A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.Peer Reviewe

Optimal map of the modular structure of complex networks

Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as many data as number of modules times number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and after, we use a Truncated Singular Value Decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allow us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.Comment: 21 pages, 10 figure

Montecarlo simulation of the role of defects as the melting mechanism

We study in this paper the melting transition of a crystal of fcc structure with the Lennard-Jones potential, by using isobaric-isothermal Monte Carlo simulations. Local and collective updates are sequentially used to optimize the convergence. We show the important role played by defects in the melting mechanism in favor of modern melting theories.Comment: 6 page, 10 figures included. Corrected version to appear in Phys. Rev.

Bounds for the time to failure of hierarchical systems of fracture

For years limited Monte Carlo simulations have led to the suspicion that the time to failure of hierarchically organized load-transfer models of fracture is non-zero for sets of infinite size. This fact could have a profound significance in engineering practice and also in geophysics. Here, we develop an exact algebraic iterative method to compute the successive time intervals for individual breaking in systems of height $n$ in terms of the information calculated in the previous height $n-1$. As a byproduct of this method, rigorous lower and higher bounds for the time to failure of very large systems are easily obtained. The asymptotic behavior of the resulting lower bound leads to the evidence that the above mentioned suspicion is actually true.Comment: Final version. To appear in Phys. Rev. E, Feb 199

Energy spectrum of turbulent fluctuations in boundary driven reduced magnetohydrodynamics

The nonlinear dynamics of a bundle of magnetic flux ropes driven by stationary fluid motions at their endpoints is studied, by performing numerical simulations of the magnetohydrodynamic (MHD) equations. The development of MHD turbulence is shown, where the system reaches a state that is characterized by the ratio between the Alfven time (the time for incompressible MHD waves to travel along the field lines) and the convective time scale of the driving motions. This ratio of time scales determines the energy spectra and the relaxation toward different regimes ranging from weak to strong turbulence. A connection is made with phenomenological theories for the energy spectra in MHD turbulence.Comment: Published in Physics of Plasma

A Review of Maser Polarization and Magnetic Fields

Through polarization observations masers are unique probes of the magnetic field in a variety of different astronomical objects, with the different maser species tracing different physical conditions. In recent years maser polarization observations have provided insights in the magnetic field strength and morphology in, among others, the envelopes around evolved stars, Planetary Nebulae (PNe), massive star forming regions and supernova remnants. More recently, maser observations have even been used to determine the magnetic field in megamaser galaxies. This review will present an overview of maser polarization observations and magnetic field determinations of the last several years and discuss the implications of the magnetic field measurements for several important fields of study, such as aspherical PNe creation and massive star formation.Comment: 10 pages, Review paper from IAU symposium 242 "Astrophysical Masers and their Environments

A Method for Calculating the Structure of (Singular) Spacetimes in the Large

A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity (\Scri{}^+) and future timelike infinity ($i^+$) are mapped to grid points on the numerical grid. The determination of the causal structure of singularities, the localization of event horizons, the extraction of radiation, and the avoidance of unphysical reflections at the outer boundary of the grid, are demonstrated with calculations of spherically symmetric models with a scalar field as matter and radiation model.Comment: 29 pages, AGG2