Shearer's point process, the hard-sphere model and a continuum Lov\'asz Local Lemma

A point process is R-dependent, if it behaves independently beyond the minimum distance R. This work investigates uniform positive lower bounds on the avoidance functions of R-dependent simple point processes with a common intensity. Intensities with such bounds are described by the existence of Shearer's point process, the unique R-dependent and R-hard-core point process with a given intensity. This work also presents several extensions of the Lov\'asz Local Lemma, a sufficient condition on the intensity and R to guarantee the existence of Shearer's point process and exponential lower bounds. Shearer's point process shares combinatorial structure with the hard-sphere model with radius R, the unique R-hard-core Markov point process. Bounds from the Lov\'asz Local Lemma convert into lower bounds on the radius of convergence of a high-temperature cluster expansion of the hard-sphere model. This recovers a classic result of Ruelle on the uniqueness of the Gibbs measure of the hard-sphere model via an inductive approach \`a la Dobrushin

Clique trees of infinite locally finite chordal graphs

We investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees. Even more, the edges of a clique tree are in bijection with the edges of the corresponding collection of finite trees. This allows us to enumerate the clique trees of a chordal graph and extend various classic characterisations of clique trees to the infinite setting

Disagreement percolation for the hard-sphere model

Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model and the Boolean model. Non-percolation of the Boolean model implies the uniqueness of the Gibbs measure and exponential decay of pair correlations and finite volume errors. Hence, lower bounds on the critical intensity for percolation of the Boolean model imply lower bounds on the critical activity for a (potential) phase transition. These lower bounds improve upon known bounds obtained by cluster expansion techniques. The proof uses a novel dependent thinning from a Poisson point process to the hard-sphere model, with the thinning probability related to a derivative of the free energy

Disagreement percolation for Gibbs ball models

We generalise disagreement percolation to Gibbs point processes of balls with varying radii. This allows to establish the uniqueness of the Gibbs measure and exponential decay of pair correlations in the low activity regime by comparison with a sub-critical Boolean model. Applications to the Continuum Random Cluster model and the Quermass-interaction model are presented. At the core of our proof lies an explicit dependent thinning from a Poisson point process to a dominated Gibbs point process.Comment: 23 pages, 0 figure Correction, from the published version, of the proof of Section

Information-Preserving Markov Aggregation

We present a sufficient condition for a non-injective function of a Markov chain to be a second-order Markov chain with the same entropy rate as the original chain. This permits an information-preserving state space reduction by merging states or, equivalently, lossless compression of a Markov source on a sample-by-sample basis. The cardinality of the reduced state space is bounded from below by the node degrees of the transition graph associated with the original Markov chain. We also present an algorithm listing all possible information-preserving state space reductions, for a given transition graph. We illustrate our results by applying the algorithm to a bi-gram letter model of an English text.Comment: 7 pages, 3 figures, 2 table

The Impact of Olfactory Disorders in the United Kingdom

Olfactory disorders are believed to affect 5% of the general population and have been shown to bear significant psychosocial consequences to sufferers. Although more common than blindness and profound deafness in the United Kingdom, the impact of these disorders has not been assessed to date and the plight of British patients has yet to be quantified. In 2012, a patient support organization, Fifth Sense, was founded to provide information and support to sufferers of chemosensory disorders. Following a recent members conference, a survey of the membership was conducted anonymously using a series of questions based on an existing olfactory disorders questionnaire. From 496 respondents, this has demonstrated high rates of depression (43%) and anxiety (45%), impairment of eating experience (92%), isolation (57%), and relationship difficulties (54%). Women appear to have significantly more issues than men in terms of social and domestic dysfunction relating to olfactory loss (P = 0.01). Qualitative disorders also affected more than 1 in 5 members with parosmia reported in 19% and phantosmia in 24%. This paper discusses the details of the British story of anosmia and other related disorders as depicted by those most affected

Progress with diamond over-coated microstrip gas chambers

We describe recent observations and measurements with Micro-Strip Gas Chambers coated, after manufacturing, with a thin diamond-like layer in order to increase their rate capability. Compared to the more widely used solution consisting in coating the insulating support with a conductive layer before photo-lithography (the so-called undercoating), over-coating has the advantage of avoiding possible problems with adherence of metals to the layer, damages during the etching process and reduced quality of the artwork resulting from imperfections or dust inclusions in the layer. Early tests have however indicated that, possibly because of damages to the layer due to electron and ion bombardment during the avalanche process, irreversible structural modifications and fatal breakdown could be encountered at very high integral radiation fluxes. The present paper summarizes these results, and describes recent developments demonstrating that a better choice of the parameters of the over-coat may allow to withstand the radiation doses anticipated for LHC detectors with the intrinsically simpler over-coating solution. We discuss also several possible applications of the use of thin, controlled resistivity layers for other families of detectors used or in development for CERN¹s high luminosity collider