Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

Estimation of inelastic seismic material properties of a surgical sea-bed from multi-component marine seismic data

To date, state-of-the-art seismic material parameter estimates from multi-component sea-bed seismic data are based on the assumption that the sea-bed consists of a fully elastic half-space. In reality, however, the shallow sea-bed generally consists of soft, unconsolidated sediments that are characterized by strong to very strong seismic attenuation. To explore the potential implications, we apply a state-of-the-art elastic decomposition algorithm to synthetic data for a range of canonical sea-bed models consisting of a viscoelastic half-space of varying attenuation. We find that in the presence of strong seismic attenuation, as quantified by Q-values of 10 or less, significant errors arise in the conventional elastic estimation of seismic properties. Tests on synthetic data indicate that these errors can be largely avoided by accounting for the inherent attenuation of the seafloor when estimating the seismic parameters. This can be achieved by replacing the real-valued expressions for the elastic moduli in the governing equations in the parameter estimation by their complex-valued viscoelastic equivalents. The practical application of our parameter procedure yields realistic estimates of the elastic seismic material properties of the shallow sea-bed, while the corresponding Q-estimates seem to be biased towards too low values, particularly for S-waves. Given that the estimation of inelastic material parameters is notoriously difficult, particularly in the immediate vicinity of the sea-bed, this is expected to be of interest and importance for civil and ocean engineering purposes.

Feasibility and electromagnetic compatibility study of the ClearPEM front-end electronics for simultaneous PET-MR imaging

In this work we present a first feasibility study of the ClearPEM technology for simultaneous PET-MR imaging. The mutual electromagnetic interference (EMI) effects between both systems were evaluated on a 7 T magnet by characterizing the response behavior of the ClearPEM detectors and front-end electronics to pulsed RF power and switched magnetic field gradients; and by analyzing the MR system performance degradation from noise pickup into the RF receiver chain, and from magnetic susceptibility artifacts caused by PET front-end materials.

L'application de la spectroscopie Raman en criminalistique pour l'analyse du colorant des fibres textiles en acrylique, coton et laine

RESUME La méthode de la spectroscopie Raman est une technique d'analyse chimique basée sur l'exploitation du phénomène de diffusion de la lumière (light scattering). Ce phénomène fut observé pour la première fois en 1928 par Raman et Krishnan. Ces observations permirent à Raman d'obtenir le Prix Nobel en physique en 1930. L'application de la spectroscopie Raman a été entreprise pour l'analyse du colorant de fibres textiles en acrylique, en coton et en laine de couleurs bleue, rouge et noire. Nous avons ainsi pu confirmer que la technique est adaptée pour l'analyse in situ de traces de taille microscopique. De plus, elle peut être qualifiée de rapide, non destructive et ne nécessite aucune préparation particulière des échantillons. Cependant, le phénomène de la fluorescence s'est révélé être l'inconvénient le plus important. Lors de l'analyse des fibres, différentes conditions analytiques ont été testées et il est apparu qu'elles dépendaient surtout du laser choisi. Son potentiel pour la détection et l'identification des colorants imprégnés dans les fibres a été confirmé dans cette étude. Une banque de données spectrale comprenant soixante colorants de référence a été réalisée dans le but d'identifier le colorant principal imprégné dans les fibres collectées. De plus, l'analyse de différents blocs de couleur, caractérisés par des échantillons d'origine inconnue demandés à diverses personnes, a permis de diviser ces derniers en plusieurs groupes et d'évaluer la rareté des configurations des spectres Raman obtenus. La capacité de la technique Raman à différencier ces échantillons a été évaluée et comparée à celle des méthodes conventionnelles pour l'analyse des fibres textiles, à savoir la micro spectrophotométrie UV-Vis (MSP) et la chromatographie sur couche mince (CCM). La technique Raman s'est révélée être moins discriminatoire que la MSP pour tous les blocs de couleurs considérés. C'est pourquoi dans le cadre d'une séquence analytique nous recommandons l'utilisation du Raman après celle de la méthode d'analyse de la couleur, à partir d'un nombre de sources lasers le plus élevé possible. Finalement, la possibilité de disposer d'instruments équipés avec plusieurs longueurs d'onde d'excitation, outre leur pouvoir de réduire la fluorescence, permet l'exploitation d'un plus grand nombre d'échantillons. ABSTRACT Raman spectroscopy allows for the measurement of the inelastic scattering of light due to the vibrational modes of a molecule when irradiated by an intense monochromatic source such as a laser. Such a phenomenon was observed for the first time by Raman and Krishnan in 1928. For this observation, Raman was awarded with the Nobel Prize in Physics in 1930. The application of Raman spectroscopy has been undertaken for the dye analysis of textile fibers. Blue, black and red acrylics, cottons and wools were examined. The Raman technique presents advantages such as non-destructive nature, fast analysis time, and the possibility of performing microscopic in situ analyses. However, the problem of fluorescence was often encountered. Several aspects were investigated according to the best analytical conditions for every type/color fiber combination. The potential of the technique for the detection and identification of dyes was confirmed. A spectral database of 60 reference dyes was built to detect the main dyes used for the coloration of fiber samples. Particular attention was placed on the discriminating power of the technique. Based on the results from the Raman analysis for the different blocs of color submitted to analyses, it was possible to obtain different classes of fibers according to the general shape of spectra. The ability of Raman spectroscopy to differentiate samples was compared to the one of the conventional techniques used for the analysis of textile fibers, like UV-Vis Microspectrophotometry (UV-Vis MSP) and thin layer chromatography (TLC). The Raman technique resulted to be less discriminative than MSP for every bloc of color considered in this study. Thus, it is recommended to use Raman spectroscopy after MSP and light microscopy to be considered for an analytical sequence. It was shown that using several laser wavelengths allowed for the reduction of fluorescence and for the exploitation of a higher number of samples.

