Clusters from higher order correlations

Given a set of variables and the correlations among them, we develop a method for finding clustering among the variables. The method takes advantage of information implicit in higher-order (not just pairwise) correlations. The idea is to define a Potts model whose energy is based on the correlations. Each state of this model is a partition of the variables and a Monte Carlo method is used to identify states of lowest energy, those most consistent with the correlations. A set of the 100 or so lowest such partitions is then used to construct a stochastic dynamics (using the adjacency matrix of each partition) whose observable representation gives the clustering. Three examples are studied. For two of them the 3$^\mathrm{rd}$ order correlations are significant for getting the clusters right. The last of these is a toy model of a biological system in which the joint action of several genes or proteins is necessary to accomplish a given process

Results of the analysis of the blood lymphocyte proliferation test data from the National Jewish Center

A new approach to the analysis of the blood beryllium lymphocyte proliferation test (LPT) was presented to the Committee to Accredit Beryllium Sensitization Testing-Beryllium Industry Scientific Advisory Committee in April, 1994. Two new outlier resistant methods were proposed for the analysis of the blood LPT and compared with the approach then in use by most labs. The National Jewish Center (NJC) agreed to provide data from a study that was underway at that time. Three groups of LPT data are considered: (1) a sample of 168 beryllium exposed (BE) workers and 20 nonexposed (NE) persons; (2) 25 unacceptable LPTs, and (3) 32 abnormal LPTs for individuals known to have chronic beryllium disease (CBD). The LAV method described in ORNL-6818 was applied to each LPT. Graphical and numerical summaries similar to those presented for the ORISE data are given. Three methods were used to identify abnormal LPTs. All three methods correctly identified the 32 known CBD cases as abnormal

Proof of the Hyperplane Zeros Conjecture of Lagarias and Wang

We prove that a real analytic subset of a torus group that is contained in its image under an expanding endomorphism is a finite union of translates of closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and Wang for real analytic varieties. Our proof uses real analytic geometry, topological dynamics and Fourier analysis.Comment: 25 page

Decay Properties of the Connectivity for Mixed Long Range Percolation Models on Zd\Z^d

In this short note we consider mixed short-long range independent bond percolation models on $\Z^{k+d}$. Let $p_{uv}$ be the probability that the edge $(u,v)$ will be open. Allowing a $x,y$-dependent length scale and using a multi-scale analysis due to Aizenman and Newman, we show that the long distance behavior of the connectivity $\tau_{xy}$ is governed by the probability $p_{xy}$. The result holds up to the critical point.Comment: 6 page

Conformations of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N; its mean squared end to end distance growing as r^2 ~ M/N. A possible collapse transition (to a region of order unity) is related to percolation in a one dimensional model with long--ranged connections. A directed version of the model is also solved exactly. Based on these results, we conjecture that the typical size of a self-avoiding polymer is reduced by the links to R > (N/M)^(nu). The number of links needed to collapse a polymer in three dimensions thus scales as N^(phi), with (phi) > 0.43.Comment: 6 pages, 3 Postscript figures, LaTe

Reconstruction of Black Hole Metric Perturbations from Weyl Curvature

Perturbation theory of rotating black holes is usually described in terms of Weyl scalars $\psi_4$ and $\psi_0$, which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials $\Psi$ in outgoing or ingoing {\it radiation gauges}. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e $\psi_4$ and $\psi_0$. We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole.Comment: 6 Pages, Revtex

Entanglement in the quantum Ising model

We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse field. When the field is sufficiently strong, the entanglement grows at most logarithmically in the number of spins. The proof utilises a transformation to a model of classical probability called the continuum random-cluster model, and is based on a property of the latter model termed ratio weak-mixing. Our proof applies equally to a large class of disordered interactions

Prevention of childhood poisoning in the home: overview of systematic reviews and a systematic review of primary studies

Unintentional poisoning is a significant child public health problem. This systematic overview of reviews, supplemented with a systematic review of recently published primary studies synthesizes evidence on non-legislative interventions to reduce childhood poisonings in the home with particular reference to interventions that could be implemented by Children's Centres in England or community health or social care services in other high income countries. Thirteen systematic reviews, two meta-analyses and 47 primary studies were identified. The interventions most commonly comprised education, provision of cupboard/drawer locks, and poison control centre (PCC) number stickers. Meta-analyses and primary studies provided evidence that interventions improved poison prevention practices. Twenty eight per cent of studies reporting safe medicine storage (OR from meta-analysis 1.57, 95% CI 1.22–2.02), 23% reporting safe storage of other products (OR from meta-analysis 1.63, 95% CI 1.22–2.17) and 46% reporting availability of PCC numbers (OR from meta-analysis 3.67, 95% CI 1.84–7.33) demonstrated significant effects favouring the intervention group. There was a lack of evidence that interventions reduced poisoning rates. Parents should be provided with poison prevention education, cupboard/drawer locks and emergency contact numbers to use in the event of a poisoning. Further research is required to determine whether improving poison prevention practices reduces poisoning rates

Second order gauge invariant gravitational perturbations of a Kerr black hole

We investigate higher than the first order gravitational perturbations in the Newman-Penrose formalism. Equations for the Weyl scalar $\psi_4,$ representing outgoing gravitational radiation, can be uncoupled into a single wave equation to any perturbative order. For second order perturbations about a Kerr black hole, we prove the existence of a first and second order gauge (coordinates) and tetrad invariant waveform, $\psi_I$, by explicit construction. This waveform is formed by the second order piece of $\psi_4$ plus a term, quadratic in first order perturbations, chosen to make $\psi_I$ totally invariant and to have the appropriate behavior in an asymptotically flat gauge. $\psi_I$ fulfills a single wave equation of the form ${\cal T}\psi_I=S,$ where ${\cal T}$ is the same wave operator as for first order perturbations and $S$ is a source term build up out of (known to this level) first order perturbations. We discuss the issues of imposition of initial data to this equation, computation of the energy and momentum radiated and wave extraction for direct comparison with full numerical approaches to solve Einstein equations.Comment: 19 pages, REVTEX. Some misprints corrected and changes to improve presentation. Version to appear in PR

Two-dimensional SIR epidemics with long range infection

We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law $p({\bf x})\sim |{\bf x}|^{-\sigma-2}$ for the probability that a site can infect another site a distance vector ${\bf x}$ apart. As in I we present detailed results for the critical case, for the supercritical case with $\sigma = 2$, and for the supercritical case with $0< \sigma < 2$. For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M. Biskup. For $\sigma=2$ we find generic power laws with $\sigma-$dependent exponents in the supercritical phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead of diverging exponentially with the distance from the critical point, the correlation length increases with an inverse power, as in an ordinary critical point. Finally we study the dependence of the critical exponents on $\sigma$ in the regime $0<\sigma <2$, and compare with field theoretic predictions. In particular we discuss in detail whether the critical behavior for $\sigma$ slightly less than 2 is in the short range universality class, as conjectured recently by F. Linder {\it et al.}. As in I we also consider a modified version of the model where only some of the contacts are long range, the others being between nearest neighbors. If the number of the latter reaches the percolation threshold, the critical behavior is changed but the supercritical behavior stays qualitatively the same.Comment: 14 pages, including 29 figure