Random simplicial complexes in the medial regime

We describe topology of random simplicial complexes in the lower and upper models in the medial regime, i.e. under the assumption that the probability parameters $p_\sigma$ approach neither $0$ nor $1$. We show that nontrivial Betti numbers of typical lower and upper random simplicial complexes in the medial regime lie in a narrow range of dimensions. For instance, an upper random simplicial complex $Y$ on $n$ vertices in the medial regime with high probability has non-vanishing Betti numbers $b_{j}(Y)$ only for $k+c <n-j<k+\log_2 k +c'$ where $k=\log_2 \ln n$ and $c, c'$ are constants. A lower random simplicial complex on $n$ vertices in the medial regime is with high probability $(k+a)$-connected and its dimension $d$ satisfies $d\sim k+\log_2 k+ a'$ where $a, \, a'$ are constants. The paper develops a new technique, based on Alexander duality, which relates the lower and upper models.Comment: 23 pages. v2 contains an updated abstrac

The Rado simplicial complex

In this paper we study a remarkable simplicial complex X on countably many vertexes. X is universal in the sense that any count- able simplicial complex is an induced subcomplex of X. Additionally, X is homogeneous, i.e. any two isomorphic finite induced subcomplexes are related by an automorphism of X. We prove that X is the unique simplicial complex which is both universal and homogeneous. The 1- skeleton of X is the well-known Rado graph. We show that a random simplicial complex on countably many vertexes is isomorphic to X with probability 1. We prove that the geometric realisation of X is homeo- morphic to an infinite dimensional simplex. We observe several curious properties of X, for example we show that X is robust, i.e. removing any finite set of simplexes leaves a simplicial complex isomorphic to X. The robustness of X leads to the hope that suitable finite approximations of X can serve as models for very resilient networks in real life applications. In a forthcoming paper [8] we study finite approximations to the Rado complex, they can potentially be useful in real life applications due to their structural stability

Mitigation and screening for environmental assessment

This article considers how, as a matter of law and policy, mitigation measures should be taken into account in determining whether a project will have significant environmental effects and therefore be subject to assessment under the EU Environmental Impact Assessment (EIA) Directive. This is not straightforward: it is problematic to distinguish clearly between an activity and the measures proposed to minimise or mitigate for the adverse consequences of the activity. The issue is a salient one in impact assessment law, but under-explored in the literature and handled with some difficulty by the courts. I argue that there is an unnecessarily and undesirably narrow approach currently taken under the EIA Directive, which could be improved upon by taking a more adaptive approach; alternatively a heightened standard of review of ‘significance’, and within this of the scope for mitigation measures to bring projects beneath the significance threshold, may also be desirable

CD103 Expression Is Required for Destruction of Pancreatic Islet Allografts by CD8+ T Cells

The mechanisms by which CD8 effector populations interact with epithelial layers is a poorly defined aspect of adaptive immunity. Recognition that CD8 effectors have the capacity to express CD103, an integrin directed to the epithelial cell-specific ligand E-cadherin, potentially provides insight into such interactions. To assess the role of CD103 in promoting CD8-mediated destruction of epithelial layers, we herein examined the capacity of mice with targeted disruption of CD103 to reject pancreatic islet allografts. Wild-type hosts uniformly rejected islet allografts, concomitant with the appearance of CD8+CD103+ effectors at the graft site. In contrast, the majority of islet allografts transplanted into CD103−/− hosts survived indefinitely. Transfer of wild-type CD8 cells into CD103−/− hosts elicited prompt rejection of long-surviving islet allografts, whereas CD103−/− CD8 cells were completely ineffectual, demonstrating that the defect resides at the level of the CD8 cell. CD8 cells in CD103−/− hosts exhibited normal effector responses to donor alloantigens in vitro and trafficked normally to the graft site, but strikingly failed to infiltrate the islet allograft itself. These data establish a causal relationship between CD8+CD103+ effectors and destruction of graft epithelial elements and suggest that CD103 critically functions to promote intragraft migration of CD8 effectors into epithelial compartments

