On the asymptotic normality of persistent Betti numbers

Persistent Betti numbers are a major tool in persistent homology, a subfield of topological data analysis. Many tools in persistent homology rely on the properties of persistent Betti numbers considered as a two-dimensional stochastic process $(r,s) \mapsto n^{-1/2} (\beta^{r,s}_q ( \mathcal{K}(n^{1/d} S_n))-\mathbb{E}[\beta^{r,s}_q ( \mathcal{K}( n^{1/d} S_n))])$. So far, pointwise limit theorems have been established in different set-ups. In particular, the pointwise asymptotic normality of (persistent) Betti numbers has been established for stationary Poisson processes and binomial processes with constant intensity function in the so-called critical (or thermodynamic) regime, see Yogeshwaran et al. [2017] and Hiraoka et al. [2018]. In this contribution, we derive a strong stabilizing property (in the spirit of Penrose and Yukich [2001] of persistent Betti numbers and generalize the existing results on the asymptotic normality to the multivariate case and to a broader class of underlying Poisson and binomial processes. Most importantly, we show that the multivariate asymptotic normality holds for all pairs $(r,s)$, $0\le r\le s<\infty$, and that it is not affected by percolation effects in the underlying random geometric graph

The autoregression bootstrap for kernel estimates of smooth nonlinear functional time series

Functional times series have become an integral part of both functional data and time series analysis. This paper deals with the functional autoregressive model of order 1 and the autoregression bootstrap for smooth functions. The regression operator is estimated in the framework developed by Ferraty and Vieu [2004] and Ferraty et al. [2007] which is here extended to the double functional case under an assumption of stationary ergodic data which dates back to Laib and Louani [2010]. The main result of this article is the characterization of the asymptotic consistency of the bootstrapped regression operator

Deguelin Attenuates Reperfusion Injury and Improves Outcome after Orthotopic Lung Transplantation in the Rat

The main goal of adequate organ preservation is to avoid further cellular metabolism during the phase of ischemia. However, modern preservation solutions do rarely achieve this target. In donor organs hypoxia and ischemia induce a broad spectrum of pathologic molecular mechanisms favoring primary graft dysfunction (PGD) after transplantation. Increased hypoxia-induced transcriptional activity leads to increased vascular permeability which in turn is the soil of a reperfusion edema and the enhancement of a pro-inflammatory response in the graft after reperfusion. We hypothesize that inhibition of the respiration chain in mitochondria and thus inhibition of the hypoxia induced mechanisms might reduce reperfusion edema and consecutively improve survival in vivo. In this study we demonstrate that the rotenoid Deguelin reduces the expression of hypoxia induced target genes, and especially VEGF-A, dose-dependently in hypoxic human lung derived cells. Furthermore, Deguelin significantly suppresses the mRNA expression of the HIF target genes VEGF-A, the pro-inflammatory CXCR4 and ICAM-1 in ischemic lungs vs. control lungs. After lung transplantation, the VEGF-A induced reperfusion-edema is significantly lower in Deguelin-treated animals than in controls. Deguelin-treated rats exhibit a significantly increased survival-rate after transplantation. Additionally, a downregulation of the pro-inflammatory molecules ICAM-1 and CXCR4 and an increase in the recruitment of immunomodulatory monocytes (CD163+ and CD68+) to the transplanted organ involving the IL4 pathway was observed. Therefore, we conclude that ischemic periods preceding reperfusion are mainly responsible for the increased vascular permeability via upregulation of VEGF. Together with this, the resulting endothelial dysfunction also enhances inflammation and consequently lung dysfunction. Deguelin significantly decreases a VEGF-A induced reperfusion edema, induces the recruitment of immunomodulatory monocytes and thus improves organ function and survival after lung transplantation by interfering with hypoxia induced signaling

Dissecting the Shared Genetic Architecture of Suicide Attempt, Psychiatric Disorders, and Known Risk Factors

Background Suicide is a leading cause of death worldwide, and nonfatal suicide attempts, which occur far more frequently, are a major source of disability and social and economic burden. Both have substantial genetic etiology, which is partially shared and partially distinct from that of related psychiatric disorders. Methods We conducted a genome-wide association study (GWAS) of 29,782 suicide attempt (SA) cases and 519,961 controls in the International Suicide Genetics Consortium (ISGC). The GWAS of SA was conditioned on psychiatric disorders using GWAS summary statistics via multitrait-based conditional and joint analysis, to remove genetic effects on SA mediated by psychiatric disorders. We investigated the shared and divergent genetic architectures of SA, psychiatric disorders, and other known risk factors. Results Two loci reached genome-wide significance for SA: the major histocompatibility complex and an intergenic locus on chromosome 7, the latter of which remained associated with SA after conditioning on psychiatric disorders and replicated in an independent cohort from the Million Veteran Program. This locus has been implicated in risk-taking behavior, smoking, and insomnia. SA showed strong genetic correlation with psychiatric disorders, particularly major depression, and also with smoking, pain, risk-taking behavior, sleep disturbances, lower educational attainment, reproductive traits, lower socioeconomic status, and poorer general health. After conditioning on psychiatric disorders, the genetic correlations between SA and psychiatric disorders decreased, whereas those with nonpsychiatric traits remained largely unchanged. Conclusions Our results identify a risk locus that contributes more strongly to SA than other phenotypes and suggest a shared underlying biology between SA and known risk factors that is not mediated by psychiatric disorders.Peer reviewe

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

On the use of multilayer Laue lenses with X-ray free electron lasers

We report on the use of multilayer Laue lenses to focus the intense X-ray Free Electron Laser (XFEL) beam at the European XFEL to a spot size of a few tens of nanometers. We present the procedure to align and characterize these lenses and discuss challenges working with the pulse trains from this unique X-ray source