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Variation
Variation or Variations may refer to: Science and mathematics * Variation (astronomy), any perturbation of the mean motion or orbit of a planet or satellite, particularly of the moon * Genetic variation, the difference in DNA among individuals or the differences between populations ** Human genetic variation, genetic differences in and among populations of humans * Magnetic variation, difference between magnetic north and true north, measured as an angle * ''p''-variation in mathematical analysis, a family of seminorms of functions * Coefficient of variation in probability theory and statistics, a standardized measure of dispersion of a probability distribution or frequency distribution * Total variation in mathematical analysis, a way of quantifying the change in a function over a subset of \mathbb^n or a measure space * Calculus of variations in mathematical analysis, a method of finding maxima and minima of functionals Arts * Variation (ballet) or pas seul, solo dance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Human Genetic Variation
Human genetic variation is the genetic differences in and among populations. There may be multiple variants of any given gene in the human population (alleles), a situation called polymorphism. No two humans are genetically identical. Even monozygotic twins (who develop from one zygote) have infrequent genetic differences due to mutations occurring during development and gene copy-number variation. Differences between individuals, even closely related individuals, are the key to techniques such as genetic fingerprinting. As of 2017, there are a total of 324 million known variants from sequenced human genomes. As of 2015, the typical difference between an individual's genome and the reference genome was estimated at 20 million base pairs (or 0.6% of the total of 3.2 billion base pairs). Comparatively speaking, humans are a genetically homogenous species. Although a small number of genetic variants are found more frequently in certain geographic regions or in people with ance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Variation
In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure. For a real-valued continuous function ''f'', defined on an interval 'a'', ''b''⊂ R, its total variation on the interval of definition is a measure of the one-dimensional arclength of the curve with parametric equation ''x'' ↦ ''f''(''x''), for ''x'' ∈ 'a'', ''b'' Functions whose total variation is finite are called functions of bounded variation. Historical note The concept of total variation for functions of one real variable was first introduced by Camille Jordan in the paper . He used the new concept in order to prove a convergence theorem for Fourier series of discontinuous periodic functions whose variation is bounded. The extension of the concept to functions of more than one variable however is not simple for various reasons. Definitions Total variation for functions of one real variable Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variation (music)
In music, variation is a formal technique where material is repeated in an altered form. The changes may involve melody, rhythm, harmony, counterpoint, timbre, orchestration or any combination of these. Variation techniques Mozart's Twelve Variations on "Ah vous dirai-je, Maman" (1785), known in the English-speaking world as "Twinkle, Twinkle, Little Star" exemplifies a number of common variation techniques. Here are the first eight bars of the theme: Melodic variation Mozart's first variation decorates and elaborates the plain melodic line: Rhythmic variation The fifth variation breaks up the steady pulse and creates syncopated off-beats: Harmonic variation The seventh variation introduces powerful new chords, which replace the simple harmonies originally implied by the theme with a prolongational series of descending fifths: Minor mode In the elaborate eighth variation, Mozart changes from the major to the parallel minor mode, while combining three techniques: count ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Variation
Genetic variation is the difference in DNA among individuals or the differences between populations. The multiple sources of genetic variation include mutation and genetic recombination. Mutations are the ultimate sources of genetic variation, but other mechanisms, such as genetic drift, contribute to it, as well. Among individuals within a population Genetic variation can be identified at many levels. Identifying genetic variation is possible from observations of phenotypic variation in either quantitative traits (traits that vary continuously and are coded for by many genes (e.g., leg length in dogs)) or discrete traits (traits that fall into discrete categories and are coded for by one or a few genes (e.g., white, pink, or red petal color in certain flowers)). Genetic variation can also be identified by examining variation at the level of enzymes using the process of protein electrophoresis. Polymorphic genes have more than one allele at each locus. Half of the genes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-variation
In mathematical analysis, ''p''-variation is a collection of seminorms on functions from an ordered set to a metric space, indexed by a real number p\geq 1. ''p''-variation is a measure of the regularity or smoothness of a function. Specifically, if f:I\to(M,d), where (M,d) is a metric space and ''I'' a totally ordered set, its ''p''-variation is : \, f \, _ = \left(\sup_D\sum_d(f(t_k),f(t_))^p\right)^ where ''D'' ranges over all finite partitions of the interval ''I''. The ''p'' variation of a function decreases with ''p''. If ''f'' has finite ''p''-variation and ''g'' is an ''α''-Hölder continuous function, then g\circ f has finite \frac-variation. The case when ''p'' is one is called total variation, and functions with a finite 1-variation are called bounded variation functions. Link with Hölder norm One can interpret the ''p''-variation as a parameter-independent version of the Hölder norm, which also extends to discontinuous functions. If ''f'' is ''α''–H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Variation
