Computing the Fréchet Distance with a Retractable Leash

All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values. We present a novel approach that avoids the detour through the decision version. This gives the first quadratic time algorithm for the Fréchet distance between polygonal curves in (Formula presented.) under polyhedral distance functions (e.g., (Formula presented.) and (Formula presented.)). We also get a (Formula presented.)-approximation of the Fréchet distance under the Euclidean metric, in quadratic time for any fixed (Formula presented.). For the exact Euclidean case, our framework currently yields an algorithm with running time (Formula presented.). However, we conjecture that it may eventually lead to a faster exact algorithm

Trans-eQTLs Reveal That Independent Genetic Variants Associated with a Complex Phenotype Converge on Intermediate Genes, with a Major Role for the HLA

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Normohomocysteinaemia and vitamin-treated hyperhomocysteinaemia are associated with similiar risks of cardiovascular events in patients with premature peripheral arterial occlusive disease. A prospective cohort study

Objectives. Mild hyperhomocysteinaemia (HHC), fasting or after methionine loading, is associated with an increased risk and severity of atherosclerotic vascular disease. Post-methionine and fasting HHC are responsive to treatment with vitamin

Blow-up profile of rotating 2D focusing Bose gases

We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed of rotation $\Omega$. First we study the behavior of the ground state when the coupling constant approaches $a\_*$ , the critical strength of the cubic nonlinearity for the focusing nonlinear Schr{\"o}dinger equation. We prove that blow-up always happens at the center of the trap, with the blow-up profile given by the Gagliardo-Nirenberg solution. In particular, the blow-up scenario is independent of $\Omega$, to leading order. This generalizes results obtained by Guo and Seiringer (Lett. Math. Phys., 2014, vol. 104, p. 141--156) in the non-rotating case. In a second part we consider the many-particle Hamiltonian for $N$ bosons, interacting with a potential rescaled in the mean-field manner $--a\_N N^{2\beta--1} w(N^{\beta} x), with$w$a positive function such that$\int\_{\mathbb{R}^2} w(x) dx = 1$. Assuming that$\beta < 1/2$and that$a\_N \to a\_*$sufficiently slowly, we prove that the many-body system is fully condensed on the Gross-Pitaevskii ground state in the limit$N \to \infty$

Exploration of the rotational power consumption of a rigid flapping wing

Accepted versio

Effects of cyclooxygenase-1 and -2 gene disruption on Helicobacter pylori-induced gastric inflammation

Background. Cyclooxygenases (COXs) play important roles in inflammation and carcinogenesis. The present study aimed to determine the effects of COX-1 and COX-2 gene disruption on Helicobacter pylori-induced gastric inflammation. Methods. Wild-type (WT), COX-1 and COX-2 heterozygous (COX-1 +/- and COX-2 +/-), and homozygous COX-deficient (COX-1 -/- and COX-2 -/-) mice were inoculated with H. pylori strain TN2 and killed after 24 weeks of infection. Uninfected WT and COX-deficient mice were used as controls. Levels of gastric mucosal inflammation, epithelial cell proliferation and apoptosis, and cytokine expression were determined. Results. COX deficiency facilitated H. pylori-induced gastritis. In the presence of H. pylori infection, apoptosis was increased in both WT and COX-deficient mice, whereas cell proliferation was increased in WT and COX-1-deficient, but not in COX-2-deficient, mice. Tumor necrosis factor (TNF)-α and interleukin-10 mRNA expression was elevated in H. pylori-infected mice, but only TNF-α mRNA expression was further increased by COX deficiency. Prostaglandin E 2 levels were increased in infected WT and COX-2-deficient mice but were at very low levels in infected COX-1-deficient mice. Leukotriene (LT) B 4 and LTC 4 levels were increased to a similar extent in infected WT and COX-deficient mice. Conclusions. COX deficiency enhances H. pylori-induced gastritis, probably via TNF-α expression. COX-2, but not COX-1, deficiency suppresses H. pylori-induced cell proliferation. © 2006 by the Infectious Diseases Society of America. All rights reserved.published_or_final_versio

Genome-wide analyses for personality traits identify six genomic loci and show correlations with psychiatric disorders

Personality is influenced by genetic and environmental factors1 and associated with mental health. However, the underlying genetic determinants are largely unknown. We identified six genetic loci, including five novel loci2,3, significantly associated with personality traits in a meta-analysis of genome-wide association studies (N = 123,132–260,861). Of these genomewide significant loci, extraversion was associated with variants in WSCD2 and near PCDH15, and neuroticism with variants on chromosome 8p23.1 and in L3MBTL2. We performed a principal component analysis to extract major dimensions underlying genetic variations among five personality traits and six psychiatric disorders (N = 5,422–18,759). The first genetic dimension separated personality traits and psychiatric disorders, except that neuroticism and openness to experience were clustered with the disorders. High genetic correlations were found between extraversion and attention-deficit– hyperactivity disorder (ADHD) and between openness and schizophrenia and bipolar disorder. The second genetic dimension was closely aligned with extraversion–introversion and grouped neuroticism with internalizing psychopathology (e.g., depression or anxiety)

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

Spatio-temporal Models of Lymphangiogenesis in Wound Healing

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a markedly different process from angiogenesis, occurring at different times and in response to different chemical stimuli. Two main hypotheses have been proposed: 1) lymphatic capillaries sprout from existing interrupted ones at the edge of the wound in analogy to the blood angiogenesis case; 2) lymphatic endothelial cells first pool in the wound region following the lymph flow and then, once sufficiently populated, start to form a network. Here we present two PDE models describing lymphangiogenesis according to these two different hypotheses. Further, we include the effect of advection due to interstitial flow and lymph flow coming from open capillaries. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from biological data. The models are then solved numerically and the results are compared with the available biological literature.Comment: 29 pages, 9 Figures, 6 Tables (39 figure files in total

Aerodynamics of the Hovering Hummingbird

Despite profound musculoskeletal differences, hummingbirds (Trochilidae) are widely thought to employ aerodynamic mechanisms similar to those used by insects. The kinematic symmetry of the hummingbird upstroke and downstroke has led to the assumption that these halves of the wingbeat cycle contribute equally to weight support during hovering, as exhibited by insects of similar size. This assumption has been applied, either explicitly or implicitly, in widely used aerodynamic models, and in a variety of empirical tests. Here we provide measurements of the wake of hovering rufous hummingbirds (Selasphorus rufus) obtained with digital particle image velocimetry that show force asymmetry: hummingbirds produce 75% of their weight support during the downstroke and only 25% during the upstroke. Some of this asymmetry is probably due to inversion of their cambered wings during upstroke. The wake of hummingbird wings also reveals evidence of leading-edge vortices created during the downstroke, indicating that they may operate at Reynolds numbers sufficiently low to exploit a key mechanism typical of insect hovering. Hummingbird hovering approaches that of insects, yet remains distinct because of effects resulting from an inherently dissimilar—avian—body plan