On central tendency and dispersion measures for intervals and hypercubes

The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for interval-valued datasets. We propose a geometrical approach in the determination of summary statistics (central tendency and dispersion measures) for interval-valued variables

An \emph{ab initio} method for locating characteristic potential energy minima of liquids

It is possible in principle to probe the many--atom potential surface using density functional theory (DFT). This will allow us to apply DFT to the Hamiltonian formulation of atomic motion in monatomic liquids [\textit{Phys. Rev. E} {\bf 56}, 4179 (1997)]. For a monatomic system, analysis of the potential surface is facilitated by the random and symmetric classification of potential energy valleys. Since the random valleys are numerically dominant and uniform in their macroscopic potential properties, only a few quenches are necessary to establish these properties. Here we describe an efficient technique for doing this. Quenches are done from easily generated "stochastic" configurations, in which the nuclei are distributed uniformly within a constraint limiting the closeness of approach. For metallic Na with atomic pair potential interactions, it is shown that quenches from stochastic configurations and quenches from equilibrium liquid Molecular Dynamics (MD) configurations produce statistically identical distributions of the structural potential energy. Again for metallic Na, it is shown that DFT quenches from stochastic configurations provide the parameters which calibrate the Hamiltonian. A statistical mechanical analysis shows how the underlying potential properties can be extracted from the distributions found in quenches from stochastic configurations

On the equivalence between 2D Yukawa and Gross-Neveu models

We study numerically on the lattice the 2D Yukawa model with the U(1) chiral symmetry and $N_F$ = 16 at infinite scalar field self-coupling. The scaling behaviour of the fermion mass, as the Yukawa coupling approaches zero, is analysed using the mean field method. It is found to agree with that of the Gross-Neveu model with the same symmetry and $N_F$. The results suggest that the 2D Yukawa models belong to the universality class of the Gross-Neveu models not only at weak scalar field self-coupling but also for a broad range of the bare parameters which is not accessible to the $1/N_F$ expansion. New universality classes might arise at the crossover to the spin model universality class, however.Comment: 18 pages, Juelich HLRZ 111/9

Interstellar dust in the BOOMERanG maps

Interstellar dust (ISD) emission is present in the mm-wave maps obtained by the BOOMERanG experiment at intermediate and high Galactic latitudes. We find that, while being sub-dominant at the lower frequencies (90,150, 240 GHz), thermal emission from ISD is dominant at 410 GHz, and is well correlated with the IRAS map at 100 µm. We find also that the angular power spectrum of ISD fluctuations at 410 GHz is a power law, and its level is negligible with respect to the angular power spectrum of the Cosmic Microwave Background (CMB) at 90 and 150 GHz