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

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

Background & 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 >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