arXiv subjects

Daniel Lazarev

Publications and source records attributed to Daniel Lazarev.

5 recordsLinked to original sources

arXiv2026

A Structural Characterization of Entropy Functionals

Entropy functionals and their associated divergences underlie many statistical methods, including maximum entropy inference, minimum divergence estimation, and goodness-of-fit testing, yet choosing among Shannon, R\'enyi, Tsallis, and more general entropies is often a matter of convention rather than structural principle. We introduce a measure theoretic framework in which admissibility requires the entropy of an input measure to be bounded above by that of its reference measure whenever the former is absolutely continuous with respect to the latter. Under generalized mean-value composition, we characterize all such entropy functionals and obtain a four-level hierarchy determined successively by the mean generator, entropy scale, and additivity assumptions. A continuous strictly monotone generator $g$ is admissible exactly when $t\mapsto g(1/t)$ is strictly convex for increasing $g$, or strictly concave for decreasing $g$. This resolves a question posed by R\'enyi (Proc. 4th Berkeley Sympos. Math. Statist. Prob., 1961) concerning which generalized means may replace the arithmetic mean in his entropy axiomatization. The same criterion is equivalent to strict convexity of an associated Csisz\'ar $f$-divergence generator and therefore yields data processing under Markov kernels with an exact equality condition. Within this hierarchy, product additivity singles out the R\'enyi family, while internal additivity, or product additivity together with arithmetic mean-value composition, singles out Shannon entropy. The characterization is constructive and yields new admissible entropy and divergence families, including integral-transform examples.

cs.IT↗

arXiv2025

Stokes' theorem as an entropy-extremizing duality

Given a manifold $\mathcal{M} \subset \mathbb{R}^n$, we consider all codimension-1 submanifolds of $\mathcal{M}$ that satisfy the generalized Stokes' theorem and show that $\partial\mathcal{M}$ uniquely maximizes the associated entropy functional. This provides an information theoretic characterization of the duality expressed by Stokes' theorem, whereby a manifold's boundary is its 'least informative' subset satisfying the Stokes relation.

math.DG↗

arXiv2023

Spatiotemporal risk prediction for infectious disease spread and mortality

With the outbreak of the COVID-19 pandemic, various studies have focused on predicting the trajectory and risk factors of the virus and its variants. Building on previous work that addressed this problem using genetic and epidemiological data, we introduce a method, Geo Score, that also incorporates geographic, socioeconomic, and demographic data to estimate infection and mortality risk by region and time. We employ gradient descent to find the optimal weights of the factors' significance in determining risk. Such spatiotemporal risk prediction is important for informed public health decision-making so that individuals are aware of the risks of travel during an epidemic or pandemic, and, perhaps more importantly, so that policymakers know how to triage limited resources during a crisis. We apply our method to New York City COVID-19 data from 2020, predicting ZIP code-level COVID-19 risk for 2021.

stat.AP↗

arXiv2023

Information Measures for Entropy and Symmetry

Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in naïve extensions of the definition of entropy from discrete to continuous settings, are byproducts of the use of probabilities, which only work in the discrete case by a fortunate coincidence. We introduce the notions of sup-normalization and information measures, which allow for the appropriate generalization of the definition of entropy that keeps with the interpretation of entropy as a subspace volume. Applying this in the context of topological groups and Haar measures, we elucidate the relationship between entropy, symmetry, and uniformity.

math.PR↗

arXiv2020

Maximum entropy production as a necessary admissibility condition for the fluid Navier-Stokes and Euler equations

In a particle physics dynamics, we assume a uniform distribution as the physical measure and a measure-theoretic definition of entropy on the velocity configuration space. This distribution is labeled as the physical solution in the remainder of the article. The dynamics is governed by an assumption of a Lagrangian formulation, with the velocity time derivatives as the momenta conjugate to the velocity configurations. From these definitions and assumptions, we show mathematically that a maximum entropy production principle selects the physical measure from among alternate solutions of the Navier-Stokes and Euler equations, but its transformation to an Eulerian frame is not established here, a topic that will be considered separately.

math-ph↗