相关论文: VC bounds on the cardinality of nearly orthogonal …
A connected Riemannian manifold M has constant vector curvature \epsilon, denoted by cvc(\epsilon), if every tangent vector v in TM lies in a 2-plane with sectional curvature \epsilon. By scaling the metric on M, we can always assume that…
By considering a certain univalent function in the open unit disk U, that maps U onto a strip domain, we introduce a new class of analytic and close-to-convex functions by means of a certain non-homogeneous Cauchy-Euler-type differential…
This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…
Motivated by a model in quantum computation we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the…
The main purpose of this paper is to prove that the point-line incidence bound due to Vinh (2011) over arbitrary finite fields can be improved in certain ranges by using tools from the VC-dimension theory. As consequences, a number of…
We give necessary and sufficient conditions for a family of inner products in a finite-dimensional vector space $V$ over an arbitrary field $\mathbb{K}$ to have an orthogonal basis relative to all the inner products. Some applications to…
We prove that the cardinality of the torsion subgroups in homology of a closed hyperbolic manifold of any dimension can be bounded by a doubly exponential function of its diameter. It would follow from a conjecture by Bergeron and Venkatesh…
The control function approach allows the researcher to identify various causal effects of interest. While powerful, it requires a strong invertibility assumption in the selection process, which limits its applicability. This paper expands…
This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on…
In analyzing a simple random walk on the Heisenberg group we encounter the problem of bounding the extreme eigenvalues of an $n\times n$ matrix of the form $M=C+D$ where $C$ is a circulant and $D$ a diagonal matrix. The discrete…
In the Orthogonal Vectors (OV) problem, we wish to determine if there is an orthogonal pair of vectors among $n$ Boolean vectors in $d$ dimensions. The OV Conjecture (OVC) posits that OV requires $n^{2-o(1)}$ time to solve, for all…
We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting we are able to define an analogue of the distributional differential and on finite…
We use the partition functions on S^1 x S^n of various conformal field theories in four and six dimensions in the limit of vanishing coupling to study the high temperature thermodynamics. Certain modular properties exhibited by the…
We control the probability of the uniform deviation between empirical and generalization performances of multi-category classifiers by an empirical L1 -norm covering number when these performances are defined on the basis of the truncated…
Modeling the spread of social contagions is central to various applications in social computing. In this paper, we study the learnability of the competitive threshold model from a theoretical perspective. We demonstrate how competitive…
We consider the problem of learning Neural Ordinary Differential Equations (neural ODEs) within the context of Linear Parameter-Varying (LPV) systems in continuous-time. LPV systems contain bilinear systems which are known to be universal…
Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…
We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…
Directed and undirected graphical models, also called Bayesian networks and Markov random fields, respectively, are important statistical tools in a wide variety of fields, ranging from computational biology to probabilistic artificial…
Non-asymptotic bounds for Gaussian and bootstrap approximation have recently attracted significant interest in high-dimensional statistics. This paper studies Berry-Esseen bounds for such approximations with respect to the multivariate…