Related papers: Local to global principle over number fields for h…

Quantifying the population density of an urban area is a fraught issue. Measures of density are often defined differently from place to place or applied inconsistently, and arguments abound over just how much of the land surrounding a city…

Stochastic expansion-based methods of uncertainty quantification, such as polynomial chaos and separated representations, require basis functions orthogonal with respect to the density of random inputs. Many modern engineering problems…

Among the variety of statistical intervals, highest-density regions (HDRs) stand out for their ability to effectively summarize a distribution or sample, unveiling its distinctive and salient features. An HDR represents the minimum size set…

This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…

We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…

This paper addresses the problem of detecting change points in the spectral density of time series, motivated by EEG analysis of seizure patients. Seizures disrupt coherence and functional connectivity, necessitating precise detection.…

The Hohenberg-Kohn theorem, a cornerstone of electronic density functional theory, concerns uniqueness of external potentials yielding given ground densities of an ${\mathcal N}$-body system. The problem is rigorously explored in a universe…

Finding the mode of a high dimensional probability distribution $D$ is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when $D$ is…

We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that are both rate-optimal and computationally efficient for…

In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means…

In order to estimate the specific intrinsic volumes of a planar Boolean model from a binary image, we consider local digital algorithms based on weighted sums of $2\times 2$ configuration counts. For Boolean models with balls as grains,…

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality \cite{AmelinoCamelia:2011bm} has been proposed as a way to consider Planckian modifications of the…

We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply…

In this paper we prove Hasse local-global principle for polynomials with coefficients in Mordell-Weil type groups over number fields like S-units, abelian varieties with trivial ring of endomorphisms and odd algebraic K-theory groups.

We present a generalization of the Li, Nunes and Vanderbilt density-matrix method to the case of a non-orthogonal set of basis functions. A representation of the real-space density matrix is chosen in such a way that only the overlap…

Crowd scenes captured by cameras at different locations vary greatly, and existing crowd models have limited generalization for unseen surveillance scenes. To improve the generalization of the model, we regard different surveillance scenes…

Predicting the local dynamics of supercooled liquids based purely on local structure is a key challenge in our quest for understanding glassy materials. Recent years have seen an explosion of methods for making such a prediction, often via…

In this paper we use Euclidean gravity to derive a simple formula for the density of black hole microstates which transform in each irreducible representation of any finite gauge group. Since each representation appears with nonzero…

This paper investigates a local central limit theorem for a normalized sequence of random variables belonging to a fixed order Wiener chaos and converging to the standard normal distribution. We prove, without imposing any additional…

We suggest a simple approach to calculate the local density of states that effectively applies to any structure created by an axially symmetric potential on a continuous graphene sheet such as circular graphene quantum dots or rings.…