The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.

Asymptotic robust inferences in the analysis of mean and covariance structures

Structural equation models are widely used in economic, socialand behavioral studies to analyze linear interrelationships amongvariables, some of which may be unobservable or subject to measurementerror. Alternative estimation methods that exploit different distributionalassumptions are now available. The present paper deals with issues ofasymptotic statistical inferences, such as the evaluation of standarderrors of estimates and chi--square goodness--of--fit statistics,in the general context of mean and covariance structures. The emphasisis on drawing correct statistical inferences regardless of thedistribution of the data and the method of estimation employed. A(distribution--free) consistent estimate of $\Gamma$, the matrix ofasymptotic variances of the vector of sample second--order moments,will be used to compute robust standard errors and a robust chi--squaregoodness--of--fit squares. Simple modifications of the usual estimateof $\Gamma$ will also permit correct inferences in the case of multi--stage complex samples. We will also discuss the conditions under which,regardless of the distribution of the data, one can rely on the usual(non--robust) inferential statistics. Finally, a multivariate regressionmodel with errors--in--variables will be used to illustrate, by meansof simulated data, various theoretical aspects of the paper.

Multi-sample analysis of moment-structures: Asymptotic validity of inferences based on second-order moments

In moment structure analysis with nonnormal data, asymptotic valid inferences require the computation of a consistent (under general distributional assumptions) estimate of the matrix $\Gamma$ of asymptotic variances of sample second--order moments. Such a consistent estimate involves the fourth--order sample moments of the data. In practice, the use of fourth--order moments leads to computational burden and lack of robustness against small samples. In this paper we show that, under certain assumptions, correct asymptotic inferences can be attained when $\Gamma$ is replaced by a matrix $\Omega$ that involves only the second--order moments of the data. The present paper extends to the context of multi--sample analysis of second--order moment structures, results derived in the context of (simple--sample) covariance structure analysis (Satorra and Bentler, 1990). The results apply to a variety of estimation methods and general type of statistics. An example involving a test of equality of means under covariance restrictions illustrates theoretical aspects of the paper.

Asymptotic behaviour of the density in a parabolic SPDE

Consider the density of the solution $X(t,x)$ of a stochastic heat equation with small noise at a fixed $t\in [0,T]$, $x \in [0,1]$.In the paper we study the asymptotics of this density as the noise is vanishing. A kind of Taylor expansion in powers of the noiseparameter is obtained. The coefficients and the residue of the expansion are explicitly calculated.In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximatingprocess and the limit one is proved. Also a suitable local integration by parts formula is developped.

Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

Mother's attachment representations of their premature infant at 6 and 18 months after birth.

The effects of premature birth on attachment have generally been examined from the infant's perspective. There is a lack of data concerning parental attachment representations toward a premature child. Because of the psychological stress engendered in parents confronted with a premature birth, we hypothesized that their attachment representations would be altered during the first months after the hospital discharge. Fifty families with a premature infant (25-33 gestation weeks) and a control group of 30 families with a full-term infant participated to the study. Perinatal risks were evaluated during hospitalization. To assess mothers' representations of their infant, the Working Model of the Child Interview (WMCI, Zeanah & Benoit, 1995 & Benoit, Zeanah, Parker, Nicholson, & Coolbear, 1997) were administered when their children were 6 and 18 months old. The severity of the perinatal risks was found to have an impact on the mothers' attachment representations. At six months, only 20% of the mothers of a prematurely born infant (30% at 18 months) had secure attachment representations, vs. 53% for the control group (57% at 18 months). Furthermore, mothers of low-risk premature infants more often had disengaged representations, whereas distorted representations were more frequent in the high-risk group of premature children. These findings suggest that the parental response to a premature birth is linked to the severity of postnatal risks. The fact that secure attachment representations are affected in mothers of low-risk infants just as much as they are in mothers of high-risk infants points to the need to conduct further studies aimed at evaluating whether preventive intervention for both low-risk and high-risk premature will be helpful.

Dynamic social representations of the 2009 H1N1 pandemic: Shifting patterns of sense-making and blame

We investigate dynamics of public perceptions of the 2009 H1N1 influenza pandemic to understand changing patterns of sense-making and blame regarding the outbreak of emerging infectious diseases. We draw on social representation theory combined with a dramaturgical perspective to identify changes in how various collectives are depicted over the course of the pandemic, according to three roles: heroes, villains and victims. Quantitative results based on content analysis of three cross-sectional waves of interviews show a shift from mentions of distant collectives (e.g., far-flung countries) at Wave 1 to local collectives (e.g., risk groups) as the pandemic became of more immediate concern (Wave 2) and declined (Wave 3). Semi-automated content analysis of media coverage shows similar results. Thematic analyses of the discourse associated with collectives revealed that many were consistently perceived as heroes, villains and victims.

