A NOTE ON RESOLVENT CONVERGENCE ON A THIN DOMAIN

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

The main-sequence rotation-colour relation in the Coma Berenices open cluster

We present the results of a photometric survey of rotation rates in the Coma Berenices (Melotte 111) open cluster, using data obtained as part of the SuperWASP exoplanetary transit-search programme. The goal of the Coma survey was to measure precise rotation periods for main-sequence F, G and K dwarfs in this intermediate-age (~600 Myr) cluster, and to determine the extent to which magnetic braking has caused the stellar spin periods to converge. We find a tight, almost linear relationship between rotation period and J - K colour with an rms scatter of only 2 per cent. The relation is similar to that seen among F, G and K stars in the Hyades. Such strong convergence can only be explained if angular momentum is not at present being transferred from a reservoir in the deep stellar interiors to the surface layers. We conclude that the coupling time-scale for angular momentum transport from a rapidly spinning radiative core to the outer convective zone must be substantially shorter than the cluster age, and that from the age of Coma onwards stars rotate effectively as solid bodies. The existence of a tight relationship between stellar mass and rotation period at a given age supports the use of stellar rotation period as an age indicator in F, G and K stars of Hyades age and older. We demonstrate that individual stellar ages can be determined within the Coma population with an internal precision of the order of 9 per cent (rms), using a standard magnetic braking law in which rotation period increases with the square root of stellar age. We find that a slight modification to the magnetic-braking power law, P ~ t0.56, yields rotational and asteroseismological ages in good agreement for the Sun and other stars of solar age for which p-mode studies and photometric rotation periods have been published.

Regularization and Bang-bang conjugate times in optimal control

Consideramos o problema de controlo óptimo de tempo mínimo para sistemas de controlo mono-entrada e controlo afim num espaço de dimensão finita com condições inicial e final fixas, onde o controlo escalar toma valores num intervalo fechado. Quando aplicamos o método de tiro a este problema, vários obstáculos podem surgir uma vez que a função de tiro não é diferenciável quando o controlo é bang-bang. No caso bang-bang os tempos conjugados são teoricamente bem definidos para este tipo de sistemas de controlo, contudo os algoritmos computacionais directos disponíveis são de difícil aplicação. Por outro lado, no caso suave o conceito teórico e prático de tempos conjugados é bem conhecido, e ferramentas computacionais eficazes estão disponíveis. Propomos um procedimento de regularização para o qual as soluções do problema de tempo mínimo correspondente dependem de um parâmetro real positivo suficientemente pequeno e são definidas por funções suaves em relação à variável tempo, facilitando a aplicação do método de tiro simples. Provamos, sob hipóteses convenientes, a convergência forte das soluções do problema regularizado para a solução do problema inicial, quando o parâmetro real tende para zero. A determinação de tempos conjugados das trajectórias localmente óptimas do problema regularizado enquadra-se na teoria suave conhecida. Provamos, sob hipóteses adequadas, a convergência do primeiro tempo conjugado do problema regularizado para o primeiro tempo conjugado do problema inicial bang-bang, quando o parâmetro real tende para zero. Consequentemente, obtemos um algoritmo eficiente para a computação de tempos conjugados no caso bang-bang.

The Politics of Poverty in the European Union: How States Respond to the Open Method of Coordination on Social Inclusion

This article assesses the responses of EU-15 member states to the poverty reduction objectives of the Open Method of Coordination (OMC) on social inclusion between 2001 and 2006. As a flexible mechanism of information sharing between governments, the OMC could not produce strong convergence. A thorough analysis of the OMC documents indeed points to the enduring power of national institutions and partisan politics, for the three dimensions of social inclusion identified by the EU (rights, labour market policies, and participation). There was however some learning and adaptation around emerging policy ideas like activation and the participation of people experiencing poverty.

ACCELERATING ITERATIVE ALGORITHMS FOR SYMMETRICAL LINEAR COMPLEMENTARITY-PROBLEMS

We propose a method for accelerating iterative algorithms for solving symmetric linear complementarity problems. The method consists in performing a one-dimensional optimization in the direction generated by a splitting method even for non-descent directions. We give strong convergence proofs and present numerical experiments that justify using this acceleration.

Error estimates for a neumann problem in highly oscillating thin domains

In this work we analyze the convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain with highly oscillatory behavior. We consider the case where the height of the domain, amplitude and period of the oscillations are all of the same order, and given by a small parameter e > 0. Using an appropriate corrector approach, we show strong convergence and give error estimates when we replace the original solutions by the first-order expansion through the Multiple-Scale Method.

Infrastructure, integration and equity: The social impact of the health and public transportation infrastructure.

