Related papers: Shrinking targets and eventually always hitting po…

We consider random dynamical systems on manifolds modeled by a skew product which have certain geometric properties and whose measures satisfy quenched decay of correlations at a sufficient rate. We prove that the limiting distribution for…

The \emph{Dominating $H$-Pattern} problem generalizes the classical $k$-Dominating Set problem: for a fixed \emph{pattern} $H$ and a given graph $G$, the goal is to find an induced subgraph $S$ of $G$ such that (1) $S$ is isomorphic to $H$,…

A fundamental question in computational geometry is for a set of input points in the Euclidean space, that is subject to discrete changes (insertion/deletion of points at each time step), whether it is possible to maintain an approximate…

We consider the minimal distance between orbits of measure preserving dynamical systems. In the spirit of dynamical shrinking target problems we identify distance rates for which almost sure asymptotic closeness properties can be ensured.…

The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points,…

We study convergence of return- and hitting-time distributions of small sets $E_{k}$ with $\mu(E_{k})\rightarrow0$ in recurrent ergodic dynamical systems preserving an infinite measure $\mu$. Some properties which are easy in finite measure…

We consider the problem of computing shortest paths in a dense motion-planning roadmap $\mathcal{G}$. We assume that~$n$, the number of vertices of $\mathcal{G}$, is very large. Thus, using any path-planning algorithm that directly searches…

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…

Via Gauge theory, we give a new proof of partial regularity for harmonic maps in dimension m>2 into arbitrary targets. This proof avoids the use of adapted frames and permits to consider targets of "minimal" C^2 regularity. The proof we…

We study the properties of `infinite-volume mixing' for two classes of intermittent maps: expanding maps $[0,1] \longrightarrow [0,1]$ with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding…

Let $\{B(\xi_n,r_n)\}_{n\ge1}$ be a sequence of random balls whose centers $\{\xi_n\}_{n\ge1}$ is a stationary process, and $\{r_n\}_{n\ge1}$ is a sequence of positive numbers decreasing to 0. Our object is the random covering set…

We investigate the problem of persistent monitoring, where a mobile agent has to survey multiple targets in an environment in order to estimate their internal states. These internal states evolve with linear stochastic dynamics and the…

Let $P$ be a set of at most $n$ points and let $R$ be a set of at most $n$ geometric ranges, such as for example disks or rectangles, where each $p \in P$ has an associated supply $s_{p} > 0$, and each $r \in R$ has an associated demand…

For the family of Double Standard Maps $f_{a,b}=2x+a+\frac{b}{\pi} \sin2\pi x \quad\pmod{1}$ we investigate the structure of the space of parameters $a$ when $b=1$ and when $b\in[0,1)$. In the first case the maps have a critical point, but…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

Duplicate detection is the problem of identifying whether a given item has previously appeared in a (possibly infinite) stream of data, when only a limited amount of memory is available. Unfortunately the infinite stream setting is…

In the Triangle-Free (Simple) 2-Matching problem we are given an undirected graph $G=(V,E)$. Our goal is to compute a maximum-cardinality $M\subseteq E$ satisfying the following properties: (1) at most two edges of $M$ are incident on each…

We derive the breakdown point for solutions of semi-discrete optimal transport problems, which characterizes the robustness of the multivariate quantiles based on optimal transport proposed in \cite{GS}. We do so under very mild…

The success of modern parallel paradigms such as MapReduce, Hadoop, or Spark, has attracted a significant attention to the Massively Parallel Computation (MPC) model over the past few years, especially on graph problems. In this work, we…

Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from the centers to given input points. Examples are $k$-Means, Geometric…