Operator algebra quantum homogeneous spaces of universal gauge groups

In this paper, we quantize universal gauge groups such as SU(\infty), as well as their homogeneous spaces, in the sigma-C*-algebra setting. More precisely, we propose concise definitions of sigma-C*-quantum groups and sigma-C*-quantum homogeneous spaces and explain these concepts here. At the same time, we put these definitions in the mathematical context of countably compactly generated spaces as well as C*-compact quantum groups and homogeneous spaces. We also study the representable K-theory of these spaces and compute it for the quantum homogeneous spaces associated to the universal gauge group SU(\infty).Comment: 14 pages. Merged with [arXiv:1011.1073

Bounded and unitary elements in pro-C^*-algebras

A pro-C^*-algebra is a (projective) limit of C^*-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-C^*-algebras can be seen as non-commutative k-spaces. An element of a pro-C^*-algebra is bounded if there is a uniform bound for the norm of its images under any continuous *-homomorphism into a C^*-algebra. The *-subalgebra consisting of the bounded elements turns out to be a C^*-algebra. In this paper, we investigate pro-C^*-algebras from a categorical point of view. We study the functor (-)_b that assigns to a pro-C^*-algebra the C^*-algebra of its bounded elements, which is the dual of the Stone-\v{C}ech-compactification. We show that (-)_b is a coreflector, and it preserves exact sequences. A generalization of the Gelfand-duality for commutative unital pro-C^*-algebras is also presented.Comment: v2 (accepted

Comparison theory and smooth minimal C*-dynamics

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of countably generated Hilbert modules over such algebras, and to a similar classification for the closures of unitary orbits of self-adjoint elements. We also obtain a structure theorem for the Cuntz semigroup in this setting, and prove a conjecture of Blackadar and Handelman: the lower semicontinuous dimension functions are weakly dense in the space of all dimension functions. These results continue to hold in the broader setting of unital simple ASH algebras with slow dimension growth and stable rank one. Our main tool is a sharp bound on the radius of comparison of a recursive subhomogeneous C*-algebra. This is also used to construct uncountably many non-Morita-equivalent simple separable amenable C*-algebras with the same K-theory and tracial state space, providing a C*-algebraic analogue of McDuff's uncountable family of II_1 factors. We prove in passing that the range of the radius of comparison is exhausted by simple C*-algebras.Comment: 30 pages, no figure

The impact of aging on the neural networks involved in gaze and emotional processing.

Normal adult aging is associated with difficulties in processing social cues to emotions such as anger and also altered motivation to focus more on positive than negative information. Gaze direction is an important modifier of the social signals conveyed by an emotion, for example, an angry face looking directly at you is considerably more threatening than an angry face looking away. In the present study we tested the hypothesis that older adults would show less neural differentiation to angry faces with direct and avert gaze compared to younger people, with the opposite prediction for happy faces. Healthy older (65-75 years; mean = 69.75) and younger (17-27 years; mean = 20.65) adults completed a functional magnetic resonance imaging experiment in which they were asked to identify happy and angry expressions displayed either with direct or averted gaze. While younger adults showed neural sensitivity to eye-gaze direction during recognition of angry expressions, older adults showed no effect of eye-gaze direction on neural response. In contrast, older adults showed sensitivity to eye-gaze direction during recognition of happy expressions but younger adults did not. Additionally, brain-behavior correlations were conducted to investigate the relationships between emotion recognition and mentalizing brain network in both age groups. Younger (but not older) adults' social cognitive performance was differentially correlated with activation in 2 brain networks when looking at angry faces with direct compared to averted gaze. These novel findings provide evidence for age-related differences in the neural substrates underlying the capacity to integrate facial affect and eye-gaze cues. The results of this study suggest that age-related differences in integrating facial cues may be related to engagement of the mentalizing network, with potentially important implications for social cognitive functioning in late adulthood

Topology and Flux of T-Dual Manifolds with Circle Actions

We present an explicit formula for the topology and H-flux of the T-dual of a general type II compactification, significantly generalizing earlier results. Our results apply to T-dualities with respect to any circle action on spacetime. As before, T-duality exchanges type IIA and type IIB string theories. A new consequence is that the T-dual spacetime is a singular space when the fixed point set is non-empty; the singularities correspond to Kaluza-Klein monopoles. We propose that the Ramond-Ramond charges of type II string theories on the singular dual are classified by twisted equivariant cohomology groups. We also include the K-theory approach.Comment: 9 pages, 1 figure, version to appear in CM

