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We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one…
We determine filtering and master equations for a quantum system interacting with wave packet of light in a continuous-mode squeezed number state. We formulate the problem of conditional evolution of a quantum system making use of model of…
We introduce a stochastic algorithm that acts as a prime number generator. The dynamics of such algorithm gives rise to a continuous phase transition which separates a phase where the algorithm is able to reduce a whole set of integers into…
Photomosaic images are a type of images consisting of various tiny images. A complete form can be seen clearly by viewing it from a long distance. Small tiny images which replace blocks of the original image can be seen clearly by viewing…
Self-organization creates new order and shifts sub-boundaries while reorganizing energy and entropy within a control volume. This article examines pathway selection and tests whether maximizing the entropy generation rate can forecast…
The idea is advanced that self-organization in complex systems can be treated as decision making (as it is performed by humans) and, vice versa, decision making is nothing but a kind of self-organization in the decision maker nervous…
We study numerically the phases and dynamics of a dense collection of self-propelled particles with soft repulsive interactions in two dimensions. The model is motivated by recent in vitro experiments on confluent monolayers of migratory…
Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production…
Particle filtering is a powerful tool for target tracking. When the budget for observations is restricted, it is necessary to reduce the measurements to a limited amount of samples carefully selected. A discrete stochastic nonlinear…
We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation…
Global food systems confront the urgent challenge of supplying sustainable, nutritious diets in the face of escalating demands. The advent of Artificial Intelligence (AI) is bringing in a personal choice revolution, wherein AI-driven…
In this paper we consider a random search process with stochastic resetting and a partially accessible target $\calU$. That is, when the searcher finds the target by attaching to its surface $\partial \calU$ it does not have immediate…
Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for machine learning study of…
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…
This book chapter introduces to the problem to which extent search strategies of foraging biological organisms can be identified by statistical data analysis and mathematical modeling. A famous paradigm in this field is the Levy Flight…
Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing…
The study of emergent behavior of swarms is of great interest for applied sciences. One of the most fundamental questions for self-organizing swarms is whether the swarms disperse or remain in a spatially cohesive configuration. In the…
We study how stochastic resetting affects first-passage processes in systems of many interacting particles. While resetting is well understood for single-particle dynamics, its consequences for collective behavior remain less clear. We…
Disorder is a pervasive characteristic of natural systems, offering a wealth of non-repeating patterns. In this study, we present a novel storage method that harnesses naturally-occurring random structures to store an arbitrary pattern in a…
We consider the statics and dynamics of a single particle trapped in a one-dimensional harmonic potential, and subjected to a driving noise with memory, that is represented by a resetting stochastic process. The finite memory of this…