Related papers: On the robustness of q-expectation values and Reny…
We consider 3d N>= 2 superconformal field theories on a branched covering of a three-sphere. The Renyi entropy of a CFT is given by the partition function on this space, but conical singularities break the supersymmetry preserved in the…
Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…
After studying some properties of the generalized exponential and logarithmic function, in particular investigating the domain where the first maintains itself real and positive, and outlining how the known dualities $q \leftrightarrow…
We combine an axiomatics of R\'{e}nyi with the $q$--deformed version of Khinchin axioms to obtain a measure of information (i.e., entropy) which accounts both for systems with embedded self-similarity and non-extensivity. We show that the…
We propose and analyze numerical schemes for the gradient flow of $Q$-tensor with the quasi-entropy. The quasi-entropy is a strictly convex, rotationally invariant elementary function, giving a singular potential constraining the…
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an…
This paper develops tools to obtain robust probabilistic estimates for queueing models at the large deviations (LD) scale. These tools are based on the recently introduced robust R\'enyi bounds, which provide LD estimates (and more…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
The aim of this paper is to investigate the q -> 1/q duality in an information-entropy theory of all q-generalized entropy functionals (Tsallis, Renyi and Sharma-Mittal measures) in the light of a representation based on generalized…
The quantum Renyi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory.…
Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms…
It has been known for some time that the usual $q$-entropy $S_q^{(n)}$ cannot be shown to converge to the continuous case. In [Phys. Rev. E 97 (2018) 012104], we have shown that the discrete $q$-entropy $\widetilde{S}_q^{(n)}$ converges to…
We present a novel robust control framework for continuous-time, perturbed nonlinear dynamical systems with uncertainty that depends nonlinearly on both the state and control inputs. Unlike conventional approaches that impose structural…
Inspired by the widespread concept of Lyapunov-Krasovskii functionals of complete type, this article proposes an alternative class of functionals, termed Lyapunov-Krasovskii functionals of robust type. Their construction aims at improving…
Randomness is a vital resource for modern day information processing, especially for cryptography. A wide range of applications critically rely on abundant, high quality random numbers generated securely. Here we show how to expand a random…
This paper develops robust inference methods for predictive regressions that address key challenges posed by endogenously persistent or heavy-tailed regressors, as well as persistent volatility in errors. Building on the Cauchy estimation…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…
We consider two types of entropy, namely, Shannon and R\'{e}nyi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More precisely, we prove that both entropies increase with…
New class of reference distribution functions for numerical approximation of the solution of the Fokker-Planck equations associated to the charged particle dynamics in tokamak are studied. The reference distribution functions are obtained…