Multivariate Hierarchical Copulas with Shocks

A transformation to obtain new multivariate hierarchical copulas, starting with an arbitrary copula, is introduced. In addition to the hierarchical structure, the presented construction principle explicitly supports singular components. These may be interpreted as the effect of local or global shocks to the underlying random variables. A large spectrum of dependence patterns can be achieved by the presented transformation, which seems promising for practical applications. Moreover, copulas arising from this construction are similarly admissible with respect to analytical tractability and sampling routines as the original copula. Finally, several well-known families of copulas may be interpreted as special cases.     

Overconvergent modular sheaves and modular forms for GL 2/F

Given a totally real field F and a prime integer p which is unramified in F, we construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of, so called, overconvergent Hilbert modular sheaves. We prove that the classical Hilbert modular forms of integral weights are overconvergent in our sense. We compare our notion with Katz’s definition of p-adic Hilbert modular forms. For F = ?, we prove that our notion of (families of) overconvergent elliptic modular forms coincides with those of R. Coleman and V. Pilloni.     

A non-isothermal Ginzburg–Landau model in superconductivity: Existence,uniqueness and asymptotic behaviour

In this paper we study a Ginzburg–Landau model which describes the behaviour of a superconducting material including thermal effects. We extend the traditional formulation of the problem, by introducing the temperature as an additional state variable. Accordingly, together with the Gor’kov–Eliashberg system, we introduce an evolution equation for the absolute temperature. We examine in detail the case which allows only variations of the concentration of superconducting electrons and of the temperature, neglecting the electromagnetic field. For this problem existence and uniqueness of the solution are shown. Finally we analyze the asymptotic behaviour of the solutions, proving that the system possesses a global attractor.     

Direct and Inverse Problems for a Phase-Field Model with Memory

We consider a semilinear integrodifferential system in non-normal form. Such a system is a generalization of the one that arises in the phase-field theory with memory. We prove an abstract existence and uniqueness theorem and a continuous dependence result for the direct problem. Reformulating the direct problem in a suitable way we prove that the identification problem admits a unique solution.     

Long‐range dependence and performance in telecom networks

Telecommunications systems have recently undergone significant innovations. These call for suitable statistical models that can properly describe the behaviour of the input traffic in a network. Here we use fractional Brownian motion (FBM) to model cumulative traffic network, thus taking into account the possible presence of long‐range dependence in the data. A Bayesian approach is devised in such a way that we are able to: (a) estimate the Hurst parameter H of the FBM; (b) estimate the overflow probability which is a parameter measuring the quality of service of a network: (c) develop a test for comparing the null hypothesis of long‐range dependence in the data versus the alternative of short‐range dependence. In order to achieve these inferential results, we elaborate an MCMC sampling scheme whose output enables us to obtain an approximation of the quantities of interest. An application to three real datasets, corresponding to three different levels of traffic, is finally considered. Copyright © 2004 John Wiley & Sons, Ltd.     

Direct and inverse problems for degenerate differential equations

We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on the abstract problem to work on \((-\infty ,\infty )\). Related inverse problems are discussed, too. All general results are applied to some systems of partial differential equations. Inverse problems for degenerate evolution integro-differential equations might be described, too.     

Objective bayesian analysis of the Yule–Simon distribution with applications

The Yule–Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, has ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule–Simon distribution. In particular, we discuss the Jeffreys prior and a loss-based prior, which has recently appeared in the literature. We illustrate the performance of the derived priors through a simulation study and the analysis of real datasets.     

Straight-Line Rectangular Drawings of Clustered Graphs

We show that every c-planar clustered graph has a straight-line c-planar drawing in which each cluster is represented by an axis-parallel rectangle, thus solving a problem posed by Eades, Feng, Lin, and Nagamochi (Algorithmica 44(1):1–32, 2006).