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Related papers: Algorithmic problems in twisted groups of Lie type

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The task of outlier detection is to find small groups of data objects that are exceptional when compared with rest large amount of data. In [38], the problem of outlier detection in categorical data is defined as an optimization problem and…

Databases · Computer Science 2007-05-23 Zengyou He , Xiaofei Xu , Shengchun Deng

We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…

Numerical Analysis · Mathematics 2016-02-02 Gil Shabat , Yaniv Shmueli , Yariv Aizenbud , Amir Averbuch

The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and…

Group Theory · Mathematics 2025-06-18 Vladimir Shpilrain

Solving symmetric Bayesian decision problems is a computationally intensive task to perform regardless of the algorithm used. In this paper we propose a method for improving the efficiency of algorithms for solving Bayesian decision…

Artificial Intelligence · Computer Science 2013-01-30 Anders L. Madsen , Finn Verner Jensen

The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this…

Computers and Society · Computer Science 2015-05-13 Yudong Sun , Bogdan Danila , Kresimir Josic , Kevin E. Bassler

A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…

Optimization and Control · Mathematics 2020-11-02 S Buchwald , G Ciaramella , Julien Salomon

Categories of partitions are combinatorial structures arising from the representation theory of certain compact quantum groups and are linked to classical diagram algebras such as the Temperley-Lieb algebra. In this paper, we present…

Data Structures and Algorithms · Computer Science 2025-02-11 Nicolas Faroß , Sebastian Volz

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial…

Rings and Algebras · Mathematics 2014-02-11 Fernando Antoneli , Michael Forger , Paola Gaviria

Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data science, image registration and biophysical simulations. Two…

Numerical Analysis · Mathematics 2021-10-15 Elena Celledoni , Ergys Çokaj , Andrea Leone , Davide Murari , Brynjulf Owren

We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical algorithm to test nilpotency of…

Group Theory · Mathematics 2019-07-16 A. S. Detinko , D. L. Flannery

The Cohn-Umans (FOCS '03) group-theoretic framework for matrix multiplication produces fast matrix multiplication algorithms from three subsets of a finite group $G$ satisfying a simple combinatorial condition (the Triple Product Property).…

Group Theory · Mathematics 2025-08-20 Jonah Blasiak , Henry Cohn , Joshua A. Grochow , Kevin Pratt , Chris Umans

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…

Group Theory · Mathematics 2019-05-14 A. S. Detinko , D. L. Flannery , E. A. O'Brien

Machine learning explorations can make significant inroads into solving difficult problems in pure mathematics. One advantage of this approach is that mathematical datasets do not suffer from noise, but a challenge is the amount of data…

Machine Learning · Computer Science 2026-05-08 Max Petschack , Alexandr Garbali , Jan de Gier

Toda equations associated with twisted loop groups are considered. Such equations are specified by Z-gradations of the corresponding twisted loop Lie algebras. The classification of Toda equations related to twisted loop Lie algebras with…

Mathematical Physics · Physics 2008-11-26 Kh. S. Nirov , A. V. Razumov

Focusing on the practical configuration needs of optimization algorithms in deep learning, this article concentrates on five major algorithms: SGD, Mini-batch SGD, Momentum, Adam, and Lion. It systematically analyzes the core advantages,…

Machine Learning · Computer Science 2025-11-27 Deng Fucheng , Wang Wanjie , Gong Ao , Wang Xiaoqi , Wang Fan

Standard Monte Carlo cluster algorithms have proven to be very effective for many different spin models, however they fail for frustrated spin systems. Recently a generalized cluster algorithm was introduced that works extremely well for…

Condensed Matter · Physics 2009-10-22 P. D. Coddington , L. Han

A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite…

Machine Learning · Computer Science 2023-11-03 David Gregoratti , Xavier Mestre , Carlos Buelga

An action of a group on a vector space partitions the latter into a set of orbits. We consider three natural and useful algorithmic "isomorphism" or "classification" problems, namely, orbit equality, orbit closure intersection, and orbit…

Data Structures and Algorithms · Computer Science 2021-10-22 Peter Bürgisser , M. Levent Doğan , Visu Makam , Michael Walter , Avi Wigderson

We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…

Group Theory · Mathematics 2017-10-20 Martin R. Bridson , David M. Evans , Martin W. Liebeck , Dan Segal

Since the braid group was discovered by E. Artin, the question of its conjugacy problem has been solved by Garside and Birman, Ko and Lee. However, the solutions given thus far are difficult to compute with a computer, since the number of…

Algebraic Geometry · Mathematics 2007-05-23 S. Kaplan , M. Teicher