Medidas autosemejantes en el plano, momentos y matrices de Hessenberg

La tesis MEDIDAS AUTOSEMEJANTES EN EL PLANO, MOMENTOS Y MATRICES DE HESSENBERG se enmarca entre las áreas de la teoría geométrica de la medida, la teoría de polinomios ortogonales y la teoría de operadores. La memoria aborda el estudio de medidas con soporte acotado en el plano complejo vistas con la óptica de las matrices infinitas de momentos y de Hessenberg asociadas a estas medidas que en la teoría de los polinomios ortogonales las representan. En particular se centra en el estudio de las medidas autosemejantes que son las medidas de equilibrio definidas por un sistema de funciones iteradas (SFI). Los conjuntos autosemejantes son conjuntos que tienen la propiedad geométrica de descomponerse en unión de piezas semejantes al conjunto total. Estas piezas pueden solaparse o no, cuando el solapamiento es pequeño la teoría de Hutchinson [Hut81] funciona bien, pero cuando no existen restricciones falla. El problema del solapamiento consiste en controlar la medida de este solapamiento. Un ejemplo de la complejidad de este problema se plantea con las convoluciones infinitas de distribuciones de Bernoulli, que han resultado ser un ejemplo de medidas autosemejantes en el caso real. En 1935 Jessen y A. Wintner [JW35] ya se planteaba este problema, lejos de ser sencillo ha sido estudiado durante más de setenta y cinco años y siguen sin resolverse las principales cuestiones planteadas ya por A. Garsia [Gar62] en 1962. El interés que ha despertado este problema así como la complejidad del mismo está demostrado por las numerosas publicaciones que abordan cuestiones relacionadas con este problema ver por ejemplo [JW35], [Erd39], [PS96], [Ma00], [Ma96], [Sol98], [Mat95], [PS96], [Sim05],[JKS07] [JKS11]. En el primer capítulo comenzamos introduciendo con detalle las medidas autosemejante en el plano complejo y los sistemas de funciones iteradas, así como los conceptos de la teoría de la medida necesarios para describirlos. A continuación se introducen las herramientas necesarias de teoría de polinomios ortogonales, matrices infinitas y operadores que se van a usar. En el segundo y tercer capítulo trasladamos las propiedades geométricas de las medidas autosemejantes a las matrices de momentos y de Hessenberg, respectivamente. A partir de estos resultados se describen algoritmos para calcular estas matrices a partir del SFI correspondiente. Concretamente, se obtienen fórmulas explícitas y algoritmos de aproximación para los momentos y matrices de momentos de medidas fractales, a partir de un teorema del punto fijo para las matrices. Además utilizando técnicas de la teoría de operadores, se han extendido al plano complejo los resultados que G. Mantica [Ma00, Ma96] obtenía en el caso real. Este resultado es la base para definir un algoritmo estable de aproximación de la matriz de Hessenberg asociada a una medida fractal u obtener secciones finitas exactas de matrices Hessenberg asociadas a una suma de medidas. En el último capítulo, se consideran medidas, μ, más generales y se estudia el comportamiento asintótico de los autovalores de una matriz hermitiana de momentos y su impacto en las propiedades de la medida asociada. En el resultado central se demuestra que si los polinomios asociados son densos en L2(μ) entonces necesariamente el autovalor mínimo de las secciones finitas de la matriz de momentos de la medida tiende a cero. ABSTRACT The Thesis work “Self-similar Measures on the Plane, Moments and Hessenberg Matrices” is framed among the geometric measure theory, orthogonal polynomials and operator theory. The work studies measures with compact support on the complex plane from the point of view of the associated infinite moments and Hessenberg matrices representing them in the theory of orthogonal polynomials. More precisely, it concentrates on the study of the self-similar measures that are equilibrium measures in a iterated functions system. Self-similar sets have the geometric property of being decomposable in a union of similar pieces to the complete set. These pieces can overlap. If the overlapping is small, Hutchinson’s theory [Hut81] works well, however, when it has no restrictions, the theory does not hold. The overlapping problem consists in controlling the measure of the overlap. The complexity of this problem is exemplified in the infinite convolutions of Bernoulli’s distributions, that are an example of self-similar measures in the real case. As early as 1935 [JW35], Jessen and Wintner posed this problem, that far from being simple, has been studied during more than 75 years. The main cuestiones posed by Garsia in 1962 [Gar62] remain unsolved. The interest in this problem, together with its complexity, is demonstrated by the number of publications that over the years have dealt with it. See, for example, [JW35], [Erd39], [PS96], [Ma00], [Ma96], [Sol98], [Mat95], [PS96], [Sim05], [JKS07] [JKS11]. In the first chapter, we will start with a detailed introduction to the self-similar measurements in the complex plane and to the iterated functions systems, also including the concepts of measure theory needed to describe them. Next, we introduce the necessary tools from orthogonal polynomials, infinite matrices and operators. In the second and third chapter we will translate the geometric properties of selfsimilar measures to the moments and Hessenberg matrices. From these results, we will describe algorithms to calculate these matrices from the corresponding iterated functions systems. To be precise, we obtain explicit formulas and approximation algorithms for the moments and moment matrices of fractal measures from a new fixed point theorem for matrices. Moreover, using techniques from operator theory, we extend to the complex plane the real case results obtained by Mantica [Ma00, Ma96]. This result is the base to define a stable algorithm that approximates the Hessenberg matrix associated to a fractal measure and obtains exact finite sections of Hessenberg matrices associated to a sum of measurements. In the last chapter, we consider more general measures, μ, and study the asymptotic behaviour of the eigenvalues of a hermitian matrix of moments, together with its impact on the properties of the associated measure. In the main result we demonstrate that, if the associated polynomials are dense in L2(μ), then necessarily follows that the minimum eigenvalue of the finite sections of the moments matrix goes to zero.

