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Random Number
A random number is generated by a random (stochastic) process such as throwing dice. Individual numbers cannot be predicted, but the likely result of generating a large quantity of numbers can be predicted by specific mathematical series and statistics. Algorithms and implementations Random numbers are frequently used in algorithms such as Knuth's 1964-developed algorithm for shuffling lists. (popularly known as ''the Knuth shuffle'' or ''the Fisher–Yates shuffle'', based on work they did in 1938). In 1999, a new feature was added to the Pentium III: a hardware-based random number generator. It has been described as "several oscillators combine their outputs and that odd waveform is sampled asynchronously." These numbers, however, were only 32 bit, at a time when export controls were on 56 bits and higher, so they were not state of the art. Common understanding In common understanding, "1 2 3 4 5" is not as random as "3 5 2 1 4" and certainly not as random as "47 88 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two Red Dice 01
2 (two) is a number, numeral (linguistics), numeral and numerical digit, digit. It is the natural number following 1 and preceding 3. It is the smallest and the only even prime number. Because it forms the basis of a Dualistic cosmology, duality, it has Religion, religious and Spirituality, spiritual significance in many Culture, cultures. Mathematics The number 2 is the second natural number after 1. Each natural number, including 2, is constructed by succession, that is, by adding 1 to the previous natural number. 2 is the smallest and the only even prime number, and the first Ramanujan prime. It is also the first superior highly composite number, and the first colossally abundant number. An integer is determined to be Parity (mathematics), even if it is Division (mathematics), divisible by two. When written in base 10, all Multiple (mathematics), multiples of 2 will end in 0, 2, 4, 6, or 8; more generally, in any even base, even numbers will end with an even digit. A dig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillators
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. The term ''vibration'' is precisely used to describe a mechanical oscillation. Oscillation, especially rapid oscillation, may be an undesirable phenomenon in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variate
In probability and statistics, a random variate or simply variate is a particular outcome or ''realization'' of a random variable; the random variates which are other outcomes of the same random variable might have different values ( random numbers). A random deviate or simply deviate is the difference of a random variate with respect to the distribution central location (e.g., mean), often divided by the standard deviation of the distribution (i.e., as a standard score). 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, where these procedures would actually provide values chosen from a uniform distribution of pseudorandom numbers. Procedures to generate random variates corresponding to a given distribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathematical definition refers to neither randomness nor variability but instead is a mathematical function (mathematics), function in which * the Domain of a function, domain is the set of possible Outcome (probability), outcomes in a sample space (e.g. the set \ which are the possible upper sides of a flipped coin heads H or tails T as the result from tossing a coin); and * the Range of a function, range is a measurable space (e.g. corresponding to the domain above, the range might be the set \ if say heads H mapped to -1 and T mapped to 1). Typically, the range of a random variable is a subset of the Real number, real numbers. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Sequence
The concept of a random sequence is essential in probability theory and statistics. The concept generally relies on the notion of a sequence of random variables and many statistical discussions begin with the words "let ''X''1,...,''Xn'' be independent random variables...". Yet as D. H. Lehmer stated in 1951: "A random sequence is a vague notion... in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests traditional with statisticians". Axiomatic probability theory ''deliberately'' avoids a definition of a random sequence. Traditional probability theory does not state if a specific sequence is random, but generally proceeds to discuss the properties of random variables and stochastic sequences assuming some definition of randomness. The Bourbaki school considered the statement "let us consider a random sequence" an abuse of language. Early history Émile Borel was one of the first mathematicians to formally address randomness in 190 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Number Generation
Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance. This means that the particular outcome sequence will contain some patterns detectable in hindsight but impossible to foresee. True random number generators can be ''Hardware random number generator, hardware random-number generators'' (HRNGs), wherein each generation is a function of the current value of a physical environment's attribute that is constantly changing in a manner that is practically impossible to model. This would be in contrast to so-called "random number generations" done by ''pseudorandom number generators'' (PRNGs), which generate numbers that only look random but are in fact predetermined—these generations can be reproduced simply by knowing the state of the PRNG. Various applications of randomness have led to the development of different methods for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi-random Sequence
