On Connection, Linearization and Duplication Coefficients of Classical Orthogonal Polynomials

In this work, we have mainly achieved the following: 1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved; 2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization problem of all orthogonal polynomials of a discrete variable; 3. we propose a method to generate the connection, linearization and duplication coefficients for q-orthogonal polynomials; 4. we propose a unified method to obtain these coefficients in a generic way for orthogonal polynomials on quadratic and q-quadratic lattices. Our algorithmic approach to compute linearization, connection and duplication coefficients is based on the one used by Koepf and Schmersau and on the NaViMa algorithm. Our main technique is to use explicit formulas for structural identities of classical orthogonal polynomial systems. We find our results by an application of computer algebra. The major algorithmic tools for our development are Zeilberger’s algorithm, q-Zeilberger’s algorithm, the Petkovšek-van-Hoeij algorithm, the q-Petkovšek-van-Hoeij algorithm, and Algorithm 2.2, p. 20 of Koepf's book "Hypergeometric Summation" and it q-analogue.

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

Automated Reasoning About Classical Mechanics

In recent years, researchers in artificial intelligence have become interested in replicating human physical reasoning talents in computers. One of the most important skills in this area is predicting how physical systems will behave. This thesis discusses an implemented program that generates algebraic descriptions of how systems of rigid bodies evolve over time. Discussion about the design of this program identifies a physical reasoning paradigm and knowledge representation approach based on mathematical model construction and algebraic reasoning. This paradigm offers several advantages over methods that have become popular in the field, and seems promising for reasoning about a wide variety of classical mechanics problems.

Self-organized sociopolitical interactions as the best way to achieve organized patterns in human social systems: going beyond the top-down control of classical political regimes

La monografía presenta la auto-organización sociopolítica como la mejor manera de lograr patrones organizados en los sistemas sociales humanos, dada su naturaleza compleja y la imposibilidad de las tareas computacionales de los regímenes políticos clásico, debido a que operan con control jerárquico, el cual ha demostrado no ser óptimo en la producción de orden en los sistemas sociales humanos. En la monografía se extrapola la teoría de la auto-organización en los sistemas biológicos a las dinámicas sociopolíticas humanas, buscando maneras óptimas de organizarlas, y se afirma que redes complejas anárquicas son la estructura emergente de la auto-organización sociopolítica.

Perfil microbiológico, prevalencia de resistencia antibiótica y patrones de susceptibilidad en infección urinaria en una población pediátrica

Introducción: El incremento de la resistencia antibiótica se considera un problema de salud pública con consecuencias clínicas y económicas, por lo tanto se determinará la prevalencia de resistencia antibiótica en Infección del Tracto Urinario (ITU, el perfil microbiológico y los patrones de susceptibilidad en una población pediátrica atendida en la Fundación Cardioinfantil. Materiales y métodos: Estudio observacional de corte transversal, retrospectivo, entre 1 mes a 18 años de edad, con diagnóstico de ITU comunitaria atendidos entre Enero de 2011 y Diciembre de 2013. Se excluyeron pacientes con dispositivos en la vía urinaria, instrumentación quirúrgica previa, trayectos fistulosos entre la vía urinaria y sistema digestivo, ITU luego de 48 horas de hospitalización y recaída clínica en tratamiento. Se estableció la prevalencia de ITU resistente y se realizó un análisis descriptivo de la información. Resultados: Se evaluaron 385 registros clínicos, con una mediana de 1.08 años (RIQ 0.8 – 4.08), el 73.5% eran niñas. La fiebre predominó (76.5%), seguido de emesis (32.0%), disuria (23.7%) y dolor abdominal (23.1%). El uropatógeno más frecuente fue E.coli (75%), seguido de Proteus mirabilis (8.5%) y Klebsiella spp. (8.3%). La Ampicilina, el Trimetropim sulfametoxazol, la Ampicilina sulbactam y el ácido nalidixico tuvieron mayor tasa de resistencia. La prevalencia de BLEE fue 5.2% y AmpC 3.9%. La prevalencia de resistencia antimicrobiana fue de 11.9%. Conclusiones: La E.coli es el uropatogeno más frecuentemente aislado en ITU, con resistencia a la ampicilina en 60.2%, cefalosporinas de primera generación en 15.5%, trimetropin sulfametoxazol en 43.9%, cefepime 4.8%. La prevalencia de resistencia antimicrobiana fue de 11.9%.

Short Term Health Shocks and School Attendance: The Case of a Dengue Fever Outbreak in Colombia.

This paper makes use of a short, sharp, unexpected health shock in the form of the 2010 Colombian Dengue outbreak to examine the direct and indirect impact of negative health shocks on behaviour of households in affected areas. Our analysis combines data from several sources in order to obtain a comprehensive picture of the influence of the outbreak, and furthermore to understand the underlying mechanisms driving the effects. Our initial analysis indicates that the outbreak had a substantial negative effect on the health status of adults and adversely affected their ability to function as usual in their daily lives. In our aggregated school data, in areas with high levels of haemorrhagic Dengue we observe a reduction innational exam attendance (last year of secondary school) and on enrolment rates in primary education. Further analysis aims to exploit detailed individual level data to gain a more in depth understanding of the precise channels through which this disease influenced the behaviour and outcomes of the poor in Colombia.

Governance and change in higher education : the debate between classical political sociology, new institutionalism and critical theories

Resumen tomado de la publicaci??n

Classical and causal inference approaches to statistical mediation analysis

Resumen tomado de la publicaci??n

Quantum similarity topological indices definition, analysis and comparison with classical molecular topological indices

Es mostra que, gracies a una extensió en la definició dels Índexs Moleculars Topològics, s'arriba a la formulació d'índexs relacionats amb la teoria de la Semblança Molecular Quàntica. Es posa de manifest la connexió entre les dues metodologies: es revela que un marc de treball teòric sòlidament fonamentat sobre la teoria de la Mecànica Quàntica es pot connectar amb una de les tècniques més antigues relacionades amb els estudis de QSPR. Es mostren els resultats per a dos casos d'exemple d'aplicació d'ambdues metodologies