Revan-degree indices on random graphs

Given a simple connected non-directed graph $G=(V(G),E(G))$, we consider two families of graph invariants: $RX_\Sigma(G) = \sum_{uv \in E(G)} F(r_u,r_v)$ (which has gained interest recently) and $RX_\Pi(G) = \prod_{uv \in E(G)} F(r_u,r_v)$ (that we introduce in this work); where $uv$ denotes the edge of $G$ connecting the vertices $u$ and $v$, $r_u$ is the Revan degree of the vertex $u$, and $F$ is a function of the Revan vertex degrees. Here, $r_u = \Delta + \delta - d_u$ with $\Delta$ and $\delta$ the maximum and minimum degrees among the vertices of $G$ and $d_u$ is the degree of the vertex $u$. Particularly, we apply both $RX_\Sigma(G)$ and R$X_\Pi(G)$ on two models of random graphs: Erd\"os-R\'enyi graphs and random geometric graphs. By a thorough computational study we show that \left and \left, normalized to the order of the graph, scale with the average Revan degree \left; here \left denotes the average over an ensemble of random graphs. Moreover, we provide analytical expressions for several graph invariants of both families in the dense graph limit.Comment: 16 pages, 10 figure

Modelling the behaviour of microbulk Micromegas in Xenon/trimethylamine gas

We model the response of a state of the art micro-hole single-stage charge amplication device (`microbulk' Micromegas) in a gaseous atmosphere consisting of Xenon/trimethylamine at various concentrations and pressures. The amplifying structure, made with photo-lithographic techniques similar to those followed in the fabrication of gas electron multipliers (GEMs), consisted of a 100 um-side equilateral-triangle pattern with 50 um-diameter holes placed at its vertexes. Once the primary electrons are guided into the holes by virtue of an optimized field configuration, avalanches develop along the 50 um-height channels etched out of the original doubly copper-clad polyimide foil. In order to properly account for the strong field gradients at the holes' entrance as well as for the fluctuations of the avalanche process (that ultimately determine the achievable energy resolution), we abandoned the hydrodynamic framework, resorting to a purely microscopic description of the electron trajectories as obtained from elementary cross-sections. We show that achieving a satisfactory description needs additional assumptions about atom-molecule (Penning) transfer reactions and charge recombination to be made

Lessons from the operation of the "Penning-Fluorescent" TPC and prospects

We have recently reported the development of a new type of high-pressure Xenon time projection chamber operated with an ultra-low diffusion mixture and that simultaneously displays Penning effect and fluorescence in the near-visible region (300 nm). The concept, dubbed `Penning-Fluorescent' TPC, allows the simultaneous reconstruction of primary charge and scintillation with high topological and calorimetric fidelity

Micromegas-TPC operation at high pressure in Xenon-trimethylamine mixtures

We present in this work measurements performed with a small Micromegas-TPC using a xenon-trimethylamine (Xe-TMA) Penning-mixture as filling gas. Measurements of gas gain and energy resolutions for 22.1 keV X-rays are presented, spanning several TMA concentrations and pressures between 1 and 10 bar. Across this pressure range, the best energy resolution and largest increase in gain at constant field (a standard figure for characterizing Penning-like energy transfers) is observed to be in the 1.5%-2.5% TMA region. A gain increase (at constant field) up to a factor 100 and a best energy resolution improved by up to a factor 3 with respect to the one previously reported in pure Xe -operated Micromegas, can be obtained. In virtue of the VUV-quenching properties of the mixture, the overall maximum gain achievable is also notably increased (up to 400 at 10bar), a factor x 3 higher than in pure Xe. In addition, preliminary measurements of the electron drift velocity in a modified setup have been performed and show good agreement with the one obtained from Magboltz. These results are of great interest for calorimetric applications in gas Xe TPCs, in particular for the search of the neutrino-less double beta decay of Xe-136.Comment: 8 pages, 7 figures, proceedin

Periodontitis and Cardiovascular Diseases. Consensus Report

Background: In Europe cardiovascular disease (CVD) is responsible for 3.9 million deaths (45% of deaths), being ischaemic heart disease, stroke, hypertension (leading to heart failure) the major cause of these CVD related deaths. Periodontitis is also a chronic non-communicable disease (NCD) with a high prevalence, being severe periodontitis, affecting 11.2% of the world's population, the sixth most common human disease. Material and Methods: There is now a significant body of evidence to support independent associations between severe periodontitis and several NCDs, in particular CVD. In 2012 a joint workshop was held between the European Federation of Periodontology (EFP) and the American Academy of Periodontology to review the literature relating periodontitis and systemic diseases, including CVD. In the last five years important new scientific information has emerged providing important emerging evidence to support these associations. Results and Conclusions: The present review reports the proceedings of the workshop jointly organised by the EFP and the World Heart Federation (WHF), which has updated the existing epidemiological evidence for significant associations between periodontitis and CVD, the mechanistic links and the impact of periodontal therapy on cardiovascular and surrogate outcomes. This review has also focused on the potential risk and complications of periodontal therapy in patients on anti thrombotic therapy and has made recommendations for dentists, physicians and for patients visiting both the dental and medical practices

Periodontitis and Cardiovascular Diseases. Consensus Report.

Background: In Europe cardiovascular disease (CVD) is responsible for 3.9 million deaths (45% of deaths), being ischaemic heart disease, stroke, hypertension (leading to heart failure) the major cause of these CVD related deaths. Periodontitis is also a chronic non-communicable disease (NCD) with a high prevalence, being severe periodontitis, affecting 11.2% of the world's population, the sixth most common human disease. Material and Methods: There is now a significant body of evidence to support independent associations between severe periodontitis and several NCDs, in particular CVD. In 2012 a joint workshop was held between the European Federation of Periodontology (EFP) and the American Academy of Periodontology to review the literature relating periodontitis and systemic diseases, including CVD. In the last five years important new scientific information has emerged providing important emerging evidence to support these associations. Results and Conclusions: The present review reports the proceedings of the workshop jointly organised by the EFP and the World Heart Federation (WHF), which has updated the existing epidemiological evidence for significant associations between periodontitis and CVD, the mechanistic links and the impact of periodontal therapy on cardiovascular and surrogate outcomes. This review has also focused on the potential risk and complications of periodontal therapy in patients on anti thrombotic therapy and has made recommendations for dentists, physicians and for patients visiting both the dental and medical practices