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In this paper, we present a toolbox for structured model reduction developed for MATLAB. In addition to structured model reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured…
In this article we give an elementary introduction to the representation theory of finite magnetic groups from a purely mathematical point of view. -- En este art\'iculo damos una introducci\'on elemental a la teor\'ia de representaciones…
A computational anatomy atlas is a set of internal organ geometries. It is based on data of real patients and complemented with virtual cases by using a some numerical approach. Atlases are in demand in computational physiology, especially…
This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary…
Rhetorical figures play a major role in our everyday communication as they make text more interesting, more memorable, or more persuasive. Therefore, it is important to computationally detect rhetorical figures to fully understand the…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
These notes form an introduction to Lie algebras and group theory. Most of the material can be found in many works by various authors given in the list of references. The reader is referred to such works for more detail.
This text provides a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous…
We provide a summary of the mathematical and computational techniques that have enabled learning reductions to effectively address a wide class of problems, and show that this approach to solving machine learning problems can be broadly…
In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…
Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort…
We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.
This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used…
In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups.
In this paper, we propose a very concise deep learning approach for collaborative filtering that jointly models distributional representation for users and items. The proposed framework obtains better performance when compared against…
Let $G$ be a connected semisimple noncompact real Lie group and let $\rho: G \longrightarrow \mathrm{SL}(V)$ be a representation on a finite dimensional vector space $V$ over $\mathbb R$, with $\rho(G)$ closed in $\mathrm{SL}(V)$.…
This paper provides a description of the algorithms employed by the Warwick AUTOMATA package for calculating the finite state automata associated with a short-lex automatic group. The aim is to provide an overview of the whole process,…
We develop a package using the computer algebra system GAP for computing the decomposition of a representation $\rho$ of a finite group $G$ over $\mathbb{C}$ into irreducibles, as well as the corresponding decomposition of the centraliser…
Current probabilistic programming languages and tools tightly couple model representations with specific inference algorithms, preventing experimentation with novel representations or mixed discrete-continuous models. We introduce a factor…
The lambda calculus since more than half a century is a model and foundation of functional programming languages. However, lambda expressions can be evaluated with different reduction strategies and thus, there is no fixed cost model nor…