Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

Parallelizing remote sensing image geometric correction

Remote sensing spatial, spectral, and temporal resolutions of images, acquired over a reasonably sized image extent, result in imagery that can be processed to represent land cover over large areas with an amount of spatial detail that is very attractive for monitoring, management, and scienti c activities. With Moore's Law alive and well, more and more parallelism is introduced into all computing platforms, at all levels of integration and programming to achieve higher performance and energy e ciency. Being the geometric calibration process one of the most time consuming processes when using remote sensing images, the aim of this work is to accelerate this process by taking advantage of new computing architectures and technologies, specially focusing in exploiting computation over shared memory multi-threading hardware. A parallel implementation of the most time consuming process in the remote sensing geometric correction has been implemented using OpenMP directives. This work compares the performance of the original serial binary versus the parallelized implementation, using several multi-threaded modern CPU architectures, discussing about the approach to nd the optimum hardware for a cost-e ective execution.

Trust region versus line search for computing the optical flow

We consider the numerical treatment of the optical flow problem by evaluating the performance of the trust region method versus the line search method. To the best of our knowledge, the trust region method is studied here for the first time for variational optical flow computation. Four different optical flow models are used to test the performance of the proposed algorithm combining linear and nonlinear data terms with quadratic and TV regularization. We show that trust region often performs better than line search; especially in the presence of non-linearity and non-convexity in the model.

Teaching fundamentals of computing theory: a constructivist approach

A Fundamentals of Computing Theory course involves different topics that are core to the Computer Science curricula and whose level of abstraction makes them difficult both to teach and to learn. Such difficulty stems from the complexity of the abstract notions involved and the required mathematical background. Surveys conducted among our students showed that many of them were applying some theoretical concepts mechanically rather than developing significant learning. This paper shows a number of didactic strategies that we introduced in the Fundamentals of Computing Theory curricula to cope with the above problem. The proposed strategies were based on a stronger use of technology and a constructivist approach. The final goal was to promote more significant learning of the course topics.

Trust region versus line search for computing the optical flow

We consider the numerical treatment of the optical flow problem by evaluating the performance of the trust region method versus the line search method. To the best of our knowledge, the trust region method is studied here for the first time for variational optical flow computation. Four different optical flow models are used to test the performance of the proposed algorithm combining linear and nonlinear data terms with quadratic and TV regularization. We show that trust region often performs better than line search; especially in the presence of non-linearity and non-convexity in the model.

On the computation of reducible invariant tori on a parallel computer

We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around the torus and, hence, its linear stability. The algorithm presents a high degree of parallelism, and the computational effort grows linearly with the number of Fourier modes needed to represent the solution. For these reasons it is a very good option to compute quasi-periodic solutions with several basic frequencies. The paper includes some examples (flows) to show the efficiency of the method in a parallel computer. In these flows we compute invariant tori of dimensions up to 5, by taking suitable sections.

Bernoulli correction to viscous losses: Radial flow between two parallel discs

For a massless fluid (density = 0), the steady flow along a duct is governed exclusively by viscous losses. In this paper, we show that the velocity profile obtained in this limit can be used to calculate the pressure drop up to the first order in density. This method has been applied to the particular case of a duct, defined by two plane-parallel discs. For this case, the first-order approximation results in a simple analytical solution which has been favorably checked against numerical simulations. Finally, an experiment has been carried out with water flowing between the discs. The experimental results show good agreement with the approximate solution

Concurrent : Easy to use Python computing environment

Concurrent aims to be a different type of task distribution system compared to what MPI like system do. It adds a simple but powerful application abstraction layer to distribute the logic of an entire application onto a swarm of clusters holding similarities with volunteer computing systems. Traditional task distributed systems will just perform simple tasks onto the distributed system and wait for results. Concurrent goes one step further by letting the tasks and the application decide what to do. The programming paradigm is then totally async without any waits for results and based on notifications once a computation has been performed.

Disseny i implementació d'un clúster high performance computing

Clúster format per una màquina principal HEAD Node més 19 nodes de càlcul de la gama SGI13 Altix14 XE Servers and Clusters, unides en una topologia de màster subordinat, amb un total de 40 processadors Dual Core i aproximadament 160Gb de RAM.

Plataforma "Cloud Computing" per la comunicació entre pares i professors (Saas)

El projecte que es presenta a continuació és el resultat fruit de la detecció d’un problema de comunicació entre les escoles (sobretot de primària) i el pares dels alumnes que hi cursen els estudis, i la necessitat de trobar-hi una solució. Amb aquesta premissa, i tenint en compte que la tecnologia cada vegada ens ofereix més i millors eines per gestionar les nostres necessitats, es porta a terme la construcció d’un servei al núvol (Saas) capaç de cobrir aquestes necessitats i de fer-ho de la manera més senzilla i eficient possible. La plataforma Aula és un servei on tant professors com pares dels alumnes poden comunicar-se i consultar la informació referent als seus alumnes (en el cas del professors), i dels seus fills (en el cas dels pares/tutors). La solució adoptada ha de ser capaç de funcionar sobre qualsevol aparell (ordinador, tablet o mòbil) i en qualsevol lloc on hi hagi connexió a Internet. No s’ha de realitzar cap tipus d’instal·lació un cop el sistema estigui funcionant, i s’hi podran registrar tants centres com siguin necessaris, així com professionals i pares dels alumnes. També s’ha valorat el manteniment mínim del sistema i la seva escalabilitat, per poder fer front a diferents volums de dades. Així doncs, el projecte Aula es presenta com una solució per gestionar el dia a dia dels professors i alumnes, però que no pretén ser substitut de cap altre sistema de gestió que pugui tenir el centre.

Extension and evaluation of JXTA protocols for supporting reliable P2P distributed computing

Peer-reviewed

Efficient Peer Selection in P2P JXTA-Based Platforms

Peer-reviewed