Direct simulation of interface dynamics: linking capillary pressure, interfacial area and surface energy

We perform direct numerical simulations of drainage by solving Navier- Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid-fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and to model the transition from stable flow to viscous fingering, we focus on the definition of macroscopic capillary pressure. When the fluids are at rest, the difference between inlet and outlet pressures and the difference between the intrinsic phase average pressure coincide with the capillary pressure. However, when the fluids are in motion these quantities are dominated by viscous forces. In this case, only a definition based on the variation of the interfacial energy provides an accurate measure of the macroscopic capillary pressure and allows separating the viscous from the capillary pressure components.

Incremental neural networks for function approximation

A new strategy for incremental building of multilayer feedforward neural networks is proposed in the context of approximation of functions from R-p to R-q using noisy data. A stopping criterion based on the properties of the noise is also proposed. Experimental results for both artificial and real data are performed and two alternatives of the proposed construction strategy are compared.

A comparative long-memory Analysis between Spanish, Mexican and U.S. interest rates

Evidence exists that many natural facts are described better as a fractal. Although fractals are very useful for describing nature, it is also appropiate to review the concept of random fractal in finance. Due to the extraordinary importance of Brownian motion in physics, chemistry or biology, we will consider the generalization that supposes fractional Brownian motion introduced by Mandelbrot.The main goal of this work is to analyse the existence of long range dependence in instantaneous forward rates of different financial markets. Concretelly, we perform an empirical analysis on the Spanish, Mexican and U.S. interbanking interest rate. We work with three time series of daily data corresponding to 1 day operations from 28th March 1996 to 21st May 2002. From among all the existing tests on this matter we apply the methodology proposed in Taqqu, Teverovsky and Willinger (1995).

Landau damping of transverse quadrupole oscillations of an elongated Bose-Einstein condensate

We have studied the interaction between the low-lying transverse collective oscillations and the thermal excitations of an elongated Bose-Einstein condensate by means of perturbation theory. We consider a cylindrical trapped condensate and calculate the transverse elementary excitations at zero temperature by solving the linearized Gross-Pitaevskii equations in two dimensions (2D). We use them to calculate the matrix elements between the thermal excited states and the quasi-2D collective modes. The Landau damping of transverse collective modes is studied as a function of temperature. At low temperatures, the corresponding damping rate is in agreement with the experimental data for the decay of the transverse quadrupole mode, but it is too small to explain the observed slow decay of the transverse breathing mode. The reason for this discrepancy is discussed.

Exact long-time behavior of a network of oscillators under random fields

We present an exact solution for the order parameters that characterize the stationary behavior of a population of Kuramotos phase oscillators under random external fields [Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39 (Springer, Berlin, 1975), p. 420]. From these results it is possible to generate the phase diagram of models with an arbitrary distribution of random frequencies and random fields.

A comparative long-memory Analysis between Spanish, Mexican and U.S. interest rates

Evidence exists that many natural facts are described better as a fractal. Although fractals are very useful for describing nature, it is also appropiate to review the concept of random fractal in finance. Due to the extraordinary importance of Brownian motion in physics, chemistry or biology, we will consider the generalization that supposes fractional Brownian motion introduced by Mandelbrot.The main goal of this work is to analyse the existence of long range dependence in instantaneous forward rates of different financial markets. Concretelly, we perform an empirical analysis on the Spanish, Mexican and U.S. interbanking interest rate. We work with three time series of daily data corresponding to 1 day operations from 28th March 1996 to 21st May 2002. From among all the existing tests on this matter we apply the methodology proposed in Taqqu, Teverovsky and Willinger (1995).

On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.

A non-linear VAD for noisy environments

This paper deals with non-linear transformations for improving the performance of an entropy-based voice activity detector (VAD). The idea to use a non-linear transformation has already been applied in the field of speech linear prediction, or linear predictive coding (LPC), based on source separation techniques, where a score function is added to classical equations in order to take into account the true distribution of the signal. We explore the possibility of estimating the entropy of frames after calculating its score function, instead of using original frames. We observe that if the signal is clean, the estimated entropy is essentially the same; if the signal is noisy, however, the frames transformed using the score function may give entropy that is different in voiced frames as compared to nonvoiced ones. Experimental evidence is given to show that this fact enables voice activity detection under high noise, where the simple entropy method fails.

Direct numerical simulations of interface dynamics to link capillary pressure and total surface energy

The flow of two immiscible fluids through a porous medium depends on the complex interplay between gravity, capillarity, and viscous forces. The interaction between these forces and the geometry of the medium gives rise to a variety of complex flow regimes that are difficult to describe using continuum models. Although a number of pore-scale models have been employed, a careful investigation of the macroscopic effects of pore-scale processes requires methods based on conservation principles in order to reduce the number of modeling assumptions. In this work we perform direct numerical simulations of drainage by solving Navier-Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid-fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and model the transition from stable flow to viscous fingering, we focus on the macroscopic capillary pressure and we compare different definitions of this quantity under quasi-static and dynamic conditions. We show that the difference between the intrinsic phase-average pressures, which is commonly used as definition of Darcy-scale capillary pressure, is subject to several limitations and it is not accurate in presence of viscous effects or trapping. In contrast, a definition based on the variation of the total surface energy provides an accurate estimate of the macroscopic capillary pressure. This definition, which links the capillary pressure to its physical origin, allows a better separation of viscous effects and does not depend on the presence of trapped fluid clusters.