Results 1  10
of
564,758
Bayes Factors
, 1995
"... In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null ..."
Abstract

Cited by 1766 (74 self)
 Add to MetaCart
In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
Abstract

Cited by 465 (1 self)
 Add to MetaCart
Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which finds such a partition A, B, C in O(n) time.
A Generalized Factor Theorem
"... In this paper we present a generalization of the factor theorem for polynomials. We show that under certain conditions for a given polynomial in the variable x there exists a factor of the form x m − b for a positive integer m and complex b.. We also show the way we may obtain quadratic factors. ..."
Abstract
 Add to MetaCart
In this paper we present a generalization of the factor theorem for polynomials. We show that under certain conditions for a given polynomial in the variable x there exists a factor of the form x m − b for a positive integer m and complex b.. We also show the way we may obtain quadratic factors.
A VIOLATION OF THE FACTORIZATION THEOREM
, 1997
"... A new mechanism for hard inclusive production, which leads to a violation of the factorization theorem, is suggested. The mechanism is illustrated by a detailed discussion of Higgs meson production in high energy deutrondeutron scattering. Numerical estimates for the effect are given for high energ ..."
Abstract
 Add to MetaCart
A new mechanism for hard inclusive production, which leads to a violation of the factorization theorem, is suggested. The mechanism is illustrated by a detailed discussion of Higgs meson production in high energy deutrondeutron scattering. Numerical estimates for the effect are given for high
Determining the Number of Factors in Approximate Factor Models
, 2000
"... In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors c ..."
Abstract

Cited by 538 (29 self)
 Add to MetaCart
In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors
Algorithms for Nonnegative Matrix Factorization
 In NIPS
, 2001
"... Nonnegative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minim ..."
Abstract

Cited by 1230 (5 self)
 Add to MetaCart
Nonnegative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown
Factoring wavelet transforms into lifting steps
 J. Fourier Anal. Appl
, 1998
"... ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This dec ..."
Abstract

Cited by 573 (8 self)
 Add to MetaCart
. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is wellknown to algebraists (and expressed by the formula); it is also used in linear systems theory in the electrical engineering community. We
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
Abstract

Cited by 1787 (72 self)
 Add to MetaCart
A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Little Bezout theorem (factor theorem)
 FORMALIZED MATHEMATICS
, 2004
"... We present a formalization of the factor theorem for univariate polynomials, also called the (little) Bezout theorem: Let r belong to a commutative ring L and p(x) be a polynomial over L. Then x − r divides p(x) iff p(r) = 0. We also prove some consequences of this theorem like that any non zero po ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
We present a formalization of the factor theorem for univariate polynomials, also called the (little) Bezout theorem: Let r belong to a commutative ring L and p(x) be a polynomial over L. Then x − r divides p(x) iff p(r) = 0. We also prove some consequences of this theorem like that any non zero
Results 1  10
of
564,758