Kernelization and Parameterized Algorithms for 3-Path Vertex Cover

A 3-path vertex cover in a graph is a vertex subset $C$ such that every path of three vertices contains at least one vertex from $C$. The parameterized 3-path vertex cover problem asks whether a graph has a 3-path vertex cover of size at most $k$. In this paper, we give a kernel of $5k$ vertices and an $O^*(1.7485^k)$-time and polynomial-space algorithm for this problem, both new results improve previous known bounds.Comment: in TAMC 2016, LNCS 9796, 201

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

Whole Genome Sequence Data From Captive Baboons Implicate RBFOX1 in Epileptic Seizure Risk

In this study, we investigate the genetic determinants that underlie epilepsy in a captive baboon pedigree and evaluate the potential suitability of this non-human primate model for understanding the genetic etiology of human epilepsy. Archived whole-genome sequence data were analyzed using both a candidate gene approach that targeted variants in baboon homologs of 19 genes (n = 20,881 SNPs) previously implicated in genetic generalized epilepsy (GGE) and a more agnostic approach that examined protein-altering mutations genome-wide as assessed by snpEff (n = 36,169). Measured genotype association tests for baboon cases of epileptic seizure were performed using SOLAR, as well as gene set enrichment analyses (GSEA) and protein–protein interaction (PPI) network construction of top association hits genome-wide (p \u3c 0.01; n = 441 genes). The maximum likelihood estimate of heritability for epileptic seizure in the pedigreed baboon sample is 0.76 (SE = 0.77; p = 0.07). Among candidate genes for GGE, a significant association was detected for an intronic SNP in RBFOX1 (p = 5.92 × 10–6; adjusted p = 0.016). For protein-altering variants, no genome-wide significant results were observed for epilepsy status. However, GSEA revealed significant positive enrichment for genes involved in the extracellular matrix structure (ECM; FDR = 0.0072) and collagen formation (FDR = 0.017), which was reflected in a major PPI network cluster. This preliminary study highlights the potential role of RBFOX1 in the epileptic baboon, a protein involved in transcriptomic regulation of multiple epilepsy candidate genes in humans and itself previously implicated in human epilepsy, both focal and generalized. Moreover, protein-damaging variants from across the genome exhibit a pattern of association that links collagen-containing ECM to epilepsy risk. These findings suggest a shared genetic etiology between baboon and human forms of GGE and lay the foundation for follow-up research

BR-squared: a practical solution to the winner’s curse in genome-wide scans

The detrimental effects of the winner’s curse, including overestimation of the genetic effects of associated variants and underestimation of sufficient sample sizes for replication studies are well-recognized in genome-wide association studies (GWAS). These effects can be expected to worsen as the field moves from GWAS into whole genome sequencing. To date, few studies have reported statistical adjustments to the naive estimates, due to the lack of suitable statistical methods and computational tools. We have developed an efficient genome-wide non-parametric method that explicitly accounts for the threshold, ranking, and allele frequency effects in whole genome scans. Here, we implement the method to provide bias-reduced estimates via bootstrap re-sampling (BR-squared) for association studies of both disease status and quantitative traits, and we report the results of applying BR-squared to GWAS of psoriasis and HbA1c. We observed over 50% reduction in the genetic effect size estimation for many associated SNPs. This translates into a greater than fourfold increase in sample size requirements for successful replication studies, which in part explains some of the apparent failures in replicating the original signals. Our analysis suggests that adjusting for the winner’s curse is critical for interpreting findings from whole genome scans and planning replication and meta-GWAS studies, as well as in attempts to translate findings into the clinical setting

Identifying the Lipidomic Effects of a Rare Loss-of-Function Deletion in ANGPTL3

Background: The identification and understanding of therapeutic targets for atherosclerotic cardiovascular disease is of fundamental importance given its global health and economic burden. Inhibition of ANGPTL3 (angiopoietin-like 3) has demonstrated a cardioprotective effect, showing promise for atherosclerotic cardiovascular disease treatment, and is currently the focus of ongoing clinical trials. Here, we assessed the genetic basis of variation in ANGPTL3 levels in the San Antonio Family Heart Study. Methods: We assayed ANGPTL3 protein levels in ≈1000 Mexican Americans from extended pedigrees. By drawing upon existing plasma lipidome profiles and genomic data we conducted analyses to understand the genetic basis to variation in ANGPTL3 protein levels, and accordingly the correlation with the plasma lipidome. Results: In a variance components framework, we identified that variation in ANGPTL3 was significantly heritable (h2=0.33, P=1.31×10-16). To explore the genetic basis of this heritability, we conducted a genome-wide linkage scan and identified significant linkage (logarithm of odds =6.18) to a locus on chromosome 1 at 90 centimorgans, corresponding to the ANGPTL3 gene location. In the genomes of 23 individuals from a single pedigree, we identified a loss-of-function variant, rs398122988 (N121Kfs*2), in ANGPTL3, that was significantly associated with lower ANGPTL3 levels (β=-1.69 SD units, P=3.367×10-13), and accounted for the linkage signal at this locus. Given the known role of ANGPTL3 as an inhibitor of endothelial and lipoprotein lipase, we explored the association of ANGPTL3 protein levels and rs398122988 with the plasma lipidome and related phenotypes, identifying novel associations with phosphatidylinositols. Conclusions: Variation in ANGPTL3 protein levels is heritable and under significant genetic control. Both ANGPTL3 levels and loss-of-function variants in ANGPTL3 have significant associations with the plasma lipidome. These findings further our understanding of ANGPTL3 as a therapeutic target for atherosclerotic cardiovascular disease

