Related papers: Lock-in Problem for Parallel Rotor-router Walks
We initiate a study of solving a row/column diagonally dominant (RDD/CDD) linear system $Mx=b$ in sublinear time, with the goal of estimating $t^{\top}x^*$ for a given vector $t\in R^n$ and a specific solution $x^*$. This setting naturally…
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…
We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…
Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…
This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be…
We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…
We study the problem of planning paths for $p$ distinguishable pebbles (robots) residing on the vertices of an $n$-vertex connected graph with $p \le n$. A pebble may move from a vertex to an adjacent one in a time step provided that it…
One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, albeit the system is translationally invariant. The effect is…
It is confirmed in this work that the graph isomorphism can be tested in polynomial time, which resolves a longstanding problem in the theory of computation. The contributions are in three phases as follows. 1. A description graph…
Consider the setting of multiple random walks (RWs) on a graph executing a certain computational task. For instance, in decentralized learning via RWs, a model is updated at each iteration based on the local data of the visited node and…
We give fast, simple, and implementable catalytic logspace algorithms for two fundamental graph problems. First, a randomized catalytic algorithm for $s\to t$ connectivity running in $\widetilde{O}(nm)$ time, and a deterministic catalytic…
We examine the hypothesis, that short-term synaptic plasticity (STSP) may generate self-organized motor patterns. We simulated sphere-shaped autonomous robots, within the LPZRobots simulation package, containing three weights moving along…
This paper proposes a data-driven motion-planning framework for nonlinear systems that constructs a sequence of overlapping invariant polytopes. Around each randomly sampled waypoint, the algorithm identifies a convex admissible region and…
In this paper, we consider discrete time quantum walks on graphs with coin focusing on the decentralized model, where the coin operation is allowed to change with the vertex of the graph. When the coin operations can be modified at every…
Quantum walks exhibit properties without classical analogues. One of those is the phenomenon of asymptotic trapping -- there can be non-zero probability of the quantum walker being localised in a finite part of the underlying graph…
Multiple dynamic pathways always exist in biological networks, but their robustness against internal fluctuations and relative stability have not been well recognized and carefully analyzed yet. Here we try to address these issues through…
The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear…
In this work, we present a constant-round algorithm for the $2$-ruling set problem in the Congested Clique model. As a direct consequence, we obtain a constant round algorithm in the MPC model with linear space-per-machine and optimal total…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
In the present work, we study random walks on complex networks subject to stochastic resetting when the resetting probability is node-dependent. Using a renewal approach, we derive the exact expressions of the stationary occupation…