Linear Extension Diameter of Downset Lattices of 2-Dimensional Posets

The linear extension diameter of a finite poset P is the maximum distance between a pair of linear extensions of P, where the distance between two linear extensions is the number of pairs of elements of P appearing in different orders in the two linear extensions. We prove a formula for the linear extension diameter of the Boolean Lattice and characterize the diametral pairs of linear extensions. For the more general case of a downset lattice D_P of a 2-dimensional poset P, we characterize the diametral pairs of linear extensions of D_P and show how to compute the linear extension diameter of D_P in time polynomial in |P|.Comment: 25 pages, 7 figure

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

LEIR electron cooler status

The electron cooler for LEIR is the first of a new generation of coolers being commissioned for fast phase space cooling of ion beams in storage rings. It is a stateof- the-art cooler incorporating all the recent developments in electron cooling technology (adiabatic expansion, electrostatic bend, variable density electron beam) and is designed to deliver up to 600 mA of electron current for the cooling and stacking of Pb54+ ions in the frame of the ions for LHC project. In this paper we present our experience with the commissioning of the new device as well as the first results of ion beam cooling with a high-intensity variable-density electron beam

Updated life history and population structure assessment of spiny dogfish, Squalus acanthias, in the Gulf of Maine

Spiny dogfish (Squalus acanthias) are considered to be the most abundant shark species in the Western North Atlantic, but recently there was a decline in biomass estimates following a nearly ten-fold increase in fishery landings. Because fishing pressure has been shown to affect population dynamics in targeted species, an update of previous life history parameters is warranted to effectively manage the population. Although updated and accurate life history parameters are important, it is crucial that these parameters are applied to the correct populations, especially when there is evidence of population structuring in the Western Atlantic. This comprehensive study addressed the need for updated and accurate life history characteristics of spiny dogfish by obtaining year round samples covering the entire size range of spiny dogfish. This also enabled examination of spatial and temporal population structuring in the Western North Atlantic. While the vertebrae of spiny dogfish provided a more accurate and precise age estimate than the dorsal fin spines used in previous studies, there was no significant difference in growth prior to or following the increase in fishing pressure. Also, there was no change in the reproductive seasonality or magnitude of morphological, histological, or physiological parameters in mature individuals over this time. However, using a suite of characteristics to define maturity, there was a decrease in size and age at maturity as well as a decrease in fecundity for female spiny dogfish in the present study compared data obtained prior to the fishing pressure. Population structuring was also observed using microsatellite regions in genomic DNA as molecular markers. With the apparent recovery of the spiny dogfish stock in the Western North Atlantic, the findings from the present study as well as a further elucidation of population structure in this region can be utilized to sustainably manage population(s) and predict the effects of fishing pressure in the future

Combinatorial Markov chains on linear extensions

We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other has a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L=S_n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in terms of discrete time Markov chain

Phosphorylation of the androgen receptor is associated with reduced survival in hormonerefractory prostate cancer patients

Cell line studies demonstrate that the PI3K/Akt pathway is upregulated in hormone-refractory prostate cancer (HRPC) and can result in phosphorylation of the androgen receptor (AR). The current study therefore aims to establish if this has relevance to the development of clinical HRPC. Immunohistochemistry was employed to investigate the expression and phosphorylation status of Akt and AR in matched hormone-sensitive and -refractory prostate cancer tumours from 68 patients. In the hormone-refractory tissue, only phosphorylated AR (pAR) was associated with shorter time to death from relapse (<i>P</i>=0.003). However, when an increase in expression in the transition from hormone-sensitive to -refractory prostate cancer was investigated, an increase in expression of PI3K was associated with decreased time to biochemical relapse (<i>P</i>=0.014), and an increase in expression of pAkt<sup>473</sup> and pAR<sup>210</sup> were associated with decreased disease-specific survival (<i>P</i>=0.0019 and 0.0015, respectively). Protein expression of pAkt<sup>473</sup> and pAR<sup>210</sup> also strongly correlated (<i>P</i><0.001, c.c.=0.711) in the hormone-refractory prostate tumours. These results provide evidence using clinical specimens, that upregulation of the PI3K/Akt pathway is associated with phosphorylation of the AR during development of HRPC, suggesting that this pathway could be a potential therapeutic target

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin