Gap probabilities for the cardinal sine

We study the zero set of random analytic functions generated by a sum of the cardinal sine functions which form an orthogonal basis for the Paley-Wiener space. As a model case, we consider real-valued Gaussian coefficients. It is shown that the asymptotic probability that there is no zero in a bounded interval decays exponentially as a function of the length.

Kuranishi type Moduli Spaces for proper CR submersions fibering over the circle

Kuranishi's fundamental result (1962) associates to any compact complex manifold X&sub&0&/sub& a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to X&sub&0&/sub&. In this paper, we give an analogous statement for Levi-flat CR manifolds fibering properly over the circle by describing explicitely an infinite-dimensional Kuranishi type local moduli space of Levi-flat CR structures. We interpret this result in terms of Kodaira-Spencer deformation theory making clear the likenesses as well as the differences with the classical case. The article ends with applications and examples.

Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians

In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians.

Speed of reaction-diffusion fronts in spatially heterogeneous media

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic results have been compared with numerical results exhibiting a good agreement. Finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities

A systematic and feasible method for computing nuclear contributions to electrical properties of polyatomic molecules

An analytic method to evaluate nuclear contributions to electrical properties of polyatomic molecules is presented. Such contributions control changes induced by an electric field on equilibrium geometry (nuclear relaxation contribution) and vibrational motion (vibrational contribution) of a molecular system. Expressions to compute the nuclear contributions have been derived from a power series expansion of the potential energy. These contributions to the electrical properties are given in terms of energy derivatives with respect to normal coordinates, electric field intensity or both. Only one calculation of such derivatives at the field-free equilibrium geometry is required. To show the useful efficiency of the analytical evaluation of electrical properties (the so-called AEEP method), results for calculations on water and pyridine at the SCF/TZ2P and the MP2/TZ2P levels of theory are reported. The results obtained are compared with previous theoretical calculations and with experimental values

Anàlisi del sistema productiu i comercial del vi de la Tarraconensis a partir de la combinació de metodologies

Des del segon quart del s. I aC i, especialment, durant el regnat d’August, es va desenvolupar a l’antiga província Tarraconensis un sistema productiu centrat en l’explotació agrària vitivinícola amb una finalitat clarament comercial. La majoria d’assentament vitivinícoles es troben emplaçats al litoral català, associats de vegades a figlinae que fabricaven les àmfores per al transport i comerç de l’excedent vinícola. No obstant, a l’àrea del Vallès Occidental i del Baix Llobregat es troben una sèrie de vil•les vinculades a la producció de vi i a la fabricació d’àmfores que han proporcionat restes molt significatives sobre la contribució d’aquesta zona a l’expansió econòmica de la província. La caracterització arqueològica i arqueomètrica d’un gran nombre d’àmfores procedents de diversos tallers ceràmics situats al Vallès Occidental i al Baix Llobregat, utilitzant diverses tècniques d’anàlisi química, mineralògica i petrogràfica, ha portat a establir quins tipus d’àmfores es van fabricar a cada taller i de quina manera. S’han identificat alguns dels processos tecnològics de la cadena operativa: la selecció i processat de les matèries primeres per conformar la pasta procedents, generalment, de l’àrea on es troba cada centre de producció, el modelatge, l’assecat i la cocció de les peces. En alguns dels casos analitzats, s’ha identificat quins tipus de contenidors van ser importants a l’establiment i la seva provinença. La integració d’aquests resultats en la base de dades analítica que disposa l’ERAAUB ha permès avaluar el grau d’estandardització dels processos tecnològics en aquesta àrea. La contrastació final amb les dades històriques i arqueològiques contribueix al coneixement arqueològic de les àmfores vinàries de la Tarraconensis i, a través d’elles, al coneixement de les societats que les van fabricar, comercialitzar i utilitzar.

