Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Hard instances of algorithms and proof systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Neural networks complemented with genetic algorithms and fuzzy systems for predicting nitrogenous effluent variables in wastewater treatment plants

This work focuses on the prediction of the two main nitrogenous variables that describe the water quality at the effluent of a Wastewater Treatment Plant. We have developed two kind of Neural Networks architectures based on considering only one output or, in the other hand, the usual five effluent variables that define the water quality: suspended solids, biochemical organic matter, chemical organic matter, total nitrogen and total Kjedhal nitrogen. Two learning techniques based on a classical adaptative gradient and a Kalman filter have been implemented. In order to try to improve generalization and performance we have selected variables by means genetic algorithms and fuzzy systems. The training, testing and validation sets show that the final networks are able to learn enough well the simulated available data specially for the total nitrogen

Algorithms and cryptographic protocols using elliptic curves

En els darrers anys, la criptografia amb corbes el.líptiques ha adquirit una importància creixent, fins a arribar a formar part en la actualitat de diferents estàndards industrials. Tot i que s'han dissenyat variants amb corbes el.líptiques de criptosistemes clàssics, com el RSA, el seu màxim interès rau en la seva aplicació en criptosistemes basats en el Problema del Logaritme Discret, com els de tipus ElGamal. En aquest cas, els criptosistemes el.líptics garanteixen la mateixa seguretat que els construïts sobre el grup multiplicatiu d'un cos finit primer, però amb longituds de clau molt menor. Mostrarem, doncs, les bones propietats d'aquests criptosistemes, així com els requeriments bàsics per a que una corba sigui criptogràficament útil, estretament relacionat amb la seva cardinalitat. Revisarem alguns mètodes que permetin descartar corbes no criptogràficament útils, així com altres que permetin obtenir corbes bones a partir d'una de donada. Finalment, descriurem algunes aplicacions, com són el seu ús en Targes Intel.ligents i sistemes RFID, per concloure amb alguns avenços recents en aquest camp.

Clustering algorithms for anti-money laundering using graph theory and social network analysis

HEMOLIA (a project under European community’s 7th framework programme) is a new generation Anti-Money Laundering (AML) intelligent multi-agent alert and investigation system which in addition to the traditional financial data makes extensive use of modern society’s huge telecom data source, thereby opening up a new dimension of capabilities to all Money Laundering fighters (FIUs, LEAs) and Financial Institutes (Banks, Insurance Companies, etc.). This Master-Thesis project is done at AIA, one of the partners for the HEMOLIA project in Barcelona. The objective of this thesis is to find the clusters in a network drawn by using the financial data. An extensive literature survey has been carried out and several standard algorithms related to networks have been studied and implemented. The clustering problem is a NP-hard problem and several algorithms like K-Means and Hierarchical clustering are being implemented for studying several problems relating to sociology, evolution, anthropology etc. However, these algorithms have certain drawbacks which make them very difficult to implement. The thesis suggests (a) a possible improvement to the K-Means algorithm, (b) a novel approach to the clustering problem using the Genetic Algorithms and (c) a new algorithm for finding the cluster of a node using the Genetic Algorithm.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Spatiotemporal order out of noise

Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

Spatiotemporal order out of noise

Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

Generating highly balanced sudoku problems as hard problems

Sudoku problems are some of the most known and enjoyed pastimes, with a never diminishing popularity, but, for the last few years those problems have gone from an entertainment to an interesting research area, a twofold interesting area, in fact. On the one side Sudoku problems, being a variant of Gerechte Designs and Latin Squares, are being actively used for experimental design, as in [8, 44, 39, 9]. On the other hand, Sudoku problems, as simple as they seem, are really hard structured combinatorial search problems, and thanks to their characteristics and behavior, they can be used as benchmark problems for refining and testing solving algorithms and approaches. Also, thanks to their high inner structure, their study can contribute more than studies of random problems to our goal of solving real-world problems and applications and understanding problem characteristics that make them hard to solve. In this work we use two techniques for solving and modeling Sudoku problems, namely, Constraint Satisfaction Problem (CSP) and Satisfiability Problem (SAT) approaches. To this effect we define the Generalized Sudoku Problem (GSP), where regions can be of rectangular shape, problems can be of any order, and solution existence is not guaranteed. With respect to the worst-case complexity, we prove that GSP with block regions of m rows and n columns with m = n is NP-complete. For studying the empirical hardness of GSP, we define a series of instance generators, that differ in the balancing level they guarantee between the constraints of the problem, by finely controlling how the holes are distributed in the cells of the GSP. Experimentally, we show that the more balanced are the constraints, the higher the complexity of solving the GSP instances, and that GSP is harder than the Quasigroup Completion Problem (QCP), a problem generalized by GSP. Finally, we provide a study of the correlation between backbone variables – variables with the same value in all the solutions of an instance– and hardness of GSP.

Statistical modelling of CSP solving algorithms performance

The goal of this work is to try to create a statistical model, based only on easily computable parameters from the CSP problem to predict runtime behaviour of the solving algorithms, and let us choose the best algorithm to solve the problem. Although it seems that the obvious choice should be MAC, experimental results obtained so far show, that with big numbers of variables, other algorithms perfom much better, specially for hard problems in the transition phase.

