Probabilistic Analysis of Facility Location on Random Shortest Path Metrics

The facility location problem is an NP-hard optimization problem. Therefore, approximation algorithms are often used to solve large instances. Such algorithms often perform much better than worst-case analysis suggests. Therefore, probabilistic analysis is a widely used tool to analyze such algorithms. Most research on probabilistic analysis of NP-hard optimization problems involving metric spaces, such as the facility location problem, has been focused on Euclidean instances, and also instances with independent (random) edge lengths, which are non-metric, have been researched. We would like to extend this knowledge to other, more general, metrics. We investigate the facility location problem using random shortest path metrics. We analyze some probabilistic properties for a simple greedy heuristic which gives a solution to the facility location problem: opening the $\kappa$ cheapest facilities (with $\kappa$ only depending on the facility opening costs). If the facility opening costs are such that $\kappa$ is not too large, then we show that this heuristic is asymptotically optimal. On the other hand, for large values of $\kappa$, the analysis becomes more difficult, and we provide a closed-form expression as upper bound for the expected approximation ratio. In the special case where all facility opening costs are equal this closed-form expression reduces to $O(\sqrt[4]{\ln(n)})$ or $O(1)$ or even $1+o(1)$ if the opening costs are sufficiently small.Comment: A preliminary version accepted to CiE 201

Estimation of conditional laws given an extreme component

Let $(X,Y)$ be a bivariate random vector. The estimation of a probability of the form $P(Y\leq y \mid X >t)$ is challenging when $t$ is large, and a fruitful approach consists in studying, if it exists, the limiting conditional distribution of the random vector $(X,Y)$, suitably normalized, given that $X$ is large. There already exists a wide literature on bivariate models for which this limiting distribution exists. In this paper, a statistical analysis of this problem is done. Estimators of the limiting distribution (which is assumed to exist) and the normalizing functions are provided, as well as an estimator of the conditional quantile function when the conditioning event is extreme. Consistency of the estimators is proved and a functional central limit theorem for the estimator of the limiting distribution is obtained. The small sample behavior of the estimator of the conditional quantile function is illustrated through simulations.Comment: 32 pages, 5 figur

Low copy numbers of complement C4 and C4A deficiency are risk factors for myositis, its subgroups and autoantibodies

Background Idiopathic inflammatory myopathies (IIM) are a group of autoimmune diseases characterised by myositis-related autoantibodies plus infiltration of leucocytes into muscles and/or the skin, leading to the destruction of blood vessels and muscle fibres, chronic weakness and fatigue. While complement-mediated destruction of capillary endothelia is implicated in paediatric and adult dermatomyositis, the complex diversity of complement C4 in IIM pathology was unknown. Methods We elucidated the gene copy number (GCN) variations of total C4, C4A and C4B, long and short genes in 1644 Caucasian patients with IIM, plus 3526 matched healthy controls using real-time PCR or Southern blot analyses. Plasma complement levels were determined by single radial immunodiffusion. Results The large study populations helped establish the distribution patterns of various C4 GCN groups. Low GCNs of C4T (C4T=2+3) and C4A deficiency (C4A=0+1) were strongly correlated with increased risk of IIM with OR equalled to 2.58 (2.28-2.91), p=5.0×10 -53 for C4T, and 2.82 (2.48-3.21), p=7.0×10 -57 for C4A deficiency. Contingency and regression analyses showed that among patients with C4A deficiency, the presence of HLA-DR3 became insignificant as a risk factor in IIM except for inclusion body myositis (IBM), by which 98.2% had HLA-DR3 with an OR of 11.02 (1.44-84.4). Intragroup analyses of patients with IIM for C4 protein levels and IIM-related autoantibodies showed that those with anti-Jo-1 or with anti-PM/Scl had significantly lower C4 plasma concentrations than those without these autoantibodies. Conclusions C4A deficiency is relevant in dermatomyositis, HLA-DRB1∗03 is important in IBM and both C4A deficiency and HLA-DRB1∗03 contribute interactively to risk of polymyositis

Transforming Growth Factor β Receptor Type 1 Is Essential for Female Reproductive Tract Integrity and Function

The transforming growth factor β (TGFβ) superfamily proteins are principle regulators of numerous biological functions. Although recent studies have gained tremendous insights into this growth factor family in female reproduction, the functions of the receptors in vivo remain poorly defined. TGFβ type 1 receptor (TGFBR1), also known as activin receptor-like kinase 5, is the major type 1 receptor for TGFβ ligands. Tgfbr1 null mice die embryonically, precluding functional characterization of TGFBR1 postnatally. To study TGFBR1–mediated signaling in female reproduction, we generated a mouse model with conditional knockout (cKO) of Tgfbr1 in the female reproductive tract using anti-Müllerian hormone receptor type 2 promoter-driven Cre recombinase. We found that Tgfbr1 cKO females are sterile. However, unlike its role in growth differentiation factor 9 (GDF9) signaling in vitro, TGFBR1 seems to be dispensable for GDF9 signaling in vivo. Strikingly, we discovered that the Tgfbr1 cKO females develop oviductal diverticula, which impair embryo development and transit of embryos to the uterus. Molecular analysis further demonstrated the dysregulation of several cell differentiation and migration genes (e.g., Krt12, Ace2, and MyoR) that are potentially associated with female reproductive tract development. Moreover, defective smooth muscle development was also revealed in the uteri of the Tgfbr1 cKO mice. Thus, TGFBR1 is required for female reproductive tract integrity and function, and disruption of TGFBR1–mediated signaling leads to catastrophic structural and functional consequences in the oviduct and uterus

Global mortality from dementia : Application of a new method and results from the Global Burden of Disease Study 2019

Introduction Dementia is currently one of the leading causes of mortality globally, and mortality due to dementia will likely increase in the future along with corresponding increases in population growth and population aging. However, large inconsistencies in coding practices in vital registration systems over time and between countries complicate the estimation of global dementia mortality. Methods We meta-analyzed the excess risk of death in those with dementia and multiplied these estimates by the proportion of dementia deaths occurring in those with severe, end-stage disease to calculate the total number of deaths that could be attributed to dementia. Results We estimated that there were 1.62 million (95% uncertainty interval [UI]: 0.41-4.21) deaths globally due to dementia in 2019. More dementia deaths occurred in women (1.06 million [0.27-2.71]) than men (0.56 million [0.14-1.51]), largely but not entirely due to the higher life expectancy in women (age-standardized female-to-male ratio 1.19 [1.10-1.26]). Due to population aging, there was a large increase in all-age mortality rates from dementia between 1990 and 2019 (100.1% [89.1-117.5]). In 2019, deaths due to dementia ranked seventh globally in all ages and fourth among individuals 70 and older compared to deaths from other diseases estimated in the Global Burden of Disease (GBD) study. Discussion Mortality due to dementia represents a substantial global burden, and is expected to continue to grow into the future as an older, aging population expands globally.Peer reviewe

Advances in ranking and selection, multiple comparisons, and reliability: methodology and applications

S. Panchapakesan has made significant contributions to ranking and selection and has published in many other areas of statistics, including order statistics, reliability theory, stochastic inequalities, and inference. Written in his honor, the twenty invited articles in this volume reflect recent advances in these areas and form a tribute to Panchapakesan's influence and impact on these areas. Thematically organized, the chapters cover a broad range of topics from: Inference; Ranking and Selection; Multiple Comparisons and Tests; Agreement Assessment; Reliability; and Biostatistics. Featurin