In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x_1, \ldots, x_N has a low discrepancy. Roughly speaking, the discrepancy of a sequence is low if the proportion of points in the sequence falling into an arbitrary set ''B'' is close to proportional to the measure of ''B'', as would happen on average (but not for particular samples) in the case of an equidistributed sequence. Specific definitions of discrepancy differ regarding the choice of ''B'' (hyperspheres, hypercubes, etc.) and how the discrepancy for every B is computed (usually normalized) and combined (usually by taking the worst value). Low-discrepancy sequences are also called quasirandom sequences, due to their common use as a replacement of uniformly distributed random numbers. The "quasi" modifier is used to denote more clearly that the values of a low-discrepancy sequence are neither random nor pseudorandom, but such sequences share some properties ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmically Random Sequence
Intuitively, an algorithmically random sequence (or random sequence) is a sequence of binary digits that appears random to any algorithm running on a (prefix-free or not) universal Turing machine. The notion can be applied analogously to sequences on any finite alphabet (e.g. decimal digits). Random sequences are key objects of study in algorithmic information theory. In measure-theoretic probability theory, introduced by Andrey Kolmogorov in 1933, there is ''no such thing'' as a random sequence. For example, consider flipping a fair coin infinitely many times. Any particular sequence, be it 0000\dots or 011010\dots, has equal probability of exactly zero. There is no way to state that one sequence is "more random" than another sequence, using the language of measure-theoretic probability. However, it is intuitively obvious that 011010\dots looks more random than 0000\dots. Algorithmic randomness theory formalizes this intuition. As different types of algorithms are sometimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York Times
''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of the longest-running newspapers in the United States, the ''Times'' serves as one of the country's Newspaper of record, newspapers of record. , ''The New York Times'' had 9.13 million total and 8.83 million online subscribers, both by significant margins the List of newspapers in the United States, highest numbers for any newspaper in the United States; the total also included 296,330 print subscribers, making the ''Times'' the second-largest newspaper by print circulation in the United States, following ''The Wall Street Journal'', also based in New York City. ''The New York Times'' is published by the New York Times Company; since 1896, the company has been chaired by the Ochs-Sulzberger family, whose current chairman and the paper's publ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Los Angeles Times
The ''Los Angeles Times'' is an American Newspaper#Daily, daily newspaper that began publishing in Los Angeles, California, in 1881. Based in the Greater Los Angeles city of El Segundo, California, El Segundo since 2018, it is the List of newspapers in the United States, sixth-largest newspaper in the U.S. and the largest in the Western United States with a print circulation of 118,760. It has 500,000 online subscribers, the fifth-largest among U.S. newspapers. Owned by Patrick Soon-Shiong and published by California Times, the paper has won over 40 Pulitzer Prizes since its founding. In the 19th century, the paper developed a reputation for civic boosterism and opposition to Trade union, labor unions, the latter of which led to the Los Angeles Times bombing, bombing of its headquarters in 1910. The paper's profile grew substantially in the 1960s under publisher Otis Chandler, who adopted a more national focus. As with other regional newspapers in California and the United Sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wired (magazine)
''Wired'' is a bi-monthly American magazine that focuses on how emerging technologies affect culture, the economy, and politics. It is published in both print and Online magazine, online editions by Condé Nast. The magazine has been in publication since its launch in January 1993. Its editorial office is based in San Francisco, California, with its business headquarters located in New York City. ''Wired'' quickly became recognized as the voice of the emerging digital economy and culture and a pace setter in print design and web design. From 1998 until 2006, the magazine and its website, ''Wired.com'', experienced separate ownership before being fully consolidated under Condé Nast in 2006. It has won multiple National Magazine Awards and has been credited with shaping discourse around the digital revolution. The magazine also coined the term Crowdsourcing, ''crowdsourcing'', as well as its annual tradition of handing out Vaporware Awards. ''Wired'' has launched several in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere lev ..., neuroscience, physics, image processing, signal processing, stochastic control, control theory, information theory, computer scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
