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Topic: Pseudorandom numbers

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	PlanetMath: pseudorandom numbers
		Generated in a digital computer by a numerical algorithm, pseudorandom numbers are not random, but should appear to be random when used in Monte Carlo calculations.
		For many scientific projects, analysis techniques are used that are extremely sensitive to patterns in the input, so when generating fake input using pseudorandom number generators, it is often necessary to use extremely good quality pseudorandom numbers.
		Such pseudorandom number generators can in fact serve as cryptosystems themselves: the requirements for such a random number generator are exactly the same as those for a stream cipher.
	www.planetmath.org /encyclopedia/PseudoRandomNumbers2.html (485 words)

	Random Number Generation - Wolfram Mathematica
		The ability to generate pseudorandom numbers is important for simulating events, estimating probabilities and other quantities, making randomized assignments or selections, and numerically testing symbolic results.
		The size of a sample returned by RandomSample is limited by the number of elements in elist, and the number of occurrences of a distinct element in that sample is limited by the number of occurrences of that element in elist.
		Methods for pseudorandom number generation typically use a recurrence relation to generate a number from the current state and to establish a new state from which the next number will be generated.
	reference.wolfram.com /mathematica/tutorial/RandomNumberGeneration.html (4223 words)

	Pseudorandom number generation with expander graphs invention
		Pseudorandom number generation typically involves using an input seed of a first bit length to produce a pseudorandom number of a second bit length.
		The second bit length of the pseudorandom number output is longer than the first bit length of the seed input due to some mathematical algorithm that is applied to the input seed.
		Although not required, pseudorandom number generation with an expander graph is facilitated by using an expander graph with good expansion properties along with a small degree (k), where the degree indicates the number of edges emanating from the vertices.
	www.freshpatents.com /Pseudorandom-number-generation-with-expander-graphs-dt20070719ptan20070165846.php (1525 words)

	Pseudorandom numbers by shift register
		Encryption of data, for example, depends on pseudorandom number generation for which finding any pattern in the number stream is extremely difficult.
		The shift-register pseudorandom number generators are calculating the successive powers of an unknown x in a finite number field called the Galois (gall-wah) of order 2 to the n.
		Pseudorandom numbers can be generated by a simple shift-register by taking successive powers of x in the field of polynomials with coefficients mod 2 modulo a prime polynomial.
	www.cs.miami.edu /~burt/learning/Csc609.022/random_numbers.html (1829 words)

	2 Introduction to Pseudorandom Numbers (Site not responding. Last check: )
		Pseudorandom - is defined as having the appearance of randomness, but nevertheless exhibiting a specific, repeatable pattern.
		Pseudorandom sequences which would fill the space are pseudorandom permutations of this set (they contain the same numbers, but in a different, ``random'' order).
		Often on vector and/or parallel computers, blocks of random numbers are generated to amortize, over many random numbers, the overhead associated with the generation of one random number.
	www.phy.ornl.gov /csep/CSEP/RN/NODE6A.html (301 words)

	CSERD Resources: Algorithms: Random Number Generation
		The process of creating numbers that simulate randomness on a computer is known as pseudorandom number generation.
		The "pseudo" in pseudo random refers to the fact that if you use a rule to generate a number, it is by definition not random, though it may appear so, and be close enough to random for all practical purposes.
		That number replaces your seed, and is used as the seed for the next random number to be generated.
	www.shodor.org /refdesk/Resources/Algorithms/RandomNumbers (374 words)

	Pseudorandomness - Wikipedia, the free encyclopedia (Site not responding. Last check: )
		With the spread of the use of computers, algorithmic pseudorandom number generators replaced random number tables, and "true" random number generators (Hardware random number generators) are only used in a few cases.
		Pseudorandom distributions can be generated deterministically from short random seeds, which are much shorter than the length of the pseudorandom output.
		This definition of pseudorandomness is used primarily in the study of pseudorandom generators.
	en.wikipedia.org /wiki/Pseudorandom (1019 words)

	Take a Chance: Science News Online, Dec. 4, 2004
		A random number is one that can't be predicted.
		Subtle correlations between the numbers the algorithm produced were being amplified by the simulation's calculations and skewing the results.
		These numbers can then be used either as the seeds for computer algorithms or as random numbers in their own right.
	www.sciencenews.org /articles/20041204/bob9.asp (2570 words)

	Pseudorandom Numbers - Wolfram Mathematica
		Mathematica has three functions for generating pseudorandom numbers that are distributed uniformly over a range of values.
		The pseudorandom numbers that Mathematica generates for a range of numbers are always uniformly distributed over the range you specify.
		An additional use of pseudorandom numbers is for selecting from a list.
	reference.wolfram.com /mathematica/tutorial/PseudorandomNumbers.html (785 words)

