Arbitrary Choice of Basic Variables in Density Functional Theory. II. Illustrative Applications

Our recent theory (Ref. 1) enables us to choose arbitrary quantities as the basic variables of the density functional theory. In this paper we apply it to several cases. In the case where the occupation matrix of localized orbitals is chosen as a basic variable, we can obtain the single-particle equation which is equivalent to that of the LDA+U method. The theory also leads to the Hartree-Fock-Kohn-Sham equation by letting the exchange energy be a basic variable. Furthermore, if the quantity associated with the density of states near the Fermi level is chosen as a basic variable, the resulting single-particle equation includes the additional potential which could mainly modify the energy-band structures near the Fermi level.Comment: 27 page

KH2PO4 + Host Matrix (Alumina / SiO2_2) Nanocomposite: Raman Scattering Insight

We report on the synthesis and Raman scattering characterization of composite materials based on the hostnanoporous matrices filled with nanostructured KH2PO4 (KDP) crystal. Silica (SiO2) and anodized aluminium oxide (AAO) were used as host matrices with various pore diameters, inter-pore spacing and morphology. The structure of the nanocomposites was investigated by X-ray diffraction and scanning electron microscopy. Raman scattering reveals the creation of one-dimensional nanostructured KDP inside the SiO2 matrix. We clearly observed the stretching {\nu}1, {\nu}3 and bending {\nu}2 vibrations of PO4 tetrahedral groups in the Raman spectrum of SiO2 + KDP. In Raman scattering spectra of AAO + KDP nanocomposite, the broad fluorescence background of AAO matrix dominates to a great extent, hindering thus the detecting of the KDP compound spectral response.Comment: 4 pages, 2 figures; 21st International Conference on Transparent Optical Networks (ICTON) 201

Feasible combinatorial matrix theory

We show that the well-known Konig's Min-Max Theorem (KMM), a fundamental result in combinatorial matrix theory, can be proven in the first order theory \LA with induction restricted to $\Sigma_1^B$ formulas. This is an improvement over the standard textbook proof of KMM which requires $\Pi_2^B$ induction, and hence does not yield feasible proofs --- while our new approach does. \LA is a weak theory that essentially captures the ring properties of matrices; however, equipped with $\Sigma_1^B$ induction \LA is capable of proving KMM, and a host of other combinatorial properties such as Menger's, Hall's and Dilworth's Theorems. Therefore, our result formalizes Min-Max type of reasoning within a feasible framework

Genome wide linkage scan for loci of musical aptitude in Finnish families: Evidence for a major locus at 4q22

ABSTRACT Background: Music perception and performance are comprehensive human cognitive functions and thus provide an excellent model system for studying human behaviour and brain function. However, the molecules involved in mediating music perception and performance are so far uncharacterized

Whole-genome sequencing to understand the genetic architecture of common gene expression and biomarker phenotypes.

Initial results from sequencing studies suggest that there are relatively few low-frequency (<5%) variants associated with large effects on common phenotypes. We performed low-pass whole-genome sequencing in 680 individuals from the InCHIANTI study to test two primary hypotheses: (i) that sequencing would detect single low-frequency-large effect variants that explained similar amounts of phenotypic variance as single common variants, and (ii) that some common variant associations could be explained by low-frequency variants. We tested two sets of disease-related common phenotypes for which we had statistical power to detect large numbers of common variant-common phenotype associations-11 132 cis-gene expression traits in 450 individuals and 93 circulating biomarkers in all 680 individuals. From a total of 11 657 229 high-quality variants of which 6 129 221 and 5 528 008 were common and low frequency (<5%), respectively, low frequency-large effect associations comprised 7% of detectable cis-gene expression traits [89 of 1314 cis-eQTLs at P < 1 × 10(-06) (false discovery rate ∼5%)] and one of eight biomarker associations at P < 8 × 10(-10). Very few (30 of 1232; 2%) common variant associations were fully explained by low-frequency variants. Our data show that whole-genome sequencing can identify low-frequency variants undetected by genotyping based approaches when sample sizes are sufficiently large to detect substantial numbers of common variant associations, and that common variant associations are rarely explained by single low-frequency variants of large effect

Second order analysis of geometric functionals of Boolean models

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.

Diabetes-specific genetic effects on obesity traits in American Indian populations: the Strong Heart Family Study

<p>Abstract</p> <p>Background</p> <p>Body fat mass distribution and deposition are determined by multiple environmental and genetic factors. Obesity is associated with insulin resistance, hyperinsulinemia, and type 2 diabetes. We previously identified evidence for genotype-by-diabetes interaction on obesity traits in Strong Heart Family Study (SHFS) participants. To localize these genetic effects, we conducted genome-wide linkage scans of obesity traits in individuals with and without type 2 diabetes, and in the combined sample while modeling interaction with diabetes using maximum likelihood methods (SOLAR 2.1.4).</p> <p>Methods</p> <p>SHFS recruited American Indians from Arizona, North and South Dakota, and Oklahoma. Anthropometric measures and diabetes status were obtained during a clinic visit. Marker allele frequencies were derived using maximum likelihood methods estimated from all individuals and multipoint identity by descent sharing was estimated using Loki. We used variance component linkage analysis to localize quantitative trait loci (QTLs) influencing obesity traits. We tested for evidence of additive and QTL-specific genotype-by-diabetes interactions using the regions identified in the diabetes-stratified analyses.</p> <p>Results</p> <p>Among 245 diabetic and 704 non-diabetic American Indian individuals, we detected significant additive gene-by-diabetes interaction for weight and BMI (<it>P </it>< 0.02). In analysis accounting for QTL-specific interaction (<it>P </it>< 0.001), we detected a QTL for weight on chromosome 1 at 242 cM (LOD = 3.7). This chromosome region harbors the adiponectin receptor 1 gene, which has been previously associated with obesity.</p> <p>Conclusion</p> <p>These results suggest distinct genetic effects on body mass in individuals with diabetes compared to those without diabetes, and a possible role for one or more genes on chromosome 1 in the pathogenesis of obesity.</p

Novel Associations of Nonstructural Loci with Paraoxonase Activity

The high-density-lipoprotein-(HDL-) associated esterase paraoxonase 1 (PON1) is a likely contributor to the antioxidant and antiatherosclerotic capabilities of HDL. Two nonsynonymous mutations in the structural gene, PON1, have been associated with variation in activity levels, but substantial interindividual differences remain unexplained and are greatest for substrates other than the eponymous paraoxon. PON1 activity levels were measured for three substrates—organophosphate paraoxon, arylester phenyl acetate, and lactone dihydrocoumarin—in 767 Mexican American individuals from San Antonio, Texas. Genetic influences on activity levels for each substrate were evaluated by association with approximately one million single nucleotide polymorphism (SNPs) while conditioning on PON1 genotypes. Significant associations were detected at five loci including regions on chromosomes 4 and 17 known to be associated with atherosclerosis and lipoprotein regulation and loci on chromosome 3 that regulate ubiquitous transcription factors. These loci explain 7.8% of variation in PON1 activity with lactone as a substrate, 5.6% with the arylester, and 3.0% with paraoxon. In light of the potential importance of PON1 in preventing cardiovascular disease/events, these novel loci merit further investigation