Structural brain connectivity and cognitive ability differences: A multivariate distance matrix regression analysis

Neuroimaging research involves analyses of huge amounts of biological data that might or might not be related with cognition. This relationship is usually approached using univariate methods, and, therefore, correction methods are mandatory for reducing false positives. Nevertheless, the probability of false negatives is also increased. Multivariate frameworks have been proposed for helping to alleviate this balance. Here we apply multivariate distance matrix regression for the simultaneous analysis of biological and cognitive data, namely, structural connections among 82 brain regions and several latent factors estimating cognitive performance. We tested whether cognitive differences predict distances among individuals regarding their connectivity pattern. Beginning with 3,321 connections among regions, the 36 edges better predicted by the individuals' cognitive scores were selected. Cognitive scores were related to connectivity distances in both the full (3,321) and reduced (36) connectivity patterns. The selected edges connect regions distributed across the entire brain and the network defined by these edges supports high-order cognitive processes such as (a) (fluid) executive control, (b) (crystallized) recognition, learning, and language processing, and (c) visuospatial processing. This multivariate study suggests that one widespread, but limited number, of regions in the human brain, supports high-level cognitive ability differences. Hum Brain Mapp, 2016. © 2016 Wiley Periodicals, Inc.

A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established.

Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.

Calibration uncertainty estimation for internal aerodynamic balance

Aerodynamic balances are employed in wind tunnels to estimate the forces and moments acting on the model under test. This paper proposes a methodology for the assessment of uncertainty in the calibration of an internal multi-component aerodynamic balance. In order to obtain a suitable model to provide aerodynamic loads from the balance sensor responses, a calibration is performed prior to the tests by applying known weights to the balance. A multivariate polynomial fitting by the least squares method is used to interpolate the calibration data points. The uncertainties of both the applied loads and the readings of the sensors are considered in the regression. The data reduction includes the estimation of the calibration coefficients, the predicted values of the load components and their corresponding uncertainties, as well as the goodness of fit.

Identification of diabetic retinopathy genes through a genome-wide association study among Mexican-Americans from Starr County, Texas

To identify genetic susceptibility loci for severe diabetic retinopathy, 286 Mexican-Americans with type 2 diabetes from Starr County, Texas completed detailed physical and ophthalmologic examinations including fundus photography for diabetic retinopathy grading. 103 individuals with moderate-to-severe non-proliferative diabetic retinopathy or proliferative diabetic retinopathy were defined as cases for this study. DNA samples extracted from study subjects were genotyped using the Affymetrix GeneChip® Human Mapping 100K Set, which includes 116,204 single nucleotide polymorphisms (SNPs) across the whole genome. Single-marker allelic tests and 2- to 8-SNP sliding-window Haplotype Trend Regression implemented in HelixTreeTM were first performed with these direct genotypes to identify genes/regions contributing to the risk of severe diabetic retinopathy. An additional 1,885,781 HapMap Phase II SNPs were imputed from the direct genotypes to expand the genomic coverage for a more detailed exploration of genetic susceptibility to diabetic retinopathy. The average estimated allelic dosage and imputed genotypes with the highest posterior probabilities were subsequently analyzed for associations using logistic regression and Fisher's Exact allelic tests, respectively. To move beyond these SNP-based approaches, 104,572 directly genotyped and 333,375 well-imputed SNPs were used to construct genetic distance matrices based on 262 retinopathy candidate genes and their 112 related biological pathways. Multivariate distance matrix regression was then used to test hypotheses with genes and pathways as the units of inference in the context of susceptibility to diabetic retinopathy. This study provides a framework for genome-wide association analyses, and implicated several genes involved in the regulation of oxidative stress, inflammatory processes, histidine metabolism, and pancreatic cancer pathways associated with severe diabetic retinopathy. Many of these loci have not previously been implicated in either diabetic retinopathy or diabetes. In summary, CDC73, IL12RB2, and SULF1 had the best evidence as candidates to influence diabetic retinopathy, possibly through novel biological mechanisms related to VEGF-mediated signaling pathway or inflammatory processes. While this study uncovered some genes for diabetic retinopathy, a comprehensive picture of the genetic architecture of diabetic retinopathy has not yet been achieved. Once fully understood, the genetics and biology of diabetic retinopathy will contribute to better strategies for diagnosis, treatment and prevention of this disease.^