	Chaos
		Pseudorandom: Referring to numbers that appear to be random (meaning they will pass numerous tests for randomness) but, sooner or later, will repeat.
		This is distinguished from a pseudorandom number generator that is deterministic.
		Next, I examined a random number generator that operates by monitoring the true physical entropy generated by the computer on which it is running.
	www.viewsfromscience.com /documents/webpages/chaos_p4.html (2525 words)

	2 Introduction to Pseudorandom Numbers
		Pseudorandom sequences which would fill the space are pseudorandom permutations of this set (they contain the same numbers, but in a different, ``random'' order).
		Thus, when problems occur, it is very difficult to isolate the problem to the random number generator because one tends to trace program execution an event step at a time, and it is only in aggregate over many random numbers that the behavior of the random number generator is flawed.
		Waxing philosophical, one wonders what number of Monte Carlo simulations may have been performed where the answers may in fact be incorrect, but not grossly incorrect, due to a flaw inherent in the random number generator used.
	www.ipp.mpg.de /de/for/bereiche/stellarator/Comp_sci/CompScience/csep/csep1.phy.ornl.gov/rn/node6.html (1094 words)

	CRA-DMP Experience
		These pseudorandom numbers constitute a sequence of values which, although they are deterministically generated, have all the appearance of being independent uniform (0,1) random variables.
		These sequences of pseudorandom numbers must be tested extensively to determine whether they mimic hte porperties of truly random numbers needed in the simulation.
		By sorting a fairly large number of samples into bins, and counting the number of observations that fall into each category, we demonstrated that the numbers were distributed evenly over each interval.
	www.cra.org /Activities/craw/dmp/awards/2003/Neuburger/research.html (470 words)

	Pseudorandom Number Generator - Programs - Brian's Casio Calculator Corner
		One class of pseudorandom number generators that has stood the test of time as both simple and “good enough” for a great many purposes are the linear congruential generators.
		Multiplying the [0,1) pseudorandom number by b-a would result in a [0,b-a) pseudorandom number, and adding a would then result in a [a,b) pseudorandom number.
		Pseudorandom numbers from any other desired distribution may be generated from the [0,1) real uniformly distributed pseudorandom numbers by applying the inverse cumulative distribution function of the distribution required.
	www.brianhetrick.com /casio/gmrandom.html (1175 words)

	Pseudorandom Numbers :: Algorithms : Gourt
		Pseudorandom sequences typically exhibit statistical randomness while being generated by an entirely deterministic causal process.
		HENKOS Pseudorandom Number Generator - Presents and evaluates this generator, intended for use as a key generator for a one-time pad cipher.
		NIST: Random Number Generation and Testing - Project to develop a battery of statistical tests to detect nonrandomness in binary sequences, to produce documentation and a software implementation of these tests, and to provide guidance in the use of these tests.
	computers.gourt.com /Algorithms/Pseudorandom-Numbers.html (596 words)

	RANDOM NUMBERS (Site not responding. Last check: )
		A particularly useful random number sequence is the uniform random number sequence.
		Because a random number sequence is supposed to be random, there cannot be any computer algorithm that iteratively computes truly random numbers.
		In most implementations of rand (), the generation of the current pseudorandom number is a function of the previously generated pseudorandom number.
	home.earthlink.net /~ddruml/random2.htm (958 words)

	Random (JMSL Numerical Library)
		Generate a pseudorandom number from a standard normal distribution using an inverse CDF method.
		Generate a pseudorandom number from a triangular distribution on the interval (0,1).
		The hypergeometric random variable x can be thought of as the number of items of a given type in a random sample of size n that is drawn without replacement from a population of size l containing m items of this type.
	www.vni.com /products/imsl/jmsl/v40/api/com/imsl/stat/Random.html (3131 words)

	Random Numbers \| World of Scientific Discovery
		In the 1950s, the RAND Corporation built a special machine to generate pseudorandom binary bits of 0 or 1 that were then used to produce a table of one million random decimal digits.
		The most common method for generating pseudorandom numbers is to use a linear congruential generator invented in 1951 by Derrick H. Lehmer (1905-1991).
		However, because there are only a finite number of possible remainders when a number is divided by m, a researcher using this method could use up all the pseudorandom numbers before finishing an experiment.
	www.bookrags.com /research/random-numbers-wsd (574 words)

	AptMath Computer Programming and Statistical Analysis home page
		However, not all algorithms for pseudorandom number generation from a specific random distribution are equally suitable for a given purpose.
		Pseudorandom number generators for the discrete uniform random number distribution have a special role in many simulations.
		Pseudorandom variates from the discrete uniform random number distribution are used in various techniques to simulate random numbers from a very wide variety of other statistical random number distributions; a few examples are the continuous uniform, normal, Student's t, chi-squared, F, Poisson, binomial, negative binomial, beta, gamma, exponential, and Weibull distributions.
	www.aptmath.com (605 words)

	Make your software behave: Playing the numbers
		A number known as the "seed" is provided to a pseudo-random number generator as an initial integer to pass through the function.
		Since this number was being used as the seed for the random number generator, the number of possible decks now reduces to 86,400,000.
		By synchronizing their program with the system clock on the server generating the pseudo-random number, they are able to reduce the number of possible combinations down to a number on the order of 200,000 possibilities.
	www.ibm.com /developerworks/library/s-playing (3818 words)

