Lower semicontinuity of the feasible set mapping of linear systems relative to their domains

This paper deals with stability properties of the feasible set of linear inequality systems having a finite number of variables and an arbitrary number of constraints. Several types of perturbations preserving consistency are considered, affecting respectively, all of the data, the left-hand side data, or the right-hand side coefficients.

Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Stability for parametric implicit vector equilibrium problems

In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters is an element of and lambda respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S : Lambda(1) x A(2) -> 2(X) for such parametric implicit vector equilibrium problems. (c) 2005 Elsevier Ltd. All rights reserved.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile

[1] We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Computing and Visualizing Solution Sets of Interval Linear Systems

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Characterizations of the Solution Sets of Generalized Convex Minimization Problems

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

RealCrono –sistema de difusão de resultados em tempo real na web

A velocidade de difusão de conteúdos numa plataforma web, assume uma elevada relevância em serviços onde a informação se pretende atualizada e em tempo real. Este projeto de Mestrado, apresenta uma abordagem de um sistema distribuído de recolher e difundir resultados em tempo real entre várias plataformas, nomeadamente sistemas móveis. Neste contexto, tempo real entende-se como uma diferença de tempo nula entre a recolha e difusão, ignorando fatores que não podem ser controlados pelo sistema, como latência de comunicação e tempo de processamento. Este projeto tem como base uma arquitetura existente de processamento e publicação de resultados desportivos, que apresentava alguns problemas relacionados com escalabilidade, segurança, tempos de entrega de resultados longos e sem integração com outras plataformas. Ao longo deste trabalho procurou-se investigar fatores que condicionassem a escalabilidade de uma aplicação web dando ênfase à implementação de uma solução baseada em replicação e escalabilidade horizontal. Procurou-se também apresentar uma solução de interoperabilidade entre sistemas e plataformas heterogêneas, mantendo sempre elevados níveis de performance e promovendo a introdução de plataformas móveis no sistema. De várias abordagens existentes para comunicação em tempo real sobre uma plataforma web, adotou-se um implementação baseada em WebSocket que elimina o tempo desperdiçado entre a recolha de informação e sua difusão. Neste projeto é descrito o processo de implementação da API de recolha de dados (Collector), da biblioteca de comunicação com o Collector, da aplicação web (Publisher) e sua API, da biblioteca de comunicação com o Publisher e por fim a implementação da aplicação móvel multi-plataforma. Com os componentes criados, avaliaram-se os resultados obtidos com a nova arquitetura de forma a aferir a escalabilidade e performance da solução criada e sua adaptação ao sistema existente.

Improving anterior deltoid activity in a musculoskeletal shoulder model - an analysis of the torque-feasible space at the sternoclavicular joint.

Modelling the shoulder's musculature is challenging given its mechanical and geometric complexity. The use of the ideal fibre model to represent a muscle's line of action cannot always faithfully represent the mechanical effect of each muscle, leading to considerable differences between model-estimated and in vivo measured muscle activity. While the musculo-tendon force coordination problem has been extensively analysed in terms of the cost function, only few works have investigated the existence and sensitivity of solutions to fibre topology. The goal of this paper is to present an analysis of the solution set using the concepts of torque-feasible space (TFS) and wrench-feasible space (WFS) from cable-driven robotics. A shoulder model is presented and a simple musculo-tendon force coordination problem is defined. The ideal fibre model for representing muscles is reviewed and the TFS and WFS are defined, leading to the necessary and sufficient conditions for the existence of a solution. The shoulder model's TFS is analysed to explain the lack of anterior deltoid (DLTa) activity. Based on the analysis, a modification of the model's muscle fibre geometry is proposed. The performance with and without the modification is assessed by solving the musculo-tendon force coordination problem for quasi-static abduction in the scapular plane. After the proposed modification, the DLTa reaches 20% of activation.

IBM's Internet of Things and Academic Initiative

IBM provide a comprehensive academic initiative, (http://www-304.ibm.com/ibm/university/academic/pub/page/academic_initiative) to universities, providing them free of charge access to a wide range of IBM Software. As part of this initiative we are currently offering free IBM Bluemix accounts, either to be used within a course, or for students to use for personal skills development. IBM Bluemix provides a comprehensive cloud based platform as a service solution set which includes the ability to quickly and easily integrate data from devices from Internet of Things ( IoT) solutions to develop and run productive and user focused web and mobile applications. If you would be interested in hearing more about IBM and Internet of Things or you would like to discuss prospective research projects that you feel would operate well in this environment, please come along to the seminar!

Projetos de controladores para sistemas de potência utilizando LMI'S

A presente dissertação tem como objetivo estudar e aprimorar métodos de projetos de controladores para sistemas de potência, sendo que esse trabalho trata da estabilidade dinâmica de sistemas de potência e, portanto, do projeto de controladores amortecedores de oscilações eletromecânicas para esses sistemas. A escolha dos métodos aqui estudados foi orientada pelos requisitos que um estabilizador de sistemas de potência (ESP) deve ter, que são robustez, descentralização e coordenação. Sendo que alguns deles tiveram suas características aprimoradas para atender a esses requisitos. A abordagem dos métodos estudados foi restringida à análise no domínio tempo, pois a abordagem temporal facilita a modelagem das incertezas paramétricas, para atender ao requisito da robustez, e também permite a formulação do controle descentralizado de maneira simples. Além disso, a abordagem temporal permite a formulação do problema de projeto utilizando desigualdades matriciais lineares (LMI’s), as quais possuem como vantagem o fato do conjunto solução ser sempre convexo e a existência de algoritmos eficientes para o cálculo de sua solução. De fato, existem diversos pacotes computacionais desenvolvidos no mercado para o cálculo da solução de um problema de inequações matriciais lineares. Por esse motivo, os métodos de projeto para controladores de saída buscam sempre colocar o problema na forma de LMI’s, tendo em vista que ela garante a obtenção de solução, caso essa solução exista.

