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Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…
We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…
In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage…
We study the common continual learning setup where an overparameterized model is sequentially fitted to a set of jointly realizable tasks. We analyze forgetting, defined as the loss on previously seen tasks, after $k$ iterations. For…
We provide a new approach, along with extensions, to results in two important papers of Worsley, Siegmund and coworkers closely tied to the statistical analysis of fMRI (functional magnetic resonance imaging) brain data. These papers…
This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special…
We investigate the one-loop effective action for a test scalar field in a general Friedmann-Lema\^itre-Robertson-Walker (FLRW) background, specifically focusing on quantum corrections up to the second order in the interaction strength. By…
We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…
We propose a semi-partitioned Generalized Method of Moments (GMM) framework for analyzing longitudinal data with time-dependent covariates, within a marginal modeling paradigm. This approach addresses limitations of both aggregated and…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
The spherical functions of the noncompact Grassmann manifolds $G_{p,q}(\mathbb F)=G/K$ over the (skew-)fields $\mathbb F=\mathbb R, \mathbb C, \mathbb H$ with rank $q\ge1$ and dimension parameter $p>q$ can be described as Heckman-Opdam…
The aim of this paper is to deepen the analysis of the asymptotic behavior of the so-called minimal random walk (MRW) using a new martingale approach. The MRW is a discrete-time random walk with infinite memory that has three regimes…
We consider the stochastic gradient descent (SGD) algorithm driven by a general stochastic sequence, including i.i.d noise and random walk on an arbitrary graph, among others; and analyze it in the asymptotic sense. Specifically, we employ…
This article presents a neural network approach for estimating the covariance function of spatial Gaussian random fields defined in a portion of the Euclidean plane. Our proposal builds upon recent contributions, expanding from the purely…
Large Language Models (LLMs) face fundamental challenges in long-context reasoning: many documents exceed their finite context windows, while performance on texts that do fit degrades with sequence length, necessitating their augmentation…
Current statistics literature on statistical inference of random fields typically assumes that the fields are stationary or focuses on models of non-stationary Gaussian fields with parametric/semiparametric covariance families, which may…
Several stochastic processes modeling molecular motors on a linear track are given by random walks (not necessarily Markovian) on quasi 1d lattices and share a common regenerative structure. Analyzing this abstract common structure, we…
It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of half-integer conformal weights. This yields representations of fermionic 2-point functions in terms of correlators of primary fields with a factorized…
The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance…
The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations…