The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

Simulation results and applications of an advection bounded scheme to practical flows

This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena.

EQUIVALENCE OF REAL MILNOR FIBRATIONS FOR QUASI-HOMOGENEOUS SINGULARITIES

We show that for real quasi-homogeneous singularities f : (R-m, 0) -> (R-2, 0) with isolated singular point at the origin, the projection map of the Milnor fibration S-epsilon(m-1) \ K-epsilon -> S-1 is given by f/parallel to f parallel to. Moreover, for these singularities the two versions of the Milnor fibration, on the sphere and on a Milnor tube, are equivalent. In order to prove this, we show that the flow of the Euler vector field plays and important role. In addition, we present, in an easy way, a characterization of the critical points of the projection (f/parallel to f parallel to) : S-epsilon(m-1) \ K-epsilon -> S-1.

Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

A transmission problem for beams on nonlinear supports

A transmission problem involving two Euler-Bernoulli equations modeling the vibrations of a composite beam is studied. Assuming that the beam is clamped at one extremity, and resting on an elastic bearing at the other extremity, the existence of a unique global solution and decay rates of the energy are obtained by adding just one damping device at the end containing the bearing mechanism.

Uso da monitorização hemodinâmica contínua não invasiva na insuficiência cardíaca descompensada

FUNDAMENTO: A avaliação clínico-hemodinâmica à beira do leito e o uso do cateter de artéria pulmonar para a estimativa de dados hemodinâmicos têm sido utilizados na insuficiência cardíaca descompensada. Entretanto, não existem dados com o uso da monitorização hemodinâmica contínua não invasiva. OBJETIVO: Comparar as medidas obtidas com a monitorização hemodinâmica não invasiva com as invasivas em pacientes com insuficiência cardíaca descompensada e refratária ao tratamento. MÉTODOS: As medidas hemodinâmicas não invasivas foram obtidas através da monitorização contínua da pressão arterial sistêmica pelo modelo de ondas de pulso (modelflow) e foram comparadas com as medidas obtidas pela passagem do cateter de artéria pulmonar, simultaneamente. RESULTADOS: Foram realizadas 56 medidas em 14 pacientes estudados em dias e horários diferentes. O índice de correlação entre as medidas da pressão arterial sistólica foi de r = 0,26 (IC 95% = 0,00 a 0,49, p = 0,0492) e da diastólica de r = 0,50 (IC 95% = 0,27 a 0,67, p < 0,0001). A correlação foi de r = 0,55 (IC 95% = 0,34 a 0,71, p 0,0001) para o índice cardíaco e de r = 0,32 (IC 95% = 0,06 a 0,53, p = 0,0178) para a resistência vascular sistêmica. CONCLUSÃO: Houve correlação entre as medidas hemodinâmicas não invasivas quando comparadas às medidas do cateter de artéria pulmonar. A monitorização hemodinâmica contínua não invasiva pode ser útil para pacientes internados com insuficiência cardíaca descompensada.

A Skyrme-like model with an exact BPS bound

We propose a new Skyrme-like model with fields taking values on the sphere S3 or, equivalently, on the group SU(2). The action of the model contains a quadratic kinetic term plus a quartic term which is the same as that of the Skyrme-Faddeev model. The novelty of the model is that it possess a first order Bogomolny type equation whose solutions automatically satisfy the second order Euler-Lagrange equations. It also possesses a lower bound on the static energy which is saturated by the Bogomolny solutions. Such Bogomolny equation is equivalent to the so-called force free equation used in plasma and solar Physics, and which possesses large classes of solutions. An old result due to Chandrasekhar prevents the existence of finite energy solutions for the force free equation on the entire three- dimensional space R3. We construct new exact finite energy solutions to the Bogomolny equations for the case where the space is the three-sphere S3, using toroidal like coordinates.

A variational approach to camera motion smoothing

[EN] In this paper we study a variational problem derived from a computer vision application: video camera calibration with smoothing constraint. By video camera calibration we meanto estimate the location, orientation and lens zoom-setting of the camera for each video frame taking into account image visible features. To simplify the problem we assume that the camera is mounted on a tripod, in such case, for each frame captured at time t , the calibration is provided by 3 parameters : (1) P(t) (PAN) which represents the tripod vertical axis rotation, (2) T(t) (TILT) which represents the tripod horizontal axis rotation and (3) Z(t) (CAMERA ZOOM) the camera lens zoom setting. The calibration function t -> u(t) = (P(t),T(t),Z(t)) is obtained as the minima of an energy function I[u] . In thIs paper we study the existence of minima of such energy function as well as the solutions of the associated Euler-Lagrange equations.

