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

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 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.

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

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

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