Related papers: On the robustness of q-expectation values and Reny…
In this paper, we study the approximation and estimation of $s$-concave densities via R\'enyi divergence. We first show that the approximation of a probability measure $Q$ by an $s$-concave densities exists and is unique via the procedure…
What is a question? According to Cox a question can be identified with the set of assertions that constitute possible answers. In this paper we propose a different approach that combines the notion that questions are requests for…
The R\'enyi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field $\lambda$ that controls the partition…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
In this lecture we briefly review the definition, consequences and applications of an entropy, $S_q$, which generalizes the usual Boltzmann-Gibbs entropy $S_{BG}$ ($S_1=S_{BG}$), basis of the usual statistical mechanics, well known to be…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
The resource theories of quantum coherence attract a lot of attention in recent years. Especially, the monotonicity property plays a crucial role here. In this paper we investigate the monotonicity property for the coherence measures…
The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
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 address the problem of distributed state estimation of a linear dynamical process in an attack-prone environment. Recent attempts to solve this problem impose stringent redundancy requirements on the measurement and communication…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
The aim of this paper is to study different estimation procedures based on $\varphi-$divergences. The dual representation of $\varphi-$divergences based on the Fenchel-Legendre duality is the main interest of this study. It provides a way…
Renyi entropies S_q are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q>=0. For (d+1)-dimensional conformal field theories, the Renyi entropies across…
We consider the problem of testing mutual independence among the components of a high-dimensional random vector. Building on the rank-based max-sum framework, we introduce fixed finite-$L_q$ power-sum statistics under three general classes…
We calculate the limiting behavior of relative Renyi entropy when the first probability distribution is close to the second one in a non-regular location-shift family which is generated by a probability distribution whose support is an…
This work investigates three aspects: (a) a network vulnerability as the non-uniform vulnerable-host distribution, (b) threats, i.e., intelligent malwares that exploit such a vulnerability, and (c) defense, i.e., challenges for fighting the…
We introduce a class of probability measures whose densities near infinity are mixtures of Pareto distributions. This class can be characterized by the Fourier transform which has a power series expansion including real powers, not only…
The effect of unstable quasiparticles in the out-of-equilibrium dynamics of certain integrable systems has been the subject of several recent studies. In this paper we focus on the stationary value of the entanglement entropy density, its…
The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values) and the fundamental entropy-like…