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

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

Knowledge and expectations of labour among primigravid women in the public health sector

Objectives. We analysed knowledge and expectations of the process and pain of labour in primigravidas attending a local midwifery obstetric unit (MOU). It was anticipated that the results of this study could inform the development of interventions aimed at improving the analgesic care of women delivering at primary health care obstetric units. Design. Qualitative analysis of data obtained from in-depth semi-structured interviews. Setting. A Cape Town MOU. Subjects. 30 black African, Xhosa-speaking primigravidas. Outcome measures. An open-ended interview guide was developed. The themes explored included previous painful experiences, knowledge of labour, expectations of and attitudes towards labour pain, and knowledge of biomedical analgesia. Results. Patients were poorly informed about the process and pain of labour. Most women appeared highly motivated concerning their ability to cope with labour. Most expected pain, but had no concept of the severity or duration of the pain, and knew very little concerning methods available for pain relief in labour. Conclusion. Women at this MOU were poorly prepared for the experience of delivery. Antenatal programmes should incorporate sensitive education concerning the process and pain of labour and the methods available to alleviate pain

Fluorides, orthodontics and demineralization: a systematic review

Objectives: To evaluate the effectiveness of fluoride in preventing white spot lesion (WSL) demineralization during orthodontic treatment and compare all modes of fluoride delivery. Data sources: The search strategy for the review was carried out according to the standard Cochrane systematic review methodology. The following databases were searched for RCTs or CCTs: Cochrane Clinical Trials Register, Cochrane Oral Health Group Specialized Trials Register, MEDLINE and EMBASE. Inclusion and exclusion criteria were applied when considering studies to be included. Authors of trials were contacted for further data. Data selection: The primary outcome of the review was the presence or absence of WSL by patient at the end of treatment. Secondary outcomes included any quantitative assessment of enamel mineral loss or lesion depth. Data extraction: Six reviewers independently, in duplicate, extracted data, including an assessment of the methodological quality of each trial. Data synthesis: Fifteen trials provided data for this review, although none fulfilled all the methodological quality assessment criteria. One study found that a daily NaF mouthrinse reduced the severity of demineralization surrounding an orthodontic appliance (lesion depth difference –70.0 µm; 95% CI –118.2 to –21.8 µm). One study found that use of a glass ionomer cement (GIC) for bracket bonding reduced the prevalence of WSL (Peto OR 0.35; 95% CI 0.15–0.84) compared with a composite resin. None of the studies fulfilled all of the methodological quality assessment criteria. Conclusions: There is some evidence that the use of a daily NaF mouthrinse or a GIC for bonding brackets might reduce the occurrence and severity of WSL during orthodontic treatment. More high quality, clinical research is required into the different modes of delivering fluoride to the orthodontic patient

Fern spore banks: implications for gametophyte establishment

Although angiosperm seed banks have been well documented, almost nothing is known about fern spore banks. This paper reviews the published evidence for spore banks and presents new observations made during a wider investigation of gametophyte establishment at two woodland sites near Edinburgh, Scotland. Analysis of soil cores has revealed the existence oflarge numbers of viable spores, of more than one species, to a depth of at least 35 em at one site and to at least 95 em at the other. Moreover, these spore banks are present throughout the year. Additional investigations in other habitats indicate that fern spore banks are widespread. The biological significance of these observations is discussed.Al contrario de lo que ocurre con los bancos de semillas de las angiospermas que están bien documentados, prácticamente no se conoce nadaacerca de los bancos deesporas de los helechos. Este artículo pasa revista a los conocimientos publicados sobre los bancos de esporas y presenta nuevas observaciones realizadas durante una amplia investigación sobre el desarrollo de los gamet6fitos en dos zonas forestales próximas a Edimburgo, (Escocia). El análisis de muestras de suelo ha revelado la existencia de grandes cantidades de esporas viables de más de una especie a profundidades de al menos 35 cm en una zona estudiada yal menos a 95 cm en otra. Además, estos bancos de esporas están presentes a lo largo de todo el afio. Otras investigaciones adicionales en otros hábitats indican que los bancos de esporas están ampliamenteextendidos. Asi mismo, se discute el significado biológico de estas observaciones

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

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

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

Gravitational lens optical scalars in terms of energy-momentum distributions

This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references in the literature where normally stringent assumptions are made on the sources. The new expressions are manifestly gauge invariant, since they are presented in terms of curvature components. We also present a method of approximation for solving the lens equations, that can be applied to any order.Comment: 17 pages, 2 figures. Titled changed. Small improvements. References added. Final version published in Phys.Rev.

Fine Structures of Shock of SN 1006 with the Chandra Observation

The north east shell of SN 1006 is the most probable acceleration site of high energy electrons (up to ~ 100 TeV) with the Fermi acceleration mechanism at the shock front. We resolved non-thermal filaments from thermal emission in the shell with the excellent spatial resolution of Chandra. The thermal component is extended widely over about ~ 100 arcsec (about 1 pc at 1.8 kpc distance) in width, consistent with the shock width derived from the Sedov solution. The spectrum is fitted with a thin thermal plasma of kT = 0.24 keV in non-equilibrium ionization (NEI), typical for a young SNR. The non-thermal filaments are likely thin sheets with the scale widths of ~ 4 arcsec (0.04 pc) and ~ 20 arcsec (0.2 pc) at upstream and downstream, respectively. The spectra of the filaments are fitted with a power-law function of index 2.1--2.3, with no significant variation from position to position. In a standard diffusive shock acceleration (DSA) model, the extremely small scale length in upstream requires the magnetic field nearly perpendicular to the shock normal. The injection efficiency (eta) from thermal to non-thermal electrons around the shock front is estimated to be ~ 1e-3 under the assumption that the magnetic field in upstream is 10 micro G. In the filaments, the energy densities of the magnetic field and non-thermal electrons are similar to each other, and both are slightly smaller than that of thermal electrons. in the same order for each other. These results suggest that the acceleration occur in more compact region with larger efficiency than previous studies.Comment: 24 pages, 11 figures, Accepted for publication in ApJ, the paper with full resolution images in http://www-cr.scphys.kyoto-u.ac.jp/member/bamba/Paper/SN1006.pd