Related papers: Statistical Mechanics of Graphity Models
We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models. The density of states is modified at each step when the energy…
We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses…
A brief review of modeling and simulation methods for a study of polymers at interfaces is provided. When studying truly multiscale problems as provided by realistic polymer systems, coarse graining is practically unavoidable. In this…
There is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and artificial…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
Motivated by the concept of geometrical frustration, we introduce a class of statistical mechanics lattice models for the glass transition. Monte Carlo simulations in three dimensions show that they display a dynamical glass transition…
From longitudinal biomedical studies to social networks, graphs have emerged as a powerful framework for describing evolving interactions between agents in complex systems. In such studies, after pre-processing, the data can be represented…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
We construct an effective Hamiltonian via Monte Carlo from a given action. This Hamiltonian describes physics in the low energy regime. We test it by computing spectrum, wave functions and thermodynamical observables (average energy and…
A new approach to describe comminution processes in general ball mills as a macroscopic canonical ensemble is proposed. Using hamiltonian method, the model is able to take simultaneously into account the internal dynamics from mechanical…
We study the statistical mechanics of a general Hamiltonian system in the context of symplectic structure of the corresponding phase space. This covariant formalism reveals some interesting correspondences between properties of the phase…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of…
The idea of a graph theoretical approach to modeling the emergence of a quantized geometry and consequently spacetime, has been proposed previously, but not well studied. In most approaches the focus has been upon how to generate a…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…