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Improving the Minimum Free Energy Principle to the Maximum Information Efficiency Principle [PDF]
EntropyFriston proposed the Minimum Free Energy Principle (FEP) based on the Variational Bayesian (VB) method. This principle emphasizes that the brain and behavior coordinate with the environment, promoting self-organization. However, it has a theoretical flaw,
Chenguang Lu
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Venus atmosphere profile from a maximum entropy principle [PDF]
Nonlinear Processes in Geophysics, 2007 The variational method with constraints recently developed by Verkley and Gerkema to describe maximum-entropy atmospheric profiles is generalized to ideal gases but with temperature-dependent specific heats.
L. N. Epele +4 more
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Mean-Field Pontryagin Maximum Principle [PDF]
Journal of Optimization Theory and Applications, 2017 International audienceWe derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ordinary differential equations and a partial differential equation of Vlasov-type with smooth interaction kernel. Such
Bongini, Mattia +3 more
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The maximum principle with lack of monotonicity
Electronic Journal of Qualitative Theory of Differential Equations, 2018 We establish a maximum principle for the weighted $(p,q)$-Laplacian, which extends the general Pucci–Serrin strong maximum principle to this quasilinear abstract setting.
Patrizia Pucci, Vicenţiu Rădulescu
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Remarks on the Maximum Entropy Principle with Application to the Maximum Entropy Theory of Ecology [PDF]
Entropy, 2017 In the first part of the paper we work out the consequences of the fact that Jaynes’ Maximum Entropy Principle, when translated in mathematical terms, is a constrained extremum problem for an entropy function H ( p ) expressing the uncertainty ...
Marco Favretti
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Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control [PDF]
PRX Quantum, 2020 Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by ...
U. Boscain, M. Sigalotti, D. Sugny
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On energy stable, maximum-principle preserving, second order BDF scheme with variable steps for the Allen-Cahn equation [PDF]
SIAM Journal on Numerical Analysis, 2020 In this work, we investigate the two-step backward differentiation formula (BDF2) with nonuniform grids for the Allen-Cahn equation. We show that the nonuniform BDF2 scheme is energy stable under the time-step ratio restriction $r_k:=\tau_k/\tau_{k-1}
Hong-lin Liao, T. Tang, Tao Zhou
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Polyconvex functionals and maximum principle
Mathematics in Engineering, 2023 Let us consider continuous minimizers $ u : \bar \Omega \subset \mathbb{R}^n \to \mathbb{R}^n $ of $ \mathcal{F}(v) = \int_{\Omega} [|Dv|^p \, + \, |{\rm det}\,Dv|^r] dx, $ with $ p > 1 $ and $ r > 0 $; then it is known that every ...
Menita Carozza +3 more
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Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations [PDF]
SIAM Journal on Scientific Computing, 2020 A new class of high-order maximum principle preserving numerical methods is proposed for solving parabolic equations, with application to the semilinear Allen--Cahn equation.
Buyang Li, Jiang Yang, Zhi Zhou
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A maximum principle related to volume growth and applications [PDF]
Annali di Matematica Pura ed Applicata, 2020 In this paper, we derive a new form of maximum principle for smooth functions on a complete noncompact Riemannian manifold M for which there exists a bounded vector field X such that ⟨∇f,X⟩≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage ...
L. Alías +2 more
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