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This paper deals with the problem of detecting non-isotropic high-dimensional geometric structure in random graphs. Namely, we study a model of a random geometric graph in which vertices correspond to points generated randomly and…

Statistics Theory · Mathematics 2020-02-25 Ronen Eldan , Dan Mikulincer

In this paper, we study the convergence properties of the Stochastic Gradient Descent (SGD) method for finding a stationary point of a given objective function $J(\cdot)$. The objective function is not required to be convex. Rather, our…

Machine Learning · Statistics 2024-09-24 Rajeeva L. Karandikar , M. Vidyasagar

In a bipartite max-min LP, we are given a bipartite graph $\myG = (V \cup I \cup K, E)$, where each agent $v \in V$ is adjacent to exactly one constraint $i \in I$ and exactly one objective $k \in K$. Each agent $v$ controls a variable…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-05-15 Patrik Floréen , Marja Hassinen , Petteri Kaski , Jukka Suomela

Applied researchers often construct a network from a random sample of nodes in order to infer properties of the parent network. Two of the most widely used sampling schemes are subgraph sampling, where we sample each vertex independently…

Statistics Theory · Mathematics 2018-02-23 Jason M. Klusowski , Yihong Wu

The specific heat of an attractive (interaction $G<0$) non-local Hubbard model is investigated. We use a two-pole approximation which leads to a set of correlation functions. In particular, the correlation function $\…

Strongly Correlated Electrons · Physics 2013-05-15 E. J. Calegari , C. O. Lobo , S. G. Magalhaes , C. M. Chaves , A. Troper

We give a distributed algorithm in the {\sf CONGEST} model for property testing of planarity with one-sided error in general (unbounded-degree) graphs. Following Censor-Hillel et al. (DISC 2016), who recently initiated the study of property…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-08-15 Reut Levi , Moti Medina , Dana Ron

We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrix for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the…

Disordered Systems and Neural Networks · Physics 2025-08-27 Luca Schaefer , Barbara Drossel

Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbours to each point of a dataset to perform their tasks. These proximity relations define a so-called…

Statistical Mechanics · Physics 2020-07-22 Vittorio Erba , Sebastiano Ariosto , Marco Gherardi , Pietro Rotondo

Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…

Data Structures and Algorithms · Computer Science 2019-02-20 Martin Furer , Shiva Prasad Kasiviswanathan

In this paper, we develop a class of decentralized algorithms for solving a convex resource allocation problem in a network of $n$ agents, where the agent objectives are decoupled while the resource constraints are coupled. The agents…

Optimization and Control · Mathematics 2018-12-18 Angelia Nedić , Alex Olshevsky , Wei Shi

Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…

Discrete Mathematics · Computer Science 2021-01-25 Michel Habib , Lalla Mouatadid , Eric Sopena , Mengchuan Zou

By introducing height dependency in the surface energy density, we propose a novel regularized variational model to simulate wetting/dewetting problems. The regularized model leads to the appearance of a precursor layer which covers the…

Analysis of PDEs · Mathematics 2022-08-18 Wei Jiang , Zhen Zhang , Zeyu Zhou

The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension…

Machine Learning · Statistics 2025-09-05 Yifan Chen , Xiaoou Cheng , Jonathan Niles-Weed , Jonathan Weare

We investigate the asymptotic behavior of sequences generated by the proximal point algorithm for convex functions in complete geodesic spaces with curvature bounded above. Using the notion of resolvents of such functions, which was…

Functional Analysis · Mathematics 2017-04-25 Yasunori Kimura , Fumiaki Kohsaka

We study the model $G_\alpha\cup G(n,p)$ of randomly perturbed dense graphs, where $G_\alpha$ is any $n$-vertex graph with minimum degree at least $\alpha n$ and $G(n,p)$ is the binomial random graph. We introduce a general approach for…

Combinatorics · Mathematics 2019-08-01 Julia Böttcher , Richard Montgomery , Olaf Parczyk , Yury Person

In this paper, based on the local comparison principle in [12], we study the local behavior of the difference of two spacelike graphs in a neighborhood of a second contact point. Then we apply it to the constant mean curvature equation in…

Analysis of PDEs · Mathematics 2017-06-14 Jingyong Zhu

The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…

Data Structures and Algorithms · Computer Science 2021-01-01 Shri Prakash Dwivedi

We study the asymmetric matrix factorization problem under a natural nonconvex formulation with arbitrary overparametrization. The model-free setting is considered, with minimal assumption on the rank or singular values of the observed…

Machine Learning · Computer Science 2023-08-22 Liwei Jiang , Yudong Chen , Lijun Ding

While there already exist randomized subspace Newton methods that restrict the search direction to a random subspace for a convex function, we propose a randomized subspace regularized Newton method for a non-convex function {and more…

Optimization and Control · Mathematics 2025-09-23 Terunari Fuji , Pierre-Louis Poirion , Akiko Takeda

The intrinsic Helmholtz free-energy functional, the centerpiece of classical density functional theory, is at best only known approximately for 3D systems. Here we introduce a method for learning a neuralnetwork approximation of this…