Isoperimetric Inequalities in Simplicial Complexes

In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high dimensional Laplacian defined by Eckmann. In particular, we present a Cheeger-type inequality, and a high-dimensional Expander Mixing Lemma. As a corollary, using the work of Pach, we obtain a connection between spectral properties of complexes and Gromov's notion of geometric overlap. Using the work of Gunder and Wagner, we give an estimate for the combinatorial expansion and geometric overlap of random Linial-Meshulam complexes

On Eigenvalues of Random Complexes

We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial-Meshulam model $X^k(n,p)$ of random $k$-dimensional simplicial complexes on $n$ vertices. We show that for $p=\Omega(\log n/n)$, the eigenvalues of these matrices are a.a.s. concentrated around two values. The main tool, which goes back to the work of Garland, are arguments that relate the eigenvalues of these matrices to those of graphs that arise as links of $(k-2)$-dimensional faces. Garland's result concerns the Laplacian; we develop an analogous result for the adjacency matrix. The same arguments apply to other models of random complexes which allow for dependencies between the choices of $k$-dimensional simplices. In the second part of the paper, we apply this to the question of possible higher-dimensional analogues of the discrete Cheeger inequality, which in the classical case of graphs relates the eigenvalues of a graph and its edge expansion. It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the higher-dimensional Laplacian spectra capture the notion of coboundary expansion - a generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov. We show that this most straightforward version of a higher-dimensional discrete Cheeger inequality fails, in quite a strong way: For every $k\geq 2$ and $n\in \mathbb{N}$, there is a $k$-dimensional complex $Y^k_n$ on $n$ vertices that has strong spectral expansion properties (all nontrivial eigenvalues of the normalised $k$-dimensional Laplacian lie in the interval $[1-O(1/\sqrt{n}),1+O(1/\sqrt{n})]$) but whose coboundary expansion is bounded from above by $O(\log n/n)$ and so tends to zero as $n\rightarrow \infty$; moreover, $Y^k_n$ can be taken to have vanishing integer homology in dimension less than $k$.Comment: Extended full version of an extended abstract that appeared at SoCG 2012, to appear in Israel Journal of Mathematic

Association of germline genetic variants with breast cancer-specific survival in patient subgroups defined by clinic-pathological variables related to tumor biology and type of systemic treatment

BACKGROUND: Given the high heterogeneity among breast tumors, associations between common germline genetic variants and survival that may exist within specific subgroups could go undetected in an unstratified set of breast cancer patients. METHODS: We performed genome-wide association analyses within 15 subgroups of breast cancer patients based on prognostic factors, including hormone receptors, tumor grade, age, and type of systemic treatment. Analyses were based on 91,686 female patients of European ancestry from the Breast Cancer Association Consortium, including 7531 breast cancer-specific deaths over a median follow-up of 8.1 years. Cox regression was used to assess associations of common germline variants with 15-year and 5-year breast cancer-specific survival. We assessed the probability of these associations being true positives via the Bayesian false discovery probability (BFDP < 0.15). RESULTS: Evidence of associations with breast cancer-specific survival was observed in three patient subgroups, with variant rs5934618 in patients with grade 3 tumors (15-year-hazard ratio (HR) [95% confidence interval (CI)] 1.32 [1.20, 1.45], P = 1.4E-08, BFDP = 0.01, per G allele); variant rs4679741 in patients with ER-positive tumors treated with endocrine therapy (15-year-HR [95% CI] 1.18 [1.11, 1.26], P = 1.6E-07, BFDP = 0.09, per G allele); variants rs1106333 (15-year-HR [95% CI] 1.68 [1.39,2.03], P = 5.6E-08, BFDP = 0.12, per A allele) and rs78754389 (5-year-HR [95% CI] 1.79 [1.46,2.20], P = 1.7E-08, BFDP = 0.07, per A allele), in patients with ER-negative tumors treated with chemotherapy. CONCLUSIONS: We found evidence of four loci associated with breast cancer-specific survival within three patient subgroups. There was limited evidence for the existence of associations in other patient subgroups. However, the power for many subgroups is limited due to the low number of events. Even so, our results suggest that the impact of common germline genetic variants on breast cancer-specific survival might be limited

Critical evaluation of key evidence on the human health hazards of exposure to bisphenol A

