Kuntze , 1754. The concept of a randomsequence is essential in probability theory and statistics . The concept generally relies on the notion of a sequence of random variable s and many statistical discussions begin with the words let X sub 1 sub ,..., X sub n sub be independent random variables... . Yet as D. H. Lehmer stated in 1951 A randomsequence is a vague notion... in which each term ... avoids a definition of a randomsequence. ref Inevitable Randomness in Discrete Mathematics ... sequence is random, but generally proceeds to discuss the properties of random variables ... the statement let us consider a randomsequence an abuse of language . ref Algorithms main ideas ... of large numbers, although he used the term collective rather than randomsequence. Using the concept of the impossibility of a gambling system , von Mises defined an infinite sequence of zeros and ones as random if it is not biased by having the frequency stability property i.e. the frequency of zeros goes to 1 2 and every sub sequence we can select from it by a proper method of selection ... Alonzo Church , On the Concept of RandomSequence, Bull. Amer. Math. Soc., 46 1940 , 254 260 ref ... of a randomsequence . Mathematical Systems Theory 5 3 246 258 ref Schnorr showed how the existence ... zeros to the front of the randomsequence the new sequence will still be considered random. Hence ... DEFAULTSORT RandomSequence Category Randomness Category Sequences and series Category Statistical ... . ref What is meant by the word Random in Mathematics and common sense by Philip J. Davis ... 7923 2210 X page 166 ref During the 20th century various technical approaches to defining random sequences ... 260 ref The sub sequence selection criterion imposed by von Mises is important, because although 0101010101... is not biased, by selecting the odd positions, we get 000000... which is not random. Von ... Alonzo Church defined it as any recursive function which having read the first N elements of the sequence ... more details
Intuitively, an algorithmically randomsequence or randomsequence is an infinite Sequence Infinite sequences in theoretical computer science sequence of binary digits that appears random to any algorithm ... used to refer to a sequence without clarification is usually taken to mean Martin L f random defined ... is denoted by RAND or MLR. History The first suitable definition of a randomsequence was given by Per ... of a randomness test test for randomness in order to define a randomsequence as one that passed ... sequence was in terms of constructive null covers he defined a sequence to be random if it is not contained ... of Kolmogorov complexity a sequence is random if there is a uniform bound on the compressibility ... incompressible if math K w geq w c math . An infinite sequence S is Martin L f random if and only if there is a constant ... . math A sequence is Martin L f random if and only if no constructive martingale succeeds on it. Note ... that a randomsequence is incompressible no prefix can be produced by a program much shorter ... describable measure 0 sets and defines a sequence to be random if it does not lie in any of these particular ... the intuition that no effective procedure should be able to make money betting against a randomsequence ..., which are not necessarily computable can make money betting on a randomsequence. Properties and examples ... of a randomsequence. RAND sup c sup the Complement set theory complement of RAND is a Measure ... 1 subset of the set of all infinite sequences. Every randomsequence is Normal number normal ... Sigma 0 2 math formula. There is a randomsequence which is math Delta 0 2 math , that is, computable ... is an example of such a sequence. No randomsequence is decidable , computably enumerable , or computably .... Every sequence is Turing reducible to some randomsequence. Ku era 1985 1989, P ter G cs G cs 1986 ... definitions of a Martin L f randomsequence is based on what is computable by some Turing ... A , a sequence B which is not only random but in fact satisfies the equivalent definitions for computability ... more details
