相关论文: Minimum correlation for any bivariate Geometric di…
The magnitude of Pearson correlation between two scalar random variables can be visually judged from the two-dimensional scatter plot of an independent and identically distributed sample drawn from the joint distribution of the two…
This paper proposes a geometric estimator of dependency between a pair of multivariate samples. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate…
Let N be a nilpotent Lie group and let S be an invariant geometric structure on N (cf. symplectic, complex or hypercomplex). We define a left invariant Riemannian metric on N compatible with S to be "minimal", if it minimizes the norm of…
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
Nonlocality is one of the main characteristic features of quantum systems involving more than one spatially separated subsystems. It is manifested theoretically as well as experimentally through violation of some local realistic inequality.…
We investigate the problem of detecting correlation between two Erd\H{o}s-R\'enyi graphs $G(n,p)$, formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are independent, while under the alternative…
Consider an open quantum system which interacts with its environment. Assuming that the experimenter has access only to the system, an interesting question is whether it is possible to detect initial correlations between the system and the…
For given a pair of nodes in a graph, the minimum non-separating path problem looks for a minimum weight path between the two nodes such that the remaining graph after removing the path is still connected. The balanced connected bipartition…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
The minimal Hamming distance between distinct $p$-ary bent functions of $2n$ variables is proved to be $p^n$ for any prime $p$. It is shown that the number of $p$-ary bent functions at the distance $p^n$ from the quadratic bent function is…
We establish minimax optimal rates of convergence for nonparametric estimation in functional ANOVA models when data from first-order partial derivatives are available. Our results reveal that partial derivatives can improve convergence…
Dependence among marginally constrained observations can break a finite-sample barrier. To formalize this phenomenon, we introduce the \emph{minimum list entropy coupling} $H(P\|Q_1,\dots,Q_m)$, the minimum conditional entropy…
We investigate minimal surfaces in products of two-spheres ${\mathbb S}^2_p\times {\mathbb S}^2_p$, with the neutral metric given by $(g,-g)$. Here ${\mathbb S}^2_p\subset {\mathbb R}^{p,3-p}$ , and $g$ is the induced metric on the sphere.…
Local porosity distributions for a three-dimensional porous medium and local porosity distributions for a two-dimensional plane-section through the medium are generally different. However, for homogeneous and isotropic media having finite…
M. Levin defined a real number $x$ that satisfies that the sequence of the fractional parts of $(2^n x)_{n\geq 1}$ are such that the first $N$ terms have discrepancy $O((\log N)^2/ N)$, which is the smallest discrepancy known for this kind…
This paper considers correlation clustering on unweighted complete graphs. We give a combinatorial algorithm that returns a single clustering solution that is simultaneously $O(1)$-approximate for all $\ell_p$-norms of the disagreement…
Marginalization of latent variables or nuisance parameters is a fundamental aspect of Bayesian inference and uncertainty quantification. In this work, we focus on scalable marginalization of latent variables in modeling correlated data,…
In this paper, we introduce the notion of negatively regionally proximal pairs of onto maps which coincides with the set of regionally proximal pair of $f^{-1}$, whenever $f$ is an homeomorphism and we prove the maximal equicontinoues…
This is a continuation of the article with the same title. In this paper, the family H is the same as in the previous paper "On Graphs with the Smallest Eigenvalue at Least $-1-\sqrt{2}$, part I". The main result is that a minimal graph…