Despite the fact that more than 5000 safety-related studies have been published on bisphenol A (BPA), there seems to be no resolution of the apparently deadlocked controversy as to whether exposure of the general population to BPA causes adverse effects due to its estrogenicity. Therefore, the Advisory Committee of the German Society of Toxicology reviewed the background and cutting-edge topics of this BPA controversy. The current tolerable daily intake value (TDI) of 0.05 mg/kg body weight [bw]/day, derived by the European Food Safety Authority (EFSA), is mainly based on body weight changes in two- and three-generation studies in mice and rats. Recently, these studies and the derivation of the TDI have been criticized. After having carefully considered all arguments, the Committee had to conclude that the criticism was scientifically not justified; moreover, recently published additional data further support the reliability of the two-and three-generation studies demonstrating a lack of estrogen-dependent effects at and below doses on which the current TDI is based. A frequently discussed topic is whether doses below 5 mg/ kg bw/day may cause adverse health effects in laboratory animals. Meanwhile, it has become clear that positive results from some explorative studies have not been confirmed in subsequent studies with higher numbers of animals or a priori defined hypotheses. Particularly relevant are some recent studies with negative outcomes that addressed effects of BPA on the brain, behavior, and the prostate in rodents for extrapolation to the human situation. The Committee came to the conclusion that rodent data can well be used as a basis for human risk evaluation. Currently published conjectures that rats are insensitive to estrogens compared to humans can be refuted. Data from toxicokinetics studies show that the half-life of BPA in adult human subjects is less than 2 hours and BPA is completely recovered in urine as BPA-conjugates. Tissue deconjugation of BPA-glucuronide and -sulfate may occur. Because of the extremely low quantities, it is only of minor relevance for BPA toxicity. Biomonitoring studies have been used to estimate human BPA exposure and show that the daily intake of BPA is far below the TDI for the general population. Further topics addressed in this article include reasons why some studies on BPA are not reproducible; the relevance of oral versus non-oral exposure routes; the degree to which newborns are at higher systemic BPA exposure; increased BPA exposure by infusions in intensive care units; mechanisms of action other than estrogen receptor activation; and the current regulatory status in Europe, as well as in the USA, Canada, Japan, New Zealand, and Australia. Overall, the Committee concluded that the current TDI for BPA is adequately justified and that the available evidence indicates that BPA exposure represents no noteworthy risk to the health of the human population, including newborns and babies

Job Insecurity: Differential Effects of Subjective and Objective Measures on Life Satisfaction Trajectories of Workers Aged 27–30 in Germany

Job insecurity has become increasingly evident in European countries in recent years. In Germany, legislation has increased insecurity through erosion of the standard employment relationship. Fixed-term contracts are central to definitions of insecurity based on atypical or precarious work but there is still limited understanding of what creates insecurity and how it affects workers. Drawing on Bourdieu’s thesis that “insecurity is everywhere”, the relationships between subjective and objective measures of insecurity are examined for their impact on the 5-year trajectories of life satisfaction of men and women in the age group 27–30. Latent growth curve analysis of data from the German Socio-Economic Panel for 2010–2014 highlights the adverse and lasting effects of subjective concerns about job insecurity on life satisfaction trajectories. This association cuts across educational groups, with far reaching implications as subjective concerns about job security permeate young worker’s lives well beyond the objective condition of being employed on a fixed-term contract

Physical activity, sedentary time and breast cancer risk: a Mendelian randomisation study

Objectives: Physical inactivity and sedentary behaviour are associated with higher breast cancer risk in observational studies, but ascribing causality is difficult. Mendelian randomisation (MR) assesses causality by simulating randomised trial groups using genotype. We assessed whether lifelong physical activity or sedentary time, assessed using genotype, may be causally associated with breast cancer risk overall, pre/post-menopause, and by case-groups defined by tumour characteristics. Methods: We performed two-sample inverse-variance-weighted MR using individual-level Breast Cancer Association Consortium case-control data from 130 957 European-ancestry women (69 838 invasive cases), and published UK Biobank data (n=91 105–377 234). Genetic instruments were single nucleotide polymorphisms (SNPs) associated in UK Biobank with wrist-worn accelerometer-measured overall physical activity (nsnps=5) or sedentary time (nsnps=6), or accelerometer-measured (nsnps=1) or self-reported (nsnps=5) vigorous physical activity. Results: Greater genetically-predicted overall activity was associated with lower breast cancer overall risk (OR=0.59; 95% confidence interval (CI) 0.42 to 0.83 per-standard deviation (SD;~8 milligravities acceleration)) and for most case-groups. Genetically-predicted vigorous activity was associated with lower risk of pre/perimenopausal breast cancer (OR=0.62; 95% CI 0.45 to 0.87,≥3 vs. 0 self-reported days/week), with consistent estimates for most case-groups. Greater genetically-predicted sedentary time was associated with higher hormone-receptor-negative tumour risk (OR=1.77; 95% CI 1.07 to 2.92 per-SD (~7% time spent sedentary)), with elevated estimates for most case-groups. Results were robust to sensitivity analyses examining pleiotropy (including weighted-median-MR, MR-Egger). Conclusion: Our study provides strong evidence that greater overall physical activity, greater vigorous activity, and lower sedentary time are likely to reduce breast cancer risk. More widespread adoption of active lifestyles may reduce the burden from the most common cancer in women