The Width of Downsets

How large an antichain can we find inside a given downset in the lattice of subsets of [n]? Sperner's theorem asserts that the largest antichain in the whole lattice has size the binomial coefficient C(n, n/2); what happens for general downsets? Our main results are a Dilworth-type decomposition theorem for downsets, and a new proof of a result of Engel and Leck that determines the largest possible antichain size over all downsets of a given size. We also prove some related results, such as determining the maximum size of an antichain inside the downset that we conjecture minimizes this quantity among downsets of a given size.Comment: 18 pages, 3 figure

Do Bare Rocks Exist on the Moon?

Astronaut surface observations and close-up images at the Apollo and Chang'e 1 landing sites confirm that at least some lunar rocks have no discernable dust cover. However, ALSEP (Apollo Lunar Surface Experiments Package) measurements as well as astronaut and LADEE (Lunar Atmosphere and Dust Environment Explorer) orbital observations and laboratory experiments possibly suggest that a fine fraction of dust is levitated and moves across and above the lunar surface. Over millions of years such dust might be expected to coat all exposed rock surfaces. This study uses thermal modeling, combined with Diviner (a Lunar Reconnaissance Orbiter experiment) orbital lunar eclipse temperature data, to further document the existence of bare rocks on the lunar surface

Rapid detection of Mycobacterium tuberculosis by recombinase polymerase amplification.

Improved access to effective tests for diagnosing tuberculosis (TB) has been designated a public health priority by the World Health Organisation. In high burden TB countries nucleic acid based TB tests have been restricted to centralised laboratories and specialised research settings. Requirements such as a constant electrical supply, air conditioning and skilled, computer literate operators prevent implementation of such tests in many settings. Isothermal DNA amplification technologies permit the use of simpler, less energy intensive detection platforms more suited to low resource settings that allow the accurate diagnosis of a disease within a short timeframe. Recombinase Polymerase Amplification (RPA) is a rapid, low temperature isothermal DNA amplification reaction. We report here RPA-based detection of Mycobacterium tuberculosis complex (MTC) DNA in <20 minutes at 39 °C. Assays for two MTC specific targets were investigated, IS6110 and IS1081. When testing purified MTC genomic DNA, limits of detection of 6.25 fg (IS6110) and 20 fg (IS1081)were consistently achieved. When testing a convenience sample of pulmonary specimens from suspected TB patients, RPA demonstrated superior accuracy to indirect fluorescence microscopy. Compared to culture, sensitivities for the IS1081 RPA and microscopy were 91.4% (95%CI: 85, 97.9) and 86.1% (95%CI: 78.1, 94.1) respectively (n = 71). Specificities were 100% and 88.6% (95% CI: 80.8, 96.1) respectively. For the IS6110 RPA and microscopy sensitivities of 87.5% (95%CI: 81.7, 93.2) and 70.8% (95%CI: 62.9, 78.7) were obtained (n = 90). Specificities were 95.4 (95% CI: 92.3,98.1) and 88% (95% CI: 83.6, 92.4) respectively. The superior specificity of RPA for detecting tuberculosis was due to the reduced ability of fluorescence microscopy to distinguish Mtb complex from other acid fast bacteria. The rapid nature of the RPA assay and its low energy requirement compared to other amplification technologies suggest RPA-based TB assays could be of use for integration into a point-of-care test for use in resource constrained settings

Motivated proteins: a web application for studying small three-dimensional protein motifs

&lt;b&gt;BACKGROUND:&lt;/b&gt; Small loop-shaped motifs are common constituents of the three-dimensional structure of proteins. Typically they comprise between three and seven amino acid residues, and are defined by a combination of dihedral angles and hydrogen bonding partners. The most abundant of these are alphabeta-motifs, asx-motifs, asx-turns, beta-bulges, beta-bulge loops, beta-turns, nests, niches, Schellmann loops, ST-motifs, ST-staples and ST-turns.We have constructed a database of such motifs from a range of high-quality protein structures and built a web application as a visual interface to this. &lt;b&gt;DESCRIPTION:&lt;/b&gt; The web application, Motivated Proteins, provides access to these 12 motifs (with 48 sub-categories) in a database of over 400 representative proteins. Queries can be made for specific categories or sub-categories of motif, motifs in the vicinity of ligands, motifs which include part of an enzyme active site, overlapping motifs, or motifs which include a particular amino acid sequence. Individual proteins can be specified, or, where appropriate, motifs for all proteins listed. The results of queries are presented in textual form as an (X)HTML table, and may be saved as parsable plain text or XML. Motifs can be viewed and manipulated either individually or in the context of the protein in the Jmol applet structural viewer. Cartoons of the motifs imposed on a linear representation of protein secondary structure are also provided. Summary information for the motifs is available, as are histograms of amino acid distribution, and graphs of dihedral angles at individual positions in the motifs. &lt;b&gt;CONCLUSION:&lt;/b&gt; Motivated Proteins is a publicly and freely accessible web application that enables protein scientists to study small three-dimensional motifs without requiring knowledge of either Structured Query Language or the underlying database schem

Email to David Rawson from Joyce Leader

Discussion on Rwanda refugees and various attempts to return them to their homes.https://digitalcommons.georgefox.edu/rawson_rwanda/1099/thumbnail.jp

A parton picture of de Sitter space during slow-roll inflation

It is well-known that expectation values in de Sitter space are afflicted by infra-red divergences. Long ago, Starobinsky proposed that infra-red effects in de Sitter space could be accommodated by evolving the long-wavelength part of the field according to the classical field equations plus a stochastic source term. I argue that--when quantum-mechanical loop corrections are taken into account--the separate-universe picture of superhorizon evolution in de Sitter space is equivalent, in a certain leading-logarithm approximation, to Starobinsky's stochastic approach. In particular, the time evolution of a box of de Sitter space can be understood in exact analogy with the DGLAP evolution of partons within a hadron, which describes a slow logarithmic evolution in the distribution of the hadron's constituent partons with the energy scale at which they are probed.Comment: 36 pages; uses iopart.cls and feynmp.sty. v2: Minor typos corrected. Matches version published in JCA

Turan densities of small hypercubes

How small can a set of vertices in the n-dimensional hypercube Qn be if it meetsevery copy of Qd? The asymptotic density of such a set (for d fixed and n large) is denoted by \gamma d.It is easy to see that \gamma d \leq 1/(d + 1), and it is known that \gamma d = 1/(d + 1) for d \leq 2, but it was recentlyshown that \gamma d &lt; 1/(d + 1) for d \geq 8. In this paper, we show that the latter phenomenon also holdsfor d = 7 and d = 6

Suspect Fits Description: Responses to Racial Profiling in New York City

A panel discussion with Darius Charney, Jesus Gonzalez, David Kennedy, Noel Leader, and Robert Perry. September 29, 201