A comparative analysis by means of quantum molecular similarity measures of density distributions derived from conventional ab initio and density functional methods

A procedure based on quantum molecular similarity measures (QMSM) has been used to compare electron densities obtained from conventional ab initio and density functional methodologies at their respective optimized geometries. This method has been applied to a series of small molecules which have experimentally known properties and molecular bonds of diverse degrees of ionicity and covalency. Results show that in most cases the electron densities obtained from density functional methodologies are of a similar quality than post-Hartree-Fock generalized densities. For molecules where Hartree-Fock methodology yields erroneous results, the density functional methodology is shown to yield usually more accurate densities than those provided by the second order Møller-Plesset perturbation theory

Optimum power allocation for parallel Gaussian channels with arbitrary input distributions

The mutual information of independent parallel Gaussian-noise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signalling constellations with limited peak-to-average ratios (m-PSK, m-QAM, etc) are used in lieu of the ideal Gaussian signals. This paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions. Such policy admits a graphical interpretation, referred to as mercury/waterfilling, which generalizes the waterfilling solution and allows retaining some of its intuition. The relationship between mutual information of Gaussian channels and nonlinear minimum mean-square error proves key to solving the power allocation problem.

Social bases of changing income distributions

On the backdrop of very little sociological concern with rising income inequality, this paper examines how key changes in sociodemographic behaviour may help shed additional light on changes in household income distribution and especially on long-term income dynamics and inter-generational mobility. The paper argues that the joint effect of rising marital homogamy in terms of human capital and labour supply contributes generally to widen the income gap between households. Only uner very restrictive conditions, namely when the labour supply of low educated women grows dis-proportionally fast, will women's earnings contribute to more equality. Finally, the paper suggests that women's rising employment commitments contribute positively to equalizing the opportunity structure both via the income effect and if quality care is available, also via more homogenous cultural and cognitive stimulation of children. Mother's work does not generally have adverse effects for children's development.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

The world distribution of income (estimated from individual country distributions)

We estimate the world distribution of income by integrating individualincome distributions for 125 countries between 1970 and 1998. Weestimate poverty rates and headcounts by integrating the density functionbelow the $1/day and $2/day poverty lines. We find that poverty ratesdecline substantially over the last twenty years. We compute povertyheadcounts and find that the number of one-dollar poor declined by 235million between 1976 and 1998. The number of $2/day poor declined by 450million over the same period. We analyze poverty across different regionsand countries. Asia is a great success, especially after 1980. LatinAmerica reduced poverty substantially in the 1970s but progress stoppedin the 1980s and 1990s. The worst performer was Africa, where povertyrates increased substantially over the last thirty years: the number of$1/day poor in Africa increased by 175 million between 1970 and 1998,and the number of $2/day poor increased by 227. Africa hosted 11% ofthe world s poor in 1960. It hosted 66% of them in 1998. We estimatenine indexes of income inequality implied by our world distribution ofincome. All of them show substantial reductions in global incomeinequality during the 1980s and 1990s.

Characterization of intonation in Karṇāṭaka music by parametrizing context-based Svara Distributions

Intonation is a fundamental music concept that has a special relevance in Indian art music. It is characteristic of the rāga and intrinsic to the musical expression of the performer. Describing intonation is of importance to several information retrieval tasks like the development of rāga and artist similarity measures. In our previous work, we proposed a compact representation of intonation based on the parametrization of the pitch histogram of a performance and demonstrated the usefulness of this representation through an explorative rāga recognition task in which we classified 42 vocal performances belonging to 3 rāgas using parameters of a single svara. In this paper, we extend this representation to employ context-based svara distributions, which are obtained with a different approach to find the pitches belonging to each svara. We quantitatively compare this method to our previous one, discuss the advantages, and the necessary melodic analysis to be carried out in future.

Dispersal probability distributions and the wave-front speed problem

The speed and width of front solutions to reaction-dispersal models are analyzed both analytically and numerically. We perform our analysis for Laplace and Gaussian distribution kernels, both for delayed and nondelayed models. The results are discussed in terms of the characteristic parameters of the models

Nonideal particle distributions from kinetic freeze-out models

In fluid dynamical models the freeze-out of particles across a three-dimensional space-time hypersurface is discussed. The calculation of final momentum distribution of emitted particles is described for freeze-out surfaces, with both spacelike and timelike normals, taking into account conservation laws across the freeze-out discontinuity.

Zenith angle distributions at Super-Kamiokande and SNO and the solution of the solar neutrino problem

We have performed a detailed study of the zenith angle dependence of the regeneration factor and distributions of events at SNO and SK for different solutions of the solar neutrino problem. In particular, we discuss the oscillatory behavior and the synchronization effect in the distribution for the LMA solution, the parametric peak for the LOW solution, etc. A physical interpretation of the effects is given. We suggest a new binning of events which emphasizes the distinctive features of the zenith angle distributions for the different solutions. We also find the correlations between the integrated day-night asymmetry and the rates of events in different zenith angle bins. The study of these correlations strengthens the identification power of the analysis.

Experimental evidences for universality of acoustic emission avalanche distributions during structural transitions

Acoustic emission avalanche distributions are studied in different alloy systems that exhibit a phase transition from a bcc to a close-packed structure. After a small number of thermal cycles through the transition, the distributions become critically stable (exhibit power-law behavior) and can be characterized by an exponent alpha. The values of alpha can be classified into universality classes, which depend exclusively on the symmetry of the resulting close-packed structure.

Distributions of avalanches in martensitic transformations

An experimental study of the acoustic emission generated during a martensitic transformation is presented. A statistical analysis of the amplitude and lifetime of a large number of signals has revealed power-law behavior for both magnitudes. The exponents of these distributions have been evaluated and, through independent measurements of the statistical lifetime to amplitude dependence, we have checked the scaling relation between the exponents. Our results are discussed in terms of current ideas on avalanche dynamics.

Sequential partitioning: an alternative to understanding size distributions of avalanches in first-order phase transitions

We study the problem of the partition of a system of initial size V into a sequence of fragments s1,s2,s3 . . . . By assuming a scaling hypothesis for the probability p(s;V) of obtaining a fragment of a given size, we deduce that the final distribution of fragment sizes exhibits power-law behavior. This minimal model is useful to understanding the distribution of avalanche sizes in first-order phase transitions at low temperatures.

Topologies for poin distributions

The concepts of void and cluster for an arbitrary point distribution in a domain D are defined and characterized by some parameters such as volume, density, number of points belonging to them, shape, etc. After assigning a weight to each void and clusterwhich is a function of its characteristicsthe concept of distance between two point configurations S1 and S2 in D is introduced, both with and without the help of a lattice in the domain D. This defines a topology for the point distributions in D, which is different for the different characterizations of the voids and clusters.