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  • Model reduction of strong-weak neurons 

    Du, Bosen; Sorensen, Danny; Cox, Steven J. (2014)
    We consider neurons with large dendritic trees that are weakly excitable in the sense that back propagating action potentials are severly attenuated as they travel from the small, strongly excitable, spike initiation zone. ...
  • The Effects of Theta Precession on Spatial Learning and Simplicial Complex Dynamics in a Topological Model of the Hippocampal Spatial Map 

    Arai, Mamiko; Brandt, Vicky; Dabaghian, Yuri (2014-06-19)
    Learning arises through the activity of large ensembles of cells, yet most of the data neuroscientists accumulate is at the level of individual neurons; we need models that can bridge this gap. We have taken spatial learning ...
  • Time-Dependent Coupling of Navier-Stokes and Darcy Flows 

    Cesmelioglu, Aycil; Girault, Vivette; Riviere, Beatrice (2013-01-11)
    A weak solution of the coupling of time-dependent incompressible Navier–Stokes equations with Darcy equations is defined. The interface conditions include the Beavers–Joseph–Saffman condition. Existence and uniqueness ...
  • An Algebraic Exploration of Dominating Sets and Vizing's Conjecture 

    Margulies, S.; Hicks, I.V. (2012-04-07)
    Systems of polynomial equations are commonly used to model combinatorial problems such as independent set, graph coloring, Hamiltonian path, and others. We formulate the dominating set problem as a system of polynomial ...
  • Ritz Value for Non-Hermitian Matrices 

    Carden, Russell L.; Embree, Mark (2012-12-12)
    Rayleigh–Ritz eigenvalue estimates for Hermitian matrices obey Cauchy interlacing, which has helpful implications for theory, applications, and algorithms. In contrast, few results about the Ritz values of non-Hermitian ...