2,905 research outputs found

    Chern numbers for two families of noncommutative Hopf fibrations

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    We consider noncommutative line bundles associated with the Hopf fibrations of SUq(2) over all Podles spheres and with a locally trivial Hopf fibration of S^3_{pq}. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SUq(2) and S^3_{pq}. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them.Comment: 6 page

    Weak in Space, Log in Time Improvement of the Lady{\v{z}}enskaja-Prodi-Serrin Criteria

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    In this article we present a Lady{\v{z}}enskaja-Prodi-Serrin Criteria for regularity of solutions for the Navier-Stokes equation in three dimensions which incorporates weak LpL^p norms in the space variables and log improvement in the time variable.Comment: 14 pages, to appea

    Variational bounds on the energy dissipation rate in body-forced shear flow

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    A new variational problem for upper bounds on the rate of energy dissipation in body-forced shear flows is formulated by including a balance parameter in the derivation from the Navier-Stokes equations. The resulting min-max problem is investigated computationally, producing new estimates that quantitatively improve previously obtained rigorous bounds. The results are compared with data from direct numerical simulations.Comment: 15 pages, 7 figure

    Relativistic Wavepackets in Classically Chaotic Quantum Cosmological Billiards

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    Close to a spacelike singularity, pure gravity and supergravity in four to eleven spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of relativistic wavepackets towards the singularity, employing flat and hyperbolic space descriptions for the quantum billiards. We find that the strongly chaotic classical billiard motion of four-dimensional pure gravity corresponds to a spreading wavepacket subject to successive redshifts and tending to zero as the singularity is approached. We discuss the possible implications of these results in the context of singularity resolution and compare them with those of known semiclassical approaches. As an aside, we obtain exact solutions for the one-dimensional relativistic quantum billiards with moving walls.Comment: 18 pages, 10 figure

    A Transgenic Rat for Investigating the Anatomy and Function of Corticotrophin Releasing Factor Circuits.

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    Corticotrophin-releasing factor (CRF) is a 41 amino acid neuropeptide that coordinates adaptive responses to stress. CRF projections from neurons in the central nucleus of the amygdala (CeA) to the brainstem are of particular interest for their role in motivated behavior. To directly examine the anatomy and function of CRF neurons, we generated a BAC transgenic Crh-Cre rat in which bacterial Cre recombinase is expressed from the Crh promoter. Using Cre-dependent reporters, we found that Cre expressing neurons in these rats are immunoreactive for CRF and are clustered in the lateral CeA (CeL) and the oval nucleus of the BNST. We detected major projections from CeA CRF neurons to parabrachial nuclei and the locus coeruleus, dorsal and ventral BNST, and more minor projections to lateral portions of the substantia nigra, ventral tegmental area, and lateral hypothalamus. Optogenetic stimulation of CeA CRF neurons evoked GABA-ergic responses in 11% of non-CRF neurons in the medial CeA (CeM) and 44% of non-CRF neurons in the CeL. Chemogenetic stimulation of CeA CRF neurons induced Fos in a similar proportion of non-CRF CeM neurons but a smaller proportion of non-CRF CeL neurons. The CRF1 receptor antagonist R121919 reduced this Fos induction by two-thirds in these regions. These results indicate that CeL CRF neurons provide both local inhibitory GABA and excitatory CRF signals to other CeA neurons, and demonstrate the value of the Crh-Cre rat as a tool for studying circuit function and physiology of CRF neurons

    High-field fMRI reveals brain activation patterns underlying saccade execution in the human superior colliculus

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    Background The superior colliculus (SC) has been shown to play a crucial role in the initiation and coordination of eye- and head-movements. The knowledge about the function of this structure is mainly based on single-unit recordings in animals with relatively few neuroimaging studies investigating eye-movement related brain activity in humans. Methodology/Principal Findings The present study employed high-field (7 Tesla) functional magnetic resonance imaging (fMRI) to investigate SC responses during endogenously cued saccades in humans. In response to centrally presented instructional cues, subjects either performed saccades away from (centrifugal) or towards (centripetal) the center of straight gaze or maintained fixation at the center position. Compared to central fixation, the execution of saccades elicited hemodynamic activity within a network of cortical and subcortical areas that included the SC, lateral geniculate nucleus (LGN), occipital cortex, striatum, and the pulvinar. Conclusions/Significance Activity in the SC was enhanced contralateral to the direction of the saccade (i.e., greater activity in the right as compared to left SC during leftward saccades and vice versa) during both centrifugal and centripetal saccades, thereby demonstrating that the contralateral predominance for saccade execution that has been shown to exist in animals is also present in the human SC. In addition, centrifugal saccades elicited greater activity in the SC than did centripetal saccades, while also being accompanied by an enhanced deactivation within the prefrontal default-mode network. This pattern of brain activity might reflect the reduced processing effort required to move the eyes toward as compared to away from the center of straight gaze, a position that might serve as a spatial baseline in which the retinotopic and craniotopic reference frames are aligned

    Core requirements for successful data linkage: an example of a triangulation method

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    OBJECTIVES: The aim was to explore the views of professional stakeholders and healthcare professionals (HCPs) on the linkage of UK National Health Service (NHS) data for paediatric pharmacovigilance purposes and to make recommendations for such a system. METHODS: A mixed methods approach including a literature review, interviews, focus groups and a three-round Delphi survey with HCPs in Scotland was followed by a triangulation process using a systematic protocol. The survey was structured using the Theoretical Domains Framework of behaviour change. Items retained after applying the matrix-based triangulation process were thematically coded. Ethical approval was granted by the North of Scotland Research Ethics Service. RESULTS: Results from 18 papers, 23 interviewees, 23 participants of focus groups and 61 completed questionnaires in the Delphi survey contributed to the triangulation process. A total of 25 key findings from all four studies were identified during triangulation. There was good convergence; 21 key findings were agreed and remained to inform recommendations. The items were coded as practical/technical (eg, decision about the unique patient identifier to use), mandatory (eg, governed by statute), essential (consistently mentioned in all studies and therefore needed to ensure professional support) or preferable. CONCLUSIONS: The development of a paediatric linked database has support from professional stakeholders and HCPs in Scotland. The triangulation identified three sets of core requirements for a new system of data linkage. An additional fourth set of 'preferable' requirements might increase engagement of HCPs and their support for the new system

    Familiäre Kavernome des Zentralnervensystems: Eine klinische und genetische Studie an 15 deutsche Familien

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    Zusammenfassung: 1928 beschrieb Hugo Friedrich Kufs erstmalig eine Familie mit zerebralen, retinalen und kutanen Kavernomen. Mittlerweile wurden über 300 weitere Familien beschrieben. Ebenfalls wurden drei Genloci 7q21-q22 (mit dem Gen CCM1), 7p15-p13 (Gen CCM2) und 3q25.2-q27 (Gen CCM3) beschrieben, in denen Mutationen zu Kavernomen führen. Das Genprodukt von CCM1 ist das Protein Krit1 (Krev Interaction Trapped 1), das über verschiedene Mechanismen mit der Angiogenese interagiert. Das neu entdeckte CCM2-Gen enkodiert ein Protein, das möglicherweise eine dem Krit1 ähnliche Funktion in der Regulation der Angiogenese hat. Das CCM3-Gen wurde noch nicht beschrieben. In dieser Arbeit werden sowohl die klinischen und genetischen Befunde bei 15 deutschen Familien beschriebe
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