Cell shape analysis of random tessellations based on Minkowski tensors

To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to the question of relationships between different stochastic models. In the context of image analysis of synthetic and biological materials, this question is central to the problem of inferring information about formation processes from spatial measurements of resulting random structures. We address this question by a theory-based simulation study of shape indices derived from Minkowski tensors for a variety of tessellation models. We focus on the relationship between two indices: an isoperimetric ratio of the empirical averages of cell volume and area and the cell elongation quantified by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for these quantities, as well as for distributions thereof and for correlations of cell shape and volume, are presented for Voronoi mosaics of the Poisson point process, determinantal and permanental point processes, and Gibbs hard-core and random sequential absorption processes as well as for Laguerre tessellations of polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data are complemented by mechanically stable crystalline sphere and disordered ellipsoid packings and area-minimising foam models. We find that shape indices of individual cells are not sufficient to unambiguously identify the generating process even amongst this limited set of processes. However, we identify significant differences of the shape indices between many of these tessellation models. Given a realization of a tessellation, these shape indices can narrow the choice of possible generating processes, providing a powerful tool which can be further strengthened by density-resolved volume-shape correlations.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 Jense

Coordinated Expression Domains in Mammalian Genomes

Gene order in eukaryotic genomes is not random. Genes showing similar expression (coexpression) patterns are often clustered along the genome. The goal of this study is to characterize coexpression clustering in mammalian genomes and to investigate the underlying mechanisms.We detect clustering of coexpressed genes across multiple scales, from neighboring genes to chromosomal domains that span tens of megabases and, in some cases, entire chromosomes. Coexpression domains may be positively or negatively correlated with other domains, within and between chromosomes. We find that long-range expression domains are associated with gene density, which in turn is related to physical organization of the chromosomes within the nucleus. We show that gene expression changes between healthy and diseased tissue samples occur in a gene density-dependent manner.We demonstrate that coexpression domains exist across multiple scales. We identify potential mechanisms for short-range as well as long-range coexpression domains. We provide evidence that the three-dimensional architecture of the chromosomes may underlie long-range coexpression domains. Chromosome territory reorganization may play a role in common human diseases such as Alzheimer's disease and psoriasis

Maternal Influences on the Transmission of Leukocyte Gene Expression Profiles in Population Samples from Brisbane, Australia

Two gene expression profiling studies designed to identify maternal influences on development of the neonate immune system and to address the population structure of the leukocyte transcriptome were carried out in Brisbane, Australia. In the first study, a comparison of 19 leukocyte samples obtained from mothers in the last three weeks of pregnancy with 37 umbilical cord blood samples documented differential expression of 7,382 probes at a false discovery rate of 1%, representing approximately half of the expressed transcriptome. An even larger component of the variation involving 8,432 probes, notably enriched for Vitamin E and methotrexate-responsive genes, distinguished two sets of individuals, with perfect transmission of the two profile types between each of 16 mother-child pairs in the study. A minor profile of variation was found to distinguish the gene expression profiles of obese mothers and children of gestational diabetic mothers from those of children born to obese mothers. The second study was of adult leukocyte profiles from a cross-section of Red Cross blood donors sampled throughout Brisbane. The first two axes in this study are related to the third and fourth axes of variation in the first study and also reflect variation in the abundance of CD4 and CD8 transcripts. One of the profiles associated with the third axis is largely excluded from samples from the central portion of the city. Despite enrichment of insulin signaling and aspects of central metabolism among the differentially expressed genes, there was little correlation between leukocyte expression profiles and body mass index overall. Our data is consistent with the notion that maternal health and cytokine milieu directly impact gene expression in fetal tissues, but that there is likely to be a complex interplay between cultural, genetic, and other environmental factors in the programming of gene expression in leukocytes of newborn children