Remarks on the classification of quasitoric manifolds up to equivariant homeomorphism

We give three sufficient criteria for two quasitoric manifolds (M,M') to be (weakly) equivariantly homeomorphic. We apply these criteria to count the weakly equivariant homeomorphism types of quasitoric manifolds with a given cohomology ring.Comment: 11 page

Bucolic Complexes

We introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. They are defined as simply connected prism complexes satisfying some local combinatorial conditions. We study various approaches to bucolic complexes: from graph-theoretic and topological perspective, as well as from the point of view of geometric group theory. In particular, we characterize bucolic complexes by some properties of their 2-skeleta and 1-skeleta (that we call bucolic graphs), by which several known results are generalized. We also show that locally-finite bucolic complexes are contractible, and satisfy some nonpositive-curvature-like properties.Comment: 45 pages, 4 figure

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

Prevalence, predictors and prognostic implications of PR interval prolongation in patients with heart failure

Aims: To determine the prevalence, incidence, predictors and prognostic implications of PR interval prolongation in patients referred with suspected heart failure. Methods and Results: Consecutive patients referred with suspected heart failure were prospectively enrolled. After excluding patients with implantable cardiac devices and atrial fibrillation, 1420 patients with heart failure and reduced ejection fraction (HeFREF) [age: median 71 (interquartile range IQR: 63-78) years; men: 71%; NT-ProBNP: 1319 (583-3378) ng/L], 1094 with heart failure and normal ejection fraction (HeFNEF) [age: 76 (70-82) years; men: 47%; NT-ProBNP: 547 (321-1171) ng/L], and 1150 without heart failure [age: 68 (60-75) years; men: 51%; NT-ProBNP: 86 (46-140) ng/L] were included. The prevalence of first degree heart block [heart-rate corrected PR interval (PRc) >200 ms] was higher in patients with heart failure (21% HeFREF, 20% HeFNEF, 9% without heart failure). In patients with HeFREF or HeFNEF, longer baseline PRc was associated with greater age, male sex, and longer QRS duration and, in those with HeFREF, treatment with amiodarone or digoxin. Patients with heart failure in the longest PRc quartile had worse survival compared to shorter PRc quartiles but PRc was not independently associated with survival in multivariable analysis. For patients without heart failure, shorter baseline PRc was independently associated with worse survival. Conclusion: PRc prolongation is common in patients with HeFREF or HeFNEF and associated with worse survival, although not an independent predictor of outcome. The results of clinical trials investigating the therapeutic potential of shortening the PR interval by pacing are awaited

Morphological and genetic divergence in Swedish postglacial stickleback (Pungitius pungitius) populations

Background: An important objective of evolutionary biology is to understand the processes that govern phenotypic variation in natural populations. We assessed patterns of morphological and genetic divergence among coastal and inland lake populations of nine-spined stickleback in northern Sweden. Coastal populations are either from the Baltic coast (n = 5) or from nearby coastal lakes (n = 3) that became isolated from the Baltic Sea (&lt; 100 years before present, ybp). Inland populations are from freshwater lakes that became isolated from the Baltic approximately 10,000 ybp; either single species lakes without predators (n = 5), or lakes with a recent history of predation (n = 5) from stocking of salmonid predators (~50 ybp).Results: Coastal populations showed little variation in 11 morphological traits and had longer spines per unit of body length than inland populations. Inland populations were larger, on average, and showed greater morphological variation than coastal populations. A principal component analysis (PCA) across all populations revealed two major morphological axes related to spine length (PC1, 47.7% variation) and body size (PC2, 32.9% variation). Analysis of PCA scores showed marked similarity in coastal (Baltic coast and coastal lake) populations. PCA scores indicate that inland populations with predators have higher within-group variance in spine length and lower within-group variance in body size than inland populations without predators. Estimates of within-group PST (a proxy for QST) from PCA scores are similar to estimates of FST for coastal lake populations but PST &gt; FST for Baltic coast populations. PST &gt; FST for PC1 and PC2 for inland predator and inland no predator populations, with the exception that PST &lt; FST for body size in inland populations lacking predators.Conclusions: Baltic coast and coastal lake populations show little morphological and genetic variation within and between groups suggesting that these populations experience similar ecological conditions and that time since isolation of coastal lakes has been insufficient to demonstrate divergent morphology in coastal lake populations. Inland populations, on the other hand, showed much greater morphological and genetic variation characteristic of long periods of isolation. Inland populations from lakes without predators generally have larger body size, and smaller spine length relative to body size, suggesting systematic reduction in spine length. In contrast, inland populations with predators exhibit a wider range of spine lengths relative to body size suggesting that this trait is responding to local predation pressure differently among these populations. Taken together the results suggest that predation plays a role in shaping morphological variation among isolated inland populations. However, we cannot rule out that a causal relationship between predation versus other genetic and environmental influences on phenotypic variation not measured in this study exists, and this warrants further investigation.</p

Constitutional Microsatellite Instability, Genotype, and Phenotype Correlations in Constitutional Mismatch Repair Deficiency

Background &amp; aims: Constitutional mismatch repair deficiency (CMMRD) is a rare recessive childhood cancer predisposition syndrome caused by germline mismatch repair variants. Constitutional microsatellite instability (cMSI) is a CMMRD diagnostic hallmark and may associate with cancer risk. We quantified cMSI in a large CMMRD patient cohort to explore genotype-phenotype correlations using novel MSI markers selected for instability in blood.Methods: Three CMMRD, 1 Lynch syndrome, and 2 control blood samples were genome sequenced to &gt;120 7 depth. A pilot cohort of 8 CMMRD and 38 control blood samples and a blinded cohort of 56 CMMRD, 8 suspected CMMRD, 40 Lynch syndrome, and 43 control blood samples were amplicon sequenced to 5000 7 depth. Sample cMSI score was calculated using a published method comparing microsatellite reference allele frequencies with 80 controls.Results: Thirty-two mononucleotide repeats were selected from blood genome and pilot amplicon sequencing data. cMSI scoring using these MSI markers achieved 100% sensitivity (95% CI, 93.6%-100.0%) and specificity (95% CI 97.9%-100.0%), was reproducible, and was superior to an established tumor MSI marker panel. Lower cMSI scores were found in patients with CMMRD with MSH6 deficiency and patients with at least 1 mismatch repair missense variant, and patients with biallelic truncating/copy number variants had higher scores. cMSI score did not correlate with age at first tumor.Conclusions: We present an inexpensive and scalable cMSI assay that enhances CMMRD detection relative to existing methods. cMSI score is associated with mismatch repair genotype but not phenotype, suggesting it is not a useful predictor of cancer risk