DAI-DEPUR: an integrated and distributed architecture for wastewater treatment plants supervision

The activated sludge process - the main biological technology usually applied towastewater treatment plants (WWTP) - directly depends on live beings (microorganisms), and therefore on unforeseen changes produced by them. It could be possible to get a good plant operation if the supervisory control system is able to react to the changes and deviations in the system and can take thenecessary actions to restore the system’s performance. These decisions are oftenbased both on physical, chemical, microbiological principles (suitable to bemodelled by conventional control algorithms) and on some knowledge (suitable to be modelled by knowledge-based systems). But one of the key problems in knowledge-based control systems design is the development of an architecture able to manage efficiently the different elements of the process (integrated architecture), to learn from previous cases (spec@c experimental knowledge) and to acquire the domain knowledge (general expert knowledge). These problems increase when the process belongs to an ill-structured domain and is composed of several complex operational units. Therefore, an integrated and distributed AIarchitecture seems to be a good choice. This paper proposes an integrated and distributed supervisory multi-level architecture for the supervision of WWTP, that overcomes some of the main troubles of classical control techniques and those of knowledge-based systems applied to real world systems

Innovació tecnològica a la construcció subterrània

Report for the scientific sojourn carried out in the International Center for Numerical Methods in Engineering (CIMNE) –state agency – from February until November 2007. The work within the project Technology innovation in underground construction can be grouped into the following tasks: development of the software for modelling underground excavation based on the discrete element method - the numerical algorithms have been implemented in the computer programs and applied to simulation of excavation using roadheaders and TBM-s -; coupling of the discrete element method with the finite element method; development of the numerical model of rock cutting taking into account of wear of rock cutting tools -this work considers a very important factor influencing effectiveness of underground works -.

Law and the practise of principle in diverse societies

Projecte de recerca elaborat a partir d’una estada a la London School of Economics and Political Science, United Kingdom, entre 2007 i 2009. L’objecte principal del projecte ha estat analitzar les implicacions jurídico-polítiques i institucionals d’una teoria de la justícia i la igualtat liberals aplicada a societats multiculturals amb un marcat predomini de la diversitat cultural. L’anàlisi desenvolupa una línia d'investigació interdisciplinar - entre el dret i la teoria política - iniciada en una tesis doctoral sobre multiculturalisme i drets de les minories culturals (UPF, 2000) que va culminar en la publicació de Group Rights as Human Rights (Springer, 2006). La recerca adopta com a punt de partida les conclusions de l'esmentada obra, en especial, la rellevància del reconeixement de drets col•lectius; tanmateix, el tipus de qüestions plantejades, l’enfoc i la metodologia emprades són substancialment diferents. En concret, s'adrecen preguntes específiques sobre el model i aspiracions del constitucionalisme democràtic i el paper del dret en contextos multiculturals. També s’atorga un pes central a la dimensió institucional dels models de gestió de la diversitat que s’analitzen, prioritzant un enfocament comparatiu a partir de l’estudi de controvèrsies concretes. L’objectiu és superar algunes limitacions importants de la literatura actual, com ara la tendència a examinar en abstracte la compatibilitat de determinades demandes amb el constitucionalisme democràtic, sense abordar el funcionament d'estratègies de gestió de la diversitat cultural emprades en contextos concrets. Els treballs producte d'aquest projecte articulen les línies bàsiques d’un model pluralista, basat en principis més que en regles, que desafia els plantejaments dominants actualment. Aquest model es caracteritza pel compromís amb la legitimitat i igualtat comparatives, rebutjant el paternalisme i les visions liberals típiques sobre el paper de la regulació. La presumpció de l’“standing” moral dels grups identitaris és fonamental per tal de considerar-los interlocutors vàlids amb interessos genuïns. També s’argumenta que la integració social en contextos multiculturals no depèn tant de l’eliminació del conflicte sinó, sobre tot, d’una gestió eficient que eviti abusos de poder sistemàtics. El model defensa el rol del dret en la institucionalització del diàleg intercultural, però admet que el diàleg no necessàriament condueix a l’acord o a una estructura reguladora coherent i uniforme. Les aspiracions del ordre jurídic pluralista són més modestes: afavorir la negociació i resolució en cada conflicte, malgrat la persistència de la fragmentació i la provisionalitat dels acords. La manca d'un marc regulador comú esdevé una virtut en la mesura que permet la interacció de diferents subordres; una interacció governada per una multiplicitat de regles no necessàriament harmòniques. Els avantatges i problemes d’aquest model s'analitzen a partir de l'anàlisi de l’estructura fragmentària de l'ordre jurídic internacional i del règim Europeu de drets humans.

The Value of Imperfection : the Wabi-Sabi Principle in Aesthetics and Learning

OER-based learning has the potential to overcome many shortcomings and problems of traditional education. It is not hampered by IP restrictions; can depend on collaborative, cumulative, iterative refinement of resources; and the digital form provides unprecedented flexibility with respect to configuration and delivery. The OER community is a progressive group of educators and learners with decades of learning research to draw from, who know that we must prepare learners for an evolving and diverse reality. Despite this OER tends to replicate the unsuccessful characteristics of traditional education. To remedy this we may need to remember the importance of imperfection, mistakes, problems, disagreement, and the incomplete for engaged learning, and relinquish our notions of perfection, acknowledging that learners learn differently and we need diverse learners. We must stretch our perceptions of quality and provide mechanisms for engaging the incredible pool of educators globally to fulfill the promise of inclusive education.

Route optimization and customization using real geographical data in Android mobile devices

Nowadays, there are several services and applications that allow users to locate and move to different tourist areas using a mobile device. These systems can be used either by internet or downloading an application in concrete places like a visitors centre. Although such applications are able to facilitate the location and the search for points of interest, in most cases, these services and applications do not meet the needs of each user. This paper aims to provide a solution by studying the main projects, services and applications, their routing algorithms and their treatment of the real geographical data in Android mobile devices, focusing on the data acquisition and treatment to improve the routing searches in off-line environments.