Related papers: Computing $S$-unit groups of orders
In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given…
Let $G$ be a finite solvable group, given through a refined consistent polycyclic presentation, and $\alpha$ an automorphism of $G$, given through its images of the generators of $G$. In this paper, we discuss algorithms for computing the…
In this paper, we examine the general algorithm for class group computations, when we do not have a small defining polynomial for the number field. Based on a result of Biasse and Fieker, we simplify their algorithm, improve the complexity…
We describe the computation of class groups and unit groups of number fields as implemented in Magma (V2.29). After quickly reviewing the main algorithms based on factor bases, relation collection, and analytic class number evaluation, we…
This paper develops a clustering algorithm for formations in team sports, with a focus on football games. Our method first clusters formations into several average formations: `442,' `4141,' `433,' `541,' and `343.' Then, each average…
We provide a simple unified approach to obtain (i) Discrete polygonal isoperimetric type inequalities of arbitrary high order. (ii) Arbitrary high order isoperimetric type inequalities for smooth curves, where both upper and lower bounds…
Here we present a very efficient method to search for Liouvillian first integrals of second order rational ordinary differential equations (rational 2ODEs). This new algorithm can be seen as an improvement to the S-function method we have…
We present a new algorithm for computing the first discrete homology group of a graph. By testing the algorithm on different data sets of random graphs, we find that it significantly outperforms other known algorithms.
In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding…
The pseudo-Frobenius numbers of a numerical semigroup are those gaps of the numerical semigroup that are maximal for the partial order induced by the semigroup. We present a procedure to detect if a given set of integers is the set of…
Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
The discrete logarithm problem in Jacobians of curves of high genus $g$ over finite fields $\FF_q$ is known to be computable with subexponential complexity $L_{q^g}(1/2, O(1))$. We present an algorithm for a family of plane curves whose…
The unit selection problem aims to identify objects, called units, that are most likely to exhibit a desired mode of behavior when subjected to stimuli (e.g., customers who are about to churn but would change their mind if encouraged). Unit…
This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SOS hierarchy in polynomial optimization, where results from…
We propose an automated method for detecting galaxy clusters in imaging surveys based on the Voronoi tessellation technique. It appears very promising, expecially for its capability of detecting clusters indipendently from their shape.…
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
Determining the number of clusters in a dataset is a fundamental issue in data clustering. Many methods have been proposed to solve the problem of selecting the number of clusters, considering it to be a problem with regard to model…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…