Shellability of noncrossing partition lattices

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank at least three.Comment: 10 page

h-vectors of generalized associahedra and non-crossing partitions

A case-free proof is given that the entries of the $h$-vector of the cluster complex $\Delta (\Phi)$, associated by S. Fomin and A. Zelevinsky to a finite root system $\Phi$, count elements of the lattice \nc of noncrossing partitions of corresponding type by rank. Similar interpretations for the $h$-vector of the positive part of $\Delta (\Phi)$ are provided. The proof utilizes the appearance of the complex $\Delta (\Phi)$ in the context of the lattice \nc, in recent work of two of the authors, as well as an explicit shelling of $\Delta (\Phi)$.Comment: 20 pages, 1 figur

Ancient technology and punctuated change: Detecting the emergence of the Edomite Kingdom in the Southern Levant.

While the punctuated equilibrium model has been employed in paleontological and archaeological research, it has rarely been applied for technological and social evolution in the Holocene. Using metallurgical technologies from the Wadi Arabah (Jordan/Israel) as a case study, we demonstrate a gradual technological development (13th-10th c. BCE) followed by a human agency-triggered punctuated "leap" (late-10th c. BCE) simultaneously across the entire region (an area of ~2000 km2). Here, we present an unparalleled, diachronic archaeometallurgical dataset focusing on elemental analysis of dozens of well-dated slag samples. Based on the results, we suggest punctuated equilibrium provides an innovative theoretical model for exploring ancient technological changes in relation to larger sociopolitical conditions-in the case at hand the emergence of biblical Edom-, exemplifying its potential for more general cross-cultural applications

Jesse E. Wrench : 1882-1958

"To some he was a teacher or a student counselor and leader, to others a civic gad-fly like Socrates whom he admired greatly, to others a champion of the poor, the underprivileged and dispossessed. To me he was a constant associate and companion for almost twenty years."--Page 36Dean Thomas A. Brady (in address at Memorial Service, Memorial Student Union, November 2, 1958)

Strategies for selection of subjects for sequencing after detection of a linkage peak

Linkage analysis has the potential to localize disease genes of interest, but the choice of which subjects to select for follow-up sequencing after identifying a linkage peak might influence the ability to find a disease gene. We compare nine different strategies for selection of subjects for follow-up sequencing using sequence data from the Genetic Analysis Workshop 17. We found that our more selective strategies, which included methods to identify case subjects more likely to be affected by genetic causes, out-performed sequencing all case and control subjects in linked pedigrees and required sequencing fewer individuals. We found that using genotype data from population control subjects had a higher benefit-cost ratio than sequencing control subjects selected as being the opposite extreme of the case subjects. We conclude that choosing case subjects for sequencing based on more selective strategies can be reliable and cost-effective

Shellability of noncrossing partition lattices

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type Dn and those of exceptional type and rank at least three

Detecting separate time scales in genetic expression data.

BACKGROUND: Biological processes occur on a vast range of time scales, and many of them occur concurrently. As a result, system-wide measurements of gene expression have the potential to capture many of these processes simultaneously. The challenge however, is to separate these processes and time scales in the data. In many cases the number of processes and their time scales is unknown. This issue is particularly relevant to developmental biologists, who are interested in processes such as growth, segmentation and differentiation, which can all take place simultaneously, but on different time scales. RESULTS: We introduce a flexible and statistically rigorous method for detecting different time scales in time-series gene expression data, by identifying expression patterns that are temporally shifted between replicate datasets. We apply our approach to a Saccharomyces cerevisiae cell-cycle dataset and an Arabidopsis thaliana root developmental dataset. In both datasets our method successfully detects processes operating on several different time scales. Furthermore we show that many of these time scales can be associated with particular biological functions. CONCLUSIONS: The spatiotemporal modules identified by our method suggest the presence of multiple biological processes, acting at distinct time scales in both the Arabidopsis root and yeast. Using similar large-scale expression datasets, the identification of biological processes acting at multiple time scales in many organisms is now possible.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are