On strongly chordal graphs that are not leaf powers

A common task in phylogenetics is to find an evolutionary tree representing proximity relationships between species. This motivates the notion of leaf powers: a graph G = (V, E) is a leaf power if there exist a tree T on leafset V and a threshold k such that uv is an edge if and only if the distance between u and v in T is at most k. Characterizing leaf powers is a challenging open problem, along with determining the complexity of their recognition. This is in part due to the fact that few graphs are known to not be leaf powers, as such graphs are difficult to construct. Recently, Nevries and Rosenke asked if leaf powers could be characterized by strong chordality and a finite set of forbidden subgraphs. In this paper, we provide a negative answer to this question, by exhibiting an infinite family \G of (minimal) strongly chordal graphs that are not leaf powers. During the process, we establish a connection between leaf powers, alternating cycles and quartet compatibility. We also show that deciding if a chordal graph is \G-free is NP-complete, which may provide insight on the complexity of the leaf power recognition problem

A comparison of arbitration procedures for risk averse disputants

We propose an arbitration model framework that generalizes many previous quantitative models of final offer arbitration, conventional arbitration, and some proposed alternatives to them. Our model allows the two disputants to be risk averse and assumes that the issue(s) in dispute can be summarized by a single quantifiable value. We compare the performance of the different arbitration procedures by analyzing the gap between the disputants' equilibrium offers and the width of the contract zone that these offers imply. Our results suggest that final offer arbitration should give results superior to those of conventional arbitration.Natural Sciences & Engineering Research Council (NSERC) Discovery Gran

Repression of Esophageal Neoplasia and Inflammatory Signaling by Anti-miR-31 Delivery In Vivo.

BACKGROUND: Overexpression of microRNA-31 (miR-31) is implicated in the pathogenesis of esophageal squamous cell carcinoma (ESCC), a deadly disease associated with dietary zinc deficiency. Using a rat model that recapitulates features of human ESCC, the mechanism whereby Zn regulates miR-31 expression to promote ESCC is examined. METHODS: To inhibit in vivo esophageal miR-31 overexpression in Zn-deficient rats (n = 12-20 per group), locked nucleic acid-modified anti-miR-31 oligonucleotides were administered over five weeks. miR-31 expression was determined by northern blotting, quantitative polymerase chain reaction, and in situ hybridization. Physiological miR-31 targets were identified by microarray analysis and verified by luciferase reporter assay. Cellular proliferation, apoptosis, and expression of inflammation genes were determined by immunoblotting, caspase assays, and immunohistochemistry. The miR-31 promoter in Zn-deficient esophagus was identified by ChIP-seq using an antibody for histone mark H3K4me3. Data were analyzed with t test and analysis of variance. All statistical tests were two-sided. RESULTS: In vivo, anti-miR-31 reduced miR-31 overexpression (P = .002) and suppressed the esophageal preneoplasia in Zn-deficient rats. At the same time, the miR-31 target Stk40 was derepressed, thereby inhibiting the STK40-NF-κΒ-controlled inflammatory pathway, with resultant decreased cellular proliferation and activated apoptosis (caspase 3/7 activities, fold change = 10.7, P = .005). This same connection between miR-31 overexpression and STK40/NF-κΒ expression was also documented in human ESCC cell lines. In Zn-deficient esophagus, the miR-31 promoter region and NF-κΒ binding site were activated. Zn replenishment restored the regulation of this genomic region and a normal esophageal phenotype. CONCLUSIONS: The data define the in vivo signaling pathway underlying interaction of Zn deficiency and miR-31 overexpression in esophageal neoplasia and provide a mechanistic rationale for miR-31 as a therapeutic target for ESCC

An Integrated Method for Accurate Determination of Melting in High-Pressure Laser Heating Experiments

We present an integrated approach for melting determination by monitoring several criteria simultaneously. In particular we combine x-ray diffraction observations with the detection of discontinuities in the optical properties by spectroradiometric measurements. This approach significantly increases the confidence of melt identification, especially with low-Z samples. We demonstrate the method with observations of melt in oxygen at 47 and 55 gigapascals