Related papers: A quantitative averaging lemma for spatially depen…
We develop geometry-of-numbers methods to count orbits in coregular vector spaces having bounded invariants over any global field. We apply these techniques to bound the average ranks and determine average Selmer group sizes of elliptic…
We study the sheaves of logarithmic vector fields along smooth cubic curves in the projective plane, and prove a Torelli-type theorem in the sense of Dolgachev-Kapranov for those with non-vanishing j-invariants.
In this paper, we present a statistical framework for modeling conditional quantiles of spatial processes assumed to be strongly mixing in space. We establish the $L_1$ consistency and the asymptotic normality of the kernel conditional…
We characterize nonforking (Morley) sequences in dependent theories in terms of a generalization of Poizat's special sequences and show that average types of Morley sequences are stationary over their domains. We characterize generically…
We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's conjecture for such Lie algebras. Also infinite-dimensional…
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
We develop a method for determining the density of squarefree values taken by certain multivariate integer polynomials that are invariants for the action of an algebraic group on a vector space. The method is shown to apply to the…
We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioned on their feature vectors, but dependent, capturing settings where e.g. these observations are collected…
This paper gives a survey on a valuation theoretical approach to local uniformization in positive characteristic, the model theory of valued fields in positive characteristic, and their connection with the valuation theoretical phenomenon…
Szemeredi's regularity lemma is one instance in a family of regularity lemmas, replacing the definition of density of a graph by a more general coefficient. Recently, Fan Chung proved another instance, a regularity lemma for clustering…
Integrable quantum field theories in 1+1 dimensions have recently become amenable to a rigorous construction, but many questions about the structure of their local observables remain open. Our goal is to characterize these local observables…
We study the reduction of non-autonomous regular Lagrangian systems by symmetries, which are generated by vector fields associated with connections in the configuration bundle of the system $Q\times\real\to\real$. These kind of symmetries…
We prove function field theorems supporting the Cohen-Lenstra heuristics for real quadratic fields, and natural strengthenings of these analogs from the affine class group to the Picard group of the associated curve. Our function field…
We prove a version of the classical Mittag-Leffler Theorem for regular functions over quaternions. Our result relies upon an appropriate notion of principal part, that is inspired by the recent definition of spherical analyticity.
This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…
Support vector machine (SVM) is a well-known statistical technique for classification problems in machine learning and other fields. An important question for SVM is the selection of covariates (or features) for the model. Many studies have…
We state and prove a Lemma in 1 variable Calculus, that justifies some arguments previously used to ilustrate non-uniqueness of some generalized physical quantities.
We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the…
We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On…
We study sample covariance matrices arising from rectangular random matrices with i.i.d. columns. It was previously known that the resolvent of these matrices admits a deterministic equivalent when the spectral parameter stays bounded away…