相关论文: Local digital algorithms applied to Boolean models

In this paper, we propose distributed algorithms that solve a system of Boolean equations over a network, where each node in the network possesses only one Boolean equation from the system. The Boolean equation assigned at any particular…

This paper deals with the robust estimation problem of a signal given noisy observations. We assume that the actual statistics of the signal and observations belong to a ball about the nominal statistics. This ball is formed by placing a…

Recent advancements in edge computing have significantly enhanced the AI capabilities of Internet of Things (IoT) devices. However, these advancements introduce new challenges in knowledge exchange and resource management, particularly…

The experimentally verified violation of Bell's inequalities apparently implies that at least one of two intuitive beliefs must be false: that effects propagating at infinite velocity do not exist, and that natural phenomena occur…

With the recent advent of a sound mathematical theory for extreme events in dynamical systems, new ways of analyzing a system's inherent properties have become available: Studying only the probabilities of extremely close Poincar\'{e}…

Measurement correlations in quantum systems can exhibit non-local behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, the explicit construction of local…

Cook's [J. Roy. Statist. Soc. Ser. B 48 (1986) 133--169] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous…

Suppose that $n$ statistical units are observed, each following the model $Y(x_j)=m(x_j)+ \epsilon(x_j),\, j=1,...,N,$ where $m$ is a regression function, $0 \leq x_1 <...<x_N \leq 1$ are observation times spaced according to a sampling…

Invoking the manifold assumption in machine learning requires knowledge of the manifold's geometry and dimension, and theory dictates how many samples are required. However, in applications data are limited, sampling may not be uniform, and…

We present an algorithm for sampling tightly confined random equilateral closed polygons in three-space which has runtime linear in the number of edges. Using symplectic geometry, sampling such polygons reduces to sampling a moment…

Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We…

Given an i.i.d. sample drawn from some probability distribution on a finite set, the best (in the sense of least variance) linear unbiased estimator (BLUE) of the average of any quantity with respect to that distribution is the sample…

We study the problem of isometrically embedding a two-dimensional Riemannian manifold into Euclidean three-space. It is shown that if Gaussian curvature vanishes to finite order and its zero set consists of two smooth curves tangent at a…

We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with…

Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that…

We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…

We compute tautological integrals over Quot schemes on curves and surfaces. After obtaining several explicit formulas over Quot schemes of dimension 0 quotients on curves (and finding a new symmetry), we apply the results to tautological…

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…

We propose a data-driven mean-curvature solver for the level-set method. This work is the natural extension to $\mathbb{R}^3$ of our two-dimensional strategy in [DOI: 10.1007/s10915-022-01952-2][1] and the hybrid inference system of [DOI:…

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…