In mathematics, the random Fibonacci sequence is a stochastic analogue of the Fibonacci sequence defined ... the rate explicitly. In 1999, Divakar Viswanath showed that the growth rate of the random Fibonacci sequence is equal to 1.1319882487943 , a mathematical constant that was later named Viswanath s constant. Description The random Fibonacci sequence is an integer randomsequence f sub n sub , where ... the random recurrence relation math f n begin cases f n 1 f n 2 , & text with probability 1 2 f n 1 f n 2 , & text with probability 1 2 . end cases math A run of the random Fibonacci sequence starts .... math Similarly to the deterministic case, the random Fibonacci sequence may be profitably described .... Their results apply to a broad class of randomsequence generating processes that includes the random ... The Embree Trefethen constant describes the qualitative behavior of the randomsequence with the recurrence ... title Random Fibonacci Sequence SloanesRef sequencenumber A078416 Category Fibonacci ... Bernoulli distribution at random with equal probability 1 2, Independence probability theory independently for different n . By a theorem of Harry Kesten and Hillel F rstenberg , random recurrent sequences ... elements of the sequence, the next element is either their sum or their difference with probability 1 2, independently of all the choices made previously. If in the random Fibonacci sequence the plus sign is chosen at each step, the corresponding run is the Fibonacci sequence F sub n sub , math ..., the result is the sequence math 1,1,0,1,1,0,1,1,0,1, ldots. math However, such patterns occur with vanishing probability in a random experiment. In a typical run, the terms will not follow ... math f n 1 choose f n M n M n 1 ldots M 3 f 1 choose f 2 , math where M sub k sub is a sequence of Independent and identically distributed random variables independent identically distributed random ... increases, the ratio of the successive terms of the Fibonacci sequence F sub n sub approaches the golden ... more details
Other uses In mathematics , a sequence is an ordered list of objects or events . Like a Set mathematics ... possibly infinite is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a Discrete mathematics discrete function mathematics function . For example, C, R, Y is a sequence of letters ..., or Infinite set infinite , such as the sequence of all even and odd numbers even ... notions of sequence, but may be excluded depending on the context. Image Cauchy sequence illustration2.svg right thumb 350px An infinite sequence of real numbers in blue . This sequence is neither increasing, nor decreasing, nor convergent, nor Cauchy sequence Cauchy . It is, however, bounded ... of which e.g. , exact sequence are not covered by the notations introduced below. In addition to identifying the elements of a sequence by their position, such as the 3rd element , elements may be given names for convenient referencing. For example a sequence might be written as a sub 1 sub , a sub ... definition of a finite sequence with terms in a set S is a function mathematics function from 1, 2, ..., n to S for some n 0. An infinite sequence in S is a function from 1, 2, ... to S . For example, the sequence of prime numbers 2,3,5,7,11, is the function 1 2 , 2 3 , 3 5 , 4 7 , 5 11 , . A sequence of a finite length n is also called an n tuple n tuple . Finite sequences include the empty sequence ... sequence or two way infinite sequence . An example is the bi infinite sequence of all even integers , 4, 2, 0, 2, 4, 6, 8 . Multiplicative Let A a sequence defined by a function f 1, 2, 3, ... 1, 2, 3, ... , such that a sub i sub f i . The sequence is multiplicative if f xy f x f y for all x , y ... of sequences A subsequence of a given sequence is a sequence formed from the given sequence by deleting ... of the sequence are a subset of an partially ordered set ordered set , then a monotonically ... more details
Infobox musical artist See Wikipedia WikiProject Musicians name The Sequence image caption image size Only for images narrower than 220 pixels background group or band alias origin Columbia, South Carolina Columbia , South Carolina , United States U.S. genre Old school hip hop br Funk years active 1979 1985 label Sugar Hill Records rap Sugar Hill associated acts Spoonie Gee website past members Angie Stone Angie Brown Stone Angie B. br Cheryl Cook Cheryl The Pearl br Gwendolyn Chisolm Blondy The Sequence is a former female old school hip hop trio signed to the Sugar Hill Records rap Sugar Hill label in the early 1980s. The group consisted of Cheryl Cook Cheryl The Pearl , Gwendolyn Chisolm Blondie , and lead singer rapper Angie Stone Angie Brown Stone Angie B. . The group originated from Columbia, South Carolina Columbia , South Carolina as a group of high school cheerleader s. Their most notable single was Funk You Up 1979 , which was the first rap record released by a female group and the second single released by Sugar Hill Records rap Sugar Hill Records . ref name Greenberg1999 Greenberg, Steve Light, Alan ed. 1999 . The VIBE History of Hip Hop . Three Rivers Press. p. 28. ISBN 0609805037 ref Elements of Funk You Up were later used by Dr. Dre for his 1995 single Keep Their Heads Ringin . ref Ego Trip s Book of Rap Lists Book of Rap Lists . 1999. Macmillan Publishers Macmillan ... song Let s Do It Again Discography Albums Sugarhill Presents the Sequence 1980 , Sugar Hill Records rap Sugar Hill The Sequence 1982 , Sugar Hill 51 Black Albums The Sequence Party 1983 , Sugar Hill Compilations Funky Sound 1995 , P Vine The Best of the Sequence 1996 , Deep Beats Monster Jam Back ... class artist id p194849 pure url yes The Sequence . Allmusic . External links http www.discogs.com artist Sequence, The Discography DEFAULTSORT Sequence, The Category African American musical groups ... Musical trios Hiphop band stub no The Sequence ... more details
