Hamiltonian cycles through prescribed edges of 4-connected maximal planar graphs

AbstractIn 1956, W.T. Tutte proved that every 4-connected planar graph is hamiltonian. Moreover, in 1997, D.P. Sanders extended this to the result that a 4-connected planar graph contains a hamiltonian cycle through any two of its edges. It is shown that Sanders’ result is best possible by constructing 4-connected maximal planar graphs with three edges a large distance apart such that any hamiltonian cycle misses one of them. If the maximal planar graph is 5-connected then such a construction is impossible

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

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

Association of TMTC2 with human nonsyndromic sensorineural hearing loss

IMPORTANCE: Sensorineural hearing loss (SNHL) is commonly caused by conditions that affect cochlear structures or the auditory nerve, and the genes identified as causing SNHL to date only explain a fraction of the overall genetic risk for this debilitating disorder. It is likely that other genes and mutations also cause SNHL. OBJECTIVE: To identify a candidate gene that causes bilateral, symmetric, progressive SNHL in a large multigeneration family of Northern European descent. DESIGN, SETTING, AND PARTICIPANTS: In this prospective genotype and phenotype study performed from January 1, 2006, through April 1, 2016, a 6-generation family of Northern European descent with 19 individuals having reported early-onset hearing loss suggestive of an autosomal dominant inheritance were studied at a tertiary academic medical center. In addition, 179 unrelated adult individuals with SNHL and 186 adult individuals reporting nondeafness were examined. MAIN OUTCOMES AND MEASURES: Sensorineural hearing loss. RESULTS: Nine family members (5 women [55.6%]) provided clinical audiometric and medical records that documented hearing loss. The hearing loss is characterized as bilateral, symmetric, progressive SNHL that reached severe to profound loss in childhood. Audiometric configurations demonstrated a characteristic dip at 1000 to 2000 Hz. All affected family members wear hearing aids or have undergone cochlear implantation. Exome sequencing and linkage and association analyses identified a fully penetrant sequence variant (rs35725509) on chromosome 12q21 (logarithm of odds, 3.3) in the TMTC2 gene region that segregates with SNHL in this family. This gene explains the SNHL occurrence in this family. The variant is also associated with SNHL in a cohort of 363 unrelated individuals (179 patients with confirmed SNHL and 184 controls, P = 7 x 10-4). CONCLUSIONS AND RELEVANCE: A previously uncharacterized gene, TMTC2, has been identified as a candidate for causing progressive SNHL in humans. This finding identifies a novel locus that causes autosomal dominant SNHL and therefore a more detailed understanding of the genetic basis of SNHL. Because TMTC2 has not been previously reported to regulate auditory function, the discovery reveals a potentially new, uncharacterized mechanism of hearing loss

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

Global metabolomic profiling targeting childhood obesity in the Hispanic population

Background: Metabolomics may unravel important biological pathways involved in the pathophysiology of childhood obesity

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

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

Parent-of-origin-specific allelic associations among 106 genomic loci for age at menarche.

Age at menarche is a marker of timing of puberty in females. It varies widely between individuals, is a heritable trait and is associated with risks for obesity, type 2 diabetes, cardiovascular disease, breast cancer and all-cause mortality. Studies of rare human disorders of puberty and animal models point to a complex hypothalamic-pituitary-hormonal regulation, but the mechanisms that determine pubertal timing and underlie its links to disease risk remain unclear. Here, using genome-wide and custom-genotyping arrays in up to 182,416 women of European descent from 57 studies, we found robust evidence (P < 5 × 10(-8)) for 123 signals at 106 genomic loci associated with age at menarche. Many loci were associated with other pubertal traits in both sexes, and there was substantial overlap with genes implicated in body mass index and various diseases, including rare disorders of puberty. Menarche signals were enriched in imprinted regions, with three loci (DLK1-WDR25, MKRN3-MAGEL2 and KCNK9) demonstrating parent-of-origin-specific associations concordant with known parental expression patterns. Pathway analyses implicated nuclear hormone receptors, particularly retinoic acid and γ-aminobutyric acid-B2 receptor signalling, among novel mechanisms that regulate pubertal timing in humans. Our findings suggest a genetic architecture involving at least hundreds of common variants in the coordinated timing of the pubertal transition

Evidence that duplications of 22q11.2 protect against schizophrenia.

A number of large, rare copy number variants (CNVs) are deleterious for neurodevelopmental disorders, but large, rare, protective CNVs have not been reported for such phenotypes. Here we show in a CNV analysis of 47 005 individuals, the largest CNV analysis of schizophrenia to date, that large duplications (1.5-3.0 Mb) at 22q11.2--the reciprocal of the well-known, risk-inducing deletion of this locus--are substantially less common in schizophrenia cases than in the general population (0.014% vs 0.085%, OR=0.17, P=0.00086). 22q11.2 duplications represent the first putative protective mutation for schizophrenia