Non-integrality of some Steinberg modules

We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a number ring is generated by integral apartments if and only if the ring is Euclidean. We also construct new cohomology classes in the top dimensional cohomology group of the special linear group of some quadratic imaginary number rings.Comment: 17 pages. To appear in Journal of Topolog

On the generalized Bykovskii presentation of Steinberg modules

We study presentations of the virtual dualizing modules of special linear groups of number rings, the Steinberg modules. Bykovskii gave a presentation for the Steinberg modules of the integers, and our main result is a generalization of this presentation to the Gaussian integers and the Eisenstein integers. We also show that this generalization does not give a presentation for the Steinberg modules of several Euclidean number rings.Comment: Minor revisions based on referee's comments. Accepted for publication at IMR

Uncertainty Analysis for the Miniaturized Laser Heterodyne Radiometer (mini-LHR)

Presented here is a sensitivity analysis for the miniaturized laser heterodyne radiometer (mini-LHR). This passive, ground-based instrument measures carbon dioxide (CO2) in the atmospheric column and has been under development at NASA/GSFC since 2009. The goal of this development is to produce a low-cost, easily-deployable instrument that can extend current ground measurement networks in order to (1) validate column satellite observations, (2) provide coverage in regions of limited satellite observations, (3) target regions of interest such as thawing permafrost, and (4) support the continuity of a long-term climate record. In this paper an uncertainty analysis of the instrument performance is presented and compared with results from three sets of field measurements. The signal-to-noise ratio (SNR) and corresponding uncertainty for a single scan are calculated to be 329.4+/-1.3 by deploying error propagation through the equation governing the SNR. Reported is an absorbance noise of 0.0024 for 6 averaged scans of field data, for an instrument precision of approximately 0.2 ppmv for CO2

Design of a 30 GHz Damped Detuned Accelerating Structure

Within the framework of the SLAC/CERN studies of 30 GHz linear colliders, an attempt has been made to scale as closely as possible the existing X-band NLC damped detuned accelerating structure to 30 GHz. A simple scaling was not possible because of mechanical and RF constraints. The 30 GHz design has 101 cells and a minimum aperture of 3.4 mm. In order to obtain acceptably small values for both the single-bunch transverse wakefield and the long-range multibunch wakefield a relatively large non-linear variation of the iris thickness was introduced in addition to the iris diameter variation. The resulting wakefield has a short-range value of 1290 V/pC/mm/m and a long range value below 10 V/pC/mm/m

Conserved Charges in the Principal Chiral Model on a Supergroup

The classical principal chiral model in 1+1 dimensions with target space a compact Lie supergroup is investigated. It is shown how to construct a local conserved charge given an invariant tensor of the Lie superalgebra. We calculate the super-Poisson brackets of these currents and argue that they are finitely generated. We show how to derive an infinite number of local charges in involution. We demonstrate that these charges Poisson commute with the non-local charges of the model

Resistance to Cancer Treatment: The Role of Somatic Genetic Events and the Challenges for Targeted Therapies

Therapeutic resistance remains a major cause of cancer-related deaths. Resistance can occur from the outset of treatment or as an acquired phenomenon after an initial clinical response. Therapeutic resistance is an almost universal phenomenon in the treatment of metastatic cancers. The advent of molecularly targeted treatments brought greater efficacy in patients whose tumors express a particular target or molecular signature. However, resistance remains a predictable challenge. This article provides an overview of somatic genomic events that confer resistance to cancer therapies. Some examples, including BCR–Abl, EML4–ALK, and the androgen receptor, contain mutations in the target itself, which hamper binding and inhibitory functions of therapeutic agents. There are also examples of somatic genetic changes in other genes or pathways that result in resistance by circumventing the inhibitor, as in resistance to trastuzumab and BRAF inhibitors. Yet other examples results in activation of cytoprotective genes. The fact that all of these mechanisms of resistance are due to somatic changes in the tumor’s genome makes targeting them selectively a feasible goal. To identify and validate these changes, it is important to obtain biopsies of clinically resistant tumors. A rational consequence of this evolving knowledge is the growing appreciation that combinations of inhibitors will be needed to anticipate and overcome therapeutic resistance