . The dominated convergence theorem does not hold for the Stratonovich ... in It form. It integral main It calculus The It integral is central to the study of stochastic ... used to denote the Stratonovich integral. Applications A very important application of stochastic ... motion . External links http www.chiark.greenend.org.uk alanb stoc calc.pdf Notes on Stochastic ... T. Szabados and B. Szekely, Stochastic integration based on simple, symmetric random walks A new approach which the authors hope is more transparent and technically less demanding. Category Stochastic ... more details
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