Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computation

We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural smoothness parameters of an associated Riemannian manifold. We then apply the method with the manifold defined by the log barrier function to the problems of (1) uniformly sampling a polytope and (2) computing its volume, the latter by extending Gaussian cooling to the manifold setting. In both cases, the total number of steps needed is O^{*}(mn^{\frac{2}{3}}), improving the state of the art. A key ingredient of our analysis is a proof of an analog of the KLS conjecture for Gibbs distributions over manifolds

Spatial Mixing of Coloring Random Graphs

We study the strong spatial mixing (decay of correlation) property of proper $q$-colorings of random graph $G(n, d/n)$ with a fixed $d$. The strong spatial mixing of coloring and related models have been extensively studied on graphs with bounded maximum degree. However, for typical classes of graphs with bounded average degree, such as $G(n, d/n)$, an easy counterexample shows that colorings do not exhibit strong spatial mixing with high probability. Nevertheless, we show that for $q\ge\alpha d+\beta$ with $\alpha>2$ and sufficiently large $\beta=O(1)$, with high probability proper $q$-colorings of random graph $G(n, d/n)$ exhibit strong spatial mixing with respect to an arbitrarily fixed vertex. This is the first strong spatial mixing result for colorings of graphs with unbounded maximum degree. Our analysis of strong spatial mixing establishes a block-wise correlation decay instead of the standard point-wise decay, which may be of interest by itself, especially for graphs with unbounded degree

Bond Breaking Kinetics in Mechanically Controlled Break Junction Experiments: A Bayesian Approach

Breakjunction experiments allow investigating electronic and spintronic properties at the atomic and molecular scale. These experiments generate by their very nature broad and asymmetric distributions of the observables of interest, and thus a full statistical interpretation is warranted. We show here that understanding the complete distribution is essential for obtaining reliable estimates. We demonstrate this for Au atomic point contacts, where by adopting Bayesian reasoning we can reliably estimate the distance to the transition state, $x{\ddag}$, the associated free energy barrier, ${\Delta}G{\ddag}$, and the curvature $\nu$ of the free energy surface. Obtaining robust estimates requires less experimental effort than with previous methods, fewer assumptions, and thus leads to a significant reassessment of the kinetic parameters in this paradigmatic atomic-scale structure. Our proposed Bayesian reasoning offers a powerful and general approach when interpreting inherently stochastic data that yield broad, asymmetric distributions for which analytical models of the distribution may be developed

Species sensitivity of zeolite minerals for uptake of mercury solutes

The uptake of inorganic Hg2+ and organometallic CH3Hg+ from aqueous solutions by 11 different natural zeolites has been investigated using a batch distribution coefficient (Kd) method and supported by a preliminary voltammetric study. The effect of mercury concentration on theKd response is shown over an environmentally appropriate concentration range of 0.1-5 ppm inorganic and organometallic Hg using a batch factor of 100 ml g−1 and 20 h equilibration. Analcime and a Na-chabazite displayed the greatest methylmercury uptakes (Kd values at 1.5 ppm of 4023 and 3456, respectively), with mordenite as the smallest at 578. All uptake responses were greater for methylmercury than for the inorganic mercuric nitrate solutions, suggesting a distinctive sensitivity of zeolites to reaction with different types of solute species. It is likely that this sensitivity is attributable to the precise nature of the resultant Hg-zeolite bonds. Additionally, both the Si-Al ratio and the Na content of the initial natural zeolite samples are shown to influence the Kd responses, with positive correlations between Kd and Na content for all zeolites excluding mordenite

Quantum speedup of classical mixing processes

Most approximation algorithms for #P-complete problems (e.g., evaluating the permanent of a matrix or the volume of a polytope) work by reduction to the problem of approximate sampling from a distribution $\pi$ over a large set $\S$. This problem is solved using the {\em Markov chain Monte Carlo} method: a sparse, reversible Markov chain $P$ on $\S$ with stationary distribution $\pi$ is run to near equilibrium. The running time of this random walk algorithm, the so-called {\em mixing time} of $P$, is $O(\delta^{-1} \log 1/\pi_*)$ as shown by Aldous, where $\delta$ is the spectral gap of $P$ and $\pi_*$ is the minimum value of $\pi$. A natural question is whether a speedup of this classical method to $O(\sqrt{\delta^{-1}} \log 1/\pi_*)$, the diameter of the graph underlying $P$, is possible using {\em quantum walks}. We provide evidence for this possibility using quantum walks that {\em decohere} under repeated randomized measurements. We show: (a) decoherent quantum walks always mix, just like their classical counterparts, (b) the mixing time is a robust quantity, essentially invariant under any smooth form of decoherence, and (c) the mixing time of the decoherent quantum walk on a periodic lattice $\Z_n^d$ is $O(n d \log d)$, which is indeed $O(\sqrt{\delta^{-1}} \log 1/\pi_*)$ and is asymptotically no worse than the diameter of $\Z_n^d$ (the obvious lower bound) up to at most a logarithmic factor.Comment: 13 pages; v2 revised several part

Helminths of the Gastrointestinal Tract of Raccoons in Southern Illinois with Management Implications of \u3ci\u3eBaylisascaris procyonis\u3c/i\u3e Occurrence

The gastrointestinal tracts of 60 raccoons (Procyon lotor) were examined for helminths. Six species were found: four species of nematodes (Arthrocephalus lotoris, Physaloptera rara, Gnathostoma procyonis, and Baylisascaris procyonis); one species of cestode (Mesocestoides variabilis); and one species of acanthocephalan (Macracanthorhynchus ingens). Baylisascaris procyonis has been implicated in the decline of woodrat populations throughout the northeast United States. As such, this parasite also may have been a factor in the extirpation of the eastern woodrat (Neotoma floridana) throughout most of southern Illinois. The frequency occurrence of Baylisascaris procyonis in our sample was unexpectedly low, 3 of 60 raccoons (5.0%), and suggests that reintroduction of eastern woodrats to formerly occupied sites in southern Illinois may not be adversely affected by this parasite

A microfluidic chip based model for the study of full thickness human intestinal tissue using dual flow

© 2016 Author(s). The study of inflammatory bowel disease, including Ulcerative Colitis and Crohn's Disease, has relied largely upon the use of animal or cell culture models; neither of which can represent all aspects of the human pathophysiology. Presented herein is a dual flow microfluidic device which holds full thickness human intestinal tissue in a known orientation. The luminal and serosal sides are independently perfused ex vivo with nutrients with simultaneous waste removal for up to 72 h. The microfluidic device maintains the viability and integrity of the tissue as demonstrated through Haematoxylin & Eosin staining, immunohistochemistry and release of lactate dehydrogenase. In addition, the inflammatory state remains in the tissue after perfusion on the device as determined by measuring calprotectin levels. It is anticipated that this human model will be extremely useful for studying the biology and tes ting novel interventions in diseased tissue