Estimation of protein coding density in a corpus of DNA sequence data

A number of experimental methods have been reported for estimating the number of genes in a genome, or the closely related coding density of a genome, defined as the fraction of base pairs in codons. Recently, DNA sequence data representative of the genome as a whole have become available for several organisms, making the problem of estimating coding density amenable to sequence analytic methods. Estimates of coding density for a single genome vary widely, so that methods with characterized error bounds have become increasingly desirable. We present a method to estimate the protein coding density in a corpus of DNA sequence data, in which a ‘coding statistic’ is calculated for a large number of windows of the sequence under study, and the distribution of the statistic is decomposed into two normal distributions, assumed to be the distributions of the coding statistic in the coding and noncoding fractions of the sequence windows. The accuracy of the method is evaluated using known data and application is made to the yeast chromosome III sequence and to C.elegans cosmid sequences. It can also be applied to fragmentary data, for example a collection of short sequences determined in the course of STS mapping.

Definitional verbal patterns for semantic relation extraction

In this paper we present a description of the role of definitional verbal patterns for the extraction of semantic relations. Several studies show that semantic relations can be extracted from analytic definitions contained in machine-readable dictionaries (MRDs). In addition, definitions found in specialised texts are a good starting point to search for different types of definitions where other semantic relations occur. The extraction of definitional knowledge from specialised corpora represents another interesting approach for the extraction of semantic relations. Here, we present a descriptive analysis of definitional verbal patterns in Spanish and the first steps towards the development of a system for the automatic extraction of definitional knowledge.

Ricercando tra i Registri

My final project is to show the development of the language and the style of the double bass and its change of role through different influences. To accomplish this I decided to make an analytic overview of those double bass players that started to use a different and not traditional approach on the instrument. Later, I focused on the bassists and composers who influenced me the most in the latest period of my study career by partly analysing their playing and their composition. Another part of my work was concerned with creating a personal connection with those musicians, who I consider idols of mine. I did this through interviews, to try to understand their creative process on the instrument and in the composition and to deeply comprehend their personal point of view about the evolution of the double bass. At the same time my interest for the compositional aspect was growing together with the necessity to discover my own voice as a musician. Subsequently I made an analysis of my compositions to underline and to get conscious about my personal influences and evolution. Concluding from this, I have created a complete overview and deepened my understanding for the modern approach in Jazz double bass.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Systematics of properties of the electron gas in deep-etched quantum wires

An efficient method is developed for an iterative solution of the Poisson and Schro¿dinger equations, which allows systematic studies of the properties of the electron gas in linear deep-etched quantum wires. A much simpler two-dimensional (2D) approximation is developed that accurately reproduces the results of the 3D calculations. A 2D Thomas-Fermi approximation is then derived, and shown to give a good account of average properties. Further, we prove that an analytic form due to Shikin et al. is a good approximation to the electron density given by the self-consistent methods.

Diffractive J/Psi photoproduction in a dual model

J/psi photoproduction is studied in the framework of the analytic S-matrix theory. The differential and integrated elastic cross sections for J/psi photoproduction are calculated from a dual amplitude with Mandelstam analyticity. It is argued that, at low energies, the background, which is the low-energy equivalent of the high-energy diffraction, replaces the Pomeron exchange. The onset of the high-energy Pomeron dominance is estimated from the fits to the data.

Exclusive J/Psi electroproduction in a dual model

Exclusive J/Psi electroproduction is studied in the framework of the analytic S-matrix theory. The differential and integrated elastic cross sections are calculated using the modified dual amplitude with Mandelstam analyticity model. The model is applied to the description of the available experimental data and proves to be valid in a wide region of the kinematical variables s, t, and Q(2). Our amplitude can be used also as a universal background parametrization for the extraction of tiny resonance signals.

Excitability transitions and wave dynamics under spatiotemporal structured noise

We present an analytic and numerical study of the effects of external fluctuations in active media. Our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction-diffusion equations. As a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise, for example, target patterns created out of noise and traveling or spiral waves sustained by noise. Our study includes the case of realistic noises with temporal and spatial structures.