dabconcept Random number may refer to A number generated for or part of a set exhibiting statistical randomness . A randomsequence obtained from a stochastic process. An algorithmically randomsequence in algorithmic information theory. The output of a random number generation random number generator . mathdab ca Nombre aleatori de Zufallszahl es N mero aleatorio id Angka acak he ms Nombor rawak ja pl Liczba losowa pt N mero aleat rio sr fi Satunnaisluku zh ... more details
point arithmetic from a pseudo randomsequence. Practical aspects For the generation of uniform random variates, see random number generation this is a bit of a misnomer, but a popular alternative ...A random variate is a particular outcome of a random variable the random variates which are other outcomes of the same random variable would have different values. Random variates are used when simulating processes driven by random influences stochastic processes . In modern applications, such simulations would derive random variates corresponding to any given probability distribution from computer procedures designed to create random variates corresponding to a Uniform distribution continuous uniform ... continuous uniform distribution of pseudorandom numbers. Procedures to generate random variates corresponding to a given distribution are known as procedures for random variate generation or pseudo random number sampling . In probability theory , a random variable is a measurable function from ..., and in statistics , those values are known as a random variates , or occasionally random deviates ... Luc Devroye Devroye ref Luc Devroye 1986 . Non Uniform Random Variate Generation . New York Springer Verlag, pp. 1 2. http cg.scs.carleton.ca luc rnbookindex.html ref defines a random variate generation ... have access to a source of random variates that are uniform distribution continuous uniformly distributed on the closed interval math 0 1 math . Then a random variate generation algorithm is any program that halts almost surely and exits with a real number X . This X is called a random variate ... a source of true randomness like certain hardware random number generator s , and instead use pseudorandom number sequences. The distinction between random variable and random variate is subtle and is not always made in the literature. It is useful when one wants to distinguish between a random variable itself with an associated probability distribution on the one hand, and random draws from that probability ... more details
A random hexamer or random hexonucleotides are for various polymerase chain reaction PCR applications such as rolling circle amplification to prime the DNA. They are oligonucleotide sequences of 6 bases which are synthesised entirely randomly to give a numerous range of sequences that have the potential to anneal at many random points on a DNA sequence and act as a primer to commence first strand cDNA synthesis. ref http www.invitrogen.com site us en home References protocols nucleic acid amplification and expression profiling pcr protocol pcr and rt pcr.html ref References reflist http www.fermentas.com en products all nucleotides primers other primers so142 random hexamer primer Category Polymerase chain reaction ... more details
Incomplete date November 2011 A random permutation is a random ordering of a set of objects, that is, a permutation valued random variable . The use of random permutations is often fundamental to fields that use randomized algorithm s such as coding theory , cryptography , and simulation . A good example of a random permutation is the shuffling of a card deck deck of cards this is ideally a random permutation of the 52 cards. Generating random permutations Entry by entry brute force One method of generating a random permutation of a set of length n uniform distribution discrete uniformly at random i.e., each of the n permutation s is equally likely to appear is to generate a sequence by taking a random number between 1 and n sequentially, ensuring that there is no repetition, and interpreting this sequence x sub 1 sub , ..., x