Related papers: Generalized Entropy Method for the Renewal Equatio…
The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…
Many learning algorithms can be represented as Markov processes, and understanding their generalization error is a central topic in learning theory. For specific continuous-time noisy algorithms, a prominent analysis technique relies on…
Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by $S = \ln \chi (x)$ with $\chi(x)$…
Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the R\'enyi entropies is expected to enhance their scope in…
Existing training criteria in automatic speech recognition(ASR) permit the model to freely explore more than one time alignments between the feature and label sequences. In this paper, we use entropy to measure a model's uncertainty, i.e.…
We study expected values of the polynomials $P_N^{}(z)=\prod_{1\leq n\leq N}(X_n^2+z^2)$ whose $2N$ zeros $\{\pm i X_k\}^{}_{k=1,...,N}$ are generated by $N$ identically distributed multi-variate mean-zero normal random variables…
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…
Recently, the author and collaborators proposed a method to construct a new conserved charge different from the Noether one for general relativistic field theory on curved space-time with energy-momentum tensor covariantly conserved, and…
We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility…
In the context of averaging an inhomogeneous cosmological model, we propose a natural measure identical to the Kullback-Leibler relative information entropy, which expresses the distinguishability of the local inhomogeneous density field…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
Statistical analysis of voluntary survey data is an important area of research in survey sampling. We consider a unified approach to voluntary survey data analysis under the assumption that the sampling mechanism is ignorable. Generalized…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
We propose utilizing entropy as a diagnostic tool to distinguish between constant and dynamical dark energy models. Entropy, a measure of the system's disorder or information content, captures the complexity and evolution of the universe.…
Analysis of the generalized Weierstrass-Enneper system includes the estimation of the degree of indeterminancy of the general analytic solution and the discussion of the boundary value problem. Several different procedures for constructing…
We show several results on convergence of the Monte Carlo method applied to consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Our method is based on combination of several new concepts. We…
Macroscopic fields like electromagnetic, MHD, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…