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Given a set $P$ of $n$ points and a set $S$ of $n$ segments in the plane, we consider the problem of computing for each segment of $S$ its closest point in $P$. The previously best algorithm solves the problem in $n^{4/3}2^{O(\log^*n)}$…
Take-off and landing are the periods of a flight where aircraft are most vulnerable to a ground based rocket attack by terrorists. While aircraft approach and depart from airports on pre-defined flight paths, there is a degree of…
We introduce the Ants Nearby Treasure Search (ANTS) problem, which models natural cooperative foraging behavior such as that performed by ants around their nest. In this problem, k probabilistic agents, initially placed at a central…
Bu{\ss} et al [KDD 2020] recently proved that the problem of computing the betweenness of all nodes of a temporal graph is computationally hard in the case of foremost and fastest paths, while it is solvable in time O(n 3 T 2 ) in the case…
We study three orientation-based shape descriptors on a set of continuously moving points: the first principal component, the smallest oriented bounding box and the thinnest strip. Each of these shape descriptors essentially defines a cost…
The exact mean time between encounters of a given particle in a system consisting of many particles undergoing random walks in discrete time is calculated, on both regular and complex networks. Analytical results are obtained both for…
The problem of optimal stopping with finite horizon in discrete time is considered in view of maximizing the expected gain. The algorithm proposed in this paper is completely nonparametric in the sense that it uses observed data from the…
We investigate the occupancy statistics of birds on a wire and on higher-dimensional substrates. In one dimension, birds land one by one on a wire and rest where they land. Whenever a newly arriving bird lands within a fixed distance of…
We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are…
Given a times series ${\bf Y}$ in $\mathbb{R}^n$, with a piece-wise contant mean and independent components, the twin problems of change-point detection and change-point localization respectively amount to detecting the existence of times…
In this paper, we propose a novel trajectory learning method that exploits motion trajectories on topological map using recurrent neural network for temporally consistent geolocalization of object. Inspired by human's ability to both be…
As we move through the world, the pattern of light projected on our eyes is complex and dynamic, yet we are still able to distinguish between moving and stationary objects. We propose that humans accomplish this by exploiting constraints…
A team of anonymous mobile agents represented by points freely moving in the plane have to gather at a single point and stop. Agents start at different points of the plane and at possibly different times chosen by the adversary. They are…
The assignment problem takes as input two finite point sets S and T and establishes a correspondence between points in S and points in T, such that each point in S maps to exactly one point in T, and each point in T maps to at least one…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
$ \newcommand{\Re}{\mathbb{R}} \newcommand{\reals}{\mathbb{R}} \newcommand{\SetX}{\mathsf{X}} \newcommand{\optX}[1]{#1^\star} \newcommand{\Qopt}{\Mh{\optX{Q}}} \newcommand{\rad}{r} \newcommand{\Mh}[1]{#1} \newcommand{\query}{q}…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
A dynamical system of points moving along the edges of a graph could be considered as a geometrical discrete dynamical system or as a discrete version of a quantum graph with localized wave packets. We study the set of such systems over…
Data-driven research in mobility has prospered in recent years, providing solutions to real-world challenges including forecasting epidemics and planning transportation. These advancements were facilitated by computational tools enabling…
We investigate the statistics of the local time $\mathcal{T} = \int_0^T \delta(x(t)) dt$ that a run and tumble particle (RTP) $x(t)$ in one dimension spends at the origin, with or without an external drift. By relating the local time to the…