Academicians and practitioners generally agree that there is a positive correlation between more and better infrastructure and economic growth. From the broader perspective of development, attempts have been made in the literature to identify the different theoretical connections and the empirical patterns that link infrastructure to productivity, on the one hand, and those that link it to social inclusion and equity, on the other hand. Infrastructure contributes to development in different ways. The capital involved is not homogeneous, nor is its effect on the distributive aspects. Water and sanitation have a particularly strong association with the health of the general population and with infant mortality, early childhood health, learning abilities and the acquisition of labour skills. With respect to transportation, the reduction of costs and travel times has a direct economic impact on economic activities of production and domestic and international distribution. That infrastructure also has a social and distributive role to play by reducing the number of fatal accidents and serious injuries in the sectors that are naturally most susceptible to them, namely, the poor. Under the broad umbrella of infrastructure, we can include a number of facilities that make possible the provision of certain services. Some of these facilities require very significant fixed capital investments; some of them are residential, while others are not necessarily. What they all have in common is the existence of networks (transportation, wiring, pipelines) and a strong convergence of physical capital and/or technology, as well as the need for major investments in periodic maintenance.

Stabilization for an ensemble of half-spin systems

Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H-1 topology. This local convergence is shown to be a weak asymptotic convergence for the H-1 topology and thus a strong convergence for the C topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium. (C) 2011 Elsevier Ltd. All rights reserved.

Black-scholes type equations

In this work we are concerned with the analysis and numerical solution of Black-Scholes type equations arising in the modeling of incomplete financial markets and an inverse problem of determining the local volatility function in a generalized Black-Scholes model from observed option prices. In the first chapter a fully nonlinear Black-Scholes equation which models transaction costs arising in option pricing is discretized by a new high order compact scheme. The compact scheme is proved to be unconditionally stable and non-oscillatory and is very efficient compared to classical schemes. Moreover, it is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. In the next chapter we turn to the calibration problem of computing local volatility functions from market data in a generalized Black-Scholes setting. We follow an optimal control approach in a Lagrangian framework. We show the existence of a global solution and study first- and second-order optimality conditions. Furthermore, we propose an algorithm that is based on a globalized sequential quadratic programming method and a primal-dual active set strategy, and present numerical results. In the last chapter we consider a quasilinear parabolic equation with quadratic gradient terms, which arises in the modeling of an optimal portfolio in incomplete markets. The existence of weak solutions is shown by considering a sequence of approximate solutions. The main difficulty of the proof is to infer the strong convergence of the sequence. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution, but without additional regularity assumptions on the solution. The results are illustrated by a numerical example.

Estudio de la tecnología IMS y diseño de una solución de telefonía multimedia

El objetivo fundamental del Proyecto Fin de Carrera es ofrecer una visión global de la arquitectura de red IMS (“IP Multimedia Subsystem”) conociendo el comportamiento de los nodos que la forman y las funcionalidades que cada uno de ellos implementa. Durante la realización del proyecto se ha tenido en cuenta que las redes IMS han transformando el sector de las telecomunicaciones debido a la gran convergencia de los servicios que ofrece. Esta tecnología presenta un amplio abanico a las aplicaciones multimedia, tanto en el entorno empresarial como residencial. Como desarrollo práctico se expone un diseño de alto nivel que consiste en la ampliación de la capacidad existente de uno de los nodos de la red IMS para un operador nacional ofreciendo el servicio ‘Business Trunking’ para grandes clientes. El objetivo destinado alcanzar con este caso práctico es el análisis del impacto que supone la inclusión de este nuevo elemento en el resto de nodos que forman la red. Consiguiendo demostrar la facilidad para el operador, a la hora de ampliar la capacidad de su red, sin olvidarnos que esto conlleva numerosos beneficios tanto a nivel de proveedor como de usuario final. The principal objective in this Final Degree Project is to provide an overview of the architect of the IMS Network, considering the behavior of nodes that integrate this network and the main functionalities that each of them implements. During the study of this Project has taken into account that IMS network has turned Telecommunications world, due to the strong convergence of the services offered. This technology shows a wide range of multimedia applications, in enterprise as much as residential environment. As a practical development a high-level design is presented. It involves the expansion of existing capacity for one of IMS network nodes for a national operator offering ‘Business Trunking’ service for enterprises. The goal to achieve in this case is to analyze the impact caused by the inclusion of this new element in the rest of the nodes within the IMS network. To manage to prove the ease of the operator, in expanding the capacity of its network, and considering IMS technology allows to obtain several benefits for both supplier and end user.

A note on the Balanced method

Recently the Balanced method was introduced as a class of quasi-implicit methods for solving stiff stochastic differential equations. We examine asymptotic and mean-square stability for several implementations of the Balanced method and give a generalized result for the mean-square stability region of any Balanced method. We also investigate the optimal implementation of the Balanced method with respect to strong convergence.

A multicultural study of stereotyping in English-speaking countries

Citizens of 9 different English-speaking countries (N = 619) evaluated the average, or typical, citizen of 5 English-speaking countries (Great Britain, Canada, Nigeria, United States, Australia) on 9 pairs of bipolar adjectives. Participants were drawn from Australia, Botswana, Canada, Kenya, Nigeria, South Africa, the United States, Zambia, and Zimbabwe. There were statistically significant similarities in the rankings of the 5 stimulus countries on 8 of the 9 adjective dimensions and a strong convergence of autostereotypes and heterostereotypes on many traits. The results relate to previous stereotyping research and traditional methods of assessing the accuracy of national stereotypes.