Diseño de una infraestructura TIC basada en virtualización

[ES] Las necesidades básicas de las empresas suelen ser las mismas, ya sea una empresa grande que pequeña, la infraestructura sobre la que montan sus procesos de negocio y las aplicaciones para gestionarlos suelen ser casi iguales. Si dividimos la infraestructura TIC de una empresa en hardware, sistema y aplicaciones, podemos ver que en la mayoría de ellas el sistema es casi idéntico. Además, gracias a la virtualización, que ha entrado de manera arrolladora en el mundo de la informática, podemos independizar totalmente el software del hardware, de forma que obtenemos una flexibilidad enorme a la hora de planificar despliegues de infraestructura. Sobre estas dos ideas, uniformidad de sistema e independencia de hardware, son sobre las que se va a desarrollar el siguiente TFG. Para el desarrollo de la primera de ellas se realizará el estudio de la infraestructura básica ( sistema) que cualquier empresa suele tener. Se intentará dar una solución que sea válida para una gran cantidad de empresas de nuestro entorno y se realizará el diseño del mismo. Con la segunda idea desarrollaremos un sistema basado en servicios, que sea lo suficientemente completa para poder dar respuesta a las necesidades vistas pero, a su vez, suficientemente flexible para que el crecimiento en capacidades o servicios se pueda realizar de forma sencilla sin que la estructura del sistema, o sus módulos deban modificarse para realizarlos. Por tanto, vamos a realizar un diseño integral y completa, de forma que será tanto de hardware como de software, haciendo énfasis en la integración de los sistemas y la interrelación entre los distintos elementos de ellos. Se dará, a su vez, la valoración económica del mismo. Por último, y como ejemplo de la flexibilidad del diseño elegido veremos dos modificaciones sobre el diseño original. El primero de ellos será una ampliación para dar mayor seguridad en cuanto a redundancia de almacenamiento y, ya en un paso definitivo, montar un CPD remoto. El segundo de ellos será un diseño de bajo coste, en el que, mantenimiento los mismos servicios, bajaremos el coste del diseño con productos con algo menos de prestaciones, pero manteniendo la solución en conjunto unos altos niveles de calidad y servicio.

A partial dependence factorial analysis to deal with selection bias in observational studis

This thesis presents a creative and practical approach to dealing with the problem of selection bias. Selection bias may be the most important vexing problem in program evaluation or in any line of research that attempts to assert causality. Some of the greatest minds in economics and statistics have scrutinized the problem of selection bias, with the resulting approaches – Rubin’s Potential Outcome Approach(Rosenbaum and Rubin,1983; Rubin, 1991,2001,2004) or Heckman’s Selection model (Heckman, 1979) – being widely accepted and used as the best fixes. These solutions to the bias that arises in particular from self selection are imperfect, and many researchers, when feasible, reserve their strongest causal inference for data from experimental rather than observational studies. The innovative aspect of this thesis is to propose a data transformation that allows measuring and testing in an automatic and multivariate way the presence of selection bias. The approach involves the construction of a multi-dimensional conditional space of the X matrix in which the bias associated with the treatment assignment has been eliminated. Specifically, we propose the use of a partial dependence analysis of the X-space as a tool for investigating the dependence relationship between a set of observable pre-treatment categorical covariates X and a treatment indicator variable T, in order to obtain a measure of bias according to their dependence structure. The measure of selection bias is then expressed in terms of inertia due to the dependence between X and T that has been eliminated. Given the measure of selection bias, we propose a multivariate test of imbalance in order to check if the detected bias is significant, by using the asymptotical distribution of inertia due to T (Estadella et al. 2005) , and by preserving the multivariate nature of data. Further, we propose the use of a clustering procedure as a tool to find groups of comparable units on which estimate local causal effects, and the use of the multivariate test of imbalance as a stopping rule in choosing the best cluster solution set. The method is non parametric, it does not call for modeling the data, based on some underlying theory or assumption about the selection process, but instead it calls for using the existing variability within the data and letting the data to speak. The idea of proposing this multivariate approach to measure selection bias and test balance comes from the consideration that in applied research all aspects of multivariate balance, not represented in the univariate variable- by-variable summaries, are ignored. The first part contains an introduction to evaluation methods as part of public and private decision process and a review of the literature of evaluation methods. The attention is focused on Rubin Potential Outcome Approach, matching methods, and briefly on Heckman’s Selection Model. The second part focuses on some resulting limitations of conventional methods, with particular attention to the problem of how testing in the correct way balancing. The third part contains the original contribution proposed , a simulation study that allows to check the performance of the method for a given dependence setting and an application to a real data set. Finally, we discuss, conclude and explain our future perspectives.