Modeling the biomechanics of fetal movements

Fetal movements in the uterus are a natural part of development and are known to play an important role in normal musculoskeletal development. However, very little is known about the biomechanical stimuli that arise during movements in utero, despite these stimuli being crucial to normal bone and joint formation. Therefore, the objective of this study was to create a series of computational steps by which the forces generated during a kick in utero could be predicted from clinically observed fetal movements using novel cine-MRI data of three fetuses, aged 20–22 weeks. A custom tracking software was designed to characterize the movements of joints in utero, and average uterus deflection of 6.95±0.41 mm due to kicking was calculated. These observed displacements provided boundary conditions for a finite element model of the uterine environment, predicting an average reaction force of 0.52±0.15 N generated by a kick against the uterine wall. Finally, these data were applied as inputs for a musculoskeletal model of a fetal kick, resulting in predicted maximum forces in the muscles surrounding the hip joint of approximately 8 N, while higher maximum forces of approximately 21 N were predicted for the muscles surrounding the knee joint. This study provides a novel insight into the closed mechanical environment of the uterus, with an innovative method allowing elucidation of the biomechanical interaction of the developing fetus with its surroundings

A C*-Algebraic Model for Locally Noncommutative Spacetimes

Locally noncommutative spacetimes provide a refined notion of noncommutative spacetimes where the noncommutativity is present only for small distances. Here we discuss a non-perturbative approach based on Rieffel's strict deformation quantization. To this end, we extend the usual C*-algebraic results to a pro-C*-algebraic framework.Comment: 13 pages, LaTeX 2e, no figure

European Society of Biomechanics S.M. Perren Award 2018: Altered biomechanical stimulation of the developing hip joint in presence of hip dysplasia risk factors

Fetal kicking and movements generate biomechanical stimulation in the fetal skeleton, which is important for prenatal musculoskeletal development, particularly joint shape. Developmental dysplasia of the hip (DDH) is the most common joint shape abnormality at birth, with many risk factors for the condition being associated with restricted fetal movement. In this study, we investigate the biomechanics of fetal movements in such situations, namely fetal breech position, oligohydramnios and primiparity (firstborn pregnancy). We also investigate twin pregnancies, which are not at greater risk of DDH incidence, despite the more restricted intra-uterine environment. We track fetal movements for each of these situations using cine-MRI technology, quantify the kick and muscle forces, and characterise the resulting stress and strain in the hip joint, testing the hypothesis that altered biomechanical stimuli may explain the link between certain intra-uterine conditions and risk of DDH. Kick force, stress and strain were found to be significantly lower in cases of breech position and oligohydramnios. Similarly, firstborn fetuses were found to generate significantly lower kick forces than non-firstborns. Interestingly, no significant difference was observed in twins compared to singletons. This research represents the first evidence of a link between the biomechanics of fetal movements and the risk of DDH, potentially informing the development of future preventative measures and enhanced diagnosis. Our results emphasise the importance of ultrasound screening for breech position and oligohydramnios, particularly later in pregnancy, and suggest that earlier intervention to correct breech position through external cephalic version could reduce the risk of hip dysplasia

Soft-mode anisotropy in the negative thermal expansion material ReO3

We use a symmetry-motivated approach to analyse neutron pair distribution function data to investigate the character of the soft phonon modes in negative thermal expansion (NTE) material ReO3. This analysis shows that its local structure is dominated by an in-phase octahedral tilting mode and that the octahedral units are far less flexible to scissoring type deformations than in the related NTE compound ScF3. The lack of flexibility in ReO3 restricts the NTE-driving phonons to a smaller region of reciprocal space, limiting the magnitude and temperature range of NTE. These results support the idea that structural flexibility is an important factor in NTE materials. Surprisingly, our results show that the local fluctuations, even at elevated temperatures, respect the symmetry and order parameter direction of the initial pressure induced phase transition in ReO3. The result indicates that the dynamic motions associated with rigid unit modes are highly anisotropic in these systems