A study of cluster analysis techniques and their applications

This thesis seeks to describe the development of an inexpensive and efficient clustering technique for multivariate data analysis. The technique starts from a multivariate data matrix and ends with graphical representation of the data and pattern recognition discriminant function. The technique also results in distances frequency distribution that might be useful in detecting clustering in the data or for the estimation of parameters useful in the discrimination between the different populations in the data. The technique can also be used in feature selection. The technique is essentially for the discovery of data structure by revealing the component parts of the data. lhe thesis offers three distinct contributions for cluster analysis and pattern recognition techniques. The first contribution is the introduction of transformation function in the technique of nonlinear mapping. The second contribution is the us~ of distances frequency distribution instead of distances time-sequence in nonlinear mapping, The third contribution is the formulation of a new generalised and normalised error function together with its optimal step size formula for gradient method minimisation. The thesis consists of five chapters. The first chapter is the introduction. The second chapter describes multidimensional scaling as an origin of nonlinear mapping technique. The third chapter describes the first developing step in the technique of nonlinear mapping that is the introduction of "transformation function". The fourth chapter describes the second developing step of the nonlinear mapping technique. This is the use of distances frequency distribution instead of distances time-sequence. The chapter also includes the new generalised and normalised error function formulation. Finally, the fifth chapter, the conclusion, evaluates all developments and proposes a new program. for cluster analysis and pattern recognition by integrating all the new features.

Effects of selection and drift on G matrix evolution in a heterogeneous environment: a multivariate Qst-Fst Test with the freshwater snail Galba truncatula.

Unraveling the effect of selection vs. drift on the evolution of quantitative traits is commonly achieved by one of two methods. Either one contrasts population differentiation estimates for genetic markers and quantitative traits (the Q(st)-F(st) contrast) or multivariate methods are used to study the covariance between sets of traits. In particular, many studies have focused on the genetic variance-covariance matrix (the G matrix). However, both drift and selection can cause changes in G. To understand their joint effects, we recently combined the two methods into a single test (accompanying article by Martin et al.), which we apply here to a network of 16 natural populations of the freshwater snail Galba truncatula. Using this new neutrality test, extended to hierarchical population structures, we studied the multivariate equivalent of the Q(st)-F(st) contrast for several life-history traits of G. truncatula. We found strong evidence of selection acting on multivariate phenotypes. Selection was homogeneous among populations within each habitat and heterogeneous between habitats. We found that the G matrices were relatively stable within each habitat, with proportionality between the among-populations (D) and the within-populations (G) covariance matrices. The effect of habitat heterogeneity is to break this proportionality because of selection for habitat-dependent optima. Individual-based simulations mimicking our empirical system confirmed that these patterns are expected under the selective regime inferred. We show that homogenizing selection can mimic some effect of drift on the G matrix (G and D almost proportional), but that incorporating information from molecular markers (multivariate Q(st)-F(st)) allows disentangling the two effects.

Multivariate QST-FST comparisons: a neutrality test for the evolution of the g matrix in structured populations.

Neutrality tests in quantitative genetics provide a statistical framework for the detection of selection on polygenic traits in wild populations. However, the existing method based on comparisons of divergence at neutral markers and quantitative traits (Q(st)-F(st)) suffers from several limitations that hinder a clear interpretation of the results with typical empirical designs. In this article, we propose a multivariate extension of this neutrality test based on empirical estimates of the among-populations (D) and within-populations (G) covariance matrices by MANOVA. A simple pattern is expected under neutrality: D = 2F(st)/(1 - F(st))G, so that neutrality implies both proportionality of the two matrices and a specific value of the proportionality coefficient. This pattern is tested using Flury's framework for matrix comparison [common principal-component (CPC) analysis], a well-known tool in G matrix evolution studies. We show the importance of using a Bartlett adjustment of the test for the small sample sizes typically found in empirical studies. We propose a dual test: (i) that the proportionality coefficient is not different from its neutral expectation [2F(st)/(1 - F(st))] and (ii) that the MANOVA estimates of mean square matrices between and among populations are proportional. These two tests combined provide a more stringent test for neutrality than the classic Q(st)-F(st) comparison and avoid several statistical problems. Extensive simulations of realistic empirical designs suggest that these tests correctly detect the expected pattern under neutrality and have enough power to efficiently detect mild to strong selection (homogeneous, heterogeneous, or mixed) when it is occurring on a set of traits. This method also provides a rigorous and quantitative framework for disentangling the effects of different selection regimes and of drift on the evolution of the G matrix. We discuss practical requirements for the proper application of our test in empirical studies and potential extensions.