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

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

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

Diffusion-Limited Growth of Microbial Colonies.

The emergence of diffusion-limited growth (DLG) within a microbial colony on a solid substrate is studied using a combination of mathematical modelling and experiments. Using an agent-based model of the interaction between microbial cells and a diffusing nutrient, it is shown that growth directed towards a nutrient source may be used as an indicator that DLG is influencing the colony morphology. A continuous reaction-diffusion model for microbial growth is employed to identify the parameter regime in which DLG is expected to arise. Comparisons between the model and experimental data are used to argue that the bacterium Bacillus subtilis can undergo DLG, while the yeast Saccharomyces cerevisiae cannot, and thus the non-uniform growth exhibited by this yeast must be caused by the pseudohyphal growth mode rather than limited nutrient availability. Experiments testing directly for DLG features in yeast colonies are used to confirm this hypothesis

Anthropometric measures in relation to Basal Cell Carcinoma: a longitudinal study

BACKGROUND: The relationship between anthropometric indices and risk of basal cell carcinoma (BCC) is largely unknown. We aimed to examine the association between anthropometric measures and development of BCC and to demonstrate whether adherence to World Health Organisation guidelines for body mass index, waist circumference, and waist/hip ratio was associated with risk of BCC, independent of sun exposure. METHODS: Study participants were participants in a community-based skin cancer prevention trial in Nambour, a town in southeast Queensland (latitude 26°S). In 1992, height, weight, and waist and hip circumferences were measured for all 1621 participants and weight was remeasured at the end of the trial in 1996. Prevalence proportion ratios were calculated using a log-binomial model to estimate the risk of BCC prior to or prevalent in 1992, while Poisson regression with robust error variances was used to estimate the relative risk of BCC during the follow-up period. RESULTS: At baseline, 94 participants had a current BCC, and 202 had a history of BCC. During the 5-year follow-up period, 179 participants developed one or more new BCCs. We found no significant association between any of the anthropometric measures or indices and risk of BCC after controlling for potential confounding factors including sun exposure. There was a suggestion that short-term weight gain may increase the risk of developing BCC for women only. CONCLUSION: Adherence to World Health Organisation guidelines for body mass index, waist circumference and waist/hip ratio is not significantly associated with occurrence of basal cell carcinomas of the skin

Modelling the potential non-breeding distribution of Spoon-billed Sandpiper Calidris pygmaea

SummaryThe Spoon-billed Sandpiper Calidris pygmaea is a ‘Critically Endangered’ migratory shorebird. The species faces an array of threats in its non-breeding range, making conservation intervention essential. However, conservation efforts are reliant on identifying the species’ key stopover and wintering sites. Using Maximum Entropy models, we predicted Spoon-billed Sandpiper distribution across the non-breeding range, using data from recent field surveys and satellite tracking. Model outputs suggest only a limited number of stopover sites are suitable for migrating birds, with sites in the Yellow Sea and on the Jiangsu coast in China highlighted as particularly important. All the previously known core wintering sites were identified by the model including the Ganges-Brahmaputra Delta, Nan Thar Island and the Gulf of Mottama. In addition, the model highlighted sites subsequently found to be occupied, and pinpointed potential new sites meriting investigation, notably on Borneo and Sulawesi, and in parts of India and the Philippines. A comparison between the areas identified as most likely to be occupied and protected areas showed that very few locations are covered by conservation designations. Known sites must be managed for conservation as a priority, and potential new sites should be surveyed as soon as is feasible to assess occupancy status. Site protection should take place in concert with conservation interventions including habitat management, discouraging hunting, and fostering alternative livelihoods.Field surveys in Russian non-breeding grounds were supported by RSPB, MHS and NABU. Field surveys in Gulf of Mottama partly supported by BBC Wildlife Fund. Satellite tagging data collection partly supported by The Biodiversity Investigation, Observation and Assessment Program (2019 - 2023) of the Ministry of Ecology and Environment of China, RSPB and a private donor. Bangladesh Spoon-billed Sandpiper Conservation Project’s fieldwork in Meghna Estuary (2015 - 2016) supported by RSPB. Data collection by EL partly supported by Basic research program (budgetary funds), projects number АААА-А19-119022190168-8 and АААА-А19-119021990093-8). PT supported by Moscow State University Grant for Leading Scientific Schools "Depository of the Living Systems" in the MSU Development Program framework. TBL was funded by the Natural Environment Research Council UK, and the IAPETUS Doctoral Training Partnership

A case of McKusick-Kaufman syndrome

McKusick-Kaufman syndrome (MKS) is an autosomal recessive multiple malformation syndrome characterized by hydrometrocolpos (HMC) and postaxial polydactyly (PAP). We report a case of a female child with MKS who was transferred to the neonatal intensive care unit of Seoul National University Children's Hospital on her 15th day of life for further evaluation and management of an abdominal cystic mass. She underwent abdominal sonography, magnetic resonance imaging, genitography and cystoscopy which confirmed HMC with a transverse vaginal septum. X-rays of the hand and foot showed bony fusion of the left third and fourth metacarpal bones, right fourth dysplastic metacarpal bone and phalanx, right PAP and hypoplastic left foot with left fourth and fifth dysplastic metatarsal bones. In addition, she had soft palate cleft, mild hydronephroses of both kidneys, hypoplastic right kidney with ectopic location and mild rotation, uterine didelphys with transverse vaginal septum and low-type imperforated anus. She was temporarily treated with ultrasound-guided transurethral aspiration of the HMC. Our patient with HMC and PAP was diagnosed with MKS because she has two typical abnormality of MKS and she has no definite complications of retinal disease, learning disability, obesity and renal failure that develop in Bardet-Biedl syndrome, but not in MKS until 33 months of age. Here, we describe a case of a Korean patient with MKS