Computations of Vector-Valued Siegel Modular Forms

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Cannabinoid receptor trafficking in peripheral cells is dynamically regulated by a binary biochemical switch

The cannabinoid G protein-coupled receptors (GPCRs) CB₁ and CB₂ are expressed in different peripheral cells. Localization of GPCRs in the cell membrane determines signaling via G protein pathways. Here we show that unlike in transfected cells, CB receptors in cell lines and primary human cells are not internalized upon agonist interaction, but move between cytoplasm and cell membranes by ligand-independent trafficking mechanisms. Even though CB receptors are expressed in many cells of peripheral origin they are not always localized in the cell membrane and in most cancer cell lines the ratios between CB₁ and CB₂ receptor gene and surface expression vary significantly. In contrast, CB receptor cell surface expression in HL60 cells is subject to significant oscillations and CB₂ receptors form oligomers and heterodimers with CB₁ receptors, showing synchronized surface expression, localization and trafficking. We show that hydrogen peroxide and other nonspecific protein tyrosine phosphatase inhibitors (TPIs) such as phenylarsine oxide trigger both CB₂ receptor internalization and externalization, depending on receptor localization. Phorbol ester-mediated internalization of CB receptors can be inhibited via this switch. In primary human immune cells hydrogen peroxide and other TPIs lead to a robust internalization of CB receptors in monocytes and an externalization in T cells. This study describes, for the first time, the dynamic nature of CB receptor trafficking in the context of a biochemical switch, which may have implications for studies on the cell-type specific effects of cannabinoids and our understanding of the regulation of CB receptor cell surface expression.

Intracavity Generation of Radially Polarized CO2 Laser Beams Based on a Simple Binary Dielectric Diffraction Grating

We present experimental results on the intracavity generation of radially polarized light by incorporation of a polarization-selective mirror in a CO2 -laser resonator. The selectivity is achieved with a simple binary dielectric diffraction grating etched in the backsurface of the mirror substrate. Very high polarization selectivity was achieved, and good agreement of simulation and experimental results is shown. The overall radial polarization purity of the generated laser beam was found to be higher than 90% .

A modified test for small-study effects in meta-analyses of controlled trials with binary endpoints

Publication bias and related bias in meta-analysis is often examined by visually checking for asymmetry in funnel plots of treatment effect against its standard error. Formal statistical tests of funnel plot asymmetry have been proposed, but when applied to binary outcome data these can give false-positive rates that are higher than the nominal level in some situations (large treatment effects, or few events per trial, or all trials of similar sizes). We develop a modified linear regression test for funnel plot asymmetry based on the efficient score and its variance, Fisher's information. The performance of this test is compared to the other proposed tests in simulation analyses based on the characteristics of published controlled trials. When there is little or no between-trial heterogeneity, this modified test has a false-positive rate close to the nominal level while maintaining similar power to the original linear regression test ('Egger' test). When the degree of between-trial heterogeneity is large, none of the tests that have been proposed has uniformly good properties.

A Faster Circular Binary Segmentation Algorithm for the Analysis of Array CGH Data

Motivation: Array CGH technologies enable the simultaneous measurement of DNA copy number for thousands of sites on a genome. We developed the circular binary segmentation (CBS) algorithm to divide the genome into regions of equal copy number (Olshen {\it et~al}, 2004). The algorithm tests for change-points using a maximal $t$-statistic with a permutation reference distribution to obtain the corresponding $p$-value. The number of computations required for the maximal test statistic is $O(N^2),$ where $N$ is the number of markers. This makes the full permutation approach computationally prohibitive for the newer arrays that contain tens of thousands markers and highlights the need for a faster. algorithm. Results: We present a hybrid approach to obtain the $p$-value of the test statistic in linear time. We also introduce a rule for stopping early when there is strong evidence for the presence of a change. We show through simulations that the hybrid approach provides a substantial gain in speed with only a negligible loss in accuracy and that the stopping rule further increases speed. We also present the analysis of array CGH data from a breast cancer cell line to show the impact of the new approaches on the analysis of real data. Availability: An R (R Development Core Team, 2006) version of the CBS algorithm has been implemented in the ``DNAcopy'' package of the Bioconductor project (Gentleman {\it et~al}, 2004). The proposed hybrid method for the $p$-value is available in version 1.2.1 or higher and the stopping rule for declaring a change early is available in version 1.5.1 or higher.

Quantifying and Comparing the Accuracy of Binary Biomarkers When Predicting a Failure Time Outcome

The positive and negative predictive value are standard measures used to quantify the predictive accuracy of binary biomarkers when the outcome being predicted is also binary. When the biomarkers are instead being used to predict a failure time outcome, there is no standard way of quantifying predictive accuracy. We propose a natural extension of the traditional predictive values to accommodate censored survival data. We discuss not only quantifying predictive accuracy using these extended predictive values, but also rigorously comparing the accuracy of two biomarkers in terms of their predictive values. Using a marginal regression framework, we describe how to estimate differences in predictive accuracy and how to test whether the observed difference is statistically significant.

Local targeting of malignant gliomas by the diffusible peptidic vector 1,4,7,10-tetraazacyclododecane-1-glutaric acid-4,7,10-triacetic acid-substance p

PURPOSE: Malignant glial brain tumors consistently overexpress neurokinin type 1 receptors. In classic seed-based brachytherapy, one to several rigid (125)I seeds are inserted, mainly for the treatment of small low-grade gliomas. The complex geometry of rapidly proliferating high-grade gliomas requires a diffusible system targeting tumor-associated surface structures to saturate the tumor, including its margins. EXPERIMENTAL DESIGN: We developed a new targeting vector by conjugating the chelator 1,4,7,10-tetraazacyclododecane-1-glutaric acid-4,7,10-triacetic acid to Arg(1) of substance P, generating a radiopharmaceutical with a molecular weight of 1,806 Da and an IC(50) of 0.88 +/- 0.34 nmol/L. Cell biological studies were done with glioblastoma cell lines. neurokinin type-1 receptor (NK1R) autoradiography was done with 58 tumor biopsies. For labeling, (90)Y was mostly used. To reduce the "cross-fire effect" in critically located tumors, (177)Lut and (213)Bi were used instead. In a pilot study, we assessed feasibility, biodistribution, and early and long-term toxicity following i.t. injection of radiolabeled 1,4,7,10-tetraazacyclododecane-1-glutaric acid-4,7,10-triacetic acid substance P in 14 glioblastoma and six glioma patients of WHO grades 2 to 3. RESULTS: Autoradiography disclosed overexpression of NK1R in 55 of 58 gliomas of WHO grades 2 to 4. Internalization of the peptidic vector was found to be specific. Clinically, the radiopharmeutical was distributed according to tumor geometry. Only transient toxicity was seen as symptomatic radiogenic edema in one patient (observation period, 7-66 months). Disease stabilization and/or improved neurologic status was observed in 13 of 20 patients. Secondary resection disclosed widespread radiation necrosis with improved demarcation. CONCLUSIONS: Targeted radiotherapy using diffusible peptidic vectors represents an innovative strategy for local control of malignant gliomas, which will be further assessed as a neoadjuvant approach.