Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)

The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible $gl(m|n)$ modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1311.424

Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond

In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary representations of the Lie superalgebra gl(mjn). Extensions to the non-unitary case are investigated. A symmetry relation between two classes of Wigner coefficients is given in terms of a ratio of dimensions.Comment: 17 page

Close encounters : spatial distances between people and a robot of mechanistic appearance

Peer reviewe

Characteristic identities for Lie (super)algebras

We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the theory, we look at the examples of the general linear Lie algebras and Lie superalgebras.Comment: 10 pages, contribution to the 30th International Colloquium on Group Theoretical Methods in Physics (Group30) in Ghent, Belgium. Journal of Physics: Conference Series (to appear

Targeting the Oxytocin System: New Pharmacotherapeutic Approaches

Deficits in social behavioral domains, such as interpersonal communication, emotion recognition, and empathy, are a characteristic symptom in several neuropsychiatric disorders, including schizophrenia and autism spectrum disorder (ASD). The neuropeptide oxytocin (OT) has emerged as a key regulator of diverse social behaviors in vertebrates and, thus, has been identified as a potential therapeutic target for improving social dysfunction. In recent years, the field of OT research has seen an explosion of scientific inquiry, producing a more comprehensive picture of oxytocinergic signaling and the pathways that regulate its release and degradation in the brain. In this review, we provide an analysis of how this information is being exploited to accelerate the discovery of novel oxytocinergic therapeutics

Reef-fidelity and migration of tiger sharks, Galeocerdo cuvier, across the Coral Sea

© The Author(s), 2014. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in PLoS One 9 (2014): e83249, doi:10.1371/journal.pone.0083249.Knowledge of the habitat use and migration patterns of large sharks is important for assessing the effectiveness of large predator Marine Protected Areas (MPAs), vulnerability to fisheries and environmental influences, and management of shark–human interactions. Here we compare movement, reef-fidelity, and ocean migration for tiger sharks, Galeocerdo cuvier, across the Coral Sea, with an emphasis on New Caledonia. Thirty-three tiger sharks (1.54 to 3.9 m total length) were tagged with passive acoustic transmitters and their localised movements monitored on receiver arrays in New Caledonia, the Chesterfield and Lord Howe Islands in the Coral Sea, and the east coast of Queensland, Australia. Satellite tags were also used to determine habitat use and movements among habitats across the Coral Sea. Sub-adults and one male adult tiger shark displayed year-round residency in the Chesterfields with two females tagged in the Chesterfields and detected on the Great Barrier Reef, Australia, after 591 and 842 days respectively. In coastal barrier reefs, tiger sharks were transient at acoustic arrays and each individual demonstrated a unique pattern of occurrence. From 2009 to 2013, fourteen sharks with satellite and acoustic tags undertook wide-ranging movements up to 1114 km across the Coral Sea with eight detected back on acoustic arrays up to 405 days after being tagged. Tiger sharks dove 1136 m and utilised three-dimensional activity spaces averaged at 2360 km3. The Chesterfield Islands appear to be important habitat for sub-adults and adult male tiger sharks. Management strategies need to consider the wide-ranging movements of large (sub-adult and adult) male and female tiger sharks at the individual level, whereas fidelity to specific coastal reefs may be consistent across groups of individuals. Coastal barrier reef MPAs, however, only afford brief protection for large tiger sharks, therefore determining the importance of other oceanic Coral Sea reefs should be a priority for future research.Funding was provided by the the Agence Francaise de Développement (http://www.afd.fr), French Pacific Fund, the CRISP program (www.crisponline.info) and QLD Fisheries

A Pilot Study with a Novel Setup for Collaborative Play of the Humanoid Robot KASPAR with children with autism