	[No title] (Site not responding. Last check: )
		NIST Special Publication (SP) 800-22, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, discusses the randomness testing of random number and pseudorandom number generators (RNGs and PRNGs) that may be used for many purposes including cryptographic, modeling, and simulation applications.
		A pseudorandom number generator produces a sequence of bits from an initial value called a seed using a known algorithm.
		The Runs test is used to determine whether the total numbers of runs of ones and zeros of various lengths is as expected for a random sequence.
	csrc.nist.gov /publications/nistbul/itl00-12.txt (1516 words)

	Stata help for random
		This is a quick reference on functions for generating random numbers.
		To generate normally distributed random numbers with mean 0 and standard deviation 1, use invnormal(uniform()).
		To generate normally distributed random numbers with mean m and standard deviation s, use m+s*invnormal(uniform()).
	www.stata.com /help.cgi?random (151 words)

	Pseudorandom Numbers
		Numbers generated by a deterministic process that appear to be random.
		One such process squares the last four digits of a phone number, extracts the middle four digits of the squared value, squares these digits and proceeds in like fashion.
		Although the resulting sequence of four digit numbers will appear to be random, it is generated deterministically and may reveal a pattern upon analysis.
	riskinstitute.ch /00012514.htm (64 words)

	Random Number Generators and XS - The Perl Journal, Summer 1997
		These numbers can be used as session keys, initialization vectors, seeds for RSA prime number generation, and so on.
		Many applications need random numbers, but not necessarily numbers unpredictable from the "inside." Quite the contrary, they often require a source of random numbers that generates the same sequence whenever you run the program.
		Pseudorandom number generators (PRNGs) are deterministic algorithms that produce such streams of repeatable (and thus predictable) numbers.
	www.foo.be /docs/tpj/issues/vol2_2/tpj0202-0008.html (1789 words)

	Random numbers
		The probability it assigns to a random number expresses an information about the expected average number of occurrences of the random number in an unlinked sequence of performances of an experiment.
		As long as a random number is within the range of a random variable X, X is a valid model for x and x is a valid realization of X.
		The same is true for sequences of random numbers, since such sequences are simply realizations of a random vector describing an experiment yielding a vector of real numbers.
	random.mat.sbg.ac.at /~ste/dipl/node9.html (910 words)

	Cryptographically Secure Random Numbers
		These issues tend to be of great concern when using a "pseudorandom" number generator: pseudorandom numbers are generated from a deterministic process and in fact, are not truly random.
		An appealing property of pseudorandom number generators is that the deterministic nature of the equations allow exact calculations of the level of difficulty of (2) or (3) above.
		Unlike pseudo-random number generators in which data is known to be non-random and the question of cryptographic security is reduced to one of measuring a degree of difficulty, a true random number generator like Really Random Numbers always has an open question: "Are the numbers really random?"
	www.sunny-beach.net /random_numbers/manual/173.htm (600 words)

	Random (Java 2 Platform SE 5.0)
		An instance of this class is used to generate a stream of pseudorandom numbers.
		The number of random bytes produced is equal to the length of the byte array.
		Linear congruential pseudo-random number generators such as the one implemented by this class are known to have short periods in the sequence of values of their low-order bits.
	java.sun.com /j2se/1.5.0/docs/api/java/util/Random.html (1127 words)

	Probability and Algorithms
		A third reason arises from cryptography: the existence of secure pseudorandom bit generators is essentially equivalent to the existence of secure private-key cryptosystems.
		For Monte Carlo simulations, one often wants pseudorandom numbers, which are numbers simulating either independent draws from a fixed probability distribution on the real line R, or more generally numbers simulating samples from a stationary random process.
		Hence the problem of constructing pseudorandom numbers is in principle reducible to that of constructing pseudorandom bits.
	www.nap.edu /openbook.php?record_id=2026&page=66 (475 words)

	RngPack: High-Quality Random Numbers for Java (Site not responding. Last check: )
		RngPack 1.1a fixes a number of serious bugs in RngPack 1.0 including an incorrect coefficient in the Ranecu implementation and an off-by-one error in the choice() method.
		RngPack is a pseudorandom number generator package for Java.
		Pseudorandom means that the "random" numbers are generated by a deterministic mathematical process, not by a fundamentally random physical process such as radioactive decay or Johnson noise.
	www.honeylocust.com /RngPack (513 words)

	CS1030 -- Lab 4: Pseudorandom Number Generator Class
		The power residue method is an alternative way of generating pseudorandom numbers.
		The lowest n digits of the result is the pseudorandom number generated and is used as the seed for the next pseudorandom number in the sequence.
		The residue of this number is 863299, the second pseudorandom number generated.
	people.msoe.edu /~taylor/cs1030s05/lab4.htm (381 words)

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