相关论文: Ergodic Effects in Token Circulation

In recent years, the problem of computing the frequencies of the induced $k$-vertex subgraphs of a graph, or \emph{$k$-graphlets}, has become central. One approach for this problem is to sample $k$-graphlets randomly. Classic algorithms for…

We consider the problem of assigning appearing times to the edges of a digraph in order to maximize the (average) temporal reachability between pairs of nodes. Motivated by the application to public transit networks, where edges cannot be…

This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem…

Given a dynamical system, we say that a performance function has property P if its time averages along orbits are maximized at a periodic orbit. It is conjectured by several authors that for sufficiently hyperbolic dynamical systems,…

We discuss conditions for unique ergodicity of a collective random walk on a continuous circle. Individual particles in this collective motion perform independent (and different in general) random walks conditioned by the assumption that…

We provide new algorithms and conditional hardness for the problem of estimating effective resistances in $n$-node $m$-edge undirected, expander graphs. We provide an $\widetilde{O}(m\epsilon^{-1})$-time algorithm that produces with high…

We consider the problem of finding the value of a maximum flow over time in a network with uniform edge lengths where the edge capacities change at specific time instants. To solve this problem, we show how to construct a condensed version…

We study smoothed analysis of distributed graph algorithms, focusing on the fundamental minimum spanning tree (MST) problem. With the goal of studying the time complexity of distributed MST as a function of the "perturbation" of the input…

We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do…

We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O(n^{2.75}) time, independent of the number of edges m inserted. For dense DAGs, this is…

We consider discrete, iterative load balancing via matchings on arbitrary graphs. Initially each node holds a certain number of tokens, defining the load of the node, and the objective is to redistribute the tokens such that eventually each…

We study a synchronous dispersion process in which $M$ particles are initially placed at a distinguished origin vertex of a graph $G$. At each time step, at each vertex $v$ occupied by more than one particle at the beginning of this step,…

In this paper, we make use of the Metropolis-type walks due to Nonaka et al. (2010) to provide a faster solution to the $S$-$T$-connectivity problem in undirected graphs (USTCON). As our main result, we propose a family of randomized…

We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…

We study the problem of maintaining robust and sparse overlay networks in fully distributed settings where nodes continuously join and leave the system. This scenario closely models real-world unstructured peer-to-peer networks, where…

A quantitative model of the mobility of functionalized particles at the interface is pivotal to understanding important systems in biology and nanotechnology. In this work, we investigate the emerging dynamics of particles anchored through…

In this paper, we report results for the wave packet dynamics in a class of quasiperiodic chains consisting of two types of weakly coupled clusters. The dynamics are studied by means of the return probability and the mean square…

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…

A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle…