相关论文: Entropy Estimate For High Dimensional Monotonic Fu…

Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…

We present a number of explicit calculations of Renyi and entanglement entropies in situations where the entangling surface intersects the boundary in $d$-dimensional Minkowski spacetime. When the boundary is a single plane we compute the…

Consider the set of all sequences of $n$ outcomes, each taking one of $m$ values, that satisfy a number of linear constraints. If $m$ is fixed while $n$ increases, most sequences that satisfy the constraints result in frequency vectors…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

We study the Euler numbers and the entropies of the non-extremal intersecting D-branes in ten-dimensions. We use the surface gravity to constrain the compactification radii. We correctly obtain the integer valued Euler numbers for these…

The aim of this work is to study a kind of refinement of the entropy conjecture, in the context of partially hyperbolic diffeomorphisms with one dimensional central direction, of d-dimensional torus. We start by establishing a connection…

In this paper non-asymptotic exact exponential estimates are derived (under minimal conditions) for the tail of deviation of the MLE distribution in the so-called natural terms: natural function, natural distance, metric entropy, Banach…

In this note, we first try to prove a uniform lower bound of nodal volume in elliptic homogenization setting. This lower bound is far from optimal. But, we can prove a constant lower bound in dimension two. Motivated by the proof, we extend…

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…

Entropy dimension is an entropy-type quantity which takes values in $[0,1]$ and classifies different levels of intermediate growth rate of complexity for dynamical systems. In this paper, we consider the complexity of skew products of…

We introduce an exactly solvable lattice model that reveals a universal finite-size scaling law for configurational entropy driven purely by geometry. Using exact enumeration via Burnside's lemma, we compute the entropy for diverse 1D, 2D,…

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular…

We establish a new monotonicity formula for minimizers of the Mumford-Shah functional in planar domains. Our formula follows the spirit of Bucur-Luckhaus, but works with the David-L\'eger entropy instead of the energy. Interestingly, this…

We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.

The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…

In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $\epsilon$-covering number of $\C([a, b]^d, B)$, in the $L_p$-metric, $1…

We explore an asymptotic behavior of R\'enyi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the problem of monotonicity is addressed under suitable moment…

Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on…

We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…

We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…