Related papers: Distances between time-series and their autocorrel…
This paper considers the inference of trends in multiple, nonstationary time series. To test whether trends are parallel to each other, we use a parallelism index based on the L2-distances between nonparametric trend estimators and their…
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based…
We study statistical inference on the similarity/distance between two time-series under uncertain environment by considering a statistical hypothesis test on the distance obtained from Dynamic Time Warping (DTW) algorithm. The sampling…
The Hellinger distance between quantum states is a significant measure in quantum information theory, known for its Riemannian and monotonic properties. It is also easier to compute than the Bures distance, another measure that shares these…
We consider the problem of determining the number of distinct distances between two point sets in $\mathbb{R}^2$ where one point set $\mathcal{P}_1$ of size $m$ lies on a real algebraic curve of fixed degree $r$, and the other point set…
The use of ordinal patterns (OPs) for analyzing the dependence structure of univariate and continuously distributed processes has gained popularity in recent years. This research goes one step further and considers the transcripts being…
We show that the cophylogenetic distance, k-interval cospeciation, is distinct from other metrics and accounts for global congruence between locally incongruent trees. The growth of the neighborhood of trees which satisfy the largest…
Measures of linear dependence (coherence) and nonlinear dependence (phase synchronization) between any number of multivariate time series are defined. The measures are expressed as the sum of lagged dependence and instantaneous dependence.…
In this paper, a time series model with coefficients that take values from random matrix ensembles is proposed. Formal definitions, theoretical solutions, and statistical properties are derived. Estimation and forecast methodologies for…
We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
The distance matrix of a graph $G$ is the matrix containing the pairwise distances between vertices. The distance eigenvalues of $G$ are the eigenvalues of its distance matrix and they form the distance spectrum of $G$. We determine the…
The curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup. We propose a new method to identify the dimensionality of curve time series based on the dynamical dependence…
Let P_1 and P_2 be two sets of points in the plane, so that P_1 is contained in a line L_1, P_2 is contained in a line L_2, and L_1 and L_2 are neither parallel nor orthogonal. Then the number of distinct distances determined by the pairs…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads…
To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between…
We reveal a general explicit relation between the statistics of delay times in one-channel reflection from a mesoscopic sample of any spatial dimension and the statistics of the eigenfunction intensities in its closed counterpart. This…
Large multidimensionality of high-throughput datasets pertaining to cell signaling and gene regulation renders it difficult to extract mechanisms underlying the complex kinetics involving various biochemical compounds (e.g., proteins,…
We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…