Related papers: A Potts Model for Night Light and Human Population
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
We study the Potts model on locally tree-like random graphs of arbitrary degree distribution. Using a population dynamics algorithm we numerically solve the problem exactly. We confirm our results with simulations. Comparisons with a…
In this paper we give a systematic review of the theory of Gibbs measures of Potts model on Cayley trees (developed since 2013) and discuss many applications of the Potts model to real world situations: mainly biology, physics, and some…
Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a new framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of…
Pairwise models like the Ising model or the generalized Potts model have found many successful applications in fields like physics, biology, and economics. Closely connected is the problem of inverse statistical mechanics, where the goal is…
When modeling the distribution of a set of data by a mixture of Gaussians, there are two possibilities: i) the classical one is using a set of parameters which are the proportions, the means and the variances; ii) the second is to consider…
The Ising and Potts models, among the most important models in statistical physics, have been used for modeling binary and multinomial data on lattices in a wide variety of disciplines such as psychology, image analysis, biology, and…
Gravity is one of the most prominent models used across various social areas, including economics, demography, mobility, politics, and other systems where spatial interactions are relevant. The model represents a flexible approach that…
In a Potts-like model of $Q$ ethnic groups, we follow Schelling (1971) and Meyer-Ortmanns (2003) and simulate the formation of ethnic ghettos as well as their prevention by an increasing social temperature.
We report on an exceptionally accurate spin-glass-type Potts model for community detection. With a simple algorithm, we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of…
Nighttime lights satellite imagery has been used for decades as a uniform, global source of data for studying a wide range of socioeconomic factors. Recently, another more terrestrial source is producing data with similarly uniform global…
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described…
We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit…
We apply a replica inference based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of "community detection" and its phase diagram. Specifically, the…
The two-dimensional Potts Model with seven states under external field is studied using a cluster algorithm. Cluster size distribution and the fluctuations in the average cluster size provide helpful information on the order of phase…
The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition…
The Potts model is frequently used to describe the behavior of image classes, since it allows to incorporate contextual information linking neighboring pixels in a simple way. Its isotropic version has only one real parameter beta, known as…
Complex systems throughout Nature display structures and functions that are built and maintained, at least in part, by optimal energies flowing through them--not specific, ideal values, rather ranges in energy rate density below which…
An approximation of the density of states for the Ising and Potts models based on the high- and low-temperature series are developed.
The photon model of light has been known for decades to be self-inconsistent and controversial theory with numerous intrinsic conflicts. This paper revises the model and explores its applicability for description of classical…