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The explosion of spatiotemporal data in the physical world requires new deep learning tools to model complex dynamical systems.
The objective of the workshop is to bring together researchers in stochastic dynamical systems, ergodic theory, SPDEs, BSDEs, nonlinear expectations and stochastic controls to interact aiming to stimu...
The aim of the symposium is to bring together specialists of various do- mains of singularity theory and mathematical foundation of complex systems representing very classical aspects of the Fields. W...
The International Conference on Statistical Properties of Nonequilibrium Dynamical Systems will be held in the South University of Science and Technology of China (SUSTC) in Shenzhen, China, from July...
In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time beh...
In this paper we describe the long time behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of the corresponding di@...
A Compactification of H′ enon Mappings in C2 as Dynamical Systems.
Dynamical systems with multiple time scales arise naturally in many domains. Models of neural systems provide the principal motivation for this paper. Most of the previous mathematical analysis of q...
In this paper, we introduce a new class of Lyapunov functionals for analyzing hybrid dynamical systems. This class can be thought of as a generalization of the Lyapunov functional introduced by Yakubo...
In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. Th...
here are two fundamental concepts in deter ministic dynamical systems: fixed point (equilibr ium point) and per iodic solutions. For stochastic dynamical systems, they correspond to fundamental ideas...
First-order SODE: OU processdX+aX(t)dt= dW(t) Three options:a >0, a= 0, a <0. First-order SPDE:du= au xx dt+dW(t, x) One option:a >0(Infinite-dimensional stable OU process.) Second-order SODE:X¨ ...
Metric Dynamical System Let be a probability space. Let be a metric dynamical system: (i) (ii) (iii) preserves th...
“Superparamagnetic limit”: As magnetic devices become smaller and smaller, the time for thermal activated switching might become too short (shorter than desired data retention time).
Due to lack of knowledge: Missing mechanisms (ignored “too small" or “too fast" or “unimportant" processes) Unresolved scales (not represented in models) Model uncertainties

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