Related papers: Partition Function Expansion on Region-Graphs and …
Bayesian nonparametric space partition (BNSP) models provide a variety of strategies for partitioning a $D$-dimensional space into a set of blocks. In this way, the data points lie in the same block would share certain kinds of homogeneity.…
The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing…
We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs…
Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
Graph-based transforms have been shown to be powerful tools in terms of image energy compaction. However, when the support increases to best capture signal dependencies, the computation of the basis functions becomes rapidly untractable.…
Statistical mechanics has grown without bounds in space. Statistical mechanics of point particles in an unbounded perfect gas is commonly accepted as a foundation for understanding many systems, including liquids like the concentrated salt…
Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties. For instance, we…
We present exact calculations of the partition function $Z$ of the $q$-state Potts model and its generalization to real $q$, the random cluster model, for arbitrary temperature on $n$-vertex ladder graphs with free, cyclic, and M\"obius…
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…
Galaxies are self-gravitating structures composed by several components encompassing spherical, axial and triaxial symmetry. Although real systems feature heterogeneous components whose properties are intimately connected, semi-analytical…
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on…
Dynamic Spectrum Access systems exploit temporarily available spectrum (`white spaces') and can spread transmissions over a number of non-contiguous sub-channels. Such methods are highly beneficial in terms of spectrum utilization. However,…
Distributed processing of large-scale graph data has many practical applications and has been widely studied. In recent years, a lot of distributed graph processing frameworks and algorithms have been proposed. While many efforts have been…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
A short review of expansion by regions is presented. It is a well-known strategy to obtain an expansion of a given multiloop Feynman integral in a given limit where some kinematic invariants and/or masses have certain scaling measured in…
The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
Perception research provides strong evidence in favor of part based representation of shapes in human visual system. Despite considerable differences among different theories in terms of how part boundaries are found, there is substantial…