Related papers: A Geometric Approach for Bounding Average Stopping…
Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this…
In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the…
How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
A survey is presented of known results concerning simple random walk on the class of distance-regular graphs. One of the highlights is that electric resistance and hitting times between points can be explicitly calculated and given strong…
We investigate the existence of periodic solutions for a class of nonlocal continuity equations, which include mean-field equations derived from systems of coupled oscillators. While periodic solutions at the particle level have been…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…
Successfully achieving bipedal locomotion remains challenging due to real-world factors such as model uncertainty, random disturbances, and imperfect state estimation. In this work, we propose a novel metric for locomotive robustness -- the…
In this paper we show that on bounded degree graphs and general trees, the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the expected supremum of the Gaussian free field…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its…
We study fully nonlinear geometric flows that deform strictly $k$-convex hypersurfaces in Euclidean space with pointwise normal speed given by a concave function of the principal curvatures. Specifically, the speeds we consider are obtained…
We provide simple and constructive proofs of Harris-type theorems on the existence and uniqueness of an equilibrium and the speed of equilibration of discrete-time and continuous-time stochastic semigroups. Our results apply both to cases…
We introduce a model for the slow relaxation of an energy landscape caused by its local interaction with a random walker whose motion is dictated by the landscape itself. By choosing relevant measures of time and potential this…
Stopping times are used in applications to model random arrivals. A standard assumption in many models is that they are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are…