Related papers: A new Algorithm for the Computation of logarithmic…

Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify…

This extends a theorem of Davenport and Erd\"os on sequences of rational integers to sequences of integral ideals in arbitrary number fields $K$. More precisely, we introduce a logarithmic density for sets of integral ideals in $K$ and…

In this paper we consider the problem of testing whether two finite groups are isomorphic. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of…

Algorithmic classifications of research publications can be used to study many different aspects of the science system, such as the organization of science into fields, the growth of fields, interdisciplinarity, and emerging topics. How to…

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…

Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gr{\"o}bner bases taking into account the valuation of K. Because of the use of the valuation, the theory of tropical Gr{\"o}bner bases…

Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…

Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for…

Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the…

In this paper, we design, analyze, and implement a variant of the two-loop L-shaped algorithms for solving two-stage stochastic programming problems that arise from important application areas including revenue management and power systems.…

Consider a matrix $\mathbf{F} \in \mathbb{K}[x]^{m \times n}$ of univariate polynomials over a field $\mathbb{K}$. We study the problem of computing the column rank profile of $\mathbf{F}$. To this end we first give an algorithm which…

We discuss a practical algorithm to compute parabolic Kazhdan-Lusztig polynomials. As an application we compute Kazhdan-Lusztig polynomials which are needed to evaluate a character formula for reductive groups due to Lusztig. Some…

We compute K-theory for ring C*-algebras in the case of higher roots of unity and thereby completely determine the K-theory for ring C*-algebras attached to rings of integers in arbitrary number fields.

We explore algorithmic aspects of a simply transitive commutative group action coming from the class field theory of imaginary hyperelliptic function fields. Namely, the Jacobian of an imaginary hyperelliptic curve defined over $\mathbb…

In this paper, we prove the existence of an efficient algorithm for the computation of $q$-expansions of modular forms of weight $k$ and level $\Gamma$, where $\Gamma \subseteq SL_{2}({\mathbb{Z}})$ is an arbitrary congruence subgroup. We…

We introduce ParK, a new large-scale solver for kernel ridge regression. Our approach combines partitioning with random projections and iterative optimization to reduce space and time complexity while provably maintaining the same…

The $p$-group generation algorithm from computational group theory is used to obtain information about large quotients of the pro-2 group $G = \text{Gal} (k^{nr,2}/k)$ for $k = \mathbb{Q}(\sqrt{d})$ with $d = -445, -1015, -1595, -2379$. In…

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. In a previous article, we gave a necessary and sufficient condition for X to be free of given rank d…

We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with…

Multiple Kernel Learning, or MKL, extends (kernelized) SVM by attempting to learn not only a classifier/regressor but also the best kernel for the training task, usually from a combination of existing kernel functions. Most MKL methods seek…