Policy attitudes, ideological values and social representations

This article reviews research on policy attitudes and ideological values from the perspective of social representations theory. In the first part of the paper, key features of lay political thinking are presented, its pragmatic imperative, its focus on communication and the social functions of shared knowledge. Objectification transforms abstract and group-neutral ideological values into concrete and socially useful knowledge, in particular stereotypes of value-conforming and value-violating groups. Such shared understandings of intergroup relations provide citizens with common reference knowledge which provides the cognitive and cultural basis of policy attitudes. Social representations theory further suggests that lay knowledge reflects the social context in which it has been elaborated (anchoring), an aspect which allows conceptualising aggregate-level differences in policy attitudes. In the second part of the paper, a model of lay conceptions of social order is outlined which organises four shared conceptions of social order, along with the stereotype-based thinking associated with each conception: Moral order, Free Market, Social diversity and Structural inequality. We conclude by arguing that policy attitudes are symbolic devices expressed to justify or to challenge existing social arrangements.

Where sound position influences sound object representations: a 7-T fMRI study.

Evidence from human and non-human primate studies supports a dual-pathway model of audition, with partially segregated cortical networks for sound recognition and sound localisation, referred to as the What and Where processing streams. In normal subjects, these two networks overlap partially on the supra-temporal plane, suggesting that some early-stage auditory areas are involved in processing of either auditory feature alone or of both. Using high-resolution 7-T fMRI we have investigated the influence of positional information on sound object representations by comparing activation patterns to environmental sounds lateralised to the right or left ear. While unilaterally presented sounds induced bilateral activation, small clusters in specific non-primary auditory areas were significantly more activated by contra-laterally presented stimuli. Comparison of these data with histologically identified non-primary auditory areas suggests that the coding of sound objects within early-stage auditory areas lateral and posterior to primary auditory cortex AI is modulated by the position of the sound, while that within anterior areas is not.

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Learning-induced plasticity in auditory spatial representations revealed by electrical neuroimaging.

Auditory spatial representations are likely encoded at a population level within human auditory cortices. We investigated learning-induced plasticity of spatial discrimination in healthy subjects using auditory-evoked potentials (AEPs) and electrical neuroimaging analyses. Stimuli were 100 ms white-noise bursts lateralized with varying interaural time differences. In three experiments, plasticity was induced with 40 min of discrimination training. During training, accuracy significantly improved from near-chance levels to approximately 75%. Before and after training, AEPs were recorded to stimuli presented passively with a more medial sound lateralization outnumbering a more lateral one (7:1). In experiment 1, the same lateralizations were used for training and AEP sessions. Significant AEP modulations to the different lateralizations were evident only after training, indicative of a learning-induced mismatch negativity (MMN). More precisely, this MMN at 195-250 ms after stimulus onset followed from differences in the AEP topography to each stimulus position, indicative of changes in the underlying brain network. In experiment 2, mirror-symmetric locations were used for training and AEP sessions; no training-related AEP modulations or MMN were observed. In experiment 3, the discrimination of trained plus equidistant untrained separations was tested psychophysically before and 0, 6, 24, and 48 h after training. Learning-induced plasticity lasted <6 h, did not generalize to untrained lateralizations, and was not the simple result of strengthening the representation of the trained lateralizations. Thus, learning-induced plasticity of auditory spatial discrimination relies on spatial comparisons, rather than a spatial anchor or a general comparator. Furthermore, cortical auditory representations of space are dynamic and subject to rapid reorganization.

Maternal interactive behaviour as a predictor of preschoolers' attachment representations among full term and premature samples.

BACKGROUND: Associations between maternal sensitivity and child attachment have been established in many samples, but the strength of the association varies across populations. The sensitivity-attachment link has never been examined at the level of representations nor among premature samples. OBJECTIVE: The present study is aimed at exploring associations between maternal interactive behaviour and children's attachment representations in a population of preterm and full-term infants. METHOD: Maternal interactive behaviour was assessed at 6 and 18 months (Ainsworth Sensitivity Scale & Care Index) and children's attachment representations were measured at 42 months (Attachment Story Completion Task) in a sample of preterm (N=48) and full-term (N=23) infants. RESULTS: Maternal unresponsiveness at 6 months and sensitivity at 18 months explained 54% of the variance of disorganized attachment representations in the full-term group but was not significantly related to attachment patterns in the preterm group. CONCLUSION: These results corroborate previous work on the causes of disorganized attachment and also point to the need to consider the development of attachment differently for children evolving in specific developmental contexts. They especially stress the importance of distinguishing between risk factors associated with the mother as opposed to the child.