Related papers: Rate-induced Tipping in Discrete-time Dynamical Sy…
Reservoir computing has been shown to be a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. Its utility is significant because in real-world scenarios, the…
Tipping points have been actively studied in various applications as well as from a mathematical viewpoint. A main technique to theoretically understand early-warning signs for tipping points is to use the framework of fast-slow stochastic…
Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. Numerical discretization of the continuous system is an integral part of subsequent analysis. Feedback…
Given $d \ge 1$, let $(A_i)_{i\ge 1}$ be a sequence of random $d\times d$ real matrices and $Q$ be a random vector in $\mathbb{R}^d$. We consider fixed points of multivariate smoothing transforms, i.e. random variables $X\in \mathbb{R}^d$…
Learning-based methods for dexterous manipulation have made notable progress in recent years. However, learned policies often still lack reliability and exhibit limited robustness to important factors of variation. One failure pattern that…
We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors…
In systems with a mixed phase space, where regular and chaotic motion coexists, regular states are coupled to the chaotic region by dynamical tunneling. We give an overview on the determination of direct regular-to-chaotic tunneling rates…
In this paper we show that the existence of a primarily discrete space-time may be a fruitful assumption from which we may develop a new approach of statistical thermodynamics in pre-relativistic conditions. The discreetness of space-time…
A dynamic crack tip equation of motion is proposed based on the autonomy of the near-tip nonlinear zone of scale $\ell_{nl}$, symmetry principles, causality and scaling arguments. Causality implies that the asymptotic linear-elastic fields…
The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability,…
Spiral waves are ubiquitous spatiotemporal patterns that occur in various excitable systems. In cardiac tissue, the formation of these spiral waves is associated with life-threatening arrhythmias, and, therefore, it is important to study…
Many robotics applications require interest points that are highly repeatable under varying viewpoints and lighting conditions. However, this requirement is very challenging as the environment changes continuously and indefinitely, leading…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…
The main result given in Theorem~1.1 is a condition for a map $X$, defined on the complement of a disk $D$ in R^2 with values in R^2, to be extended to a topological embedding of R^2, not necessarily surjective. The map $X$ is supposed to…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
Inertial-aided systems require continuous motion excitation among other reasons to characterize the measurement biases that will enable accurate integration required for localization frameworks. This paper proposes the use of informative…
We consider a periodically-forced 1-D Langevin equation that possesses two stable periodic solutions in the absence of noise. We ask the question: is there a most likely noise-induced transition path between these periodic solutions that…
This paper analyzes the evolution of inter-event times (IETs) in linear systems under region-based self-triggered control (RBSTC). In this control method, the state space is partitioned into a finite number of conic regions and each region…
A prioritized inverse kinematics (PIK) solution can be considered as a (regulation or output tracking) control law of a dynamical system with prioritized multiple outputs. We propose a method that guarantees that a joint trajectory…
Conventional trajectory planning approaches for autonomous vehicles often assume a fixed vehicle model that remains constant regardless of the vehicle's location. This overlooks the critical fact that the tires and the surface are the two…