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We present a novel segmentation algorithm based on a hierarchical representation of images. The main contribution of this work is to explore the capabilities of the A Contrario reasoning when applied to the segmentation problem, and to…

Computer Vision and Pattern Recognition · Computer Science 2013-05-07 Juan Cardelino , Vicent Caselles , Marcelo Bertalmio , Gregory Randall

Cluster analysis is one of the essential tasks in data mining and knowledge discovery. Each type of data poses unique challenges in achieving relatively efficient partitioning of the data into homogeneous groups. While the algorithms for…

Machine Learning · Computer Science 2018-12-11 Ruben A. Gevorgyan , Yenok B. Hakobyan

Block matrix structure is commonly arising is various physics and engineering applications. There are various advantages in preserving the blocks structure while computing the inversion of such partitioned matrices. In this context, using…

Numerical Analysis · Mathematics 2023-11-22 R. Thiru Senthil

We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…

Quantum Physics · Physics 2019-09-11 Juan Miguel Arrazola , Timjan Kalajdzievski , Christian Weedbrook , Seth Lloyd

Rectangular spectral collocation (RSC) methods have recently been proposed to solve linear and nonlinear differential equations with general boundary conditions and/or other constraints. The involved linear systems in RSC become extremely…

Numerical Analysis · Mathematics 2015-10-22 Kui Du

In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…

Combinatorics · Mathematics 2021-10-15 Bingchen Qian , Xin Wang , Gennian Ge

In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a…

Optimization and Control · Mathematics 2018-09-25 Mahyar Fazlyab , Manfred Morari , Victor M. Preciado

The aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-08-16 Christophe Cérin , Jean-Christophe Dubacq , Jean-Louis Roch , the SafeScale Collaboration

We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…

Data Structures and Algorithms · Computer Science 2021-09-13 Kaan Gokcesu , Hakan Gokcesu

The availability of larger and larger graph datasets, growing exponentially over the years, has created several new algorithmic challenges to be addressed. Sequential approaches have become unfeasible, while interest on parallel and…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-03-26 Alessio Guerrieri , Alberto Montresor

Incomplete factorizations have long been popular general-purpose algebraic preconditioners for solving large sparse linear systems of equations. Guaranteeing the factorization is breakdown free while computing a high quality preconditioner…

Numerical Analysis · Mathematics 2025-02-04 Jennifer Scott , Miroslav Tůma

We present a graph bisection and partitioning algorithm based on graph neural networks. For each node in the graph, the network outputs probabilities for each of the partitions. The graph neural network consists of two modules: an embedding…

Machine Learning · Computer Science 2021-12-09 Alice Gatti , Zhixiong Hu , Tess Smidt , Esmond G. Ng , Pieter Ghysels

In this paper, we introduce innovative approaches for accelerating the Jacobi method for matrix diagonalization, specifically through the formulation of large matrix diagonalization as a Semi-Markov Decision Process and small matrix…

We consider the problem of finding the optimal diagonal preconditioner for a positive definite matrix. Although this problem has been shown to be solvable and various methods have been proposed, none of the existing approaches are scalable…

Numerical Analysis · Mathematics 2024-11-07 Wenzhi Gao , Zhaonan Qu , Madeleine Udell , Yinyu Ye

We consider three distinct and well studied problems concerning network structure: community detection by modularity maximization, community detection by statistical inference, and normalized-cut graph partitioning. Each of these problems…

Physics and Society · Physics 2013-11-13 M. E. J. Newman

In recent research, the parallel performances of sweeping-type algorithms for high-frequency time-harmonic wave problems have been improved by departing from standard layer-type domain decomposition and introducing a new sweeping strategy…

Numerical Analysis · Mathematics 2023-04-03 Ruiyang Dai

Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…

Signal Processing · Electrical Eng. & Systems 2018-03-01 Stephen Kruzick , José M. F. Moura

We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical…

Data Structures and Algorithms · Computer Science 2023-06-22 Thorsten Wißmann , Ulrich Dorsch , Stefan Milius , Lutz Schröder

We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…

Data Structures and Algorithms · Computer Science 2017-04-10 Zeyuan Allen-Zhu , Yuanzhi Li , Rafael Oliveira , Avi Wigderson

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

Optimization and Control · Mathematics 2019-08-30 Yu-Chao Tang , Guo-Rong Wu , Chuan-Xi Zhu