T. E. Harris' contributions to interacting particle systems and percolation

Interacting particle systems and percolation have been among the most active areas of probability theory over the past half century. Ted Harris played an important role in the early development of both fields. This paper is a bird's eye view of his work in these fields, and of its impact on later research in probability theory and mathematical physics.Comment: Published in at http://dx.doi.org/10.1214/10-AOP593 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Metagenomic Analysis of the Structure and Function of the Human Gut Microbiota in Crohn's Disease

Inflammatory bowel diseases (IBD), such as Crohn’s disease, are chronic, immunologically mediated disorders that have severe medical consequences. The current hypothesis is that these diseases are due to an overly aggressive immune response to a subset of commensal enteric bacteria. Studies to date on IBD have suggested that the disorder may be caused by a combination of bacteria and host susceptibility; however the etiologies of these diseases remain an enigma. In this application, we propose to develop and demonstrate the ability to profile Crohn’s disease at an unprecedented molecular level by elucidation of specific biomarkers (bacterial strains, genes, or proteins) that correlate to disease symptoms. To achieve this goal, we will employ a multidisciplinary approach based on metagenomic and metaproteomic molecular tools to elucidate the composition of the commensal microbiota in monozygotic twins that are either healthy or exhibit Crohn’s disease (for concordant, both are diseased; for discordant, one is healthy and one is diseased). The central hypotheses of this proposal are (1) that specific members and/or functional activities of the gastrointestinal (GI) microbiota differ in patients with Crohn’s disease as compared to healthy individuals, and (2) that it will be possible to elucidate microbial signatures which correlate with the occurrence and progression of this disease by integration of data obtained from 16S rRNA based molecular fingerprinting, metagenomics, and metaproteomics approaches. To address these hypotheses, three specific aims are proposed: 1) Obtain data on community gene content (metagenome) in a subset of healthy twins and twins with Crohn’s Disease to assess potential differences in the metabolic capabilities of the gut microbiota associated with CD, 2) Obtain data on community protein content (metaproteome) in a subset of healthy twins and twins with Crohn’s Disease to assess the state of expressed proteins associated with CD, 3) Apply various statistical clustering and classification methods to correlate/associate microbial community composition, gene and protein content with patient metadata, including metabolite profiles and clinical phenotype. The ultimate goal of these efforts is to identify novel biomarkers for non-invasive diagnostics of CD and to eventually identify drug targets (i.e. bacterial strains) for cure or suppression of disease symptoms

Exclusion processes in higher dimensions: Stationary measures and convergence

There has been significant progress recently in our understanding of the stationary measures of the exclusion process on $Z$. The corresponding situation in higher dimensions remains largely a mystery. In this paper we give necessary and sufficient conditions for a product measure to be stationary for the exclusion process on an arbitrary set, and apply this result to find examples on $Z^d$ and on homogeneous trees in which product measures are stationary even when they are neither homogeneous nor reversible. We then begin the task of narrowing down the possibilities for existence of other stationary measures for the process on $Z^d$. In particular, we study stationary measures that are invariant under translations in all directions orthogonal to a fixed nonzero vector. We then prove a number of convergence results as $t\to\infty$ for the measure of the exclusion process. Under appropriate initial conditions, we show convergence of such measures to the above stationary measures. We also employ hydrodynamics to provide further examples of convergence.Comment: Published at http://dx.doi.org/10.1214/009117905000000341 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

A reconnaissance space sensing investigation of crustal structure for a strip from the eastern Sierra Nevada to the Colorado Plateau

The author has identified the following significant results. Research progress in an investigation using ERTS-1 MSS imagery to study regional tectonics and related natural resources is summarized. Field reconnaissance guided by analysis of ERTS-1 imagery has resulted in development of a tectonic model relating strike-slip faulting to crustal extension in the southern Basin Range Province. The tectonics of the northern Death Valley-Furnace Creek Fault Zone and spacially associated volcanism and mercury mineralization were also investigated. Field work in the southern Sierra Nevada has confirmed the existence of faults and diabase dike swarms aligned along several major lineaments first recognized in ERTS-1 imagery. Various image enhancement and analysis techniques employed in the study of ERTS-1 data are summarized

Finitely dependent coloring

We prove that proper coloring distinguishes between block-factors and finitely dependent stationary processes. A stochastic process is finitely dependent if variables at sufficiently well-separated locations are independent; it is a block-factor if it can be expressed as an equivariant finite-range function of independent variables. The problem of finding non-block-factor finitely dependent processes dates back to 1965. The first published example appeared in 1993, and we provide arguably the first natural examples. More precisely, Schramm proved in 2008 that no stationary 1-dependent 3-coloring of the integers exists, and conjectured that no stationary k-dependent q-coloring exists for any k and q. We disprove this by constructing a 1-dependent 4-coloring and a 2-dependent 3-coloring, thus resolving the question for all k and q. Our construction is canonical and natural, yet very different from all previous schemes. In its pure form it yields precisely the two finitely dependent colorings mentioned above, and no others. The processes provide unexpected connections between extremal cases of the Lovasz local lemma and descent and peak sets of random permutations. Neither coloring can be expressed as a block-factor, nor as a function of a finite-state Markov chain; indeed, no stationary finitely dependent coloring can be so expressed. We deduce extensions involving d dimensions and shifts of finite type; in fact, any non-degenerate shift of finite type also distinguishes between block-factors and finitely dependent processes

How likely is an i.i.d. degree sequence to be graphical?

Given i.i.d. positive integer valued random variables D_1,...,D_n, one can ask whether there is a simple graph on n vertices so that the degrees of the vertices are D_1,...,D_n. We give sufficient conditions on the distribution of D_i for the probability that this be the case to be asymptotically 0, {1/2} or strictly between 0 and {1/2}. These conditions roughly correspond to whether the limit of nP(D_i\geq n) is infinite, zero or strictly positive and finite. This paper is motivated by the problem of modeling large communications networks by random graphs.Comment: Published at http://dx.doi.org/10.1214/105051604000000693 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org