Modification and Developer Metrics at the Function Level: Metrics for the Study of the Evolution of a Software Project

Software evolution, and particularly its growth, has been mainly studied at the file (also sometimes referred as module) level. In this paper we propose to move from the physical towards a level that includes semantic information by using functions or methods for measuring the evolution of a software system. We point out that use of functions-based metrics has many advantages over the use of files or lines of code. We demonstrate our approach with an empirical study of two Free/Open Source projects: a community-driven project, Apache, and a company-led project, Novell Evolution. We discovered that most functions never change; when they do their number of modifications is correlated with their size, and that very few authors who modify each; finally we show that the departure of a developer from a software project slows the evolution of the functions that she authored.

Integration of design tools and knowledge capture into a CAD system: a case study

onceptual design phase is partially supported by product lifecycle management/computer-aided design (PLM/CAD) systems causing discontinuity of the design information flow: customer needs — functional requirements — key characteristics — design parameters (DPs) — geometric DPs. Aiming to address this issue, it is proposed a knowledge-based approach is proposed to integrate quality function deployment, failure mode and effects analysis, and axiomatic design into a commercial PLM/CAD system. A case study, main subject of this article, was carried out to validate the proposed process, to evaluate, by a pilot development, how the commercial PLM/CAD modules and application programming interface could support the information flow, and based on the pilot scheme results to propose a full development framework.

Approach to integrate product conceptual design information into a computer-aided design system

Commercial computer-aided design systems support the geometric definition of product, but they lack utilities to support initial design stages. Typical tasks such as customer need capture, functional requirement formalization, or design parameter definition are conducted in applications that, for instance, support ?quality function deployment? and ?failure modes and effects analysis? techniques. Such applications are noninteroperable with the computer-aided design systems, leading to discontinuous design information flows. This study addresses this issue and proposes a method to enhance the integration of design information generated in the early design stages into a commercial computer-aided design system. To demonstrate the feasibility of the approach adopted, a prototype application was developed and two case studies were executed.

Adaptive control system based on lineal control theory for the path-following problem of a car-like mobile robot

The objective of this paper is to design a path following control system for a car-like mobile robot using classical linear control techniques, so that it adapts on-line to varying conditions during the trajectory following task. The main advantages of the proposed control structure is that well known linear control theory can be applied in calculating the PID controllers to full control requirements, while at the same time it is exible to be applied in non-linear changing conditions of the path following task. For this purpose the Frenet frame kinematic model of the robot is linearised at a varying working point that is calculated as a function of the actual velocity, the path curvature and kinematic parameters of the robot, yielding a transfer function that varies during the trajectory. The proposed controller is formed by a combination of an adaptive PID and a feed-forward controller, which varies accordingly with the working conditions and compensates the non-linearity of the system. The good features and exibility of the proposed control structure have been demonstrated through realistic simulations that include both kinematics and dynamics of the car-like robot.

