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We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…

Numerical Analysis · Mathematics 2023-05-05 H. Harbrecht , M. Multerer , O. Schenk , Ch. Schwab

Symmetric and sparse tensors arise naturally in many domains including linear algebra, statistics, physics, chemistry, and graph theory. Symmetric tensors are equal to their transposes, so in the $n$-dimensional case we can save up to a…

Mathematical Software · Computer Science 2025-01-27 Radha Patel , Willow Ahrens , Saman Amarasinghe

We consider multidimensional optimization problems that are formulated in the framework of tropical mathematics to minimize functions defined on vectors over a tropical semifield (a semiring with idempotent addition and invertible…

Optimization and Control · Mathematics 2018-05-29 Nikolai Krivulin

Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to…

Numerical Analysis · Mathematics 2021-08-23 Lev I. Vysotsky , Alexander V. Smirnov , Eugene E. Tyrtyshnikov

Motivated by the classical work of Halmos on functional monadic Boolean algebras we derive three basic sup-semilattice constructions, among other things the so-called powersets and powerset operators. Such constructions are extremely useful…

Rings and Algebras · Mathematics 2022-07-13 Michal Botur , Jan Paseka , Richard Smolka

We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…

Numerical Analysis · Mathematics 2011-06-01 J. Bailey , M. A. Iwen , C. V. Spencer

A unified method of calculating structure functions from commutation relations of deformed single-mode oscillator algebras is presented. A natural approach to building coherent states associated to deformed algebras is then deduced.

Mathematical Physics · Physics 2012-11-15 J. D. Bukweli-Kyemba , M. N. Hounkonnou

As the first step in automated natural language processing, representing words and sentences is of central importance and has attracted significant research attention. Different approaches, from the early one-hot and bag-of-words…

Computation and Language · Computer Science 2019-11-06 Wenye Li , Senyue Hao

We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary…

Optimization and Control · Mathematics 2023-07-17 Andrzej Cegielski

We consider a Wilson-Dirac operator with improved chiral properties. We show that, for arbitrarily rough gauge fields, it satisfies the index theorem if we identify the zero modes with the small real eigenvalues of the fermion operator and…

High Energy Physics - Lattice · Physics 2009-10-31 P. Hernandez

We consider weighted tiling systems to represent functions from graphs to a commutative semiring such as the Natural semiring or the Tropical semiring. The system labels the nodes of a graph by its states, and checks if the neighbourhood of…

Formal Languages and Automata Theory · Computer Science 2020-10-01 C. Aiswarya , Paul Gastin

This paper introduces semi-ring dictionaries, a powerful class of compositional and purely functional collections that subsume other collection types such as sets, multisets, arrays, vectors, and matrices. We developed SDQL, a statically…

Programming Languages · Computer Science 2022-03-23 Amir Shaikhha , Mathieu Huot , Jaclyn Smith , Dan Olteanu

We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary…

High Energy Physics - Theory · Physics 2015-01-26 Miguel S. Costa , Joao Penedones , David Poland , Slava Rychkov

Semantic parsing aims to map natural language utterances onto machine interpretable meaning representations, aka programs whose execution against a real-world environment produces a denotation. Weakly-supervised semantic parsers are trained…

Computation and Language · Computer Science 2019-09-11 Bailin Wang , Ivan Titov , Mirella Lapata

We introduce a generalization of the notion of operad that we call a contractad, whose set of operations is indexed by connected graphs and whose composition rules are numbered by contractions of connected subgraphs. We show that many…

Algebraic Topology · Mathematics 2024-07-24 Denis Lyskov

We describe an abstract loop-based intermediate representation that can express fused implementations of relational algebra expressions on sets and bags (multisets). The loops are abstracted away from physical data structures thus making it…

Programming Languages · Computer Science 2025-02-12 James Dong , Fredrik Kjolstad

This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze structures in another part. The survey is broad enough to…

Commutative Algebra · Mathematics 2015-12-11 Neil Epstein

We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to…

High Energy Physics - Theory · Physics 2015-09-03 Miguel S. Costa , Tobias Hansen

This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model…

Machine Learning · Statistics 2019-08-12 Pierre Humbert , Julien Audiffren , Laurent Oudre , Nicolas Vayatis

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…

Operator Algebras · Mathematics 2009-07-30 Meghna Mittal , Vern Paulsen