Fast and accurate modelling of longitudinal and repeated measures neuroimaging data

Despite the growing importance of longitudinal data in neuroimaging, the standard analysis methods make restrictive or unrealistic assumptions (e.g., assumption of Compound Symmetry—the state of all equal variances and equal correlations—or spatially homogeneous longitudinal correlations). While some new methods have been proposed to more accurately account for such data, these methods are based on iterative algorithms that are slow and failure-prone. In this article, we propose the use of the Sandwich Estimator (SwE) method which first estimates the parameters of interest with a simple Ordinary Least Square model and second estimates variances/covariances with the “so-called” SwE which accounts for the within-subject correlation existing in longitudinal data. Here, we introduce the SwE method in its classic form, and we review and propose several adjustments to improve its behaviour, specifically in small samples. We use intensive Monte Carlo simulations to compare all considered adjustments and isolate the best combination for neuroimaging data. We also compare the SwE method to other popular methods and demonstrate its strengths and weaknesses. Finally, we analyse a highly unbalanced longitudinal dataset from the Alzheimer's Disease Neuroimaging Initiative and demonstrate the flexibility of the SwE method to fit within- and between-subject effects in a single model. Software implementing this SwE method has been made freely available at http://warwick.ac.uk/tenichols/SwE

A Closed-Form Solution of the Multi-Period Portfolio Choice Problem for a Quadratic Utility Function

In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed and no assumption on the distribution is imposed. All expressions are presented in terms of the conditional mean vectors and the conditional covariance matrices. If the multivariate process of the asset returns is independent it is shown that in the case without a riskless asset the solution is presented as a sequence of optimal portfolio weights obtained by solving the single-period Markowitz optimization problem. The process dynamics are included only in the shape parameter of the utility function. If a riskless asset is present then the multi-period optimal portfolio weights are proportional to the single-period solutions multiplied by time-varying constants which are depending on the process dynamics. Remarkably, in the case of a portfolio selection with the tangency portfolio the multi-period solution coincides with the sequence of the simple-period solutions. Finally, we compare the suggested strategies with existing multi-period portfolio allocation methods for real data.Comment: 38 pages, 9 figures, 3 tables, changes: VAR(1)-CCC-GARCH(1,1) process dynamics and the analysis of increasing horizon are included in the simulation study, under revision in Annals of Operations Researc

Associations between biological markers of prenatal stress and infant negative emotionality are specific to sex

Purpose Fetal programming is the idea that environmental stimuli can alter the development of the fetus, which may have a long-term effect on the child. We have recently reported that maternal prenatal cortisol predicts infant negative emotionality in a sex-dependent manner: high prenatal cortisol was associated with increased negative emotionality in females, and decreased negative emotionality in males. This study aims to test for this sex-specific effect in a different cohort, and investigate whether sex differences in fetal programming may be specific to glucocorticoid mechanisms by also examining a maternal salivary alpha-amylase (sAA) by sex interaction. Methods 88 pregnant women (mean gestational age = 27.4 weeks, SD = 7.4) collected saliva samples at home over two working days to be assayed for the hormone cortisol (range = 0.13–88.22 nmol/l) and the enzyme alpha-amylase (range = 4.57–554.8 units/ml). Samples were collected at waking, 30-min post-waking and 12 h post-waking. Two months after birth participants reported infant negative emotionality using the distress to limits subscale of the Infant Behavior Questionnaire. Results The interaction between maternal prenatal cortisol and infant sex to predict distress to limits approached significance (p = 0.067). In line with our previous finding there was a positive association between prenatal cortisol and negative emotionality in females, and a negative association in males. The interaction between sAA and sex to predict distress was significant (p = 0.025), and the direction of effect was the same as for the cortisol data; high sAA associated with increased negative emotionality in females and reduced negative emotionality in males. Conclusions In line with our previous findings, this research adds to an emerging body of literature, which suggests that fetal programming mechanisms may be sex-dependent. This is the first study to demonstrate that maternal prenatal sAA may be an important biomarker for infant behavior, and the findings have implications for understanding sex differences in developmental psychopathology

Secret Sharing over Fast-Fading MIMO Wiretap Channels

Secret sharing over the fast-fading MIMO wiretap channel is considered. A source and a destination try to share secret information over a fast-fading MIMO channel in the presence of a wiretapper who also makes channel observations that are different from but correlated to those made by the destination. An interactive authenticated unrestricted public channel is also available for use by the source and destination in the secret sharing process. This falls under the "channel-type model with wiretapper" considered by Ahlswede and Csiszar. A minor extension of their result (to continuous channel alphabets) is employed to evaluate the key capacity of the fast-fading MIMO wiretap channel. The effects of spatial dimensionality provided by the use of multiple antennas at the source, destination, and wiretapper are then investigated.Comment: Revision submitted to EURASIP Journal on Wireless Communications and Networking, Special Issue on Wireless Physical Layer Security, Sept. 2009. v.3: Fixes to proofs. Matthieu Bloch added as co-author for contributions to proof

A systematic approach to mapping recessive disease genes in individuals from outbred populations

The identification of recessive disease-causing genes by homozygosity mapping is often restricted by lack of suitable consanguineous families. To overcome these limitations, we apply homozygosity mapping to single affected individuals from outbred populations. In 72 individuals of 54 kindred ascertained worldwide with known homozygous mutations in 13 different recessive disease genes, we performed total genome homozygosity mapping using 250,000 SNP arrays. Likelihood ratio Z-scores (ZLR) were plotted across the genome to detect ZLR peaks that reflect segments of homozygosity by descent, which may harbor the mutated gene. In 93% of cases, the causative gene was positioned within a consistent ZLR peak of homozygosity. The number of peaks reflected the degree of inbreeding. We demonstrate that disease-causing homozygous mutations can be detected in single cases from outbred populations within a single ZLR peak of homozygosity as short as 2 Mb, containing an average of only 16 candidate genes. As many specialty clinics have access to cohorts of individuals from outbred populations, and as our approach will result in smaller genetic candidate regions, the new strategy of homozygosity mapping in single outbred individuals will strongly accelerate the discovery of novel recessive disease genes

Synchronization of coupled limit cycles

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.Comment: Journal of Nonlinear Science, accepte