Related papers: Spectral Entropy via Random Spanning Forests
The scale invariance of natural images suggests an analogy to the statistical mechanics of physical systems at a critical point. Here we examine the distribution of pixels in small image patches and show how to construct the corresponding…
We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as $S_d=-\sum_n \rho_{nn}\ln \rho_{nn}$ with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the…
Non-equilibrium stochastic dynamics of several active Brownian systems are modeled in terms of non-linear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for…
We study the problem of estimating the density $f(\boldsymbol x)$ of a random vector ${\boldsymbol X}$ in $\mathbb R^d$. For a spanning tree $T$ defined on the vertex set $\{1,\dots ,d\}$, the tree density $f_{T}$ is a product of bivariate…
Cortical networks exhibit synchronized activity which often occurs in spontaneous events in the form of spike avalanches. Since synchronization has been causally linked to central aspects of brain function such as selective signal…
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy…
The apparent thermalization of the particles produced in hadronic collisions can be obtained by quantum entanglement of the partons of the initial state once a fast hard collision is produced. The scale of the hard collision is related to…
Most methods for estimating configurational entropy from molecular simulation data yield upper limits except for harmonic systems where they are exact. Problems arise at diffusive systems and the presence of conformational transitions.…
We propose methods for density estimation and data synthesis using a novel form of unsupervised random forests. Inspired by generative adversarial networks, we implement a recursive procedure in which trees gradually learn structural…
The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy cost inequality and…
We present new insights into causal inference in the context of Heterogeneous Treatment Effects by proposing natural variants of Random Forests to estimate the key conditional distributions. To achieve this, we recast Breiman's original…
A framework for relativistic thermodynamics and statistical physics is built by first exploiting the symmetries between energy and momentum in the derivation of the Boltzmann distribution, then using Einstein's energy-momentum relationship…
We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs--Shannon entropy into more general framework - Renyi's information entropy. We address the…
This paper presents a brand new nonparametric density estimation strategy named the best-scored random forest density estimation whose effectiveness is supported by both solid theoretical analysis and significant experimental performance.…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
We study spanning trees on Sierpinski graphs (i.e., finite approximations to the Sierpinski gasket) that are chosen uniformly at random. We construct a joint probability space for uniform spanning trees on every finite Sierpinski graph and…
The Jarzynski identity can be applied to instances when a microscopic system is pulled repeatedly but quickly along some coordinate, allowing the calculation of an equilibrium free energy profile along the pulling coordinate from a set of…
We demonstrate that a machine learning framework based on kernel ridge regression can encode and predict the self-energy of one-dimensional Hubbard models using only mean-field features such as static and dynamic Hartree-Fock quantities and…
A spectral solution method is proposed to solve a previuously developed non-equilibrium statistical model describing partial thermalization of produced charged hadrons in relativistic heavy-ion collisions, thus improving the accuracy of the…
We provide a generalized treatment of uncertainties, von Neumann entropy, and squeezing in entangled bipartite pure state of two-level atoms. We observe that when the bipartite state is entangled, though the von Neumann entropy of the…