A Note on Polarization Vectors in Quantum Electrodynamics

A photon of momentum k can have only two polarization states, not three. Equivalently, one can say that the magnetic vector potential A must be divergence free in the Coulomb gauge. These facts are normally taken into account in QED by introducing two polarization vectors epsilon_\lambda(k) with lambda in {1,2}, which are orthogonal to the wave-vector k. These vectors must be very discontinuous functions of k and, consequently, their Fourier transforms have bad decay properties. Since these vectors have no physical significance there must be a way to eliminate them and their bad decay properties from the theory. We propose such a way here.Comment: 6 pages late

There are No Unfilled Shells in Hartree-Fock Theory

Hartree-Fock theory is supposed to yield a picture of atomic shells which may or may not be filled according to the atom's position in the periodic table. We prove that shells are always completely filled in an exact Hartree-Fock calculation. Our theorem generalizes to any system having a two-body interaction that, like the Coulomb potential, is repulsive.Comment: 5 pages, VBEHLMLJPS--16/July/9

Bose-Einstein Quantum Phase Transition in an Optical Lattice Model

Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an external potential, such as that presented by an optical lattice. We present a model of this phenomenon which we are able to analyze rigorously. The system is a hard core lattice gas at half-filling and the optical lattice is modeled by a periodic potential of strength $\lambda$. For small $\lambda$ and temperature, BEC is proved to occur, while at large $\lambda$ or temperature there is no BEC. At large $\lambda$ the low-temperature states are in a Mott insulator phase with a characteristic gap that is absent in the BEC phase. The interparticle interaction is essential for this transition, which occurs even in the ground state. Surprisingly, the condensation is always into the $p=0$ mode in this model, although the density itself has the periodicity of the imposed potential.Comment: RevTeX4, 13 pages, 2 figure

What is marine biodiversity? Towards common concepts and their implications for assessing biodiversity status

Biodiversity' is one of the most common keywords used in environmental sciences, spanning from research to management, nature conservation, and consultancy. Despite this, our understanding of the underlying concepts varies greatly, between and within disciplines as well as among the scientists themselves. Biodiversity can refer to descriptions or assessments of the status and condition of all or selected groups of organisms, from the genetic variability, to the species, populations, communities, and ecosystems. However, a concept of biodiversity also must encompass understanding the interactions and functions on all levels from individuals up to the whole ecosystem, including changes related to natural and anthropogenic environmental pressures. While biodiversity as such is an abstract and relative concept rooted in the spatial domain, it is central to most international, European, and national governance initiatives aimed at protecting the marine environment. These rely on status assessments of biodiversity which typically require numerical targets and specific reference values, to allow comparison in space and/or time, often in association with some external structuring factors such as physical and biogeochemical conditions. Given that our ability to apply and interpret such assessments requires a solid conceptual understanding of marine biodiversity, here we define this and show how the abstract concept can and needs to be interpreted and subsequently applied in biodiversity assessments

Engineered G protein coupled receptors reveal independent regulation of internalization, desensitization and acute signaling

BACKGROUND: The physiological regulation of G protein-coupled receptors, through desensitization and internalization, modulates the length of the receptor signal and may influence the development of tolerance and dependence in response to chronic drug treatment. To explore the importance of receptor regulation, we engineered a series of G(i)-coupled receptors that differ in signal length, degree of agonist-induced internalization, and ability to induce adenylyl cyclase superactivation. All of these receptors, based on the kappa opioid receptor, were modified to be receptors activated solely by synthetic ligands (RASSLs). This modification allows us to compare receptors that have the same ligands and effectors, but differ only in desensitization and internalization. RESULTS: Removal of phosphorylation sites in the C-terminus of the RASSL resulted in a mutant that was resistant to internalization and less prone to desensitization. Replacement of the C-terminus of the RASSL with the corresponding portion of the mu opioid receptor eliminated the induction of AC superactivation, without disrupting agonist-induced desensitization or internalization. Surprisingly, removal of phosphorylation sites from this chimera resulted in a receptor that is constitutively internalized, even in the absence of agonist. However, the receptor still signals and desensitizes in response to agonist, indicating normal G-protein coupling and partial membrane expression. CONCLUSIONS: These studies reveal that internalization, desensitization and adenylyl cyclase superactivation, all processes that decrease chronic G(i)-receptor signals, are independently regulated. Furthermore, specific mutations can radically alter superactivation or internalization without affecting the efficacy of acute G(i )signaling. These mutant RASSLs will be useful for further elucidating the temporal dynamics of the signaling of G protein-coupled receptors in vitro and in vivo

Segmentation of the Retinal Vasculature within Spectral-Domain Optical Coherence Tomography Volumes of Mice

Automated approaches for the segmentation of the retinal vessels are helpful for longitudinal studies of mice using spectral-domain optical coherence tomography (SD-OCT). In the SD-OCT volumes of human eyes, the retinal vasculature can be readily visualized by creating a projected average intensity image in the depth direction. The created projection images can then be segmented using standard approaches. However, in the SD-OCT volumes of mouse eyes, the creation of projection images from the entire volume typically results in very poor images of the vasculature. The purpose of this work is to present and evaluate three machine-learning approaches, namely baseline, single-projection, and all-layers approaches, for the automated segmentation of retinal vessels within SD-OCT volumes of mice. Twenty SD-OCT volumes (400 × 400 × 1024 voxels) from the right eyes of twenty mice were obtained using a Bioptigen SD-OCT machine (Morrisville, NC) to evaluate our methods. The area under the curve (AUC) for the receiver operating characteristic (ROC) curves of the all-layers approach, 0.93, was significantly larger than the AUC for the single-projection (0.91) and baseline (0.88) approach with p < 0.05