Some Curvature Problems in Semi-Riemannian Geometry

In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the construction of Lorentzian metrics which satisfy the dominant energy condition.Comment: 25 pages, LaTeX, 4 figure

Bovine pericardium retail preserved in glutaraldehyde and used as a vascular patch

<p>Abstract</p> <p>Background</p> <p>In this study we evaluated the performance of bovine pericardium preserved in glutaraldehyde used as a vascular patch.</p> <p>Methods</p> <p>Fourteen young pigs, six females and eight males, weighting 10.3 - 18.4 kg were used in our study. We implanted three remnants in each pig, two in the abdominal aorta and one was juxtaposed to the peritoneum. The smooth face (SF) and rough face (RF) of each remnant were implanted turned to the vessel inner portion and one remnant was juxtaposed to the peritoneum. The animals were sacrificed in 4.5 - 8 months after surgery (75 - 109 kg). The remnants were assessed for aorta wall, fibroses formation in inner apposition and calcification related to the face turned to the vessel inner portion.</p> <p>Results</p> <p>The rough face showed a lower dilatation level compared to the face implanted in adjacent aorta. There was no difference between intensity and/or incidence of graft calcification when the superficies were compared. The bovine pericardium preserved in glutaraldehyde did not show alterations in its structure when implanted with different faces turned to the inner portion of vessel.</p> <p>Conclusion</p> <p>When turned to the inner portion of the vessel, the rough face of the remnant presented a lower dilatation in relation to the adjacent aorta and a better quality of endothelium layer and did not show a difference between intensity and/or incidence of graft calcification.</p

Existence of Integral mm-Varifolds minimizing ∫∣A∣p\int |A|^p and ∫∣H∣p\int |H|^p, p>mp>m, in Riemannian Manifolds

We prove existence and partial regularity of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2\leq mm$, under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in $\mathbb{R}^S$ involving $\int |H|^p$, to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.Comment: 33 pages; this second submission corresponds to the published version of the paper, minor typos are fixe

Stationary Black Holes: Uniqueness and Beyond

The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.Comment: Major update of the original version by Markus Heusler from 1998. Piotr T. Chru\'sciel and Jo\~ao Lopes Costa succeeded to this review's authorship. Significantly restructured and updated all sections; changes are too numerous to be usefully described here. The number of references increased from 186 to 32

Uniaxial versus biaxial character of nematic equilibria in three dimensions

We study global minimizers of the Landau–de Gennes (LdG) energy functional for nematic liquid crystals, on arbitrary three-dimensional simply connected geometries with topologically non-trivial and physically relevant Dirichlet boundary conditions. Our results are specific to an asymptotic limit coined in terms of a dimensionless temperature and material-dependent parameter, t and some constraints on the material parameters, and we work in the t→∞ limit that captures features of the widely used Lyuksyutov constraint (Kralj and Virga in J Phys A 34:829–838, 2001). We prove (i) that (re-scaled) global LdG minimizers converge uniformly to a (minimizing) limiting harmonic map, away from the singular set of the limiting map; (ii) we have points of maximal biaxiality and uniaxiality near each singular point of the limiting map; (iii) estimates for the size of “strongly biaxial” regions in terms of the parameter t. We further show that global LdG minimizers in the restricted class of uniaxial Q-tensors cannot be stable critical points of the LdG energy in this limit

Spatiotemporally Controlled Cardiac Conduction Block Using High-Frequency Electrical Stimulation

