Related papers: A note on correlation and local dimensions
Quantum information leverages properties of quantum behaviors in order to perform useful tasks such as secure communication and randomness certification. Nevertheless, not much is known about the intricate geometric features of the set…
With the recent advent of a sound mathematical theory for extreme events in dynamical systems, new ways of analyzing a system's inherent properties have become available: Studying only the probabilities of extremely close Poincar\'{e}…
We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or $\textit{modal-sets}$, of…
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial…
We study the entanglement of formation for arbitrary dimensional bipartite mixed unknown states. Experimentally measurable lower and upper bounds for entanglement of formation are derived.
Given a language, which in this article is a set of strings of some fixed length, we study the problem of producing its elements by a procedure in which each position has its own local rule. We introduce a way of measuring how much…
When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by…
We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures like quantum discord and quantum work deficit in two qubits and higher dimensional systems. We show that determination of…
We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the…
Some recent attempts at measuring non local weak values via local measurements are discussed and shown to be less robust than standard weak measurements. A method for measuring some non local weak values via non local measurements (non…
Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix.…
We discuss discrete Morrey spaces and their generalizations, and we prove necessary and sufficient conditions for the inclusion property among these spaces through an estimate for the characteristic sequences.
Tests of local realism and their applications aim for very high confidence in their results even in the presence of potentially adversarial effects. For this purpose, one can measure a quantity that reflects the amount of violation of local…
Optimal designs for generalized linear models require a prior knowledge of the regression parameters. At certain values of the parameters we propose particular assumptions which allow to derive a locally optimal design for a model without…
How can we characterize different types of correlation between quantum systems? Since correlations cannot be generated locally, we take any real function of a multipartite state which cannot increase under local operations to measure a…
This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizontal variation are considered. The investigations provide…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…