sub n sub as the permutation math begin pmatrix 1 & 2 & 3 & cdots ... retries whenever the random number picked is a repeat of a number already selected. This can ... , one chooses a number j at random between 1 and n &minus i 1 and sets x sub i sub equal to the j ... items uniformly at random without retries, known as the Knuth shuffle , is to start with any permutation ... over all such permutations. Statistics on random permutations Fixed points main Rencontres ... distributed random permutation approaches a Poisson distribution with expected value 1 as n grows ... random processes, the quality of the resulting distribution of an implementation of a randomized algorithm ... possible randomness test s for random permutations, such as some of the Diehard tests . A typical ... genetics Golomb Dickman constant Perfect shuffle Random permutation statistics Shuffle Shuffling algorithms Shuffling algorithms random sort method, iterative exchange method External links http mathworld.wolfram.com RandomPermutation.html Random permutation at MathWorld http www.techuser.net randpermgen.html Random permutation generation detailed and practical explanation of Knuth shuffle ... more details
Refimprove date July 2011 Image Random vs sequential access.svg thumb right Random access compared to sequential access . In computer science , random access sometimes called direct access is the ability to access an element at an arbitrary position in a sequence mathematics sequence in equal time, independent of sequence size. The position is arbitrary in the sense that it is unpredictable, thus the use of the term random in random access . The opposite is sequential access , where a remote element takes longer time to access. ref http technet.microsoft.com en us library cc938619.aspx ref A typical illustration of this distinction is to compare an ancient scroll parchment scroll sequential all material prior to the data needed must be unrolled and the book random can be immediately flipped open to any random page paper page . A more modern example is a cassette tape sequential&mdash you have to fast forward through earlier songs to get to later ones and a CD random access&mdash you can skip to the track you want . In data structure s, random access implies the ability to access any entry in a List computing list in constant i.e. independent of its position in the list and of list s size, i.e. Big O notation math O 1 math time. Very few data structures can guarantee this, other than array data structure array s and related structures like dynamic array s . Random access is critical to many algorithms such as binary search , integer sorting or sieve of Eratosthenes . Other data structures, such as linked list s, sacrifice random access to make for efficient inserts, deletes, or reordering of data. Self balancing binary search tree s may provide an acceptable compromise, where access time is equal for any member of a collection and only grows logarithmically with its size. See also direct access Data stream RAM machine References reflist Category Computer data ar de Wahlfreier Zugriff es Acceso aleatorio fr Acc s direct it Accesso casuale he hu V letlen ... more details
on factors such as programmed probabilities Pseudo random number generator s create the sequence ...Refimprove date November 2010 About the feature in role playing games Random Encounter disambiguation Random Encounter A random encounter is a feature commonly used in various role playing game s whereby encounters with non player character NPC enemies or other dangers occur sporadically and at random. In general, random encounters are used to simulate the challenges associated with being in a hazardous ... and makeup as opposed to a placed encounter . Frequent random encounters are common in games like ... Fantasy series. Role playing games Random encounters sometimes called wandering monsters were ... offshoots to this day. Random encounters are usually determined by the gamemaster by rolling dice against a random encounter table . The tables are usually based on terrain and or time weather , and have ... section date March 2010 Random encounters were incorporated into early role playing video game s and have ... 2009 12 10 accessdate 2010 11 09 ref Placed and random encounters were both used in 1981s Wizardry ... 1980s, random encounters made up the bulk of battles in genre defining games such as Dragon Warrior ... 23 accessdate 2010 11 09 ref Random encounters happen when the player is traversing the game world often ... differently than with enemies. Random encounters are random in the respect that players cannot anticipate ... character . In some games, items can be found to increase or decrease the frequency of random .... Random encounters often occur more frequently in cave s, forest s, and swamp s than in open plain s. The simplest sort of random encounter algorithm would be as follows Each step, set X to a random integer between 0 and 99. If in plains, and X 8, a random encounter occurs. If in swamp, desert, or forest, and X 16, a random encounter occurs. The problem with this algorithm is that random encounters .... Random encounters in rapid succession are considered undesirable ref cite web url ... more details
