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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Entropy-Dissipation Informed Neural Networks for McKean-Vlasov type PDEs
McKean-Vlasov型 偏微分方程 熵耗散 信息神经网络
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2023/4/13
We extend the concept of self-consistency for the Fokker-Planck equation (FPE) [Shen et al., 2022] to the more general McKean-Vlasov equation (MVE). While FPE describes the macroscopic behavior of par...
ENTROPY OF COUPLED MAP LATTICES
Coupled map lattice Pesin formula Ruelle inequality
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2015/9/29
The entropy of coupled map lattices with respect to the group
of space-time translations is considered. We use the notion of generalized
Lyapunov spectra ([11]) to prove the analogue of Ruelle inequ...
THE ENTROPY THEORY OF SYMBOLIC EXTENSIONS
ENTROPY THEORY SYMBOLIC EXTENSIONS
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2015/9/29
Fix a topological system (X, T), with its space K(X, T) of Tinvariant Borel probabilities. If (Y, S) is a symbolic system (subshift) and ϕ : (Y, S) → (X, T) is a topological extension (factor map...
SYMBOLIC EXTENSION ENTROPY:Cr EXAMPLES,PRODUCTS AND FLOWS
SYMBOLIC EXTENSION ENTROPY Cr EXAMPLES PRODUCTS FLOWS
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2015/9/29
Adapting techniques of Misiurewicz, for 1 ≤ r < ∞ we give an explicit construction of Cr maps with positiveresidual entropy. We also establish the behavior of symbolic extension entropy with respect t...
Zd SHIFTS OF FINITE TYPE WITHOUT EQUAL ENTROPY FULL SHIFT FACTORS
Zd SHIFTS FINITE TYPE ENTROPY FULL SHIFT
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2015/9/29
For d ≥ 2, we use results of Hochman and Meyerovitch to construct examples of Zd shifts of finite type of entropy log N, N ∈ N, which cannot factor topologically onto the Zd Bernoulli shift on N symbo...
BOWEN’S ENTROPY-CONJUGACY CONJECTURE IS TRUE UP TO FINITE INDEX
BOWEN’S ENTROPY CONJUGACY CONJECTURE FINITE INDEX
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2015/9/29
For a topological dynamical system (X, f), consisting of a continuous map f : X → X, and a (not necessarily compact) set Z ⊂ X, Bowen [2] defined a dimension-like version of entropy,hX(f, Z). In...
Entropy and random feedback
Convex function matrix spectrum application linear controller design
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2015/8/11
The gamma-entropy is a convex function of matrices that is closely related to the Frobenius and spectral (maximum singular value) norms. It comes up in several applications such as central H-infinity ...
Entropy and Renormalized Solutions for the p(x)-Kaokacuab Equation with Measure Data
Variable exponents Entropy solutions Renormalized solutions Exist- ence Uniqueness
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2015/5/4
In this paper we prove the existence and uniqueness of both entropy solutions and renormalized solutions for the p(x)-Laplacian equation with variable exponents and a signed measure in L 1 (Ω) +...
Acyclic edge-coloring using entropy compression
Acyclic edge-coloring entropy compression Combinatorics
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2012/6/29
An edge-coloring of a graph G is acyclic if it is a proper edge-coloring of G and every cycle contains at least three colors. We prove that every graph with maximum degree Delta has an acyclic edge-co...
Lowering topological entropy over subsets revisited
entropy principal extension lowerable hereditarily lowerable
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2012/6/19
Let $(X, T)$ be a topological dynamical system. Denote by $h (T, K)$ and $h^B (T, K)$ the covering entropy and dimensional entropy of $K\subseteq X$, respectively. $(X, T)$ is called D-{\it lowerable}...
Entropy, Lyapunov exponents and the volume growth of boundary distortion under the action of dynamical systems
Lyapunov exponents the volume growth of boundary distortion the action of dynamical systems
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2012/4/17
We study the connection between the Lyapunov exponents and the volume growth of boundary distortion of regions in the phase space of the dynamical system.
Bayesian interpretation of Generalized empirical likelihood by maximum entropy
Bayesian interpretation Generalized empirical likelihood maximum entropy
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2012/3/1
We study a parametric estimation problem related to moment condition models. As an alternative to the generalized empirical likelihood (GEL) and the generalized method of moments (GMM), a Bayesian app...
Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups
Residually nilpotent group entropy of automorphisms of groups pseudo-Anosov dilatation
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2011/9/15
Abstract: We study the word length entropy of automorphisms of residually nilpotent groups, and how the entropy of such group automorphisms relates to the entropy of induced automorphisms on various n...
Supremum of Perelman's entropy and Kahler-Ricci flow on a Fano manifold
Kahler-Ricci flow Kahler-Ricci solitons Perelman entropy
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2011/9/15
Abstract: In this paper, we extend the method in [TZhu5] to study the energy level $L(\cdot)$ of Perelman's entropy $\lambda(\cdot)$ for K\"ahler-Ricci flow on a Fano manifold. Consequently, we first ...
Time relaxation of a phase-field model with entropy balance
phase-field model entropy balance Analysis of PDEs
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2011/9/14
Abstract: We deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations: the first ...