In this paper we analyze replica symmetry breaking in attractor neural networks with non-monotone activation function. We study the non-monotone version of the Edinburgh model, which allows the control of the domains of attraction by the stability parameter K, and we compute, at one step of symmetry breaking, storage capacity and, for the strongly dilute model, the domains of attraction of the stable fixed points.

Collocation and quadrature methods for Cauchy singular integral equations on an interval with variable coefficients are studied. Convergence rates are proved in weighted uniform and uniform norms.

Retrieving of temperature profiles from radiance data obtained by interferograms is an important problem in remote sensing of atmosphere. The great amount of data to process and the ill-conditioning of the problem demand objective procedures able to reduce the error of the retrieval. In this paper we use generalized singular value decomposition (GSVD), which is able to deal with deficient-rank smoothing functionals in order to regularize the problem and the L-curve criterion for choosing the optimal regularization parameter and then the proper amount of smoothing. Some test problems of temperature inversion are carried out to examine the effectiveness of the methods considered; to this purpose we use some indicators based on the bias and variance of the output temperature. We show that the objective L-curve criterion does not perform fully satisfactory in estimating the optimal regularization parameter and then in reducing output error at best. In any case GSVD plus L-curve criterion prove effective in reducing output error (with respect to the ordinary least squares method). In particular, reduction of variance over troposphere and stratosphere is high for all tested cases; reduction of bias depends on the first-guess profile. An important role in the latter is played by the choice of deficient-rank smoothing functional.

progetto coordinato da D. Mansutti con 4 UU.OO. - titolo del progetto della U.O. dell'IAC, "Modelli numerici per la cristallizzazione da fuso in microgravita': modello globale, convezione naturale nel fuso e propagazione di onde nel cristallo".

We consider a class of integral equations of Volterra type with constant coefficients containing a logarithmic difference kernel. This equation can be transformed into an equivalent singular equation of Cauchy type which allows us to give the explicit formula for the solution. The numerical method proposed in this paper consists of applying the Lagrange interpolation to the inner Cauchy type singular integral in the latter formula after subtracting the singularity. For the error of this method weighted norm estimates as well as estimates on discrete subsets of knots are given. The paper concludes with some numerical examples. © 1995 Rocky Mountain Mathematics Consortium.

Reaction-diffusion systems with cross-diffusion are analyzed here for modeling the population dynamics of epidemic systems. In this paper specific attention is devoted to the numerical analysis and simulation of such systems to show that, far from possible pathologies, the qualitative behaviour of the systems may well interpret the dynamics of real systems.

Boundedness and convergence of the extended Lagrange interpolating operator are investigated in the space L_u,t^p of Sobolev type.

The authors study the convergence and the stability of a collocation and a discrete collocation method for Cauchy singular integral equations with weakly singular perturbation kernel in some weighted uniform norms. Uniform error estimates are also given.

Viene descritta una metodologia basata sull'analisi semantica e sull'uso delle radici lessicali per costruire un thesaurus estraendo parole chiave da testi di un archivio bibliografico.

Using the simulated annealing technique we re-examine the role played by the minimization of the physicochemical distances between amino acids during the origin of the organization of the genetic code. The results are discussed in the context of the various hypotheses proposed to explain how amino acids were allocated in the genetic code.