The Epstein-Glaser causal approach to the light-front QED(4). I: Free theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

On the structure of analytic vectors for the Schrodinger representation

This article deals with the structure of analytic and entire vectors for the Schrodinger representations of the Heisenberg group. Using refined versions of Hardy's theorem and their connection with Hermite expansions we obtain very precise representation theorems for analytic and entire vectors.

Comparison between complex amplitude envelope representation and complex analytic signal representation in studying pulsed Gaussian beam

Analytic propagation expressions of pulsed Gaussian beam are deduced by using complex amplitude envelope representation and complex analytic signal representation. Numerical calculations are given to illustrate the differences between them. The results show that the major difference between them is that there exists singularity in the beam obtained by using complex amplitude envelope representation. It is also found that singularity presents near propagation axis in the case of broadband and locates far from propagation axis in the case of narrowband. The critical condition to determine what representation should be adopted in studying pulsed Gaussian beam is also given. (C) 2004 Elsevier B.V. All rights reserved.

The representation of majorities and minorities in the British press: A content analytic approach

A content analysis examined the way majorities and minorities are represented in the British press. An analysis of the headlines of five British newspapers, over a period of five years, revealed that the words 'majority' and 'minority' appeared 658 times. Majority headlines were most frequent (66%), more likely to emphasize the numerical size of the majority, to link majority status with political groups, to be described with positive evaluations, and to cover political issues. By contrast, minority headlines were less frequent (34%), more likely to link minority status with ethnic groups and to other social issues, and less likely to be described with positive evaluations. The implications of examining how real-life majorities and minorities are represented for our understanding of experimental research are discussed. Copyright (C) 2004 John Wiley Sons, Ltd.

The representation of majorities and minorities in the British Press:a content analytic approach

A content analysis examined the way majorities and minorities are represented in the British press. An analysis of the headlines of five British newspapers, over a period of five years, revealed that the words ‘majority’ and ‘minority’ appeared 658 times. Majority headlines were most frequent (66% ), more likely to emphasize the numerical size of the majority, to link majority status with political groups, to be described with positive evaluations, and to cover political issues. By contrast, minority headlines were less frequent (34%), more likely to link minority status with ethnic groups and to other social issues, and less likely to be described with positive evaluations. The implications of examining how real-life majorities and minorities are represented for our understanding of experimental research are discussed.

Improving governance : practical methods and an analytic framework for the enhancement of democracy

Seven endemic governance problems are shown to be currently present in governments around the globe and at any level of government as well (for example municipal, federal). These problems have their roots traced back through more than two thousand years of political, specifically ‘democratic’, history. The evidence shows that accountability, transparency, corruption, representation, campaigning methods, constitutionalism and long-term goals were problematic for the ancient Athenians as well as modern international democratisation efforts encompassing every major global region. Why then, given the extended time period humans have had to deal with these problems, are they still present? At least part of the answer to this question is that philosophers, academics and NGOs as well as MNOs have only approached these endemic problems in a piecemeal manner with a skewed perspective on democracy. Their works have also been subject to the ebbs and flows of human history which essentially started and stopped periods of thinking. In order to approach the investigation of endemic problems in relation to democracy (as the overall quest of this thesis was to generate prescriptive results for the improvement of democratic government), it was necessary to delineate what exactly is being written about when using the term ‘democracy’. It is common knowledge that democracy has no one specific definition or practice, even though scholars and philosophers have been attempting to create a definition for generations. What is currently evident, is that scholars are not approaching democracy in an overly simplified manner (that is, it is government for the people, by the people) but, rather, are seeking the commonalities that democracies share, in other words, those items which are common to all things democratic. Following that specific line of investigation, the major practiced and theoretical versions of democracy were thematically analysed. After that, their themes were collapsed into larger categories, at which point the larger categories were comparatively analysed with the practiced and theoretical versions of democracy. Four democratic ‘particles’ (selecting officials, law, equality and communication) were seen to be present in all practiced and theoretical democratic styles. The democratic particles fused with a unique investigative perspective and in-depth political study created a solid conceptualisation of democracy. As such, it is argued that democracy is an ever-present element of any state government, ‘democratic’ or not, and the particles are the bodies which comprise the democratic element. Frequency- and proximity-based analyses showed that democratic particles are related to endemic problems in international democratisation discourse. The linkages between democratic particles and endemic problems were also evident during the thematic analysis as well historical review. This ultimately led to the viewpoint that if endemic problems are mitigated the act may improve democratic particles which might strengthen the element of democracy in the governing apparatus of any state. Such may actively minimise or wholly displace inefficient forms of government, leading to a government specifically tailored to the population it orders. Once the theoretical and empirical goals were attained, this thesis provided some prescriptive measures which government, civil society, academics, professionals and/or active citizens can use to mitigate endemic problems (in any country and at any level of government) so as to improve the human condition via better democratic government.

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Analyticity of the Schrodinger propagator on the Heisenberg group

We discuss the analytic extension property of the Schrodinger propagator for the Heisenberg sublaplacian and some related operators. The result for the sublaplacian is proved by interpreting the sublaplacian as a direct integral of an one parameter family of dilated special Hermite operators.

Fractional Hilbert transform extensions and associated analytic signal construction

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations. (C) 2013 Elsevier B.V. All rights reserved.

Syntax-Based Analytic Reading of Musical Scores

As part of a larger research project in musical structure, a program has been written which "reads" scores encoded in an input language isomorphic to music notation. The program is believed to be the first of its kind. From a small number of parsing rules the program derives complex configurations, each of which is associated with a set of reference points in a numerical representation of a time-continuum. The logical structure of the program is such that all and only the defined classes of events are represented in the output. Because the basis of the program is syntactic (in the sense that parsing operations are performed on formal structures in the input string), many extensions and refinements can be made without excessive difficulty. The program can be applied to any music which can be represented in the input language. At present, however, it constitutes the first stage in the development of a set of analytic tools for the study of so-called atonal music, the revolutionary and little understood music which has exerted a decisive influence upon contemporary practice of the art. The program and the approach to automatic data-structuring may be of interest to linguists and scholars in other fields concerned with basic studies of complex structures produced by human beings.

Linguistics and Information Theory: Analytic advantages

The analytic advantages of central concepts from linguistics and information theory, and the analogies demonstrated between them, for understanding patterns of retrieval from full-text indexes to documents are developed. The interaction between the syntagm and the paradigm in computational operations on written language in indexing, searching, and retrieval is used to account for transformations of the signified or meaning between documents and their representation and between queries and documents retrieved. Characteristics of the message, and messages for selection for written language, are brought to explain the relative frequency of occurrence of words and multiple word sequences in documents. The examples given in the companion article are revisited and a fuller example introduced. The signified of the sequence stood for, the term classically used in the definitions of the sign, as something standing for something else, can itself change rapidly according to its syntagm. A greater than ordinary discourse understanding of patterns in retrieval is obtained.