We study transport properties such as conductance and diffusion of complex networks such as scale-free and Erdős-Rényi networks. We consider the equivalent conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P (k) ∼ k−λ and Erdős-Rényi networks in which each link has the same unit resistance. Our theoretical analysis for scale-free networks ...

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. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback-Leibler divergence over projective measurement statisti...

Estimating entropies is important in many fields including statistical physics, machine learning and statistics. While the Shannon logarithmic entropy is the most fundamental, other Rényi entropies are also of importance. In this paper, we derive a bias corrected estimator for a subset of Rényi entropies. The advantage of the estimator is demonstrated via theoretical and experimental considerat...

We propose a natural relaxation of differential privacy based on the Rényi divergence. Closely related notions have appeared in several recent papers that analyzed composition of differentially private mechanisms. We argue that the useful analytical tool can be used as a privacy definition, compactly and accurately representing guarantees on the tails of the privacy loss. We demonstrate that th...

The Rényi information measures are characterized in terms of their Shannon counterparts, and properties of the former are recovered from first principle via the associated properties of the latter. Motivated by this characterization, a two-sensor composite hypothesis testing problem is presented, and the optimal worst case miss-detection exponent is obtained in terms of a Rényi divergence.

We consider the generalized differential entropy of normalized sums of independent and identically distributed (IID) continuous random variables. We prove that the Rényi entropy and Tsallis entropy of order α (α > 0) of the normalized sum of IID continuous random variables with bounded moments are convergent to the corresponding Rényi entropy and Tsallis entropy of the Gaussian limit, and obtai...

Since their introduction in the early sixties [20], the Rényi entropies have been used in many contexts, ranging from information theory to astrophysics, turbulence phenomena and others. In this note, we enlighten the main connections between Rényi entropies and nonlinear diffusion equations. In particular, it is shown that these relationships allow to prove various functional inequalities in s...

We provide a variational characterization for the various Rényi information measures via their Shannon counterparts, and demonstrate how properties of the former can be recovered from first principle via the associated properties of the latter. Motivated by this characterization, we give a new operational interpretation for the Rényi divergence in a twosensor composite hypothesis testing framew...

Instability, fear of falling and fall injuries are common problems for the older population and individuals with chronic disabilities. Development of screening tools and outcome measures of balance performance and fall risk has become of great interest for health professionals and researchers in the field of rehabilitation. Although linear modeling is desirable due to its simplicity, however, m...