We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random

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 Hummel-Zucker consistency theory and dynamical systems theory. In particular, it is shown that, when a certain

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

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

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

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 ...

ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing

We consider a new nonlinear relaxation for the Constrained Maximum-Entropy 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

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

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