senses in which a sequence X sub n sub of random variables can converge to a random ...In probability and statistics , a random variable or stochastic variable is, roughly speaking, a Variable ... variables, a random variable conceptually does not have a single, fixed value even if unknown rather ..., a random variable can be thought of in one of the following ways The frequentist statistics frequentist ... the center more likely . Random variables can be classified as either Discrete random variable discrete i.e. it may assume any of a specified list of exact values or as Continuous random variable continuous ... function describing the possible values of a random variable and their associated probabilities is known as a probability distribution . The realizations of a random variable, i.e. the results of randomly choosing values according to the variable s probability distribution are called random variate s. A random variable s possible values might represent the possible outcomes of a yet to be performed ... random process e.g. rolling a die , or the subjective randomness that results from incomplete knowledge of a quantity. The meaning of the probabilities assigned to the potential values of a random ... in use. The basic concept of random variable in statistics is real number real valued . However, one can consider arbitrary types such as indicator random variable boolean values , Covariance matrix Complex random vectors complex numbers , random vector vectors , random matrix matrices , randomsequence sequences , random tree trees , random compact set sets , random shape shapes , random manifold manifolds , random function functions , and stochastic process processes . The term random ... , a set of indexed random variables typically indexed by time or space . This more general concept ... many of the basic elements of analysis are non numerical. These general random variables are typically parameterized as sets of real valued random variables often more specifically as random vector s . For example ... more details
In probability theory &ndash specifically in the theory of stochastic process es, a stationary sequence is a randomsequence whose joint probability distribution is Invariant mathematics invariant over time. If a randomsequence X sub j sub is stationary then the following holds math begin align & qquad F X n,X n 1 , dots,X n N 1 x n, x n 1 , dots,x n N 1 & F X n k ,X n k 1 , dots,X n k N 1 x n, x n 1 , dots,x n N 1 , end align math where F is the joint cumulative distribution function of the random variable s in the subscript. If a sequence is stationary then it is wide sense stationary . If a sequence is stationary then it has a constant mean which may not be finite math E X n mu quad text for all n . math See also Stationary process References Probability and Random Processes with Application to Signal Processing Third Edition by Henry Stark and John W. Woods. Prentice Hall, 2002. Category Sequences and series Category Stochastic processes Category Time series analysis probability stub ... more details
Image Random Walk example.svg thumb right 420px Example of eight random walks in one dimension starting ... axis . File 2D Random Walk 400x400.ogv thumb right 300px An animated example of a Brownian motion like random walk on a torus A random walk is a mathematical formalisation of a trajectory that consists of taking successive random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating random walk hypothesis stock and the financial status of a gambler can all be modeled as random walks. The term random walk was first introduced by Karl Pearson in 1905. ref Pearson, K. 1905 . The problem of the Random Walk. Nature. 72 , 294. ref Random walks have been used in many fields ecology , economics , psychology ... 