We introduce a geometry of interaction model given by an algebra of clauses equipped with resolution (following \cite{Girard95d}) which proofs of Elementary Linear Logic can be interpreted into. In order to extend geometry of interaction computation (the so called {\em execution formula}) to a wider class of programs in the algebra than just those coming from proofs, we define a variant of execution (called {\em weak execution}). Its application to any program of clauses is shown to terminate with a bound on the number of steps which is elementary in the size of the program. We establish that weak execution coincides with standard execution on programs coming from proofs.

The Italian Ministry of Education in collaboration of the Italian National Research Council are engaged in joint activities concerning the modeling, design and prototype implementation of an adaptive e-framework supporting the interactions of various actors of the national teacher training system. The framework includes patterns of static and adaptive versions for resources-services allocation and management.

The Infrared Atmospheric Sounding Interferometer (IASI) has 8461 potential channels to be exploited for inversions of geophysical parameters. In this paper we analyse two different strategies for their reduction. The first one looks for suitable spectral ranges where the inverse problem is as linear as possible; the second one is based on the cluster analysis theory. Our aim is to minimise the potential information loss evaluated by directly comparing the retrieved temperature and water vapour profiles on a complete set of test atmospheres.

A particle-based model for mesoscopic fluid dynamics is used to simulate steady and unsteady flows around a circular and a square cylinder in a two-dimensional channel for a range of Reynolds numbers between 10 and 130. Numerical results for the recirculation length, the drag coefficient, and the Strouhal number are reported and compared with previous experimental measurements and computational fluid dynamics data. The good agreement demonstrates the potential of this method for the investigation of complex flows.

The phase separation process which follows a sudden quench inside the coexistence region is considered for a binary fluid subjected to an applied shear flow. This issue is studied in the framework of the convection-diffusion equation based on a Ginzburg-Landau free energy functional in the approximation scheme introduced by Bray and Humayun [Plays. Rev. Lett. 68, 1559 (1992)]. After an early stage where domains furin and shear effects become effective the system enters a scaling regime where the typical domains sizes L-parallel to, L-perpendicular to along the flow and perpendicular to it grow as t(5/4) and t(1/4). The structure factor is characterized by the existence of four peaks, similarly to previous theoretical and experimental observations, and by exponential tails at large wavevectors.

The conformational properties of a semiflexible polymer chain, anchored at one end in a uniform force field, are studied in a simple two-dimensional model. Recursion relations are derived for the partition function and then iterated numerically. We calculate the angular fluctuations of the polymer about the direction of the force field and the average polymer configuration as functions of the bending rigidity, chain length, chain orientation at the anchoring point. and field strength.

We apply lattice Boltzmann method to study the phase separation of a two-dimensional binary fluid mixture in shear flow. The algorithm can simulate systems described by the Navier-Stokes and convection-diffusion equations. We propose a new scheme for imposing the shear flow which has the advantage of preserving mass and momentum conservation on the boundary walls without introducing slip velocities. We study how the steady Velocity profile is reached. Our main results show the presence of two typical length scales in the phase separation process, corresponding to domains with two different thicknesses.

We consider a simple exchangeable model, which accounts for heterogeneity and dependence. Based on this model, we show how, and in which sense, situations of negative aging arise in a natural way from conditions of heterogeneity among items.

We use a framework that takes into account the effects of deformation of both the solid and fluid in the solidification process, to study the solidification of a semi-infinite layer of fluid. It is shown that the time required for solidification, and the final location of the interface are significantly different form the predictions of the classical Stefan problem. A detailed numerical solution of the initial-boundary value problem is provided for a variety of values for non-dimensional parameters relevant for freezing water.

The problem of inverse statistics (statistics of distances for which the signal fluctuations are larger than a certain threshold) in differentiable signals with power law spectrum, E(k) approximately k(-alpha), 3< or =alpha<5, is discussed. We show that for these signals, with random phases, exit-distance moments follow a bifractal distribution. We also investigate two dimensional turbulent flows in the direct cascade regime, which display a more complex behavior. We give numerical evidences that the inverse statistics of 2D turbulent flows is described by a multifractal probability distribution; i.e., the statistics of laminar events is not simply captured by the exponent alpha characterizing the spectrum.

The mathematical model of some environmental physics problems is represented by a singular integral equation with an oscillatory kernel. We investigate a method for the numerical evaluation of Cauchy principal value integrals of oscillatory functions. The method is based on an interpolatory procedure at the zeros of the orthogonal polynomials with respect to a Jacobi weight. In this way, we obtain a procedure that is numerically stable and the algorithm can be implemented in a fast way yielding satisfactory numerical results. Bounds of the error and of the amplification factor are also provided.

Using the de la Vallèe Poussin interpolation at the Chebyshev zeros, the authors construct polynomial interpolating wavelets and give the corresponding decomposition and reconstruction algorithms. The involved matrices can be diagonalized by sine and cosine orthogonal matrices. So the algorithms can be realized using fast sine and cosine transforms.

An inverse diffusion problem that appears in Magnetic Resonance dosimetry is studied. The problem is shown to be equivalent to a deconvolution problem with a known kernel. To cope with the singularity of the kernel, nonlinear regularization functionals are considered which can provide regular solutions, reproduce steep gradients and impose positivity constraints. A fast deterministic algorithm for solving the involved non-convex minimization problem is used. Accurate restorations on real 256×256 images are obtained by the algorithm in a few minutes on a 266-MHz PC that allow to precisely quantitate the relative absorbed dose.

Recent studies have demonstrated the potential of dynamic contrast-enhanced magnetic resonance imaging (MRI) describing pulmonary perfusion. However, breathing motion, susceptibility artifacts, and a low signal-to-noise ratio (SNR) make automatic pixel-by-pixel analysis difficult. In the present work, we propose a novel method to compensate for breathing motion. In order to test the feasibility of this method, we enrolled 53 patients with pulmonary embolism (N = 24), chronic obstructive pulmonary disease (COPD) (N = 14), and acute pneumonia (N = 15). A crucial part of the method, an automatic diaphragm detection algorithm, was evaluated in all 53 patients by two independent observers. The accuracy of the method to detect the diaphragm showed a success rate of 92%. Furthermore, a Bayesian noise reduction technique was implemented and tested. This technique significantly reduced the noise level without removing important clinical information. In conclusion, the combination of a motion correction method and a Bayesian noise reduction method offered a rapid, semiautomatic pixel-by-pixel analysis of the lungs with great potential for research and clinical use. © 2001 Wiley-Liss, Inc.