A priori ratemaking using bivariate poisson regression models

In automobile insurance, it is useful to achieve a priori ratemaking by resorting to gene- ralized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper exa- mines an a priori ratemaking procedure when including two di®erent types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tari® system might be a®ected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.

Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

A priori parameterisation of the CERES soil-crop models and tests against several European data sets

Mechanistic soil-crop models have become indispensable tools to investigate the effect of management practices on the productivity or environmental impacts of arable crops. Ideally these models may claim to be universally applicable because they simulate the major processes governing the fate of inputs such as fertiliser nitrogen or pesticides. However, because they deal with complex systems and uncertain phenomena, site-specific calibration is usually a prerequisite to ensure their predictions are realistic. This statement implies that some experimental knowledge on the system to be simulated should be available prior to any modelling attempt, and raises a tremendous limitation to practical applications of models. Because the demand for more general simulation results is high, modellers have nevertheless taken the bold step of extrapolating a model tested within a limited sample of real conditions to a much larger domain. While methodological questions are often disregarded in this extrapolation process, they are specifically addressed in this paper, and in particular the issue of models a priori parameterisation. We thus implemented and tested a standard procedure to parameterize the soil components of a modified version of the CERES models. The procedure converts routinely-available soil properties into functional characteristics by means of pedo-transfer functions. The resulting predictions of soil water and nitrogen dynamics, as well as crop biomass, nitrogen content and leaf area index were compared to observations from trials conducted in five locations across Europe (southern Italy, northern Spain, northern France and northern Germany). In three cases, the model’s performance was judged acceptable when compared to experimental errors on the measurements, based on a test of the model’s root mean squared error (RMSE). Significant deviations between observations and model outputs were however noted in all sites, and could be ascribed to various model routines. In decreasing importance, these were: water balance, the turnover of soil organic matter, and crop N uptake. A better match to field observations could therefore be achieved by visually adjusting related parameters, such as field-capacity water content or the size of soil microbial biomass. As a result, model predictions fell within the measurement errors in all sites for most variables, and the model’s RMSE was within the range of published values for similar tests. We conclude that the proposed a priori method yields acceptable simulations with only a 50% probability, a figure which may be greatly increased through a posteriori calibration. Modellers should thus exercise caution when extrapolating their models to a large sample of pedo-climatic conditions for which they have only limited information.

Inversió cega de funcions no-lineals mitjançant un procés de Gaussianització

En aquest treball es presenta un nou mètode per a la inversió cega de funcions no-lineals mitjançant la gaussianització del senyal observat. El mètode es basa en restituir el caràcter aproximadament gaussià que presenta un senyal filtrat, gràcies al teorema del límit central,que ha vist canviada la seva distribució per l’efecte d’una funció no-lineal. Inicialment, doncs,aquest mètode és útil per a la inversió de sistemes de Wiener, tot i que en els darrers experiments realitzats s’han obtingut resultats interessants en sistemes purament no-lineals. El treball presenta dues possibles parametritzacions, la primera basada en xarxes neurals i la segona en polinomis. En els dos casos s’aconsegueix invertir la funció desconeguda sense tenir cap coneixement a priori ni del senyal original, ni del filtre, ni de la funció no-lineal que volem invertir.

La raó circular

És un text epistemològic sobre les qüestions cognitives circulars que apareixen: a) Quan el subjecte forma part de l’objecte estudiat; b) En la recerca de les bases del coneixement; c) Al voler justificar la inducció; d) En algunes interpretacions filosòfiques i científiques. S’hi explica l’estat del punt a) el més problemàtic, i s’aclareixen els altres tres punts: els b) i c) pel fet científic que l’evolució cognitiva humana ha anat acoblada a l’evolució biològica, la qual ha generat els a priori kantians i altres innatismes. El d) perquè la formació del coneixement i de la ciència es progressiva, passant una i altra vegada sobre el que ja s’havia tractat però ascendint alhora i ampliant el panorama, tal com fa una escala de cargol.

Avaluació dels algorismes d'encaminament per a una NoC amb topologia Mesh 2D

Aquest projecte presenta una avaluació de les diferents alternatives d'encaminament per a una NoC amb una topologia mesh 2D. Per tal d'exposar aquestes alternatives s'ha estudiat la composició d'un router implementat amb l'algorisme determinista XY i s'ha adaptat per tal que aquest suportés els algorismes parcialment adaptatius West First, North Last i Negative First. Un cop tenim els routers implementats es disposa un estudi dels diferents algorismes i com cadascun d'aquests actuen en front uns mateixos estímuls per tal de crear una comparativa entre ells que ens faciliti una elecció a priori.

