Relations between three-point configuration space shear and convergence statistics

With the growing interest in and ability of using weak lensing studies to probe the non-Gaussian properties of the matter density field, there is an increasing need for the study of suitable statistical measures, e.g. shear three-point statistics. In this paper we establish the relations between the three-point configuration space shear and convergence statistics, which are an important missing link between different weak lensing three-point statistics and provide an alternative way of relating observation and theory. The method we use also allows us to derive the relations between other two- and three-point correlation functions. We show the consistency of the relations obtained with already established results and demonstrate how they can be evaluated numerically. As a direct application, we use these relations to formulate the condition for E/B-mode decomposition of lensing three-point statistics, which is the basis for constructing new three-point statistics which allow for exact E/B-mode separation. Our work applies also to other two-dimensional polarization fields such as that of the Cosmic Microwave Background.Comment: 17 pages, 5 figures, submitted to A&

Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole

Toroidal multipoles are a topic of increasing interest in the nanophotonics and metamaterials communities. In this paper, we separate out the toroidal multipole components of multipole expansions in polar coordinates (two- and three-dimensional) by expanding the Bessel or spherical Bessel functions. We discuss the formation of the lowest order of magnetic anapoles from the interaction between the magnetic toroidal dipole and the magnetic dipole. Our method also reveals that there are higher order current configurations other than the electric toroidal multipole that have the same radiation characteristics as the pure electric dipole. Furthermore, we find that the anapole condition requires that there is a perfect cancellation of all higher order current configurations

Amino acid residues 24-31 but not palmitoylation of cysteines 30 and 45 are required for membrane anchoring of glutamic acid decarboxylase, GAD65.

The smaller isoform of the GABA synthesizing enzyme glutamic acid decarboxylase, GAD65, is synthesized as a soluble protein that undergoes post-translational modification(s) in the NH2-terminal region to become anchored to the membrane of small synaptic-like microvesicles in pancreatic beta cells, and synaptic vesicles in GABA-ergic neurons. A soluble hydrophilic form, a soluble hydrophobic form, and a hydrophobic firmly membrane-anchored form have been detected in beta cells. A reversible and hydroxylamine sensitive palmitoylation has been shown to distinguish the firmly membrane-anchored form from the soluble yet hydrophobic form, suggesting that palmitoylation of cysteines in the NH2-terminal region is involved in membrane anchoring. In this study we use site-directed mutagenesis to identify the first two cysteines in the NH2-terminal region, Cys 30 and Cys 45, as the sites of palmitoylation of the GAD65 molecule. Mutation of Cys 30 and Cys 45 to Ala results in a loss of palmitoylation but does not significantly alter membrane association of GAD65 in COS-7 cells. Deletion of the first 23 amino acids at the NH2 terminus of the GAD65 30/45A mutant also does not affect the hydrophobicity and membrane anchoring of the GAD65 protein. However, deletion of an additional eight amino acids at the NH2 terminus results in a protein which is hydrophilic and cytosolic. The results suggest that amino acids 24-31 are required for hydrophobic modification and/or targeting of GAD65 to membrane compartments, whereas palmitoylation of Cys 30 and Cys 45 may rather serve to orient or fold the protein at synaptic vesicle membranes

Scalable Coordinated Beamforming for Dense Wireless Cooperative Networks

To meet the ever growing demand for both high throughput and uniform coverage in future wireless networks, dense network deployment will be ubiquitous, for which co- operation among the access points is critical. Considering the computational complexity of designing coordinated beamformers for dense networks, low-complexity and suboptimal precoding strategies are often adopted. However, it is not clear how much performance loss will be caused. To enable optimal coordinated beamforming, in this paper, we propose a framework to design a scalable beamforming algorithm based on the alternative direction method of multipliers (ADMM) method. Specifically, we first propose to apply the matrix stuffing technique to transform the original optimization problem to an equivalent ADMM-compliant problem, which is much more efficient than the widely-used modeling framework CVX. We will then propose to use the ADMM algorithm, a.k.a. the operator splitting method, to solve the transformed ADMM-compliant problem efficiently. In particular, the subproblems of the ADMM algorithm at each iteration can be solved with closed-forms and in parallel. Simulation results show that the proposed techniques can result in significant computational efficiency compared to the state- of-the-art interior-point solvers. Furthermore, the simulation results demonstrate that the optimal coordinated beamforming can significantly improve the system performance compared to sub-optimal zero forcing beamforming