511 research outputs found

    Natural convection in a vertical slot: accurate solution of the linear stability equations

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    The linear stability of natural convection in a fluid between vertical hot and cold walls was studied using a collocation method. Seven figure accurate results for monotonic disturbances were obtained by Ruth (1979) using numerical power series, but this method is intrinsically limited and failed for Pr ? 10 . In contrast, Chebyshev collocation converges more rapidly and allows the computation of results at higher Pr for which oscillatory disturbances dominate. Accurate results are now obtained across the entire Prandtl number range. These match the zero and infinite Pr asymptotes which are also refined here

    Skirting subsets of the plane, with application to marginal stability curves

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    An easily implemented algorithm is described for tracing the margin of a plane region defined by a predicate. Given a point inside and one outside, a sequence of marginal points is produced. The algorithm is a modified specialization of the `simplicial decomposition' method for n equations in n+1 dimensions. The case n=1 has special properties and its importance motivates their present exploitation. It is directly applicable to finding level curves. It does not require differentiability and copes well with cusps. Two questions of accuracy are the proximity of the outputs to the margin and the proximity of the margin to the output set. The first is answered precisely. The second is complicated and predicate-dependent, but is addressed in practical terms by adaptivity, which also improves the scheme's efficiency

    Afferent specific role of NMDA receptors for the circuit integration of hippocampal neurogliaform cells.

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    This is the final version of the article. Available from Nature Publishing Group via the DOI in this record.Appropriate integration of GABAergic interneurons into nascent cortical circuits is critical for ensuring normal information processing within the brain. Network and cognitive deficits associated with neurological disorders, such as schizophrenia, that result from NMDA receptor-hypofunction have been mainly attributed to dysfunction of parvalbumin-expressing interneurons that paradoxically express low levels of synaptic NMDA receptors. Here, we reveal that throughout postnatal development, thalamic, and entorhinal cortical inputs onto hippocampal neurogliaform cells are characterized by a large NMDA receptor-mediated component. This NMDA receptor-signaling is prerequisite for developmental programs ultimately responsible for the appropriate long-range AMPAR-mediated recruitment of neurogliaform cells. In contrast, AMPAR-mediated input at local Schaffer-collateral synapses on neurogliaform cells remains normal following NMDA receptor-ablation. These afferent specific deficits potentially impact neurogliaform cell mediated inhibition within the hippocampus and our findings reveal circuit loci implicating this relatively understudied interneuron subtype in the etiology of neurodevelopmental disorders characterized by NMDA receptor-hypofunction.Proper brain function depends on the correct assembly of excitatory and inhibitory neurons into neural circuits. Here the authors show that during early postnatal development in mice, NMDAR signaling via activity of long-range synaptic inputs onto neurogliaform cells is required for their appropriate integration into the hippocampal circuitry.We thank Daniel Abebe for mouse colony maintenance and Kurt Auville for additional assistance with confocal imaging. We thank UNC Vector Core and Ed Boyden, MIT, Cambridge, MA, USA for generously providing AAV9-syn-Chrimson-TdTomato and AAV9-syn-Chronos-GFP. This work was supported by an intramural award to C.J.M. from the Eunice Kennedy–Shriver National Institute of Child Health and Human Development and a Competitive Fellowship Award to J.C.W. from the National Institute of Neurological Disorders and Strok
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