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.This article describes a pilot study in which a novel experimental setup, involving an autonomous humanoid robot, KASPAR, participating in a collaborative, dyadic video game, was implemented and tested with children with autism, all of whom had impairments in playing socially and communicating with others. The children alternated between playing the collaborative video game with a neurotypical adult and playing the same game with the humanoid robot, being exposed to each condition twice. The equipment and experimental setup were designed to observe whether the children would engage in more collaborative behaviours while playing the video game and interacting with the adult than performing the same activities with the humanoid robot. The article describes the development of the experimental setup and its first evaluation in a small-scale exploratory pilot study. The purpose of the study was to gain experience with the operational limits of the robot as well as the dyadic video game, to determine what changes should be made to the systems, and to gain experience with analyzing the data from this study in order to conduct a more extensive evaluation in the future. Based on our observations of the childrens’ experiences in playing the cooperative game, we determined that while the children enjoyed both playing the game and interacting with the robot, the game should be made simpler to play as well as more explicitly collaborative in its mechanics. Also, the robot should be more explicit in its speech as well as more structured in its interactions. Results show that the children found the activity to be more entertaining, appeared more engaged in playing, and displayed better collaborative behaviours with their partners (For the purposes of this article, ‘partner’ refers to the human/robotic agent which interacts with the children with autism. We are not using the term’s other meanings that refer to specific relationships or emotional involvement between two individuals.) in the second sessions of playing with human adults than during their first sessions. One way of explaining these findings is that the children’s intermediary play session with the humanoid robot impacted their subsequent play session with the human adult. However, another longer and more thorough study would have to be conducted in order to better re-interpret these findings. Furthermore, although the children with autism were more interested in and entertained by the robotic partner, the children showed more examples of collaborative play and cooperation while playing with the human adult.Peer reviewe

Pharmacological evaluation of novel bioisosteres of an adamantanyl benzamide P2X7 receptor antagonist

Adamantanyl benzamide 1 was identified as a potent P2X7R antagonist but failed to progress further due to poor metabolic stability. We describe the synthesis and SAR of a series of bioisosteres of benzamide 1 to explore improvements in the pharmacological properties of this lead. Initial efforts investigated a series of heteroaromatic bioisosteres, which demonstrated improved physicochemical properties but reduced P2X7R antagonism. Installation of bioisosteric fluorine on the adamantane bridgeheads was well tolerated and led to a series of bioisosteres with improved physicochemical properties and metabolic stability. Trifluorinated benzamide 34 demonstrated optimal physicochemical parameters, superior metabolic stability (ten times longer than lead benzamide 1), and an improved physicokinetic profile and proved effective in the presence of several known P2X7R polymorphisms

Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)

Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary generators, on finite dimensional type 1 unitary irreducible representations.We compare our results with existingworks that deal with only subsets of the class of type 1 unitary representations, all of which only present explicit matrix elements for elementary generators. Our work therefore provides an important extension to existing methods, and thus highlights the strength of our techniques which exploit the characteristic identities

Exploring drivers of litter decomposition in a greening Arctic: Results from a transplant experiment across a tree-line (Forthcoming)

Decomposition of plant litter is a key control over carbon (C) storage in the soil. The biochemistry of the litter being produced, the environment in which the decomposition is taking place, and the community composition and metabolism of the decomposer organisms exert a combined influence over decomposition rates. As deciduous shrubs and trees are expanding into tundra ecosystems as a result of regional climate warming, this change in vegetation represents a change in litter input to tundra soils and a change in the environment in which litter decomposes. To test the importance of litter biochemistry and environment in determining litter mass loss, we reciprocally transplanted litter between heath (Empetrum nigrum), shrub (Betula nana) and forest (Betula pubescens) at a sub-arctic tree-line in Sweden. As expansion of shrubs and trees promotes deeper snow, we also used a snow fence experiment in a tundra heath environment to understand the importance of snow depth, relative to other factors, in the decomposition of litter. Our results show that B. pubescens and B. nana leaf litter decomposed at faster rates than E. nigrum litter across all environments, while all litter species decomposed at faster rates in the forest and shrub environments than in the tundra heath. The effect of increased snow on decomposition was minimal, leading us to conclude that microbial activity over summer in the productive forest and shrub vegetation is driving increased mass loss compared to the heath. Using B. pubescens and E. nigrum litter, we demonstrate that degradation of carbohydrate-C is a significant driver of mass loss in the forest. This pathway was less prominent in the heath, which is consistent with observations that tundra soils typically have high concentrations of ‘labile’ C. This experiment suggests that further expansion of shrubs and trees may stimulate the loss of undecomposed carbohydrate-C in the tundra.REF Compliant by Deposit in Stirling's Repositor