A vertex algebra attached to the flag manifold and Lie algebra cohomology

Each flag manifold carries a unique algebra of chiral differential operators. Continuing along the lines of arXiv:0903.1281 we compute the vertex algebra structure on the cohomology of this algebra. The answer is: the tensor product of the center and a subalgebra; the center is isomorphic, as a commutative associative algebra, to the cohomology of the corresponding maximal nilpotent Lie algebra; the subalgebra is the vacuum module over the corresponding affine Lie algebra of critical level and 0 central character. We next find the Friedan-Martinec-Shenker-Borisov bosonization of the cohomology algebra in case of the projective line and show that this algebra vanishes nonperturbatively, thus verifying a suggestion by Witten.Comment: a reference adde

Localization of affine W-algebras

We introduce the notion of an asymptotic algebra of chiral differential operators. We then construct, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone. We compute the space of global sections of this algebra thereby proving a localization theorem for affine W-algebras at the critical level.Comment: 36 page

A chiral Borel-Weil-Bott theorem

We compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold. This is applied to (1) finding the character of $G$-integrable irreducible highest weight modules over the affine Lie algebra at the critical level, and (2) computing a certain elliptic genus of the flag manifold. The main tool is a result that interprets the Drinfeld-Sokolov reduction as a derived functor.Comment: Some considerable reworking. A final version to appear in Adv. in Mat

New Tardigrade Opsins and Differential Expression Analyses Show Ontogenic Variation in Light Perception

Abstract Opsins are light-sensitive proteins involved in many photoreceptive processes, including, but not limited to, vision and regulation of circadian rhythms. Arthropod (e.g., insects, spiders, centipedes, and crabs) opsins have been extensively researched, but the relationships and function of opsins found in lineages that are evolutionarily closely related to the arthropods remains unclear. Multiple, independent, opsin duplications are known in Tardigrada (the water bears), evidencing that protostome opsin duplications are not limited to the Arthropoda. However, the relationships, function, and expression of these new opsins are still unknown. Here, we use two tardigrade transcriptomes with deep coverage to greatly expand our knowledge of the diversity of tardigrade opsins. We reconstruct the phylogenetic relationships of the tardigrade opsins and investigate their ontogenetic expression. We found that while tardigrades have multiple opsins that evolved from lineage-specific duplications of well-understood arthropod opsins, their expression levels change during ontogeny such that most of these opsins are not co-temporally expressed. Co-temporal expression of multiple opsins underpins color vision in Arthropoda and Vertebrata. Our results clearly show duplications of both rhabdomeric and ciliary opsins within Tardigrada, forming clades specific to both the Heterotardigrada and Eutardigrada in addition to multiple independent duplications within genera. However, lack of co-temporal, ontogenetic, expression suggests that while tardigrades possess multiple opsins, they are unlikely to be able to distinguish color

Opportunities to demonstrate expertise and job satisfaction of community pharmacists in Japan and England

Background: In response to anticipated increased health needs as a consequence of aging populations, and associated rising co-morbidity and medicines use, in both Japan and the UK potential extended roles for community pharmacy are part of health policy agendas. It is widely perceived that community pharmacists do not fully utilize their expertise, which may limit their contribution to health care in their communities and also impact negatively on their own job satisfaction. Purpose: The aim of this qualitative study was to identify operations that are perceived as opportunities to demonstrate expertise (ODE) and/or sources of job satisfaction by pharmacists in Japan and England, and explore associated system and contextual factors. Methods: Data were gathered with purposively selected pharmacists in Japan and England. An initial questionnaire was forwarded which guided subsequent face-to-face semi-structured interviews. These were audio-recoded to enable qualitative analytical procedures. Results: There were 18 participants in England and 13 in Japan. There was a notable association between ODE and job satisfaction. However, ODE was not a sufficient condition for job satisfaction. Conclusion: In order for pharmacists to be satisfied with their jobs, not only ODE but also additional contextual factors, i.e. recognition of professionalism, autonomy and positive collaboration were also needed. The findings can inform initiatives in the development of pharmacy services that would be positive for pharmacists whilst potentially contributing to wider public health objectives

