Mathematics

Throttling is a graph optimization problem, where the throttling number of a graph is the minimum sum or minimum product of the number of vertices in an initial set and the time required to complete a certain graph operation. A…

We present some developments in the study of chaotic dynamics following the solution of a conjecture of Newhouse on the measures maximizing the entropy of smooth surface diffeomorphisms. We focus on \emph{strong positive recurrence}, a…

In this paper we study the potential measures and the Laplace transforms of the occupation times of a refracted-reflected spectrally negative L\'evy process when the process is observed at the arrival epochs of two independent Poisson…

A straightforward and computationally efficient indirect method based on STM sensitivity analysis is introduced for designing fuel-optimal low-thrust transfers under high-fidelity dynamics. Conventional indirect approaches require explicit…

We introduce a discrete-energy Sobolev space $\mathcal{W}^{1,p}_{\mathscr V}(T)$ on Ahlfors regular snowtrees, a class of metric trees where every arc is a snowflake of the same type. Our main result shows that, for every partition…

We study the compositionality of global dynamics through attractor lattices and order structures of recurrent dynamics in product and skew-product systems using Conley theory. For product systems, these structures can be characterized…

Given two Banach spaces $X$ and $E$, one can associate a numerical invariant $\mathcal{CR}(X, E)$, called the coarse embeddability ratio, which provides a criterion for coarse and uniform embeddability. We compute the coarse embeddability…

This work is about the shape optimization of long tubular objects in electromagnetic chirality (em-chirality). Em-chirality is a property of individual scattering objects or metamaterials describing their qualitatively different response to…

Let $\mathbb{H}_{n+1}$ denote a computable copy of the $(n+1)$-clique free universal homogeneous Henson graph, $G$ denote a finite subgraph of $\mathbb{H}_{n+1}$, and $k(G,n)$ denote the big Ramsey degree of $G$ in $\mathbb{H}_{n+1}$. We…

We investigate four-dimensional electrostatic systems arising as spatial factors of static Einstein--Maxwell spacetimes with cosmological constant. Assuming that the electric field is everywhere collinear with the gradient of the lapse…

We investigate matrices with entries in a number field such that some positive power has all its entries in the corresponding ring of integers. Our work generalizes previous results in several directions and we find applications to…

The difference in gauge between two observers of the same physical system can be thought of as a group element acting on their common vector representations. Recovering that group element from a finite, noisy list of paired observations may…

We prove a version of the Dvoretzky-Kiefer-Wolfowitz inequality for Markov chains with a regenerative structure. Suppose we have a regenerative Markov chain with stationary distribution $\pi$. Given a functional $\theta$ on the state space…

Consider a nonparametric regression model with one-dimensional covariates and a continuous regression function. Assume that the regression function from the left of the covariate support starts equal to zero and then changes at some unknown…

This is a geometric retelling of Konyagin and Sevast'yanov's proof of Andrew's theorem, which is a tight upper bound on the number of vertices of a d-dimensional lattice polytope in terms of its volume.

We present $\texttt{bucket-graph-spprc}$ ($\texttt{bgspprc}$ for short), an open-source, header-only C++23 library for the shortest path problem with resource constraints (SPPRC), the pricing subproblem at the heart of branch-cut-and-price…

We prove a Nekhoroshev type result for a time quasiperiodic perturbation of an integrable Hamiltonian system. More precisely, we assume that the integrable part is analytic and fulfills a generic nondegeneracy condition introduced by…

We study the squared singular value spectrum of a product of non-square random matrices, a setting that also corresponds to the feature covariance eigenvalues of a deep linear neural network at initialization. We first take a proportional…

We consider the finite-time optimal control of stochastic systems subject to a probabilistic constraint on the trajectories' safety. Such formulations are known as joint chance constrained optimal control problems. The common practice is to…

For a compactly supported probability measure $\mu$ on the $d$-dimensional space $\mathbb{R}^d$, the average distance problem asks us to minimize the average distance functional over all compact, connected, $\Sigma \subseteq \mathbb{R}^d$…