1984. ref ref name 6 Weiss G. H., Aspects and Applications of the Random Walk North Holland, Amsterdam 1994. ref ref name 7 Cox D. R., Renewal Theory Methuen, London 1962. ref Random walks explain ... model for the recorded Stochastic process stochastic activity . Various different types of random walks are of interest. Often, random walks are assumed to be Markov chain s or Markov process es, but other, more complicated walks are also of interest. Some random walks are on graph theory graphs , others on the line, in the plane, or in higher dimensions, while some random walks are on group theory groups . Random walks also vary with regard to the time parameter. Often, the walk is in discrete ... take their steps at random times, and in that case the position math X t math is defined for the continuum of times math t ge 0 math . Specific cases or limits of random walks include the drunkard s walk and L vy flight . Random walks are related to the diffusion models and are a fundamental topic in discussions of Markov process es. Several properties of random walks, including dispersal distributions, first passage times and encounter rates, have been extensively studied. Lattice random walk ... more details
wiktionary randomRandom can refer to Randomness , the property of lacking any sort of order. Science and technology Random number Random variable dev random , a Unix device file See also Category Randomness Places Random Lake , Wisconsin Random Island , Canada The former name of Brighton, Vermont Music Random musician Random band Random Lady Sovereign song , a song by Lady Sovereign Random , a song by Gary Numan released as a bonus track on his album The Pleasure Principle Gary Numan album The Pleasure Principle Random , a song from the 311 album 311 album by the band 311 Random , a tribute album to Gary Numan Other Robert Random , a Canadian actor Random comics , a fictional character in the Marvel Universe Random, Prince of The Chronicles of Amber Amber , in the novels of Roger Zelazny Random Dent Random Frequent Flyer Dent , the daughter of Arthur Dent in the Hitchhikers Guide book Mostly Harmless Random House , Book Publisher Random refers to things in no sense or order. For example, if someone were to shout out cream cheese in the middle of a business presentation, that would be considered an act of randomness. See also Non sequitur , for which random is a common synonym with today s youth. disambig ko pt Random ... more details
Random Hero may refer to Random Hero band , an American rock band formed in Denver, Colorado in 2005 Ryan Dunn or Random Hero, American reality television personality and daredevil disambig ... more details
Random Encounter may refer to Random encounter , a method governing encounters with enemies in many RPG video games Random Encounter film Random Encounter film , a 1998 Crime thriller film Random Encounter comic Random Encounter comic , a comic published by Viper Comics Random Encounter band , a Russian American video game inspired rock group that features an accordion disambiguation ... more details
coord 52.33 5.824 display title DEFAULTSORT Hacking At Random Category Free software events Category Hacker conventions compu conference stub fr Hacking at Random ... more details
Random Thoughts may refer to Music Random Thoughts Shulman album Random Thoughts Shulman album Random Thoughts Faye Wong album Random Thoughts Faye Wong album Random Thoughts Koolism album Random Thoughts Koolism album Random Thoughts Don Pullen album Random Thoughts Don Pullen album Random Thoughts , song by Steve Kuhn from Non Fiction Steve Kuhn album Non Fiction Steve Kuhn album Other uses Random Thoughts Star Trek Voyager Random Thoughts Star Trek Voyager , episode of Star Trek Voyager Random Thoughts , columns by Richard Felder in the quarterly journal Chemical Engineering Education See also A Random Thought on the Segregation Cases , a 1952 memo by William Rehnquist Racing thoughts , rapid thought patterns that often occur in manic, hypomanic, or mixed episodes Random Thoughts of a Fascist Hyena , book by Constantine Fitzgibbon Ink Blots and Random Thoughts , album by Darryl Tonemah Random Thoughts Before a Fatal Crash , Caitl n R. Kiernan bibliography story by Caitl n R. Kiernan first published in Sirenia Digest disambig ... more details
Probabilistic In mathematics and computer science , a random tree is a tree graph theory tree or Arborescence graph theory arborescence that is formed by a stochastic process . Types of random trees include Uniform spanning tree , a spanning tree of a given graph in which each different tree is equally likely to be selected Random minimal spanning tree , spanning trees of a graph formed by choosing random edge weights and using the minimum spanning tree for those weights Random binary tree , binary trees with a given number of nodes, formed by inserting the nodes in a random order or by selecting all possible trees uniformly at random Recursive tree Random recursive tree , increasingly labelled trees, which can be generated using a simple stochastic growth rule. Treap or randomized