Symmetry of Quantum Torus with Crossed Product Algebra

In this paper, we study the symmetry of quantum torus with the concept of crossed product algebra. As a classical counterpart, we consider the orbifold of classical torus with complex structure and investigate the transformation property of classical theta function. An invariant function under the group action is constructed as a variant of the classical theta function. Then our main issue, the crossed product algebra representation of quantum torus with complex structure under the symplectic group is analyzed as a quantum version of orbifolding. We perform this analysis with Manin's so-called model II quantum theta function approach. The symplectic group Sp(2n,Z) satisfies the consistency condition of crossed product algebra representation. However, only a subgroup of Sp(2n,Z) satisfies the consistency condition for orbifolding of quantum torus.Comment: LaTeX 17pages, changes in section 3 on crossed product algebr

Morita Equivalence of Noncommutative Supertori

In this paper we study the extension of Morita equivalence of noncommutative tori to the supersymmetric case. The structure of the symmetry group yielding Morita equivalence appears to be intact but its parameter field becomes supersymmetrized having both body and soul parts. Our result is mainly in the two dimensional case in which noncommutative supertori have been constructed recently: The group $SO(2,2,V_{\Z}^0)$, where $V_{\Z}^0$ denotes Grassmann even number whose body part belongs to ${\Z}$, yields Morita equivalent noncommutative supertori in two dimensions.Comment: LaTeX 18 pages, the version appeared in JM

Blunted neural response to anticipation, effort and consummation of reward and aversion in adolescents with depression symptomatology

Neural reward function has been proposed as a possible biomarker for depression. However how the neural response to reward and aversion might differ in young adolescents with current symptoms of depression is as yet unclear. 33 adolescents were recruited. 17 scoring low on the Mood and Feelings Questionnaire (MFQ) (Low Risk: LR) and 16 scoring high on the MFQ (High Risk: HR). Our fMRI task measured; anticipation (pleasant/unpleasant cue), effort (achieve a pleasant taste or avoid an unpleasant taste) and consummation (pleasant/unpleasant tastes) in Regions of Interest; ventral medial prefrontal cortex (vmPFC), pregenual cingulate cortex (pgACC), the insula and ventral striatum. We also examined whole brain group differences. In the ROI analysis we found reduced activity in the HR group in the pgACC during anticipation and reduced pgACC and vmPFC during effort and consummation. In the whole brain analysis we also found reduced activity in the HR group in the prefrontal cortex and the precuneus during anticipation. We found reduced activity in the hippocampus during the effort phase and in the anterior cingulate/frontal pole during consummation in the HR group. Increased anhedonia measures correlated with decreased pgACC activity during consummation in the HR group only. Our results are the first to show that adolescents with depression symptoms have blunted neural responses during the anticipation, effort and consummation of rewarding and aversive stimuli. This study suggests that interventions in young people at risk of depression, that can reverse blunted responses, might be beneficial as preventative strategies

Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory

N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop triangles, one-loop boxes, and two-loop diagonal boxes can be cast as simple one- and two- parametric integrals over a single propagator in configuration space. We observe that the two-loop Wilson-loop "hard-diagram" corresponds to a four-loop hexagon Feynman diagram. Guided by the diagrammatic correspondence of the configuration-space propagator and loop Feynman diagrams, we derive Feynman parameterizations of complicated planar and non-planar Feynman diagrams which simplify their evaluation. For illustration, we compute numerically a four-loop hexagon scalar Feynman diagram.Comment: 20 pages, many figures. Two references added. Published versio

Theta Vectors and Quantum Theta Functions

In this paper, we clarify the relation between Manin's quantum theta function and Schwarz's theta vector in comparison with the kq representation, which is equivalent to the classical theta function, and the corresponding coordinate space wavefunction. We first explain the equivalence relation between the classical theta function and the kq representation in which the translation operators of the phase space are commuting. When the translation operators of the phase space are not commuting, then the kq representation is no more meaningful. We explain why Manin's quantum theta function obtained via algebra (quantum tori) valued inner product of the theta vector is a natural choice for quantum version of the classical theta function (kq representation). We then show that this approach holds for a more general theta vector with constant obtained from a holomorphic connection of constant curvature than the simple Gaussian one used in the Manin's construction. We further discuss the properties of the theta vector and of the quantum theta function, both of which have similar symmetry properties under translation.Comment: LaTeX 21 pages, give more explicit explanations for notions given in the tex

The holographic principle

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.Comment: 52 pages, 10 figures, invited review for Rev. Mod. Phys; v2: reference adde

WNT signalling in prostate cancer

Genome sequencing and gene expression analyses of prostate tumours have highlighted the potential importance of genetic and epigenetic changes observed in WNT signalling pathway components in prostate tumours-particularly in the development of castration-resistant prostate cancer. WNT signalling is also important in the prostate tumour microenvironment, in which WNT proteins secreted by the tumour stroma promote resistance to therapy, and in prostate cancer stem or progenitor cells, in which WNT-β-catenin signals promote self-renewal or expansion. Preclinical studies have demonstrated the potential of inhibitors that target WNT receptor complexes at the cell membrane or that block the interaction of β-catenin with lymphoid enhancer-binding factor 1 and the androgen receptor, in preventing prostate cancer progression. Some WNT signalling inhibitors are in phase I trials, but they have yet to be tested in patients with prostate cancer

TRY plant trait database - enhanced coverage and open access

Plant traits-the morphological, anatomical, physiological, biochemical and phenological characteristics of plants-determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait-based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits-almost complete coverage for 'plant growth form'. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait-environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Measurement of the B0 anti-B0 oscillation frequency using l- D*+ pairs and lepton flavor tags

The oscillation frequency Delta-md of B0 anti-B0 mixing is measured using the partially reconstructed semileptonic decay anti-B0 -> l- nubar D*+ X. The data sample was collected with the CDF detector at the Fermilab Tevatron collider during 1992 - 1995 by triggering on the existence of two lepton candidates in an event, and corresponds to about 110 pb-1 of pbar p collisions at sqrt(s) = 1.8 TeV. We estimate the proper decay time of the anti-B0 meson from the measured decay length and reconstructed momentum of the l- D*+ system. The charge of the lepton in the final state identifies the flavor of the anti-B0 meson at its decay. The second lepton in the event is used to infer the flavor of the anti-B0 meson at production. We measure the oscillation frequency to be Delta-md = 0.516 +/- 0.099 +0.029 -0.035 ps-1, where the first uncertainty is statistical and the second is systematic.Comment: 30 pages, 7 figures. Submitted to Physical Review

Enriched job design, high involvement management and organizational performance: The mediating roles of job satisfaction and well-being

The relationship between organizational performance and two dimensions of the 'high performance work system' - enriched job design and high involvement management (HIM) - is widely assumed to be mediated by worker well-being. We outline the basis for three models: mutual-gains, in which employee involvement increases well-being and this mediates its positive relationship with performance; conflicting outcomes, which associates involvement with increased stress for workers, accounting for its positive performance effects; and counteracting effects, which associates involvement with increased stress and dissatisfaction, reducing its positive performance effects. These are tested using the UK's Workplace Employment Relations Survey 2004. Job satisfaction mediates the relationship between enriched job design and four performance indicators, supporting the mutual gains model; but HIM is negatively related to job satisfaction and this depresses a positive relationship between HIM and the economic performance measures, supporting a counteracting effects model. Finally, HIM is negatively related to job-related anxiety-comfort and enriched job design is unrelated to it. © The Author(s) 2012