Related papers: Parallel Kac's Walk Generates PRU

The circadian clocks keeping time of day in many living organisms rely on self-sustained biochemical oscillations which can be entrained by external cues, such as light, to the 24-hour cycle induced by Earth rotation. However, environmental…

We introduce and study a family of random processes on trees we call hipster random walks, special instances of which we heuristically connect to the min-plus binary trees introduced by Robin Pemantle and studied by Auffinger and Cable…

Recently it has been shown that Repeat-Until-Success (RUS) circuits can approximate a given single-qubit unitary with an expected number of $T$ gates of about $1/3$ of what is required by optimal, deterministic, ancilla-free decompositions…

In order to tackle the problem of sampling from heavy tailed, high dimensional distributions via Markov Chain Monte Carlo (MCMC) methods, Yang, Latuszy\'nski, and Roberts (2022) (arXiv:2205.12112) introduces the stereographic projection as…

The concept of Secret Unknown Ciphers (SUCs) was introduced a decade ago as a new visionary concept without devising practical real-world examples. The major contribution of this work is to show the feasibility of "self-mutating" unknown…

Robotic Additive Manufacturing (AM) has emerged as a scalable and customizable construction method in the last decade. However, current AM design methods rely on pre-conceived (A priori) toolpath of the structure, often developed via…

We study properties of a non-Markovian random walk $X^{(n)}_l$, $l =0,1,2, >...,n$, evolving in discrete time $l$ on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the…

The step-reinforced random walk (SRRW), where each step may replicate a randomly chosen past step, exhibits complex dependencies on the history. This paper introduces a generalized SRRW on groups, incorporating arbitrary transformations of…

We prove that a group of injection-locked oscillators, each modelled using a nonlinear phase macromodel, responds as a single oscillator to small external perturbations. More precisely, we show that any group of injection-locked oscillators…

Industrial embedded systems are typically used to execute simple control algorithms due to their low computational resources. Despite these limitations, the implementation of advanced control techniques such as Model Predictive Control…

This thesis examines edge-reinforced random walks with some modifications to the standard definition. An overview of known results relating to the standard model is given and the proof of recurrence for the standard linearly edge-reinforced…

For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…

One technique to visualize the training of neural networks is to perform PCA on the parameters over the course of training and to project to the subspace spanned by the first few PCA components. In this paper we compare this technique to…

Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…

We present a novel mechanism to improve the accuracy of the recently-introduced class of graph random features (GRFs). Our method induces negative correlations between the lengths of the algorithm's random walks by imposing antithetic…

Pedestrian tracking has long been considered an important problem, especially in security applications. Previously,many approaches have been proposed with various types of sensors. One popular method is Pedestrian Dead Reckoning(PDR) [1]…

We consider the continuous time random walk model (CTRW) of tracer's motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported in Holzner et al. Phys. Rev. E 92, 013015…

We propose an approach to design a Model Predictive Controller (MPC) for constrained Linear Time Invariant systems performing an iterative task. The system is subject to an additive disturbance, and the goal is to learn to satisfy state and…

Sub-categories of mathematical topology, like the mathematical theory of chaos, offer interesting applications devoted to information security. In this research work, we have introduced a new chaos-based pseudorandom number generator…

We study the first order phase transition of the fixed-connectivity triangulated surface model using the Parallel Tempering Monte Carlo (PTMC) technique on relatively large lattices. From the PTMC results, we find that the transition is…