Rapid Mixing for Lattice Colorings with Fewer Colors

We provide an optimally mixing Markov chain for 6-colorings of the square lattice on rectangular regions with free, fixed, or toroidal boundary conditions. This implies that the uniform distribution on the set of such colorings has strong spatial mixing, so that the 6-state Potts antiferromagnet has a finite correlation length and a unique Gibbs measure at zero temperature. Four and five are now the only remaining values of q for which it is not known whether there exists a rapidly mixing Markov chain for q-colorings of the square lattice.Comment: Appeared in Proc. LATIN 2004, to appear in JSTA

Isolation of tributyltin-degrading bacteria citrobacter braakii and enterobacter cloacae from butyltin-polluted sediment

Tributyltin compound (TBT) released into the aquatic environment is generally degraded by bacteria in water and sediment. The isolation of TBT-degrading bacteria from TBT polluted sediment leads to the indication of specific potential TBT degraders. Two new strains of bacteria designated as B2 and B3 were successfully isolated using glycerol medium containing tributyltin chloride (TBTC) at 130 μM from contaminated sediment collected from Bowling Basin in Glasgow. The observed degradation after 14 days of the microcosm from the sediment and the isolated bacteria were investigated at an initial concentration of 1 μM TBTC. It was found that TBT was degraded by the bacterial strains B2 and B3 at 8.3 and 16.9 %, respectively. The results indicate that B2 and B3 are effective as TBT degraders. EC50 of B2 and B3 in water were 88.73 and 112.53 μM TBTC, which were significantly higher than the concentration of TBT measured at the basin, suggesting a low effect of TBT on the growth and activity of bacteria. After identification using API 20E and 16S sequencing, the bacterial isolate strain B2 is Citrobacter braakii and B3 is Enterobacter cloacae. Therefore, this study has discovered two species of high resistance TBT degrader which have never been previously studied or isolated based upon TBT degradation ability

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

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

Technical management techniques for identification and control of industrial safety and pollution hazards

Constructive recommendations are suggested for pollution problems from offshore energy resources industries on outer continental shelf. Technical management techniques for pollution identification and control offer possible applications to space engineering and management

Ablation debris control by means of closed thick film filtered water immersion

The performance of laser ablation generated debris control by means of open immersion techniques have been shown to be limited by flow surface ripple effects on the beam and the action of ablation plume pressure loss by splashing of the immersion fluid. To eradicate these issues a closed technique has been developed which ensured a controlled geometry for both the optical interfaces of the flowing liquid film. This had the action of preventing splashing, ensuring repeatable machining conditions and allowed for control of liquid flow velocity. To investigate the performance benefits of this closed immersion technique bisphenol A polycarbonate samples have been machined using filtered water at a number of flow velocities. The results demonstrate the efficacy of the closed immersion technique: a 93% decrease in debris is produced when machining under closed filtered water immersion; the average debris particle size becomes larger, with an equal proportion of small and medium sized debris being produced when laser machining under closed flowing filtered water immersion; large debris is shown to be displaced further by a given flow velocity than smaller debris, showing that the action of flow turbulence in the duct has more impact on smaller debris. Low flow velocities were found to be less effective at controlling the positional trend of deposition of laser ablation generated debris than high flow velocities; but, use of excessive flow velocities resulted in turbulence motivated deposition. This work is of interest to the laser micromachining community and may aide in the manufacture of 2.5D laser etched patterns covering large area wafers and could be applied to a range of wavelengths and laser types

X-Ray Synchrotron Emitting Fe-Rich Ejecta in SNR RCW 86

Supernova remnants may exhibit both thermal and nonthermal X-ray emission. We present Chandra observations of RCW 86. Striking differences in the morphology of X-rays below 1 keV and above 2 keV point to a different physical origin. Hard X-ray emission is correlated fairly well with the edges of regions of radio emission, suggesting that these are the locations of shock waves at which both short-lived X-ray emitting electrons, and longer-lived radio-emitting electrons, are accelerated. Soft X-rays are spatially well-correlated with optical emission from nonradiative shocks, which are almost certainly portions of the outer blast wave. These soft X-rays are well fit with simple thermal plane-shock models. Harder X-rays show Fe K alpha emission and are well described with a similar soft thermal component, but a much stronger synchrotron continuum dominating above 2 keV, and a strong Fe K alpha line. Quantitative analysis of this line and the surrounding continuum shows that it cannot be produced by thermal emission from a cosmic-abundance plasma; the ionization time is too short, as shown both by the low centroid energy (6.4 keV) and the absence of oxygen lines below 1 keV. Instead, a model of a plane shock into Fe-rich ejecta, with a synchrotron continuum, provides a natural explanation. This requires that reverse shocks into ejecta be accelerating electrons to energies of order 50 TeV. We show that maximum energies of this order can be produced by radiation-limited diffusive shock acceleration at the reverse shocks.Comment: ApJ, accepted; full resolution images in http://spider.ipac.caltech.edu/staff/rho/rcw86chandra.p