binary search tree, a data structure that uses random choices to simulate a random binary tree for non random update sequences Rapidly exploring random tree , a fractal space filling pattern used as a data structure for searching high dimensional spaces Brownian tree , a fractal tree structure created by diffusion limited aggregation processes Random forest , a machine learning classifier based on choosing random subsets of variables for each tree and using the most frequent tree output as the overall classification Branching process , a model of a population in which each individual has a random number of children mathdab Category Trees graph theory Category Probabilistic data structures Category Random graphs ... more details
In probability theory , random element is a generalization of the concept of random variable to more complicated spaces than the simple real line. The concept was introduced by harvs first Maurice last ... random outcomes of experience can be described by number or a finite set of numbers, to schemes where outcomes of experience represent, for example, random vector vectors , function mathematics function ... , and also Set mathematics sets or collections of sets. The modern day usage of random ... ,&thinsp P be a probability space , and E ,&thinsp a measurable space . A random element with values ... X &thinsp &thinsp B &thinsp &thinsp . Sometimes random elements with values in math E math are called math E math valued random variables. Note if math E, mathcal E mathbb R , mathcal B mathbb ... algebra , then the definition of random element is the classical definition of random variable . The definition of a random element math X math with values in a Banach space math B math is typically ... Omega rightarrow B math , from a probability space, is a random element if math f circ X math is a random ... measurable function weakly measurable . Random elements of the various nature Random variable Discrete random variable Continuous random variable Complex random variable Simple random variable Random vector Random matrix theory Random matrix Random function Random process Random field Random measure Random set Random closed set Random compact set Random point Random figure ref name Stoyan Stoyan, D., and Stoyan, H. 1994 Fractals, Random Shapes and Point Fields. Methods of Geometrical Statistics . Chichester, New York John Wiley & Sons. ISBN 0 471 93757 6 ref Random shape ref name Stoyan Random finite set Random finite abstract set Random set of events References Reflist Literature refbegin cite ... de Banach These . Paris. Prokhorov Yu.V. 1999 Random element. Probability and Mathematical statistics ... as the Prokhorov reference listed above, with perhaps some additions Category Random process theory ... more details
last Halton first J. title Algorithm 247 Radical inverse quasi random point sequence publisher ... we pair them up, we get a sequence of points in a unit square frac 2 , frac 3 , frac 4 , frac 2 3 , frac ... other methods have been proposed one of the most prominent solutions is the scrambled Halton sequence, which uses permutations of the coefficients used in the construction of the standard sequence. Implementation ... last Niederreiter first Harald title Random number generation and quasi Monte Carlo methods publisher ... more details
Expert subject Mathematics date November 2008 A random Vector field field is a generalization of a stochastic ... on some manifold . At its most basic, discrete case, a random field is a list of random number s whose indices are mapped onto a space of n dimensions . Values in a random field are usually spatially ... of a covariance structure, many different types of which may be modeled in a random field. More generally, the values might be defined over a continuous domain, and the random field might be thought of as a function valued random variable. Definition and Examples Given a probability space math Omega, mathcal F , pi math , an X valued random field is a collection of X valued random variable s indexed by elements in a topological space T . That is, a random field F is a collection math F t t in T math where each math F t math is an X valued random variable. Several kinds of random fields exist, among them the Markov random field MRF , Gibbs random field GRF , conditional random field CRF , and Gaussian random field . An MRF exhibits the Markovian property math pi X i x i X j x j, i neq j pi X i x i partial i , , math where math partial i math is a set of neighbours of the random variable X sub i sub . In other words, the probability that a random variable assumes a value depends on the other random variables only through the ones that are its immediate neighbours. The probability of a random variable in an MRF is given by math pi X i x i partial i frac pi omega sum omega pi omega , math where is the same realization of , except for random variable X sub i sub . It is difficult ... by Julian Besag in 1974. Applications Random fields are of great use in studying natural processes by the Monte Carlo method , in which the random fields correspond to naturally spatially varying ... of centimeters. A further common use of random fields is in the generation of computer graphics, particularly ... Series B 36, 2 May 1974 , 192 236. cite book author Adler, RJ & Taylor, Jonathan title Random Fields ... more details
