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A Discrete Binary Version of The Particle Swarm Algorithm
 PROC. OF CONF. ON SYSTEM, MAN, AND CYBERNETICS, 4104–4109
, 1997
"... The particle swarm algorithm adjusts the trajectories of a population of “particles” through a problem space on the basis of information about each particle’s previous best performance and the best previous performance of its neighbors. Previous versions of the particle swarm have operated in contin ..."
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Cited by 339 (2 self)
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in continuous space, where trajectories are defined as changes in position on some number of dimensions. The present paper reports a reworking of the algorithm to operate on discrete binary variables. In the binary version, trajectories are changes in the probability that a coordinate will take on a zero or one
Monotonicity, thinning and discrete versions of the Entropy Power Inequality
, 2009
"... We consider the entropy of sums of independent discrete random variables, in analogy with Shannon’s Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for Poisson variables. We show that some natural analogues of the Entr ..."
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Cited by 10 (1 self)
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We consider the entropy of sums of independent discrete random variables, in analogy with Shannon’s Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for Poisson variables. We show that some natural analogues
On Symplectic and Multisymplectic Structures and Their Discrete Versions in Lagrangian Formalism
, 2001
"... Abstract We introduce the Euler–Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference discrete counterparts in the relevant regularly disc ..."
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Abstract We introduce the Euler–Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference discrete counterparts in the relevant regularly
A DISCRETE VERSION OF AN OPEN PROBLEM AND SEVERAL ANSWERS
"... D. D. Thang, T. T. Dat, and D. A. Tuan, Notes on an integral inequality, J. Inequal. Pure Appl. Math. 7 (2006), no. 4, Art. 120; Available online at ..."
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Cited by 1 (0 self)
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D. D. Thang, T. T. Dat, and D. A. Tuan, Notes on an integral inequality, J. Inequal. Pure Appl. Math. 7 (2006), no. 4, Art. 120; Available online at
ON THE DISCRETE VERSION OF GENERALIZED KIGURADZE’S LEMMA
"... Abstract:The Kiguaradze’s lemma for quasidifferences of a real sequence is presented. Some examples illustrating the result are included. Key words: quasidifferences, difference equation, nonoscillatory solution. In the last few years there has been increasing interest in the study of qualitative ..."
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Abstract:The Kiguaradze’s lemma for quasidifferences of a real sequence is presented. Some examples illustrating the result are included. Key words: quasidifferences, difference equation, nonoscillatory solution. In the last few years there has been increasing interest in the study of qualitative behaviour of solutions of difference equations. In many papers (see for example [24], [611]) the following Kiguradze’s Lemma is used to prove the main results. Let N = {0, 1,...}, N(a) = {a, a + 1,...}, where a ∈ N. Lemma 1. (see [1, Th.1.8.11]) Let x be defined on N(a), and x(n)> 0 with ∆ m x(n) on constant sign on N(a) and not identically zero. Then, there exists an integer l, 0 ≤ l ≤ m with m + l odd for ∆ m x(n) ≤ 0 or m + l even for ∆ m x(n) ≥ 0 and such that ∆ i x(n)> 0 for all large n ∈ N(a), 1 ≤ i ≤ l − 1, (−1) l+i ∆ i x(n)> 0 for all n ∈ N(a), l ≤ i ≤ m − 1. Let ri (i = 1, 2,..., m) be positive real sequences. For any real sequence x we denote L0x(n) = x(n), Lix(n) = ri(n)∆Li−1x(n), i = 1, 2,..., m, n ∈ N. The sequences Lix are called quasidifferences of x. For quasidifferences we can prove similar result, which we formulate as
the second equality is by FubiniTonelli. A discrete version is
"... The material mostly come from [1], [2], [3] and wikipedia. ..."
Efficient exact stochastic simulation of chemical systems with many species and many channels
 J. Phys. Chem. A
, 2000
"... There are two fundamental ways to view coupled systems of chemical equations: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more comm ..."
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Cited by 427 (5 self)
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There are two fundamental ways to view coupled systems of chemical equations: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more
An image segmentation method based on a discrete version of the topological derivative
 In World Congress Structural and Multidisciplinary Optimization 6, Rio de Janeiro. International Society for Structural and Multidisciplinary Optimization
, 2005
"... Computed tomography (CT) and magnetic resonance imaging (MRI) have introduced 3D data sets into clinical radiology. 3D data sets provide information for analysis not available in 2D imaging and challenge the traditional 2D viewing and interpretation used in most clinical environments. Despite the 3D ..."
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) should facilitate the segmentation process, medical images are relatively di#cult to segment for several undesired properties like low signaltonoise and contrasttonoise ratios and multiple and discontinuous edges. Our aim in this paper is to present an image segmentation method based on a discrete
The discrete version of Ostrowski’s inequality in normed linear spaces
 JOURNAL OF INEQUALITIES IN PURE AND APPLIED MATHEMATICS
, 2002
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On a discrete version of Tanaka’s theorem for maximal functions
 Proc. Amer. Math. Soc
"... ar ..."
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