Search results for "Matrices"

On the empirical spectral distribution for certain models related to sample covariance matrices with different correlations

2021

Given [Formula: see text], we study two classes of large random matrices of the form [Formula: see text] where for every [Formula: see text], [Formula: see text] are iid copies of a random variable [Formula: see text], [Formula: see text], [Formula: see text] are two (not necessarily independent) sets of independent random vectors having different covariance matrices and generating well concentrated bilinear forms. We consider two main asymptotic regimes as [Formula: see text]: a standard one, where [Formula: see text], and a slightly modified one, where [Formula: see text] and [Formula: see text] while [Formula: see text] for some [Formula: see text]. Assuming that vectors [Formula: see t…

Global functional variation in alpine vegetation

2021

International audience; Questions. What are the functional trade-offs of vascular plant species in global alpine ecosystems? How is functional variation related to vegetation zones, climatic groups and biogeographic realms? What is the relative contribution of macroclimate and evolutionary history in shaping the functional variation of alpine plant communities? Location. Global. Methods. We compiled a data set of alpine vegetation with 5,532 geo-referenced plots, 1,933 species and six plant functional traits. We used principal component analysis to quantify functional trade-offs among species and trait probability density to assess the functional dissimilarity of alpine vegetation in differ…

Determinant and inverse of a sum of matrices with applications in economics and statistics

1978

In this note we present some useful tools concerning the determinant and the inverse of the sum of two matrices. Some of the results shown here are found in the statistical and econometric literature, but often without proof and without a clear statement of the conditions under which they hold. Some other results, however, are believed to be original. A number of applications in the fields of economics and statistics are given.

On the ∗-cocharacter sequence of 3×3 matrices

2000

Abstract Let M 3 (F) be the algebra of 3×3 matrices with involution * over a field F of characteristic zero. We study the ∗ -polynomial identities of M 3 (F) , where ∗=t is the transpose involution, through the representation theory of the hyperoctahedral group B n . After decomposing the space of multilinear ∗ -polynomial identities of degree n under the B n -action, we determine which irreducible B n -modules appear with non-zero multiplicity. In symbols, we write the nth ∗ -cocharacter χ n (M 3 (F),*)=∑ r=0 n ∑ λ⊢r,h(λ)⩽6 μ⊢n−r,h(μ)⩽3 m λ,μ χ λ,μ , where λ and μ are partitions of r and n−r , respectively, χ λ,μ is the irreducible B n -character associated to the pair (λ,μ) and m λ,μ ⩾0 i…

Entanglement dynamics and relaxation in a few-qubit system interacting with random collisions

2008

The dynamics of a single qubit interacting by a sequence of pairwise collisions with an environment consisting of just two more qubits is analyzed. Each collision is modeled in terms of a random unitary operator with a uniform probability distribution described by the uniform Haar measure. We show that the purity of the system qubit as well as the bipartite and the tripartite entanglement reach time averaged equilibrium values characterized by large instantaneous fluctuations.These equilibrium values are independent of the order of collision among the qubits. The relaxation to equilibrium is analyzed also in terms of an ensemble average of random collision histories. Such average allows for…

Indexed Two-Dimensional String Matching

2016

Relationship between socioeconomic factors and intelligence of preschoolers: A cohort study in the Serbian context

2020

The aim of the current research is to analyse the relationship between the socioeconomic status (SES) of parents and intellectual abilities (IQ) of preschool children of Serbian territory, and in particular how SES factors relate to preschool children’s IQ measured with Raven’s Coloured Progressive Matrices (CPM), in the different age groups. The research included 430 parents and 430 preschool children. A confirmatory factor analysis of the SES questionnaire revealed five factors: educational and professional status of father and mother, residential and educational status of the family, sport status of parents and comfort of family housing. No gender differences in IQ levels were found in c…

Systematic review and meta-analysis found that malnutrition was associated with poor cognitive development

2021

Aim: Malnutrition is a major public health issue that has been associated with high susceptibility for impaired brain development and mental functioning. However, to date studies on this topic have not been collated and appraised. This systematic review and meta-analysis investigated the association between malnutrition and cognitive development. Methods: We searched the MEDLINE, Scopus, CINAHL, Embase PsycINFO and Cochrane Library databases in English up to 8 December 2020. All studies reporting an association between nutritional status and cognitive development were included. p values of less than 0.05 were considered statistically significant and the results are reported as standardised …

A note on k-generalized projections

2007

Abstract In this note, we investigate characterizations for k -generalized projections (i.e., A k  =  A ∗ ) on Hilbert spaces. The obtained results generalize those for generalized projections on Hilbert spaces in [Hong-Ke Du, Yuan Li, The spectral characterization of generalized projections, Linear Algebra Appl. 400 (2005) 313–318] and those for matrices in [J. Benitez, N. Thome, Characterizations and linear combinations of k -generalized projectors, Linear Algebra Appl. 410 (2005) 150–159].

Efficient Online Laplacian Eigenmap Computation for Dimensionality Reduction in Molecular Phylogeny via Optimisation on the Sphere

2019

Reconstructing the phylogeny of large groups of large divergent genomes remains a difficult problem to solve, whatever the methods considered. Methods based on distance matrices are blocked due to the calculation of these matrices that is impossible in practice, when Bayesian inference or maximum likelihood methods presuppose multiple alignment of the genomes, which is itself difficult to achieve if precision is required. In this paper, we propose to calculate new distances for randomly selected couples of species over iterations, and then to map the biological sequences in a space of small dimension based on the partial knowledge of this genome similarity matrix. This mapping is then used …