Related papers: RepLAB: a computational/numerical approach to repr…

In this article we show how to compute a matrix representation and the implicit equation by means of the method developed in [Botbol: arXiv:1007.3437], using the computer algebra system Macaulay2 \cite{M2}. As it is probably the most…

Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first…

We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…

We describe different optimization techniques to perform the assembly of finite element matrices in Matlab and Octave, from the standard approach to recent vectorized ones, without any low level language used. We finally obtain a simple and…

We introduce an algorithm to decompose orthogonal matrix representations of the symmetric group over the reals into irreducible representations, which as a by-product also computes the multiplicities of the irreducible representations. The…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…

These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…

We describe a general approach for computing generators for elimination ideals associated with matrix and hypermatrix spectral decomposition constraints. We derive from these generators iterative procedures for approximating the spectral…

Routines for computation of Weber's parabolic cylinder functions and their derivatives are implemented in Matlab for both moderate and great values of the argument. Standard, real solutions are considered. Tables of values are included.

This paper presents a MATLAB toolbox for computing the conformal mapping from a given polygonal multiply connected domain onto a circular multiply connected domain and its inverse. The toolbox can be used for multiply connected domains with…

The decomposition of representations of compact classical Lie groups into representations of finite subgroups is discussed. A Mathematica package is presented that can be used to compute these branching rules using the Weyl character…

The use of machine learning is becoming increasingly common in computational materials science. To build effective models of the chemistry of materials, useful machine-based representations of atoms and their compounds are required. We…

Existing algorithms for explaining the output of image classifiers perform poorly on inputs where the object of interest is partially occluded. We present a novel, black-box algorithm for computing explanations that uses a principled…

We investigate the task of retrieving information from compositional distributed representations formed by Hyperdimensional Computing/Vector Symbolic Architectures and present novel techniques which achieve new information rate bounds.…

On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…

We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…

Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…

Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…

Convex optimization is an essential tool for machine learning, as many of its problems can be formulated as minimization problems of specific objective functions. While there is a large variety of algorithms available to solve convex…