Related papers: Phase transitions in Paradigm models
Comparative and evolutive ecologists are interested in the distribution of quantitative traits among related species. The classical framework for these distributions consists of a random process running along the branches of a phylogenetic…
Decision making in modern stochastic systems, including e-commerce platforms, financial markets and healthcare systems, has evolved into a multifaceted process that combines information acquisition and adaptive information sources. This…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
Inference-time scaling has achieved remarkable success in language models, yet its adaptation to diffusion models remains underexplored. We observe that the efficacy of recent Sequential Monte Carlo (SMC)-based methods largely stems from…
The spontaneous formation and subsequent growth, dissolution, merger and competition of social groups bears similarities to physical phase transitions in metastable finite systems. We examine three different scenarios, percolation, spinodal…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
A deterministic temporal process can be determined by its trajectory, an element in the product space of (a) initial condition $z_0 \in \mathcal{Z}$ and (b) transition function $f: (\mathcal{Z}, \mathcal{T}) \to \mathcal{Z}$ often…
We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main…
We consider a three dimensional, generalized version of the original SPP model for collective motion. By extending the factors influencing the ordering, we investigate the case when the movement of the self-propelled particles (SPP-s)…
Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this…
Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition…
This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an…
The abrupt outbreak and transmission of biological diseases has always been a long-time concern of humankind. For long, mathematical modeling has served as a simple and yet efficient tool to investigate, predict, and control spread of…
Recent work on modeling influence propagation focus on progressive models, i.e., once a node is influenced (active) the node stays in that state and cannot become inactive. However, this assumption is unrealistic in many settings where…
Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the…
We introduce a novel type of abnormal agents that proceed in the opposite direction of that defined for the normal agents. A new order parameter, $y$, is introduced to describe the characteristic of the system. Many interesting phenomenons…
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying…
A critical issue in the evolution of software models is change propagation: given a primary change that is made to a model in order to meet a new or changed requirement, what additional secondary changes are needed to maintain consistency…