Related papers: A Dynamical Systems Approach for Most Probable Esc…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
We consider the problem of minimizing the asymptotic exit rate with which the controlled-diffusion process of a stochastically perturbed multi-channel dynamical system exits from a given bounded open domain. In particular, for a class of…
Safe UAV navigation is challenging due to the complex environment structures, dynamic obstacles, and uncertainties from measurement noises and unpredictable moving obstacle behaviors. Although plenty of recent works achieve safe navigation…
This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving…
Dynamic path planning must remain reliable in the presence of sensing noise, uncertain localization, and incomplete semantic perception. We propose a practical, implementation-friendly planner that operates on occupancy grids and optionally…
The aim of this work is to revise but also explore even further the escape dynamics in the H\'{e}non-Heiles system. In particular, we conduct a thorough and systematic numerical investigation distinguishing between trapped (ordered and…
In this paper we develop a metastability theory for a class of stochastic reaction-diffusion equations exposed to small multiplicative noise. We consider the case where the unperturbed reaction-diffusion equation features multiple…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…
This paper examines the use of operator-theoretic approaches to the analysis of chaotic systems through the lens of their unstable periodic orbits (UPOs). Our approach involves three data-driven steps for detecting, identifying, and…
We study the detailed path-wise behavior of the discrete-time Langevin algorithm for non-convex Empirical Risk Minimization (ERM) through the lens of metastability, adopting some techniques from Berglund and Gentz (2003. For a particular…
We pursue our study of integrable weak noise theories of directed polymer and interacting particle stochastic models in the 1D KPZ universality class. Here we focus on the $q$-TASEP in either continuous or discrete time. Each particle on…
Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems are now routinely used as evidence for low dimensional chaos . Extracting accurate dynamical information…
Optimal paths for the classical Onsager-Machlup function determining most probable paths between points on a manifold are only explicitly identified for specific processes, for example the Riemannian Brownian motion. This leaves out large…
The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…
Deterministic chaotic dynamics presumes that the state space can be partitioned arbitrarily finely. In a physical system, the inevitable presence of some noise sets a finite limit to the finest possible resolution that can be attained. Much…
We report a simulation study on the narrow escape kinetics of a Chiral Active Particle (CAP) confined to a circular domain with a narrow escape opening. The studys main objective is to optimize the CAPs escape changes as a function of the…
Stochastic and soft optimal policies resulting from entropy-regularized Markov decision processes (ER-MDP) are desirable for exploration and imitation learning applications. Motivated by the fact that such policies are sensitive with…
We investigate the evolution of families of periodic orbits in a bisymmetrical potential made up of a two-dimensional harmonic oscillator with only one quartic perturbing term, in a number of resonant cases. Our main objective is to compute…
Using path-integral methods, a formula is deduced for the noise-induced escape rate from an attracting fixed point across an unstable fixed point in one-dimensional maps. The calculation starts from the trace formula for the eigenvalues of…
In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the…