Correct rounding of values to the nearest representable value avoids systematic biases in calculations and slows the growth of errors. Rounding ties to even removes the statistical bias that can occur in adding similar figures. Directed rounding was intended as an aid with checking error bounds, for instance in interval arithmetic. It is also used in the implementation of some functions. The mathematical basis of the operations enabled high precision multiword arithmetic subroutines to be built relatively easily. The single and double precision formats were designed to be easy to sort without using floating-point hardware.
floating pointfloating-pointfloating-point number
IN: Handbook of Quantitative Science and Technology Research: The Use of Publication and Patent Statistics in Studies of S&T Systems. Ed. Henk Moed. Dordrecht: Kluwer Academic. Hyland, K. (2004). Disciplinary Discourses: Social Interactions in Academic Writing. New edition. University of Michigan Press/ESL. Klein, J.T. (1990). Interdisciplinarity: History, Theory, and Practice. Detroit: Wayne State University Press. Leydesdorff, L. & Rafols, I. (2008). A global map of science based on the ISI subject categories. Journal of the American Society for Information Science and Technology. Lindholm-Romantschuk, Y. (1998).
Telecommunication is the transmission of signs, signals, messages, words, writings, images and sounds or information of any nature by wire, radio, optical or electromagnetic systems. Telecommunication occurs when the exchange of information between communication participants includes the use of technology. It is transmitted either electrically over physical media, such as cables, or via electromagnetic radiation. Such transmission paths are often divided into communication channels which afford the advantages of multiplexing.
evolvedtheory of evolutionevolutionary theory
In addition to being a major source of variation, mutation may also function as a mechanism of evolution when there are different probabilities at the molecular level for different mutations to occur, a process known as mutation bias. If two genotypes, for example one with the nucleotide G and another with the nucleotide A in the same position, have the same fitness, but mutation from G to A happens more often than mutation from A to G, then genotypes with A will tend to evolve. Different insertion vs. deletion mutation biases in different taxa can lead to the evolution of different genome sizes. Developmental or mutational biases have also been observed in morphological evolution.
This technique for testing the statistical significance of results was developed in the early 20th century. The term significance does not imply importance here, and the term statistical significance is not the same as research, theoretical, or practical significance. For example, the term clinical significance refers to the practical importance of a treatment effect. Statistical significance dates to the 1700s, in the work of John Arbuthnot and Pierre-Simon Laplace, who computed the p-value for the human sex ratio at birth, assuming a null hypothesis of equal probability of male and female births; see for details.
SASSAS Enterprise MinerSAS Software
In a 2005 article for the Journal of Marriage and Family comparing statistical packages from SAS and its competitors Stata and SPSS, Alan C. Acock wrote that SAS programs provide "extraordinary range of data analysis and data management tasks," but were difficult to use and learn. SPSS and Stata, meanwhile, were both easier to learn (with better documentation) but had less capable analytic abilities, though these could be expanded with paid (in SPSS) or free (in Stata) add-ons. Acock concluded that SAS was best for power users, while occasional users would benefit most from SPSS and Stata. A comparison by the University of California, Los Angeles, gave similar results.
TuringTuring, Alan Turing, Alan
Alan Mathison Turing (23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. Turing is widely considered to be the father of theoretical computer science and artificial intelligence. Despite these accomplishments, he was never fully recognized in his home country during his lifetime due to his homosexuality, which was then a crime in the UK.
Mathematics: Random numbers are also employed where their use is mathematically important, such as sampling for opinion polls and for statistical sampling in quality control systems. Computational solutions for some types of problems use random numbers extensively, such as in the Monte Carlo method and in genetic algorithms. Medicine: Random allocation of a clinical intervention is used to reduce bias in controlled trials (e.g., randomized controlled trials). Religion: Although not intended to be random, various forms of divination such as cleromancy see what appears to be a random event as a means for a divine being to communicate their will. (See also Free will and Determinism).
Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation. In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language.
operational researchoperation researchmanagement science
Department of Labor Bureau of Labor Statistics.
Some kinds of statistical tests employ calculations based on ranks. Examples include: The distribution of values in decreasing order of rank is often of interest when values vary widely in scale; this is the rank-size distribution (or rank-frequency distribution), for example for city sizes or word frequencies. These often follow a power law. Some ranks can have non-integer values for tied data values. For example, when there is an even number of copies of the same data value, the above described fractional statistical rank of the tied data ends in ½.
In probability theory and statistics, stochastic matrices are used to describe sets of probabilities; for instance, they are used within the PageRank algorithm that ranks the pages in a Google search. Matrix calculus generalizes classical analytical notions such as derivatives and exponentials to higher dimensions. Matrices are used in economics to describe systems of economic relationships. A major branch of numerical analysis is devoted to the development of efficient algorithms for matrix computations, a subject that is centuries old and is today an expanding area of research. Matrix decomposition methods simplify computations, both theoretically and practically.
Similarly, psychologists have found that due to cognitive bias people are more likely to remember notable or unusual examples rather than typical examples. Thus, even when accurate, anecdotal evidence is not necessarily representative of a typical experience. Accurate determination of whether an anecdote is typical requires statistical evidence. Misuse of anecdotal evidence is an informal fallacy and is sometimes referred to as the "person who" fallacy ("I know a person who..."; "I know of a case where..." etc.) which places undue weight on experiences of close peers which may not be typical.
Data transformation (statistics). Winsorizing.
Recently they have also sponsored a machine-learned ranking competition "Internet Mathematics 2009" based on their own search engine's production data. Yahoo has announced a similar competition in 2010. As of 2008, Google's Peter Norvig denied that their search engine exclusively relies on machine-learned ranking. Cuil's CEO, Tom Costello, suggests that they prefer hand-built models because they can outperform machine-learned models when measured against metrics like click-through rate or time on landing page, which is because machine-learned models "learn what people say they like, not what people actually like".
learnassociative learninglearning process
In these environments, learning is favored because the fish are predisposed to learn the specific spatial cues where they live. Machine learning, a branch of artificial intelligence, concerns the construction and study of systems that can learn from data.
The term is also used, especially in the description of algorithms, to mean associative array or "abstract array", a theoretical computer science model (an abstract data type or ADT) intended to capture the essential properties of arrays. Arrays have better cache locality as compared to linked lists. The first digital computers used machine-language programming to set up and access array structures for data tables, vector and matrix computations, and for many other purposes.
Growth curve (statistics). Regression analysis includes a large group of methods for predicting future values of a variable using information about other variables. These methods include both parametric (linear or non-linear) and non-parametric techniques. Autoregressive moving average with exogenous inputs (ARMAX). Composite forecasts. Cooke's method. Delphi method. Forecast by analogy. Scenario building. Statistical surveys. Technology forecasting. Artificial neural networks. Group method of data handling. Support vector machines. Data mining. Machine learning. Pattern recognition. Simulation. Prediction market.