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2,149
Nonlinear relaxation in population dynamics
 Fractals
, 2003
"... We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized LotkaVolterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interac ..."
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Cited by 2 (2 self)
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We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized LotkaVolterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random
The Dynamics of Nonlinear Relaxation Labeling Processes
, 1997
"... We present some new results which definitively explain the behavior of the classical, heuristic nonlinear relaxation labeling algorithm of Rosenfeld, Hummel, and Zucker in terms of the HummelZucker consistency theory and dynamical systems theory. In particular, it is shown that, when a certain symm ..."
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Cited by 39 (11 self)
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We present some new results which definitively explain the behavior of the classical, heuristic nonlinear relaxation labeling algorithm of Rosenfeld, Hummel, and Zucker in terms of the HummelZucker consistency theory and dynamical systems theory. In particular, it is shown that, when a certain
BREATHING PATTERNS IN NONLINEAR RELAXATION
"... Abstract. In numerical experiments involving nonlinear solitary waves propagating through nonhomogeneous media one observes “breathing ” in the sense of the amplitude of the wave going up and down on a much faster scale than the motion of the wave – see Fig. 2 below. In this paper we investigate thi ..."
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Cited by 2 (0 self)
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this phenomenon in the simplest case of stationary waves in which the evolution corresponds to relaxation to a nonlinear ground state. The particular model is the popular δ0 impurity in the cubic nonlinear Schrödinger equation on the line. We give asymptotics of the amplitude on a finite but relevant time
Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images.
 IEEE Trans. Pattern Anal. Mach. Intell.
, 1984
"... AbstractWe make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a latticelike physical system. The assignment of an energy function in the physical system determines its Gibbs di ..."
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Cited by 5126 (1 self)
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mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical
Optical Flow through Nonlinear Relaxation
"... A novel multiconstraint approach to the estimation of optical flow is presented, which is based on normal flow relaxation. An architecture for a parallel implementation of the algorithm is suggested, in which relaxation is accomplished by a mesh grid of simple computational units, one for each image ..."
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A novel multiconstraint approach to the estimation of optical flow is presented, which is based on normal flow relaxation. An architecture for a parallel implementation of the algorithm is suggested, in which relaxation is accomplished by a mesh grid of simple computational units, one for each
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1211 (13 self)
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the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
Impulses and Physiological States in Theoretical Models of Nerve Membrane
 Biophysical Journal
, 1961
"... ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing excitabi ..."
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Cited by 505 (0 self)
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ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing
Using Continuous Nonlinear Relaxations to Solve Constrained MaximumEntropy Sampling Problems
 Mathematical Programming, Series A
, 1998
"... We consider a new nonlinear relaxation for the Constrained MaximumEntropy Sampling Problem  the problem of choosing the s × s principal submatrix with maximal determinant from a given n × n positive definite matrix, subject to linear constraints. We implement a branchandboun ..."
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Cited by 10 (6 self)
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We consider a new nonlinear relaxation for the Constrained MaximumEntropy Sampling Problem  the problem of choosing the s × s principal submatrix with maximal determinant from a given n × n positive definite matrix, subject to linear constraints. We implement a branch
Using Convex Nonlinear Relaxations in the Global Optimization of Nonconvex Generalized Disjunctive Programs
"... In this paper we present a framework to generate tight convex relaxations for nonconvex generalized disjunctive programs. The proposed methodology builds on our recent work on bilinear and concave generalized disjunctive programs for which strong linear relaxations can be generated and extends its a ..."
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Cited by 1 (1 self)
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application by allowing nonlinear relaxations. This is particular important for those cases in which the convex envelopes of the nonconvex functions arising in the formulations are nonlinear (e.g. fractional terms). This extension is now possible by using the latest developments in convex disjunctive
CharacteristicBased Numerical Schemes for Hyperbolic Systems With Nonlinear Relaxation
, 1997
"... In order to embark the development of characteristic based schemes for hyperbolic systems with nonlinear stiff source terms we have studied a prototype onedimensional discretevelocity Boltzmann equation. We show that the method can be evaluated at the cost of an explicit scheme and that yield accu ..."
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Cited by 4 (3 self)
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systems with nonlinear relaxation [5]. These systems are characterized by the presence of multiple scales in the problem depending on the relaxation time ffl. The flow starts out at the frozen limit (t=ffl ! 0) and relaxes to the equilibrium limit (t=ffl ! 1). When at least one of these scales is much
Results 1  10
of
2,149