Related papers: Phase diagram of a Schelling segregation model
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
A novel mechanism for cell differentiation is proposed, based on the dynamic clustering in a globally coupled chaotic system. A simple model with metabolic reaction, active transport of chemicals from media, and cell division is found to…
By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient…
We propose and study a model for the equilibrium statistical mechanics of a pressurised semiflexible polymer ring. The Hamiltonian has a term which couples to the algebraic area of the ring and a term which accounts for bending…
The Schelling model of segregation between two groups of residential agents (Schelling 1971; Schelling 1978) reflects the most abstract view of the non-economic forces of residential migrations: be close to people of 'your own'. The model…
Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…
The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions. Analytically, this function is shown to have a…
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure. We define such a phase…
We propose a novel model-based clustering approach for samples of time series. We assume as a unique commonality that two observations belong to the same group if structural changes in their behaviours happen at the same time. We resort to…
A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble,…
Finite mixture models that allow for a broad range of potentially non-elliptical cluster distributions is an emerging methodological field. Such methods allow for the shape of the clusters to match the natural heterogeneity of the data,…
Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent…
We consider a collective behavior model in which individuals try to imitate each others' velocity and have a preferred speed. We show that a phase change phenomenon takes place as diffusion decreases, bringing the system from a "disordered"…
The lattice spin model, with nearest neighbor ferromagnetic exchange and long range dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon…
This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…
Many time-evolving systems in nature, society and technology leave traces of the interactions within them. These interactions form temporal networks that reflect the states of the systems. In this work, we pursue a coarse-grained…
We apply a recently proposed criterion for the existence of phase transitions, which is based on the properties of the saddles of the energy landscape, to a simplified model of a system with gravitational interactions, referred to as the…
Some models of clustering processes are formulated and analytically solved employing generating functions methods. Those models include events which result from combined action of the coagulation and fragmentation processes. Fragmentation…
We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to…