Related papers: Statistical Mechanics of Graphity Models
We discuss several ways of illustrating fundamental concepts in statistical and thermal physics by considering various models and algorithms. We emphasize the importance of replacing students' incomplete mental images by models that are…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…
A set of Pauli stings is well characterized by the graph that encodes its commutatitivity structure, i.e., by its frustration graph. This graph provides a natural interface between graph theory and quantum information, which we explore in…
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic…
The state of a thermodynamic system being characterized by its set of extensive variables $q^{i}(i=1,...,n) ,$ we write the associated intensive variables $\gamma_{i},$ the partial derivatives of the entropy $ S(q^{1},...,q^{n}) \equiv…
In loop quantum gravity (LQG), states of the gravitational field are represented by labeled graphs called spin networks. Their dynamics can be described by a Hamiltonian constraint, { which acts on the spin network states modifying both…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
Probabilistic graphical models (PGMs) have become a popular tool for computational analysis of biological data in a variety of domains. But, what exactly are they and how do they work? How can we use PGMs to discover patterns that are…
Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…
Graph drawings are commonly used to visualize relational data. User understanding and performance are linked to the quality of such drawings, which is measured by quality metrics. The tacit knowledge in the graph drawing community about…
Starting from an important research path, we consider gravity as a collective phenomenon governed by statistical mechanics. While previous studies have focussed on the thermodynamic heat flow across a 2d-horizon as perceived by a single,…
We analyse the statistical physics of a two dimensional lattice based gas with long range interactions. The particles interact in a way analogous to Queens on a chess board. The long range nature of the interaction gives the mathematics of…
In this work we show that there is a direct relationship between a graph's topology and the free energy of a spin system on the graph. We develop a method of separating topological and enthalpic contributions to the free energy, and find…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…
We propose statistical systems based on $p$-adic numbers. In the systems, the Hamiltonian is a standard real number which is given by a map from the $p$-adic numbers. Therefore we can introduce the temperature as a real number and calculate…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…