相关论文: Sharp Bounds on Arimoto's Conditional R\'{e}nyi En…

We study the entanglement entropy, the R\'enyi entropy, and the mutual (R\'enyi) information of Dirac fermions on a 2 dimensional torus in the presence of constant gauge fields. We derive their general formulas using the equivalence between…

In their recent paper [Phys. Rev. E 99 (2019) 032134], T. Oikinomou and B. Bagci have argued that R\'enyi entropy is ill-suited for inference purposes because it is not consistent with the Shore{ Johnson axioms of statistical estimation…

Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the R\'enyi entropy, which measures the diversity of a statistical ensemble. We derive a mathematical relation…

We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…

We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…

We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…

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.…

R\'enyi entropy is a one-parameter generalization of Shannon entropy, which has been used in various fields of physics. Despite its wide applicability, the physical interpretations of the R\'enyi entropy are not widely known. In this paper,…

The entropic moments of the probability density of a quantum system in position and momentum spaces describe not only some fundamental and/or experimentally accessible quantities of the system, but also the entropic uncertainty measures of…

The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…

Fundamental results on secret sharing schemes (SSSs) are discussed in the setting where security and share size are measured by (conditional) min-entropies. We first formalize a unified framework of SSSs based on (conditional) R\'enyi…

Specially customised Entropies are widely applied in measuring the degree of uncertainties existing in the frame of discernment. However, all of these entropies regard the frame as a whole that has already been determined which dose not…

Majorization is a stochastic ordering relation that compares the relative diversity of probability distributions with numerous applications in econometrics, spectral theory, and ecology. It is well-known that the majorization partial order…

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the R\'enyi entropy is presented that uses transport arguments from normal densities and a change of variable by…

For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the R\'enyi divergence of infinite order. In terms of densities $p_n$ of $Z_n$,…

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…

Sharpness (of the loss minima) is a common measure to investigate the generalization of neural networks. Intuitively speaking, the flatter the landscape near the minima is, the better generalization might be. Unfortunately, the correlation…

Under the Bayesian brain hypothesis, behavioural variations can be attributed to different priors over generative model parameters. This provides a formal explanation for why individuals exhibit inconsistent behavioural preferences when…

A comparative study of one-dimensional quantum structures which allow analytic expressions for the position and momentum R\'{e}nyi $R(\alpha)$ and Tsallis $T(\alpha)$ entropies, focuses on extracting the most characteristic physical…