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Topological defects are singularities within a field that cannot be removed by continuous transformations. The definition of these irregularities requires an ordered reference configuration, calling into question whether they exist in…

Soft Condensed Matter · Physics 2025-01-06 Vinay Vaibhav , Arabinda Bera , Amelia C. Y. Liu , Matteo Baggioli , Peter Keim , Alessio Zaccone

We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…

Mathematical Physics · Physics 2011-10-17 Scott A. Norris , Stephen J. Watson

Mapping of spatial hotspots, i.e., regions with significantly higher rates of generating cases of certain events (e.g., disease or crime cases), is an important task in diverse societal domains, including public health, public safety,…

Machine Learning · Statistics 2021-10-12 Yiqun Xie , Shashi Shekhar , Yan Li

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…

Algebraic Topology · Mathematics 2020-06-15 Chengyuan Wu , Carol Anne Hargreaves

We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…

Optimization and Control · Mathematics 2018-09-25 John Duchi , Feng Ruan

A major problem in the study of complex socioeconomic systems is represented by privacy issues$-$that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this…

This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…

General Topology · Mathematics 2021-03-18 Svetlana V. Butler

Adaptive Resonance Theory (ART) is considered as an effective approach for realizing continual learning thanks to its ability to handle the plasticity-stability dilemma. In general, however, the clustering performance of ART-based…

Machine Learning · Computer Science 2022-07-08 Naoki Masuyama , Narito Amako , Yuna Yamada , Yusuke Nojima , Hisao Ishibuchi

In this paper we continue to develop the following general approach. We study asymptotic behavior of the errors of sampling recovery not for an individual smoothness class, how it is usually done, but for the collection of classes, which…

Numerical Analysis · Mathematics 2026-01-14 V. Temlyakov

This paper investigates a general robust one-shot aggregation framework for distributed and federated Independent Component Analysis (ICA) problem. We propose a geometric median-based aggregation algorithm that leverages $k$-means…

Machine Learning · Computer Science 2025-05-28 Dian Jin , Xin Bing , Yuqian Zhang

A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the…

Numerical Analysis · Mathematics 2023-06-13 Deyue Zhang , Yan Chang , Yukun Guo

We study the localization of a cluster of activated vertices in a graph, from adaptively designed compressive measurements. We propose a hierarchical partitioning of the graph that groups the activated vertices into few partitions, so that…

Machine Learning · Statistics 2014-02-17 Akshay Krishnamurthy , James Sharpnack , Aarti Singh

Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat…

Machine Learning · Statistics 2017-11-15 Yongjin Park , Joel S. Bader

This paper studies the possibility of detecting and isolating topology failures (including link failures and node failures) of a networked system from subsystem measurements, in which subsystems are of fixed high-order linear dynamics, and…

Systems and Control · Electrical Eng. & Systems 2021-01-27 Yuan Zhang , Yuanqing Xia , Jinhui Zhang , Jun Shang

We develop a model in which interactions between nodes of a dynamic network are counted by non homogeneous Poisson processes. In a block modelling perspective, nodes belong to hidden clusters (whose number is unknown) and the intensity…

Machine Learning · Statistics 2017-07-11 Marco Corneli , Pierre Latouche , Fabrice Rossi

We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods…

Machine Learning · Computer Science 2023-11-27 Xiang Zhang , Qiao Wang

Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…

Molecular Networks · Quantitative Biology 2009-11-10 Konstantin Klemm , Stefan Bornholdt

Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the…

Machine Learning · Statistics 2016-11-15 Vicente Zarzoso , Pierre Comon

We prove a compactness result with respect to $\Gamma$-convergence for a class of integral functionals which are expressed as a sum of a local and a non-local term. The main feature is that, under our hypotheses, the local part of the…

Analysis of PDEs · Mathematics 2022-12-23 Andrea Braides , Gianni Dal Maso

In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature…

Computation · Statistics 2023-03-08 Hai-Dang Dau , Nicolas Chopin