Wikify date April 2010 Orphan date December 2008 A random stimulus is any of a class of creativity techniques that explore randomization. Most of their names start with word randomrandom word, random heuristic, random picture, random sound, etc. In each random creativity technique the user is presented with a random stimulus and explores associations that has a potential to bring novel ideas. The power of random stimulus is that it can lead you to explore some useful associations that could never be explored intentionally. Random Word technique is the simplest technique of this class where a randomly picked word is used to generate new associations. By getting a random word and thinking how ... direction from that you would normally. ref Ray, 1989 ref Low tech implementations of the random ... use computers, random number generators, and availabiliy of internet resources to extend the potential of this technique. Simple random techniques are classified by modality of association Verbal, Visual, Audial, Kinesthetic . Multi modal techniques combine different modalities, e.g. random article, website, or video. ref Kosorukoff, 2000 ref Random article link is an example of this kind of technique implemented by MediaWiki software. The best tool to explore a random website creativity ... Kosorukoff, 2000 Goldberg, 2002 ref views random stimulus creativity techniques as mutation operators ..., it is the share of random stimuli that were useful among all presented. The innovation rate depends on the distribution from which the random stimuli are sampled. Improving innovation rate ... http www.brainstorming.co.uk tutorials randomwebsitetutorial.html How to use the Random Website technique ... Mangle.ca 2002 http thatrandomwebsite.com That Random Website 2008 http randomwebsite.net randomwebsite.net 2005 http tools.blackhat seo.com strategies Random strategies , a website implementing the oblique strategies Eno & Schmidt, 1975 http werdomaker.com Werdomaker , A random word website utilizing ... more details
Unreferenced date December 2009 In mathematics , an ergodic sequence is a certain type of integer sequence , having certain equidistribution properties. Definition Let math A a j math be an infinite, strictly increasing sequence of positive integers. Then, given an integer q , this sequence is said to be ergodic mod q if, for all integers math 1 leq k leq q math , one has math lim t to infty frac N A,t,k,q N A,t frac 1 q math where math N A,t mbox card a j in A a j leq t math and cardinality card is the count the number of elements of a set, so that math N A,t math is the number of elements in the sequence A that are less than or equal to t , and math N A,t,k,q mbox card a j in A a j leq t, , a j mod q k math so math N A,t,k,q math is the number of elements in the sequence A , less than t , that are equivalent to k modulo q . That is, a sequence is an ergodic sequence if it becomes uniformly distributed mod q as the sequence is taken to infinity. An equivalent definition is that the sum math lim t to infty frac 1 N A,t sum j a j leq t exp frac 2 pi ika j q 0 math vanish for every integer k with math k mod q ne 0 math . If a sequence is ergodic for all q , then it is sometimes said to be ergodic for periodic systems . Examples The sequence of positive integers is ergodic for all q . Almost all Bernoulli sequence s, that is, sequences associated with a Bernoulli process , are ergodic for all q . That is, let math Omega,Pr math be a probability space of random variable s over two letters math 0,1 math . Then, given math omega in Omega math , the random variable math X j omega math is 1 with some probability p and is zero with some probability 1 p this is the definition of a Bernoulli process. Associated with each math omega math is the sequence of integers math mathbb Z omega n in mathbb Z X n omega 1 math Then almost every sequence math mathbb Z omega math is ergodic. See ... Sequence Category Ergodic theory Category Sequences and series ... more details
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