Related papers: Products of Random Matrices for Disordered Systems
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal…
While many classical notions of learnability (e.g., PAC learnability) are distribution-free, utilizing the specific structures of an input distribution may improve learning performance. For example, a product distribution on a…
The systematic approach for the off-perturbative calculations in disordered systems is developed. The proposed scheme is applied for the random temperature and the random field ferromagnetic Ising models. It is shown that away from the…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
The software Randentropy is designed to estimate inequality in a random system where several individuals interact moving among many communities and producing dependent random quantities of an attribute. The overall inequality is assessed by…
Structurally random matrices (SRMs) are a practical alternative to fully random matrices (FRMs) when generating compressive sensing measurements because of their computational efficiency and their universality with respect to the sparsifing…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos,…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
We use series expansions to study dynamics of equilibrium and non-equilibrium systems on networks. This analytical method enables us to include detailed non-universal effects of the network structure. We show that even low order…
A transition matrix can be constructed through the partial contraction of two given quantum states. We analyze and compare four different definitions of entropy for transition matrices, including (modified) pseudo entropy, SVD entropy, and…
Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with…
Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
Transfer entropy (TE) captures the directed relationships between two variables. Partial transfer entropy (PTE) accounts for the presence of all confounding variables of a multivariate system and infers only about direct causality. However,…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…