An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions

In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real space. The incrementality comes from the first part of the algorithm, where a complex cylindrical tree is constructed by refining a previous complex cylindrical tree with a polynomial constraint. We have implemented our algorithm in Maple. The experimentation shows that the proposed algorithm outperforms existing ones for many examples taken from the literature

An Algorithm for Computing the Limit Points of the Quasi-component of a Regular Chain

For a regular chain $R$, we propose an algorithm which computes the (non-trivial) limit points of the quasi-component of $R$, that is, the set $\bar{W(R)} \setminus W(R)$. Our procedure relies on Puiseux series expansions and does not require to compute a system of generators of the saturated ideal of $R$. We focus on the case where this saturated ideal has dimension one and we discuss extensions of this work in higher dimensions. We provide experimental results illustrating the benefits of our algorithms

Business complexity and geographic expansion in banking

Utilizando datos confidenciales españoles de supervisión, este trabajo examina el efecto sobre el riesgo bancario de la complejidad geográfica y empresarial, y su interacción e importancia relativa, donde el grado de complejidad se basa en la estructura corporativa de las filiales del grupo bancario. Los resultados muestran que, mientras la complejidad empresarial genera un mayor riesgo, la complejidad geográfica genera beneficios de diversificación, por lo que reduce el riesgo. Sin embargo, la complejidad geográfica no es buena por sí sola, ya que depende de cómo se desarrolle. Una mayor complejidad empresarial en el extranjero en relación con la nacional puede contrarrestar estos beneficios de diversificación. En la misma línea, centrarse en el extranjero en áreas en las que el grupo no tiene experiencia en el ámbito nacional también se traduce en un mayor riesgo.Using Spanish confidential supervisory data, this paper examines the effect of geographic and business complexity, their interaction and relative importance for banks’ risk, where the degree of complexity stems from the corporate structure of banking groups affiliates. The results show that while business complexity results in higher risk, geographic complexity gives rise to diversification benefits, thus lowering risk. However, geographic complexity alone is not enough, as its effect depends on how it interacts with business complexity. Higher business complexity abroad in relation to that at home may counterbalance the benefits of diversification. In the same vein, focusing abroad on areas in which the group does not have expertise at home also results in higher risk

Parallel Integer Polynomial Multiplication

We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this new approach

Computing differential characteristic sets by change of ordering

submitted to the Journal of Symbolic ComputationWe describe an algorithm for converting a characteristic set of a prime differential ideal from one ranking into another. This algorithm was implemented in many different languages and has been applied within various software and projects. It permitted to solve formerly unsolved problems