相关论文: Zero-one laws for eventually always hitting points…

Let $\mathcal X$ be an infinite locally compact separable metric space with metric $\rho$ and let $f : \mathcal X \longrightarrow \mathcal X$ be a continuous weakly mixing map. Let $\beta = \sup \big\{ \rho(x, y): \{x, y \} \subset \mathcal…

We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal…

We study coming down from infinity for coordinated particle systems. In a coordinated particle system, particles live on a set of sites $V$ and are able to coalesce, migrate, reproduce, and die. The dynamics of these events are coordinated…

This paper introduces a novel reachability problem for the scenario involving two agents, where one agent follows another agent using a feedback strategy. The geometry of the reachable set for an agent, termed \emph{dependent reachable…

We study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks)…

In dynamical systems, shrinking target sets and pointwise recurrent sets are two important classes of dynamically defined subsets. In this article we introduce a mild condition on the linear parts of the affine mappings that allow us to…

Finite time coherent sets [8] have recently been defined by a measure based objective function describing the degree that sets hold together, along with a Frobenius-Perron transfer operator method to produce optimally coherent sets. Here we…

This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…

This paper presents a state-of-the-art algorithm for the vertex enumeration problem of arrangements, which is based on the proposed new pivot rule, called the Zero rule. The Zero rule possesses several desirable properties: i) It gets rid…

In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ball with a linear…

Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories that can be made all-loop finite, leading to a severe reduction of the free parameters. We review the investigation of FUTs based on SU(5) in the context of…

A simple algorithm is described to target any desired operation point for simple one-dimensional and two-dimensional dynamical systems. What makes the algorithm unique is the fact that it targets any desired point, not merely a…

A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite…

For a functional $\E$ and a peak selection that picks up a global maximum of $\E$ on varying cones, we study the convergence up to a subsequence to a critical point of the sequence generated by a mountain pass type algorithm. Moreover, by…

Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…

We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the…

Let $(B_{i})$ be a sequence of measurable sets in a probability space $(X,\mathcal{B}, \mu)$ such that $\sum_{n=1}^{\infty} \mu (B_{i}) = \infty$. The classical Borel-Cantelli lemma states that if the sets $B_{i}$ are independent, then $\mu…

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method…

In this paper, the existence of perfect and quasi-perfect splitter sets in finite abelian groups is studied, motivated by their application in coding theory for flash memory storage. For perfect splitter sets we view them as splittings of…