L’ètica de la investigació aeroespacial: anàlisi de dades, de justificacions oficials i de criteris ètics

Treball de recerca realitzat per una alumna d’ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l’any 2008. La recerca aeroespacial avui forma part d’un complex aparell productiu i institucional. Però, quin paper ha de jugar aquesta activitat aristocràtica en un món de desigualtats i d’injustícies socials? Quin paper hi juga, de fet? Quins mecanismes i quins criteris hi ha darrere les decisions en aquest àmbit? Disposem de criteris ètics per avaluar-ne l’oportunitat? En la mesura que un pressupost implica una quantificació en diners de les prioritats d’una societat, és necessari avaluar èticament les inversions en aquest àmbit. Per poder respondre sense simplificar els interrogants plantejats, calia dividir la recerca en tres parts: investigació sobre els organismes públics i els programes concrets que s’encarreguen de gestionar la recerca en matèria aeroespacial; a partir d’aquí, determinació de les justificacions de la recerca que oferien aquestes institucions i anàlisi d’aquestes justificacions a la llum de les dades històriques de què disposem, i, finalment, després d’una consulta prèvia amb especialistes en la matèria, avaluació ètica de les qüestions plantejades a partir dels criteris d’alguns dels filòsofs principals en l’àmbit de l’ètica. L’anàlisi ètica de les dades assolides s’ha desenvolupat considerant, entre altres, criteris d’utilitat, de responsabilitat, de prudència i de justícia. Finalment, s’ha cregut oportú cedir la paraula al criteri aristotèlic de prudència, segons el qual és impossible i indesitjable establir a priori una avaluació d’allò que està bé o malament, ja que l’encert ètic sempre restarà pendent d’una valoració molt acurada de les circumstàncies de l’acció, valoració que, d’altra banda, caldrà actualitzar constantment en funció dels canvis històrics, socials i econòmics.

Indicadors de l'estructura sòcio-afectiva en el rendiment dels esports col·lectius

The present work carries out an analysis about which elements of the socioaffective structure take more importance for different male team sports coaches. Data obtaining carries out by using a survey applied directly by interview. In the first part, the interviewed coaches were asked to point out the indicators of the stated structure they considered more important, using a previous selection. In the second part, using a qualitative technique, the interviewed coaches were asked to explain own strategies to work, to control or to evaluate the indicators they pointed out as important in the first part. Analysis show that most of the coaches gave great importance to this structure (80% of the values are over 4 points on a top 5 points scale), and all of them had their own strategies to deal with the structure in their sports.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

On the density distribution across space: a probabilistic approach

This paper aims at providing a Bayesian parametric framework to tackle the accessibility problem across space in urban theory. Adopting continuous variables in a probabilistic setting we are able to associate with the distribution density to the Kendall's tau index and replicate the general issues related to the role of proximity in a more general context. In addition, by referring to the Beta and Gamma distribution, we are able to introduce a differentiation feature in each spatial unit without incurring in any a-priori definition of territorial units. We are also providing an empirical application of our theoretical setting to study the density distribution of the population across Massachusetts.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Un aspecte semàntic dels termes generals : la rigidesa

L'objectiu de la recerca és determinar quina és la noció de rigidesa més adient per als termes generals. Els termes generals són els que, per oposició als termes singulars, es poden aplicar a més d'un individu o exemplar, com per exemple 'tigre', 'aigua', 'bolígraf'. Des de Kripke es considera que alguns termes singulars, com els noms propis, són rígids. Un terme singular és rígid quan designa el mateix individu o objecte en tot món possible. Així 'Sòcrates' és un terme rígid perquè designa el mateix individu, Sòcrates, en tota circumstància contrafàctica. Kripke va proposar que alguns termes generals, com els termes de gènere natural, tals com 'aigua', 'calor' o 'tigre' també són rígids, però no va donar cap formulació precisa de la rigidesa per a termes generals. Des de llavors s'han proposat bàsicament dues concepcions de la rigidesa per a aquests termes: la que els considera designadors rígids i la que els considera aplicadors rígids. L'anàlisi de les dues concepcions pretén determinar quina és la millor comprensió de la rigidesa per a aquests termes, resultant la concepció dels aplicadors rígids indesitjable fonamentalment pels seus compromisos metafísics i allunyats de la semàntica.