A Correlation between the Emission Intensity of Self-Assembled Germanium Islands and the Quality Factor of Silicon Photonic Crystal Nanocavities

We present a comparative micro-photoluminescence study of the emission intensity of self-assembled germanium islands coupled to the resonator mode of two-dimensional silicon photonic crystal defect nanocavities. The emission intensity is investigated for cavity modes of L3 and Hexapole cavities with different cavity quality factors. For each of these cavities many nominally identical samples are probed to obtain reliable statistics. As the quality factor increases we observe a clear decrease in the average mode emission intensity recorded under comparable optical pumping conditions. This clear experimentally observed trend is compared with simulations based on a dissipative master equation approach that describes a cavity weakly coupled to an ensemble of emitters. We obtain evidence that reabsorption of photons emitted into the cavity mode is responsible for the observed trend. In combination with the observation of cavity linewidth broadening in power dependent measurements, we conclude that free carrier absorption is the limiting effect for the cavity mediated light enhancement under conditions of strong pumping.Comment: 8 pages, 5 figure

Calculation of pure dephasing for excitons in quantum dots

Pure dephasing of an exciton in a small quantum dot by optical and acoustic phonons is calculated using the ``independent boson model''. Considering the case of zero temperature the dephasing is shown to be only partial which manifests itself in the polarization decaying to a finite value. Typical dephasing times can be assigned even though the spectra exhibits strongly non-Lorentzian line shapes. We show that the dephasing from LO phonon scattering, occurs on a much larger time scale than that of dephasing due to acoustic phonons which for low temperatures are also a more efficient dephasing mechanism. The typical dephasing time is shown to strongly depend on the quantum dot size whereas the electron phonon ``coupling strength'' and external electric fields tend mostly to effect the residual coherence. The relevance of the dephasing times for current quantum information processing implementation schemes in quantum dots is discussed

P-shell carriers assisted dynamic nuclear spin polarization in single quantum dots at zero external magnetic field

Repeated injection of spin polarized carriers in a quantum dot leads to the polarization of nuclear spins, a process known as dynamic nuclear spin polarization (DNP). Here, we report the first observation of p-shell carrier assisted DNP in single QDs at zero external magnetic field. The nuclear field - measured by using the Overhauser shift of the singly charged exciton state of the QDs - continues to increase, even after the carrier population in the s-shell saturates. This is also accompanied by an abrupt increase in nuclear spin buildup time as p-shell emission overtakes that of the s-shell. We attribute the observation to p-shell electrons strongly altering the nuclear spin dynamics in the QD, supported by numerical simulation results based on a rate equation model of coupling between electron and nuclear spin system. DNP with p-shell carriers could open up avenues for further control to increase the degree of nuclear spin polarization in QDs.Comment: 23 pages, 6 figure

Duality in finite-dimensional spin glasses

We present an analysis leading to a conjecture on the exact location of the multicritical point in the phase diagram of spin glasses in finite dimensions. The conjecture, in satisfactory agreement with a number of numerical results, was previously derived using an ansatz emerging from duality and the replica method. In the present paper we carefully examine the ansatz and reduce it to a hypothesis on analyticity of a function appearing in the duality relation. Thus the problem is now clearer than before from a mathematical point of view: The ansatz, somewhat arbitrarily introduced previously, has now been shown to be closely related to the analyticity of a well-defined function.Comment: 12 pages, 3 figures; A reference added; to appear in J. Stat. Phy

Electron-hole correlation effects in the emission of light from quantum wires

We present a self-consistent treatment of the electron-hole correlations in optically excited quantum wires within the ladder approximation, and using a contact potential interaction. The limitations of the ladder approximation to the excitonic low-density region are largely overcome by the introduction of higher order correlations through self consistency. We show relevance of these correlations in the low-temperature emission, even for high density relevant in lasing, when large gain replaces excitonic absorption.Comment: 4 paes 3 figure