Background: Methods for the electrical inhibition of cardiac excitation have long been sought to control excitability and conduction, but to date remain largely impractical. High-amplitude alternating current (AC) stimulation has been known to extend cardiac action potentials (APs), and has been recently exploited to terminate reentrant arrhythmias by producing reversible conduction blocks. Yet, low-amplitude currents at similar frequencies have been shown to entrain cardiac tissues by generation of repetitive APs, leading in some cases to ventricular fibrillation and hemodynamic collapse in vivo. Therefore, an inhibition method that does not lead to entrainment – irrespective of the stimulation amplitude (bound to fluctuate in an in vivo setting) – is highly desirable. Methodology/Principal Findings: We investigated the effects of broader amplitude and frequency ranges on the inhibitory effects of extracellular AC stimulation on HL-1 cardiomyocytes cultured on microelectrode arrays, using both sinusoidal and square waveforms. Our results indicate that, at sufficiently high frequencies, cardiac tissue exhibits a binary response to stimulus amplitude with either prolonged APs or no effect, thereby effectively avoiding the risks of entrainment by repetitive firing observed at lower frequencies. We further demonstrate the ability to precisely define reversible local conduction blocks in beating cultures without influencing the propagation activity in non-blocked areas. The conduction blocks were spatiotemporally controlled by electrode geometry and stimuli duration, respectively, and sustainable for long durations (300 s). Conclusion/Significance: Inhibition of cardiac excitation induced by high-frequency AC stimulation exhibits a binary response to amplitude above a threshold frequency, enabling the generation of reversible conduction blocks without the risks of entrainment. This inhibition method could yield novel approaches for arrhythmia modeling in vitro, as well as safer and more efficacious tools for in vivo cardiac mapping and radio-frequency ablation guidance applications

EDGAR: A software framework for the comparative analysis of prokaryotic genomes

Blom J, Albaum S, Doppmeier D, et al. EDGAR: a software framework for the comparative analysis of prokaryotic genomes. BMC Bioinformatics. 2009;10(1): 154.Background:The introduction of next generation sequencing approaches has caused a rapid increase in the number of completely sequenced genomes. As one result of this development, it is now feasible to analyze large groups of related genomes in a comparative approach. A main task in comparative genomics is the identification of orthologous genes in different genomes and the classification of genes as core genes or singletons. Results: To support these studies EDGAR – ''Efficient Database framework for comparative Genome Analyses using BLAST score Ratios'' – was developed. EDGAR is designed to automatically perform genome comparisons in a high throughput approach. Comparative analyses for 582 genomes across 75 genus groups taken from the NCBI genomes database were conducted with the software and the results were integrated into an underlying database. To demonstrate a specific application case, we analyzed ten genomes of the bacterial genus Xanthomonas, for which phylogenetic studies were awkward due to divergent taxonomic systems. The resultant phylogeny EDGAR provided was consistent with outcomes from traditional approaches performed recently and moreover, it was possible to root each strain with unprecedented accuracy. Conclusion: EDGAR provides novel analysis features and significantly simplifies the comparative analysis of related genomes. The software supports a quick survey of evolutionary relationships and simplifies the process of obtaining new biological insights into the differential gene content of kindred genomes. Visualization features, like synteny plots or Venn diagrams, are offered to the scientific community through a web-based and therefore platform independent user interface http://edgar.cebitec.uni-bielefeld.de webcite, where the precomputed data sets can be browsed

Genetic Diversity and Linkage Disequilibrium in Chinese Bread Wheat (Triticum aestivum L.) Revealed by SSR Markers

Two hundred and fifty bread wheat lines, mainly Chinese mini core accessions, were assayed for polymorphism and linkage disequilibrium (LD) based on 512 whole-genome microsatellite loci representing a mean marker density of 5.1 cM. A total of 6,724 alleles ranging from 1 to 49 per locus were identified in all collections. The mean PIC value was 0.650, ranging from 0 to 0.965. Population structure and principal coordinate analysis revealed that landraces and modern varieties were two relatively independent genetic sub-groups. Landraces had a higher allelic diversity than modern varieties with respect to both genomes and chromosomes in terms of total number of alleles and allelic richness. 3,833 (57.0%) and 2,788 (41.5%) rare alleles with frequencies of <5% were found in the landrace and modern variety gene pools, respectively, indicating greater numbers of rare variants, or likely new alleles, in landraces. Analysis of molecular variance (AMOVA) showed that A genome had the largest genetic differentiation and D genome the lowest. In contrast to genetic diversity, modern varieties displayed a wider average LD decay across the whole genome for locus pairs with r2>0.05 (P<0.001) than the landraces. Mean LD decay distance for the landraces at the whole genome level was <5 cM, while a higher LD decay distance of 5–10 cM in modern varieties. LD decay distances were also somewhat different for each of the 21 chromosomes, being higher for most of the chromosomes in modern varieties (<5∼25 cM) compared to landraces (<5∼15 cM), presumably indicating the influences of domestication and breeding. This study facilitates predicting the marker density required to effectively associate genotypes with traits in Chinese wheat genetic resources