Objective Assessment of Olfactory Function Using Functional Magnetic Resonance Imaging=Estudio objetivo del olfato mediante resonancia magnética funcional

Objective: To show the results of a device that generates automated olfactory stimuli suitable for functional magnetic resonance imaging (fMRI) experiments. Material and methods: Te n normal volunteers, 5 women and 5 men, were studied. The system allows the programming of several sequences, providing the capability to synchronise the onset of odour presentation with acquisition by a trigger signal of the MRI scanner. The olfactometer is a device that allows selection of the odour, the event paradigm, the time of stimuli and the odour concentration. The paradigm used during fMRI scanning consisted of 15-s blocks. The odorant event took 2 s with butanol, mint and coffee. Results: We observed olfactory activity in the olfactory bulb, entorhinal cortex (4%), amygdala (2.5%) and temporo-parietal cortex, especially in the areas related to emotional integration. Conclusions: The device has demonstrated its effectiveness in stimulating olfactory areas and its capacity to adapt to fMRI equipment.RESUMEN Objetivo: Mostrar los resultados del olfatómetro capaz de generar tareas olfativas en un equipo de resonancia magnética funcional (fMRI). Material y métodos: Estudiamos 10 sujetos normales: 5 varones y 5 mujeres. El olfatómetro está dise ̃ nado para que el estímulo que produce se sincronice con el equipo de fMRI mediante la se ̃ nal desencadenante que suministra el propio equipo. El olfatómetro es capaz de: selec- cionar el olor, secuenciar los distintos olores, programar la frecuencia y duración de los olores y controlar la intensidad del olor. El paradigma utilizado responde a un dise ̃ no de activación asociada a eventos, en el que la duración del bloque de activación y de reposo es de 15 s. La duración del estímulo olfativo (butanol, menta o café) es de 2 segundos, durante toda la serie que consta de 9 ciclos. Resultados: Se ha observado reactividad (contraste BOLD) en las diferentes áreas cerebrales involucradas en las tareas olfativas: bulbo olfatorio, córtex entorrinal (4%), amigdala (2,5%) y córtex temporoparietal. Las áreas relacionadas con integración de las emociones tienen una reactividad mayor. Conclusiones: El dispositivo propuesto nos permite controlar de forma automática y sincronizada los olores necesarios para estudiar la actividad de las áreas olfatorias cerebrales mediante fMRI.

Analysis of a thermal system through remote laboratories

This paper describes the experiences using remote laboratories for thorough analysis of a thermal system, including disturbances. Remote laboratories for education in subjects of control, is a common resorted method, used by universities. This method is applied to offer a flexible service in schedules so as to obtain greater and better results of available resources. Remote laboratories have been used for controlling physical devices remotely. Furthermore, remote labs have been used for transfer function identification of real equipment. Nevertheless, remote analyses of disturbances have not been done. The aim of this contribution is thereby to apply the experience of remote laboratories in the study of disturbances. Some experiments are carried out to demonstrate the effectiveness in using remote laboratories for complete analysis of a thermal system. Considering the remote access to thermal system, “Sistema de Laboratorios a Distancia” (SLD) was used.

Monte Carlo simulation on a system of hard cylinders at a very high packing fraction

Using the Monte Carlo method the behavior of a system of true hard cylinders has been studied. Values of the length-to-breadth ratio L/D and packing fraction η have been chosen similar to those of real nematic liquid crystals. Results include radial distribution function g(r), structure factor S(k), and orientational order parameter M. These results lead to the conclusion that the hard cylinder model may be a useful reference for real mesomorphic phases.

Bare-tether cathodic contact through thermoionic emission by low work-function materials

A new material, C12A7 : electride, which might present a work function as low as 0.6 eV and moderately high temperature stability, was recently proposed as coating for floating bare tethers. Arising from heating under space operation, current is emitted by thermionic emission along a thus coated cathodic segment. A preliminary study on the space-charge-limited (SCL) double layer in front of the cathodic segment is presented using Langmuir’s SCL electron current between cylindrical electrodes and orbital-motion-limited ion-collection sheath. A detailed calculation of current and bias profiles along the entire tether length is carried out with ohmic effects and the transition from SCL to full Richardson-Dushman emission included. Analysis shows that in the simplest drag mode, under typical orbital and tether conditions, thermionic emission leads to a short cathodic section and may eliminate the need for an active cathodic device and its corresponding gas feed requirements and power subsystem, which results in a truly “propellant-less” tether system for such basic applications as de-orbiting low earth orbit satellites.

Low work-function coating for an entirely propellantless bare electrodynamic tether

We present the possibility of a low work-function material, calcium aluminate electride, being used for a coating on a bare electrodynamic tether system. Analyses suggest that the coating would eliminate the need for an active cathodic device like a hollow cathode and, consequently, eliminate the need for an expellant to the hollow cathode, thus resulting in an electrodynamic tether system that requires no consumables. Applications include on-orbit power generation and deorbiting debris from low Earth orbit in a simple and trouble-free manner.

