science, a function f ( n ) {\displaystyle f(n)} is said to exhibit quasi-polynomial growth when it has an upper bound of the form f ( n ) = 2 O ( ( log ...
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Polylogarithmic function (category Polynomial stubs)
produces a function with quasi-polynomial growth, and algorithms with this as their time complexity are said to take quasi-polynomial time. All polylogarithmic...
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theorem on groups of polynomial growth, first proved by Mikhail Gromov, characterizes finitely generated groups of polynomial growth, as those groups which...
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Time complexity (redirect from Polynomial time)
require superpolynomial time. Quasi-polynomial time algorithms are algorithms whose running time exhibits quasi-polynomial growth, a type of behavior that...
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say that G has a polynomial growth rate. The infimum k 0 {\displaystyle k_{0}} of such k's is called the order of polynomial growth. According to Gromov's...
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details. Two metric spaces are quasi-isometric if there exists a quasi-isometry between them. The property of being quasi-isometric behaves like an equivalence...
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ecology, etc. Rational curves are subdivided according to the degree of the polynomial. Line Plane curves of degree 2 are known as conics or conic sections and...
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Height function (redirect from Height of a polynomial)
properties of polynomials". Illinois Journal of Mathematics. 7 (4): 681–701. doi:10.1215/ijm/1255645104. Zbl 0117.04003. Néron, André (1965). "Quasi-fonctions...
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turn that various properties of growth, such as polynomial growth, the degree of polynomial growth, and exponential growth, are isomorphism invariants of...
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Generating function (redirect from Generating polynomial)
functions precisely corresponds to the generating functions that enumerate quasi-polynomial sequences of the form f n = p 1 ( n ) ρ 1 n + ⋯ + p ℓ ( n ) ρ ℓ n ...
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quadratic growth at infinity. From this, elementary complex analysis can be used to show that g {\displaystyle g} must actually be a quadratic polynomial. Thus...
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Golden ratio (section Minimal polynomial)
an algebraic integer. It has minimal polynomial x 2 − x − 1. {\displaystyle x^{2}-x-1.} This quadratic polynomial has two roots, φ {\displaystyle \varphi...
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integer programs with few variables in time polynomial in the number of constraints. Eugene M. Luks for a polynomial time graph isomorphism algorithm for graphs...
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identity of the complexity classes formed by taking "polynomial time" and "non-deterministic polynomial time" as least upper bounds. Simulating an NP-algorithm...
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interpolation Padua points — set of points in R2 with unique polynomial interpolant and minimal growth of Lebesgue constant Hermite interpolation Birkhoff interpolation...
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Dehn function (section Growth types of functions)
the length of that relation (see pp. 79–80 in ). The growth type of the Dehn function is a quasi-isometry invariant of a finitely presented group. The...
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{\displaystyle P=0} . To avoid the solution of a transcendental function, a polynomial Taylor expansion to the second-order in P {\displaystyle P} is used for...
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others. Theorems which use quasi-isometry invariants to prove algebraic results about groups, for example: Gromov's polynomial growth theorem; Stallings' ends...
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(unemployment) as a function of the independent variable (GDP growth) is given in polynomial least squares. Econometric theory uses statistical theory and...
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"Jump PDA's, deterministic context-free languages, principal AFDLs and polynomial time recognition (Extended Abstract)," Proceedings of the fifth annual...
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{\displaystyle \mathbb {P} ^{n}} of some finite family of homogeneous polynomials that generate a prime ideal, the defining ideal of the variety. A projective...
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randomized polynomial time algorithm, but not by a deterministic one: see Dyer, Martin; Frieze, Alan; Kannan, Ravi (January 1991). "A Random Polynomial-time...
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bundle on projective space whose global sections are the homogeneous polynomials of degree 1 (that is, linear functions) in variables x 0 , … , x n {\displaystyle...
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Polynomial regression, Muthukrishnan". Maths behind Polynomial regression. Retrieved 30 Jan 2024. "Mathematics of Polynomial Regression". Polynomial Regression...
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dispersion Quasi-birth–death process Quasi-experiment Quasi-experimental design – see Design of quasi-experiments Quasi-likelihood Quasi-maximum likelihood...
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deviate somewhat from Zipf's law. Such empirical distributions are said to be quasi-Zipfian. In 1913, the German physicist Felix Auerbach observed an inverse...
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equations Sine-Gordon equation Sturm–Liouville theory of orthogonal polynomials and separable partial differential equations Universal differential equation...
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are: the Lorenz attractor population growth (i.e. logistic map) parameter plane of complex quadratic polynomials with Mandelbrot set. In quantum mechanics...
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differential geometry. They can also be defined as implicit equations, often polynomial equations (which spawned algebraic geometry). Analytic geometry also makes...
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Dries and Alex Wilkie's treatment of Gromov's theorem on groups of polynomial growth. Nonstandard analysis was used by Larry Manevitz and Shmuel Weinberger...
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