Not All Saturated 3-Forests Are Tight

A basic statement in graph theory is that every inclusion-maximal forest is connected, i.e. a tree. Using a definiton for higher dimensional forests by Graham and Lovasz and the connectivity-related notion of tightness for hypergraphs introduced by Arocha, Bracho and Neumann-Lara in, we provide an example of a saturated, i.e. inclusion-maximal 3-forest that is not tight. This resolves an open problem posed by Strausz

A Rapid and Computationally Inexpensive Method to Virtually Implant Current and Next-Generation Stents into Subject-Specific Computational Fluid Dynamics Models

Computational modeling is often used to quantify hemodynamic alterations induced by stenting, but frequently uses simplified device or vascular representations. Based on a series of Boolean operations, we developed an efficient and robust method for assessing the influence of current and next-generation stents on local hemodynamics and vascular biomechanics quantified by computational fluid dynamics. Stent designs were parameterized to allow easy control over design features including the number, width and circumferential or longitudinal spacing of struts, as well as the implantation diameter and overall length. The approach allowed stents to be automatically regenerated for rapid analysis of the contribution of design features to resulting hemodynamic alterations. The applicability of the method was demonstrated with patient-specific models of a stented coronary artery bifurcation and basilar trunk aneurysm constructed from medical imaging data. In the coronary bifurcation, we analyzed the hemodynamic difference between closed-cell and open-cell stent geometries. We investigated the impact of decreased strut size in stents with a constant porosity for increasing flow stasis within the stented basilar aneurysm model. These examples demonstrate the current method can be used to investigate differences in stent performance in complex vascular beds for a variety of stenting procedures and clinical scenarios

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

Inhaled nitric oxide to treat intermediate risk pulmonary embolism: A multicenter randomized controlled trial

Objective To test the hypothesis that adjunctive inhaled NO would improve RV function and viability in acute PE. Methods This was a randomized, placebo-controlled, double blind trial conducted at four academic hospitals. Eligible patients had acute PE without systemic arterial hypotension but had RV dysfunction and a treatment plan of standard anticoagulation. Subjects received either oxygen plus 50 parts per million nitrogen (placebo) or oxygen plus 50 ppm NO for 24 h. The primary composite endpoint required a normal RV on echocardiography and a plasma troponin T concentration <14 pg/mL. The secondary endpoint required a blood brain natriuretic peptide concentration <90 pg/mL and a Borg dyspnea score ≤ 2. The sample size of N = 76 tested if 30% more patients treated with NO would achieve the primary endpoint with 80% power and alpha = 5%. Results We randomized 78 patients and after two withdrawals, 38 were treated per protocol in each group. Patients were well matched for baseline conditions. At 24 h, 5/38 (13%) of patients treated with placebo and 9/38 (24%) of patients treated with NO reached the primary endpoint (P = 0.375). The secondary endpoint was reached in 34% with placebo and 13% of the NO (P = 0.11). In a pre-planned post-hoc analysis, we examined how many patients with RV hypokinesis or dilation at enrollment resolved these abnormalities; 29% more patients treated with NO resolved both abnormalities at 24 h (P = 0.010, Cochrane's Q test). Conclusions In patients with severe submassive PE, inhaled nitric oxide failed to increase the proportion of patients with a normal troponin and echocardiogram but increased the probability of eliminating RV hypokinesis and dilation on echocardiography

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

Scientific Guidance on the data required for the risk assessment of flavourings to be used in or on foods

Following a request from the European Commission, EFSA developed a new scientific guidance to assist applicants in the preparation of applications for the authorisation of flavourings to be used in or on foods. This guidance applies to applications for a new authorisation as well as for a modification of an existing authorisation of a food flavouring, submitted under Regulation (EC) No 1331/2008. It defines the scientific data required for the evaluation of those food flavourings for which an evaluation and approval is required according to Article 9 of Regulation (EC) No 1334/2008. This applies to flavouring substances, flavouring preparations, thermal process flavourings, flavour precursors, other flavourings and source materials, as defined in Article 3 of Regulation (EC) No 1334/2008. Information to be provided in all applications relates to: (a) the characterisation of the food flavouring, including the description of its identity, manufacturing process, chemical composition, specifications, stability and reaction and fate in foods; (b) the proposed uses and use levels and the assessment of the dietary exposure and (c) the safety data, including information on the genotoxic potential of the food flavouring, toxicological data other than genotoxicity and information on the safety for the environment. For the toxicological studies, a tiered approach is applied, for which the testing requirements, key issues and triggers are described. Applicants should generate the data requested in each section to support the safety assessment of the food flavouring. Based on the submitted data, EFSA will assess the safety of the food flavouring and conclude whether or not it presents risks to human health and to the environment, if applicable, under the proposed conditions of use

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 &lt; 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