Integration of congestion pricing and intertemporal preference rate in social welfare function

Assessing social benefits in transport policy implementation has been studied by many researchers using theoretical or empirical measures. However, few of them measure social benefit using different discount rates including the inter-temporal preferences rate of users, the private investment discount rate and the inter-temporal preferences rate of the government. In general, the social discount rate used is the same for all social actors. Therefore, this paper aims to assess a new method by integrating different types of discount rate belonging to different social actors in order to measure the real benefits of each actor in the short, medium and long term. A dynamic simulation is provided by a strategic Land-Use and Transport Interaction (LUTI) model. The method is tested by optimizing a cordon toll scheme in Madrid considering socio- economic efficiency and environmental criteria. Based on the modified social welfare function (WF), the effects on the measure of social benefits are estimated and compared with the classical WF results as well. The results of this research could be a key issue to understanding the relationship between transport system policies and social actors' benefits distribution in a metropolitan context. The results show that the use of more suitable discount rates for each social actor had an effect on the selection and definition of optimal strategy of congestion pricing. The usefulness of the measure of congestion toll declines more quickly overtime.

Integration of congestion pricing and intertemporal preferences rate integration in social welfare function

Many researchers have used theoretical or empirical measures to assess social benefits in transport policy implementation. However, few have measured social benefits by using discount rates, including the intertemporal preference rate of users, the private investment discount rate, and the intertemporal preference rate of the government. In general, the social discount rate used is the same for all social actors. This paper aims to assess a new method by integrating different types of discount rates belonging to different social actors to measure the real benefits of each actor in the short term, medium term, and long term. A dynamic simulation is provided by a strategic land use and transport interaction model. The method was tested by optimizing a cordon toll scheme in Madrid, Spain. Socioeconomic efficiency and environmental criteria were considered. On the basis of the modified social welfare function, the effects on the measure of social benefits were estimated and compared with the classical welfare function measures. The results show that the use of more suitable discount rates for each social actor had an effect on the selection and definition of optimal strategy of congestion pricing. The usefulness of the measure of congestion toll declines more quickly over time. This result could be the key to understanding the relationship between transport system policies and the distribution of social actors? benefits in a metropolitan context.

The type II secretion system (Xcp) of Pseudomonas putida is active and involved in the secretion of phosphatases.

The genome of the Gram-negative bacterium Pseudomonas putida harbours a complete set of xcp genes for a type II protein secretion system (T2SS). This study shows that expression of these genes is induced under inorganic phosphate (Pi ) limitation and that the system enables the utilization of various organic phosphate sources. A phosphatase of the PhoX family, previously designated UxpB, was identified, which was produced under low Pi conditions and transported across the cell envelope in an Xcp-dependent manner demonstrating that the xcp genes encode an active T2SS. The signal sequence of UxpB contains a twin-arginine translocation (Tat) motif as well as a lipobox, and both processing by leader peptidase II and Tat dependency were experimentally confirmed. Two different tat gene clusters were detected in the P.?putida genome, of which one, named tat-1, is located adjacent to the uxpB and xcp genes. Both Tat systems appeared to be capable of transporting the UxpB protein. However, expression of the tat-1 genes was strongly induced by low Pi levels, indicating a function of this system in survival during Pi starvation.

The type II secretion system (Xcp) of Pseudomonas putida is active and involved in the secretion of phosphatases.

The genome of the Gram-negative bacterium Pseudomonas putida harbours a complete set of xcp genes for a type II protein secretion system (T2SS). This study shows that expression of these genes is induced under inorganic phosphate (Pi ) limitation and that the system enables the utilization of various organic phosphate sources. A phosphatase of the PhoX family, previously designated UxpB, was identified, which was produced under low Pi conditions and transported across the cell envelope in an Xcp-dependent manner demonstrating that the xcp genes encode an active T2SS. The signal sequence of UxpB contains a twin-arginine translocation (Tat) motif as well as a lipobox, and both processing by leader peptidase II and Tat dependency were experimentally confirmed. Two different tat gene clusters were detected in the P.?putida genome, of which one, named tat-1, is located adjacent to the uxpB and xcp genes. Both Tat systems appeared to be capable of transporting the UxpB protein. However, expression of the tat-1 genes was strongly induced by low Pi levels, indicating a function of this system in survival during Pi starvation.

Performance metrics for small-signal stability assessment of DC-distributed power-system-architecture comparisons

The objective of this paper is to provide performance metrics for small-signal stability assessment of a given system architecture. The stability margins are stated utilizing a concept of maximum peak criteria (MPC) derived from the behavior of an impedance-based sensitivity function. For each minor-loop gain defined at every system interface, a single number to state the robustness of stability is provided based on the computed maximum value of the corresponding sensitivity function. In order to compare various power-architecture solutions in terms of stability, a parameter providing an overall measure of the whole system stability is required. The selected figure of merit is geometric average of each maximum peak value within the system. It provides a meaningful metrics for system comparisons: the best system in terms of robust stability is the one that minimizes this index. In addition, the largest peak value within the system interfaces is given thus detecting the weakest point of the system in terms of robustness.