3-D geometry reconstruction using a color image stereo pair and partial differential equations

[EN] In this work, we present a new model for a dense disparity estimation and the 3-D geometry reconstruction using a color image stereo pair. First, we present a brief introduction to the 3-D Geometry of a camera system. Next, we propose a new model for the disparity estimation based on an energy functional. We look for the local minima of the energy using the associate Euler-Langrage partial differential equations. This model is a generalization to color image of the model developed in, with some changes in the strategy to avoid the irrelevant local minima. We present some numerical experiences of 3-D reconstruction, using this method some real stereo pairs.

Dense disparity map estimation respecting image discontinuities

[EN] We present an energy based approach to estimate a dense disparity map from a set of two weakly calibrated stereoscopic images while preserving its discontinuities resulting from image boundaries. We first derive a simplified expression for the disparity that allows us to estimate it from a stereo pair of images using an energy minimization approach. We assume that the epipolar geometry is known, and we include this information in the energy model. Discontinuities are preserved by means of a regularization term based on the Nagel-Enkelmann operator. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method The resulting parabolic problem has a unique solution. In order to reduce the risk to be trapped within some irrelevant local minima during the iterations, we use a focusing strategy based on a linear scalespace. Experimental results on both synthetic and real images arere presented to illustrate the capabilities of this PDE and scale-space based method.

A variational approach to 3D geometry reconstruction from two or multiple views

[EN] In the last years we have developed some methods for 3D reconstruction. First we began with the problem of reconstructing a 3D scene from a stereoscopic pair of images. We developed some methods based on energy functionals which produce dense disparity maps by preserving discontinuities from image boundaries. Then we passed to the problem of reconstructing a 3D scene from multiple views (more than 2). The method for multiple view reconstruction relies on the method for stereoscopic reconstruction. For every pair of consecutive images we estimate a disparity map and then we apply a robust method that searches for good correspondences through the sequence of images. Recently we have proposed several methods for 3D surface regularization. This is a postprocessing step necessary for smoothing the final surface, which could be afected by noise or mismatch correspondences. These regularization methods are interesting because they use the information from the reconstructing process and not only from the 3D surface. We have tackled all these problems from an energy minimization approach. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method.

A PDE model for computing the optical flow

[EN] In this paper we present a new model for optical flow calculation using a variational formulation which preserves discontinuities of the flow much better than classical methods. We study the Euler-Lagrange equations asociated to the variational problem. In the case of quadratic energy, we show the existence and uniqueness of the corresponding evolution problem. Since our method avoid linearization in the optical flow constraint, it can recover large displacement in the scene. We avoid convergence to irrelevant local minima by embedding our method into a linear scale-space framework and using a focusing strategy from coarse to fine scales.

Reconstrucción 3-D a partir de un par estéreo de imágenes en color utilizando ecuaciones en derivadas parciales

[ES] En este trabajo proponemos un nuevo modelo para el cálculo de la disparidad y la reconstrucción 3-D a partir de un sistema estéreo compuesto por 2 imágenes en color. Proponemos un nuevo modelo para el cálculo de la disparidad basado en un criterio de energía. Para calcular los mínimos de este funcional de energía utilizamos la ecuación en derivadas parciales de Euler-Langrage asociada. Este modelo es una extensión a imágenes color del modelo desarrollado en "L. Alvarez, R. Deriche, J. Sánchez and J. Weickert, Dense disparity map estimation respecting image discontinuities : A PDE and Scale-Space Based Approach. INRIA Rapport de Recherche Nº 3874, 2000". Con algunos cambios en la estrategia parav evitar caer en mínimos locales de la energía. Por último presentamos algunas experiencias numéricas de la reconstrucción 3-D obtenida con este método en algunos pares estéreos de imágenes reales.

3-D Boundary element-finite element method for the dynamic analysis of piled buildings.

[EN]A boundary element-finite element model is presented for the three-dimensional dynamic analysis of piled buildings in the frequency domain. Piles are modelled as compressible Euler-Bernoulli beams founded on a linear, isotropic, viscoelastic, zoned-homogeneous, unbounded layered soil, while multi-storey buildings are assumed to be comprised of vertical compressible piers and rigid slabs.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.