相关论文: Understanding Chicken Walks on n x n Grid: Hamilto…

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…

Let $P$ be a set of $n$ points in the plane where each point $p$ of $P$ is associated with a radius $r_p>0$.The transmission graph $G=(P,E)$ of $P$ is defined as the directed graph such that $E$ contains an edge from $p$ to $q$ if and only…

This work aims to assess the risks of Covid-19 disease spread in diverse daily-life situations (referred to as scenarios) involving crowds of maskless pedestrians, mostly outdoors. More concretely, we develop a method to infer the global…

The interaction among spreading processes on a complex network is a nontrivial phenomenon of great importance. It has recently been realized that cooperative effects among infective diseases can give rise to qualitative changes in the…

One important feature of the mammalian immune system is the highly specific binding of antigens to antibodies. Antibodies generated in response to one infection may also provide some level of cross immunity to other infections. One model to…

The most frequent infectious diseases in humans - and those with the highest potential for rapid pandemic spread - are usually transmitted via droplets during close proximity interactions (CPIs). Despite the importance of this transmission…

We consider the problem of packing node-disjoint directed paths in a directed graph. We consider a variant of this problem where each path starts within a fixed subset of root nodes, subject to a given bound on the length of paths. This…

Animals foraging alone are hypothesized to optimize the encounter rates with resources through L\'evy walks. However, the issue of how the interactions between multiple foragers influence their search efficiency is still not completely…

We study an Eulerian walker on a square lattice, starting from an initially randomly oriented background using Monte Carlo simulations. We present evidence that, that, for large number of steps $N$, the asymptotic shape of the set of sites…

Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear…

We consider the problem of predicting an individual's identity from accelerometry data collected during walking. In a previous paper we introduced an approach that transforms the accelerometry time series into an image by constructing its…

Navigating our physical environment requires changing directions and turning. Despite its ecological importance, we do not have a unified theoretical account of non-straight-line human movement. Here, we present a unified optimality…

It is well known that the distribution of simple random walks on $\bf{Z}$ conditioned on returning to the origin after $2n$ steps does not depend on $p= P(S_1 = 1)$, the probability of moving to the right. Moreover, conditioned on…

Gait synchronization in pedestrians is influenced by biomechanical, environmental, and cognitive factors. Studying gait in ecological settings provides insights often missed in controlled experiments. This study tackles the challenges of…

Infections depend on interactions between pathogen and host proteins, but comprehensively mapping these interactions is challenging and labor intensive. Many biological networks have hierarchical, scale-free structure, so we developed a…

The main purpose of this thesis is to study the interplay between geometric properties of infinite graphs and analytic and probabilistic objects such as transition operators, harmonic functions and random walks on these graphs. For a…

Malaria is transmitted to vertebrates via a mosquito bite, during which rod-like and crescent-shaped parasites, called sporozoites, are injected into the skin of the host. Searching for a blood capillary to penetrate, sporozoites move…

Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient…

Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…

Pathogen outbreaks (i.e., outbreaks of bacteria and viruses) in hospitals can cause high mortality rates and increase costs for hospitals significantly. An outbreak is generally noticed when the number of infected patients rises above an…