In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the standard deviation \sigma to the mean \mu (or its absolute value, The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, and in neuroscience. Definition The coefficient of variation (CV) is defined as the ratio of the standard deviation \ \sigma to the mean \ \mu , c_ = \frac. It shows the extent of variability in relation to the mean of the population. The coefficient of variation should be computed only for data measured on scales that have a meaningful zer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variation (horse)
Variation (1827–1847) was a British Thoroughbred racehorse and broodmare who won the classic Oaks Stakes at Epsom Downs Racecourse in 1830. The Oaks was Variation's racing debut and she went on to win a total of eight races from fifteen starts. Her other successes included three match races, the Oatlands Stakes, and two editions of the Garden Stakes at Newmarket Racecourse. Her best performance was probably her win in the 1831 Garden Stakes in which she defeated a very strong field over a distance of two miles. She was retired from racing in 1833 and had some success as a broodmare. Background Variation was a bay mare bred in 1827 either by Mr Nowell or by William Scott Stonehewer, Sr. Stonehewer, a "great sporting man" from a "good old Yorkshire family", owned her during her racing career. She was the eighth foal produced by her dam, a daughter of Beningbrough named Johanna Southcote (1811–1834). Variation was the only classic winner sired by Bustard, a horse which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variation (linguistics)
Variation is a characteristic of language: there is more than one way of saying the same thing. Speakers may vary pronunciation ( accent), word choice (lexicon), or morphology and syntax (sometimes called "grammar"). But while the diversity of variation is great, there seem to be boundaries on variation – speakers do not generally make drastic alterations in sentence word order or use novel sounds that are completely foreign to the language being spoken. Linguistic variation does not equate with language ungrammaticality, but speakers are still (often unconsciously) sensitive to what is and is not possible in their native lect. Variationists study how a language changes by observing it. This is accomplished by looking at authentic data. For example, variation is studied by looking at linguistic and social environments, then the data is analyzed as the change occurs. Variation in research programs must be malleable due to the nature of language itself. This is because language i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Variation
Magnetic declination, or magnetic variation, is the angle on the horizontal plane between magnetic north (the direction the north end of a magnetized compass needle points, corresponding to the direction of the Earth's magnetic field lines) and true north (the direction along a meridian towards the geographic North Pole). This angle varies depending on position on the Earth's surface and changes over time. Somewhat more formally, Bowditch defines variation as “the angle between the magnetic and geographic meridians at any place, expressed in degrees and minutes east or west to indicate the direction of magnetic north from true north. The angle between magnetic and grid meridians is called grid magnetic angle, grid variation, or grivation.” By convention, declination is positive when magnetic north is east of true north, and negative when it is to the west. '' Isogonic lines'' are lines on the Earth's surface along which the declination has the same constant value, and li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Diversity
Genetic diversity is the total number of genetic characteristics in the genetic makeup of a species, it ranges widely from the number of species to differences within species and can be attributed to the span of survival for a species. It is distinguished from ''genetic variability'', which describes the tendency of genetic characteristics to vary. Genetic diversity serves as a way for populations to adapt to changing environments. With more variation, it is more likely that some individuals in a population will possess variations of alleles that are suited for the environment. Those individuals are more likely to survive to produce offspring bearing that allele. The population will continue for more generations because of the success of these individuals. The academic field of population genetics includes several hypotheses and theories regarding genetic diversity. The neutral theory of evolution proposes that diversity is the result of the accumulation of neutral substitutions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variation (astronomy)
In astronomy, the variation of the Moon is one of the principal perturbations in the motion of the Moon. Discovery The variation was discovered by Tycho Brahe, who noticed that, starting from a lunar eclipse in December 1590, at the times of syzygy (new or full moon), the apparent velocity of motion of the Moon (along its orbit as seen against the background of stars) was faster than expected. On the other hand, at the times of first and last quarter, its velocity was correspondingly slower than expected. (Those expectations were based on the lunar tables widely used up to Tycho's time. They took some account of the two largest irregularities in the Moon's motion, i.e. those now known as the equation of the center and the evection, see also Lunar theory - History.) Variation The main visible effect (in longitude) of the variation of the Moon is that during the course of every month, at the octants of the Moon's phase that follow the syzygies (i.e. halfway between the new or t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
