Expanding an abridged life table

A question of interest in the demographic and actuarial fields is the estimation of the age-specific mortality pattern when data are given in age groups. Data can be provided in such a form usually because of systematic fluctuations caused by age heaping. This is a phenomenon usual to vital registrations related to age misstatements, usually preferences of ages ending in multiples five. Several techniques for expanding an abridged life table to a complete one are proposed in the literature. Although many of these techniques are considered accurate and are more or less extensively used, they have never been simultaneously evaluated. This work provides a critical presentation, an evaluation and a comparison of the performance of these techniques. For that purpose, we consider empirical data sets for several populations with reliable analytical documentation. Departing from the complete sets of qx-values, we form the abridged ones. Then we apply each one of the expanding techniques considered to these abridged data sets and finally we compare the results with the corresponding complete empirical values.abridged life table, age-specific mortality pattern, complete life table, expanding method, interpolation, life tables, parametric models, probability of dying, splines

Reduced order isogeometric analysis approach for PDEs in parametrized domains

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe

Comparison of shape parametrization techniques for fluid-structure interaction problems

This master thesis describes the development in the framework of Fluid- Structure Interaction (FSI) problems of an efficient and flexible technique treating the fluid-structure interface and mesh motion problems. The main idea is to build, through a new hierarchical approach, a tool with accurate identication capabilities for both the structural rigid movement (translation/rotation) and the elastic deformation (displacement), with the possibility of facing arbitrary structural and fluid discretization schemes. Starting from a review of the state of the art methods, used for these applications, the different shape representation techniques applied, like Free Form Deformation (FFD), Radial Basis Function (RBF) and Inverse Distance Weighting (IDW) are introduced and then compared to test their performances in terms of computational costs and achievable mesh quality. Then, in order to reduce the complexity of the geometrical model and its description, ad hoc innovative optimization techniques, like a selective approach of the RBF interpolation sites as well as a domain-decomposition approach for FFD, are presented showing clear reductions in term of computational costs. Some applications and test-cases, solved by using an open-source Finite Element library (LifeV), dealing with unsteady viscous (internal and external) flows, characterized by different Reynolds number, are shown to highlight the quality and the accuracy of the methods and their stability. For the implementation of the schemes developed, an efficient C++ object oriented code language was used, relying also on Trilinos packages

Splines and local approximation of the earth's gravity field

Bibliography: pages 214-220.The Hilbert space spline theory of Delvos and Schempp, and the reproducing kernel theory of L. Schwartz, provide the conceptual foundation and the construction procedure for rotation-invariant splines on Euclidean spaces, splines on the circle, and splines on the sphere and harmonic outside the sphere. Spherical splines and surface splines such as multi-conic functions, Hardy's multiquadric functions, pseudo-cubic splines, and thin-plate splines, are shown to be largely as effective as least squares collocation in representing geoid heights or gravity anomalies. A pseudo-cubic spline geoid for southern Africa is given, interpolating Doppler-derived geoid heights and astro-geodetic deflections of the vertical. Quadrature rules are derived for the thin-plate spline approximation (over a circular disk, and to a planar approximation) of Stokes's formula, the formulae of Vening Meinesz, and the L₁ vertical gradient operator in the analytical continuation series solution of Molodensky's problem

Análisis de armónicas dinámicas con filtros de respuesta impulsional finita diseñados con O-splines

Los splines son esenciales en procesamiento de señales. No solamente se usan ven el muestreo e interpolación de señales, sino también en el diseño de filtros, en procesamiento de imágenes, y el análisis multiresolución. Aquí presentamos una nueva clase de splines. Se les llama O-splines porque sus nodos están separados por un ciclo fundamental. Se usan como muestreadores de estados óptimos, en el sentido de que sus coeficientes ofrecen en cada instante de tiempo las derivadas del segmento de señal que aseguran la mejor aproximación de Taylor alrededor de un punto, o la mejor interpolación de Hermite entre dos puntos. Los O-splines corresponden a la respuesta impulsional de los filtros de la Transformada de Tiempo Discreto de Taylor-Fourier (DTTFT). Los pasabajas coinciden con los núcleos centrales de interpolación de Lagrange, los cuáles convergen a la función Seno Cardenal, respuesta impulsional del filtro ideal. Y sus derivadas convergen a su vez a los diferenciadores ideales pasabajas. Los O-splines pasabanda son splines armónicos, pues son simples modulaciones de un pasabajas en cada frecuencia armónica. En este artículo se presenta la solución en forma cerrada de los O-splines pasabajas. Con ella se reduce enormemente la complejidad computacional de la DTTFT y se pueden obtener O-splines de orden elevado. Con ellos se pueden diseñar filtros pasabanda muy cercanos al ideal, en cualquier frecuencia. Los O-splines definen una escalera de espacios muy útiles para el análisis multiresolución, y el análisis tiempo-frecuencia. El artículo ilustra algunos ejemplos de diversa naturaleza. Por supuesto que una nueva familia de onduletas obtenidas a partir de los O-splines está en camino

Solving, Estimating and Selecting Nonlinear Dynamic Economic Models without the Curse of Dimensionality

A welfare analysis of a risky policy is impossible within a linear or linearized model and its certainty equivalence property. The presented algorithms are designed as a toolbox for a general model class. The computational challenges are considerable and I concentrate on the numerics and statistics for a simple model of dynamic consumption and labor choice. I calculate the optimal policy and estimate the posterior density of structural parameters and the marginal likelihood within a nonlinear state space model. My approach is even in an interpreted language twenty time faster than the only alternative compiled approach. The model is estimated on simulated data in order to test the routines against known true parameters. The policy function is approximated by Smolyak Chebyshev polynomials and the rational expectation integral by Smolyak Gaussian quadrature. The Smolyak operator is used to extend univariate approximation and integration operators to many dimensions. It reduces the curse of dimensionality from exponential to polynomial growth. The likelihood integrals are evaluated by a Gaussian quadrature and Gaussian quadrature particle filter. The bootstrap or sequential importance resampling particle filter is used as an accuracy benchmark. The posterior is estimated by the Gaussian filter and a Metropolis- Hastings algorithm. I propose a genetic extension of the standard Metropolis-Hastings algorithm by parallel random walk sequences. This improves the robustness of start values and the global maximization properties. Moreover it simplifies a cluster implementation and the random walk variances decision is reduced to only two parameters so that almost no trial sequences are needed. Finally the marginal likelihood is calculated as a criterion for nonnested and quasi-true models in order to select between the nonlinear estimates and a first order perturbation solution combined with the Kalman filter.stochastic dynamic general equilibrium model, Chebyshev polynomials, Smolyak operator, nonlinear state space filter, Curse of Dimensionality, posterior of structural parameters, marginal likelihood