Tensor products of subspace lattices and rank one density

We show that, if $M$ is a subspace lattice with the property that the rank one subspace of its operator algebra is weak* dense, $L$ is a commutative subspace lattice and $P$ is the lattice of all projections on a separable infinite dimensional Hilbert space, then the lattice $L\otimes M\otimes P$ is reflexive. If $M$ is moreover an atomic Boolean subspace lattice while $L$ is any subspace lattice, we provide a concrete lattice theoretic description of $L\otimes M$ in terms of projection valued functions defined on the set of atoms of $M$. As a consequence, we show that the Lattice Tensor Product Formula holds for \Alg M and any other reflexive operator algebra and give several further corollaries of these results.Comment: 15 page

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

Intra-annual patterns of tracheid size in the Mediterranean tree Juniperus thurifera as an indicator of seasonal water stress

Because climate can affect xylem cell anatomy, series of intra-annual cell anatomical features have the potential to retrospectively supply seasonal climatic information. In this study, we explored the ability to extract information about water stress conditions from tracheid features of the Mediterranean conifer Juniperus thurifera L. Tracheidograms of four climatic years from two drought-sensitive sites in Spain were compared to evaluate whether it is possible to link intra-annual cell size patterns to seasonal climatic conditions. Results indicated site-specific anatomical adjustment such as smaller and thicker tracheids at the dryer site but also showed a strong climatic imprint on the intra-annual pattern of tracheid size. Site differences in cell size reflected expected structural adjustments against cavitation failures. Differences between intra-annual patterns, however, indicated a response to seasonal changes in water availability whereby cells formed under drought conditions were smaller and thicker, and vice versa. This relationship was more manifest and stable at the dryer sit

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Load-bearing capacity of a red-yellow latosol cultivated with coffee plants subjected to different weed managements

It is essential to know the levels of pressure applied to the soil by different weed managements to adapt the management of coffee plantations in a sustainable manner. The objectives of this study were: a) to generate load-bearing capacity models of a Red-Yellow Latosol (Oxisol) submitted to different weed managements and b) to determine which weed management resulted in higher compression. The study was conducted at the Experimental Farm of EPAMIG, located near the community Farias, in Lavras-MG (latitude 21° 14' 43" S and longitude 44° 59' 59" W and altitude of 919 m). The soil is a Red-Yellow Latosol (LVA) cultivated with coffee plantation using Topazio MG 1190 coffee variety, since 2006. We evaluated five weed managements, three being through mechanical control (harrow (GD), mowing (RÇ) and brush (TC)) and two by chemical control (post-emergence herbicide (HPos) and pre emergence herbicide (HPre)). To obtain the load-bearing capacity models, 10 undisturbed soil samples were randomly collected in the 0-3, 10-13 and 25-28 cm layers between the rows. The load-bearing capacity models which indicated a higher compaction were: in the 0-3 cm layer, TC and GD; in the 10-13 cm layer, HPre, HPos and RÇ and in the 25-28 cm layer, GD. The load-bearing capacity models that indicated greater susceptibility to compaction were: in the 0-3 cm layer, HPos; in the 10-13 cm layer, GD and TC and in the 25-28 cm layer, HPre

Massive Star Formation

This chapter reviews progress in the field of massive star formation. It focuses on evidence for accretion and current models that invoke high accretion rates. In particular it is noted that high accretion rates will cause the massive young stellar object to have a radius much larger than its eventual main sequence radius throughout much of the accretion phase. This results in low effective temperatures which may provide the explanation as to why luminous young stellar objects do not ionized their surroundings to form ultra-compact H II regions. The transition to the ultra-compact H II region phase would then be associated with the termination of the high accretion rate phase. Objects thought to be in a transition phase are discussed and diagnostic diagrams to distinguish between massive young stellar objects and ultra-compact H II regions in terms of line widths and radio luminosity are presented.Comment: 21 pages, 6 figures, chapter in Diffuse Matter from Star Forming Regions to Active Galaxies - A Volume Honouring John Dyson, Edited by T.W. Hartquist, J. M. Pittard, and S. A. E. G. Falle. Series: Astrophysics and Space Science Proceedings. Springer Dordrecht, 2007, p.6