1,457 research outputs found

    Dimensions and singular traces for spectral triples, with applications to fractals

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    Given a spectral triple (A,D,H), the functionals on A of the form a -> tau_omega(a|D|^(-t)) are studied, where tau_omega is a singular trace, and omega is a generalised limit. When tau_omega is the Dixmier trace, the unique exponent d giving rise possibly to a non-trivial functional is called Hausdorff dimension, and the corresponding functional the (d-dimensional) Hausdorff functional. It is shown that the Hausdorff dimension d coincides with the abscissa of convergence of the zeta function of |D|^(-1), and that the set of t's for which there exists a singular trace tau_omega giving rise to a non-trivial functional is an interval containing d. Moreover, the endpoints of such traceability interval have a dimensional interpretation. The corresponding functionals are called Hausdorff-Besicovitch functionals. These definitions are tested on fractals in R, by computing the mentioned quantities and showing in many cases their correspondence with classical objects. In particular, for self-similar fractals the traceability interval consists only of the Hausdorff dimension, and the corresponding Hausdorff-Besicovitch functional gives rise to the Hausdorff measure. More generally, for any limit fractal, the described functionals do not depend on the generalized limit omega.Comment: latex, 36 pages, no figures, to appear on Journ. Funct. Analysi

    Kinking of a Crack Out of an Interface,”

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    Kinking of a plane strain crack out of the interface between two dissimilar isotropi

    Effectiveness and resource requirements of test, trace and isolate strategies for COVID in the UK

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    We use an individual-level transmission and contact simulation model to explore the effectiveness and resource requirements of various test-trace-isolate (TTI) strategies for reducing the spread of SARS-CoV-2 in the UK, in the context of different scenarios with varying levels of stringency of non-pharmaceutical interventions. Based on modelling results, we show that selfisolation of symptomatic individuals and quarantine of their household contacts has a substantial impact on the number of new infections generated by each primary case. We further show that adding contact tracing of non-household contacts of confirmed cases to this broader package of interventions reduces the number of new infections otherwise generated by 5–15%. We also explore impact of key factors, such as tracing application adoption and testing delay, on overall effectiveness of TTI

    Pathogenic challenge reveals immune trade-off in mussels exposed to reduced seawater pH and increased temperature

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    Mussels tolerant to seawater pH's that are projected to occur by 2300 due to ocean acidification.•Exposure to pH 6.50 reduced mussel immune response, yet in the absence of a pathogen.•Subsequent pathogenic challenge led to a reversal of immune suppression at pH 6.50.•Study highlights the importance of undertaking multiple stressor exposures.•Shows a need to consider physiological trade-offs and measure responses functionall

    Effectiveness and resource requirements of test, trace and isolate strategies for COVID in the UK.

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    We use an individual-level transmission and contact simulation model to explore the effectiveness and resource requirements of various test-trace-isolate (TTI) strategies for reducing the spread of SARS-CoV-2 in the UK, in the context of different scenarios with varying levels of stringency of non-pharmaceutical interventions. Based on modelling results, we show that self-isolation of symptomatic individuals and quarantine of their household contacts has a substantial impact on the number of new infections generated by each primary case. We further show that adding contact tracing of non-household contacts of confirmed cases to this broader package of interventions reduces the number of new infections otherwise generated by 5-15%. We also explore impact of key factors, such as tracing application adoption and testing delay, on overall effectiveness of TTI

    Endurance exercise accelerates myocardial tissue oxygenation recovery and reduces ischemia reperfusion injury in mice

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    Exercise training offers cardioprotection against ischemia and reperfusion (I/R) injury. However, few essential signals have been identified to underscore the protection from injury. In the present study, we hypothesized that exercise-induced acceleration of myocardial tissue oxygenation recovery contributes to this protection. C57BL/6 mice (4 weeks old) were trained on treadmills for 45 min/day at a treading rate of 15 m/min for 8 weeks. At the end of 8-week exercise training, mice underwent 30-min left anterior descending coronary artery occlusion followed by 60-min or 24-h reperfusion. Electron paramagnetic resonance oximetry was performed to measure myocardial tissue oxygenation. Western immunoblotting analyses, gene transfection, and myography were examined. The oximetry study demonstrated that exercise markedly shortened myocardial tissue oxygenation recovery time following reperfusion. Exercise training up-regulated Kir6.1 protein expression (a subunit of ATP-sensitive K(+)channel on vascular smooth muscle cells, VSMC sarc-K(ATP)) and protected the heart from I/R injury. In vivo gene transfer of dominant negative Kir6.1AAA prolonged the recovery time and enlarged infarct size. In addition, transfection of Kir6.1AAA increased the stiffness and reduced the relaxation capacity in the vasculature. Together, our study demonstrated that exercise training up-regulated Kir6.1, improved tissue oxygenation recovery, and protected the heart against I/R injury. This exercise-induced cardioprotective mechanism may provide a potential therapeutic intervention targeting VSMC sarc-K(ATP) channels and reperfusion recovery
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