Females are an under-represented research model and the mechanisms through which sleep loss impairs cognition are not clear. Since levels of reproductive hormones and the estrous cycle are sensitive to sleep loss and necessary for learning and memory, we hypothesized that sleep deprivation impacts learning and memory in female mice by interfering with the estrous cycle. We used the object recognition task to assess learning and memory in female mice during separate phases of the estrous cycle and after sleep loss. Mice in metestrus/diestrus attended to sample objects less than mice in proestrus/estrus during object acquisition, the first phase of the object recognition task. Subsequently, during the recognition phase of the task, only mice in proestrus/estrus displayed a preference for the novel object. Sleep deprivation for 12h immediately before the object recognition task reduced time attending to sample objects and novel object preference for mice in proestrus/estrus, without changing length of the estrous cycle. These results show that sleep deprived mice in proestrus/estrus had learning deficits and memory impairments, like mice in metestrus/diestrus. Since sleep deprivation did not disrupt the estrous cycle, however, results did not support the hypothesis. Cognitive impairments due to acute sleep loss were not due to alterations to the estrous cycle.

SUMMARYWe prove a rather general mean-value formula in the theory of elasticity, which expresses the value of the displacement at the centre of a sphere in terms of certain combinations of integral averages over the sphere itself of the traction and the displacement. We also establish the corresponding converse to this mean-value formula under minimal smoothness assumptions on the displacement.

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Through Borel summation methods, we analyze the Boussinesq equations for coupled fluid velocity and temperature fields:We prove that an equivalent system of integral equations in the Borel variable p ∈ R + dual to 1/t has a unique solution in a class of exponentially bounded functions, implying the existence of a classical solution to (1) in a complex t-region that includes a real positive time axis segment. For analytic initial data and forcing, it is shown that the solution is Borel summable, implying that that formal series in powers of t is Gevrey-1 asymptotic, and within the time interval of existence, the solution remains analytic with the same analyticity strip width as the initial data and forcing. We also determine conditions on the integral equation solution that improve the estimate for existence time.

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