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  • A Topological Model of the Hippocampal Cell Assembly Network 

    Babichev, Andrey; Ji, Daoyun; Mémoli, Facundo; Dabaghian, Yuri A. (2016)
    It is widely accepted that the hippocampal place cells' spiking activity produces a cognitive map of space. However, many details of this representation's physiological mechanism remain unknown. For example, it is believed ...
  • Levetiracetam mitigates doxorubicin-induced DNA and synaptic damage in neurons 

    Manchon, Jose Felix Moruno; Dabaghian, Yuri; Uzor, Ndidi-Ese; Kesler, Shelli R.; Wefel, Jeffrey S.; Tsvetkov, Andrey S. (2016)
    Neurotoxicity may occur in cancer patients and survivors during or after chemotherapy. Cognitive deficits associated with neurotoxicity can be subtle or disabling and frequently include disturbances in memory, attention, ...
  • Topological Schemas of Cognitive Maps and Spatial Learning 

    Babichev, Andrey; Cheng, Sen; Dabaghian, Yuri A. (2016)
    Spatial navigation in mammals is based on building a mental representation of their environment-a cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains ...
  • The Minimalᅠk-Core Problem for Modelingᅠ k-Assemblies 

    Wood, Cynthia I.; Hicks, Illya V. (2015)
    The concept of cell assembly was introduced by Hebb and formalized mathematically by Palm in the framework of graph theory. In the study of associative memory, a cell assembly is a group of neurons that are strongly connected ...
  • Cytoplasmic sphingosine-1-phosphate pathway modulates neuronal autophagy 

    Manchon, Jose Felix Moruno; Uzor, Ndidi-Ese; Dabaghian, Yuri; Furr-Stimming, Erin E.; Finkbeiner, Steven; Tsvetkov, Andrey S. (2015)
    Autophagy is an important homeostatic mechanism that eliminates long-lived proteins, protein aggregates and damaged organelles. Its dysregulation is involved in many neurodegenerative disorders. Autophagy is therefore a ...
  • A Matrix-Free Trust-Region SQP Method for Equality Constrained Optimization 

    Heinkenschloss, Matthias; Ridzal, Denis (2014)
    We develop and analyze a trust-region sequential quadratic programming (SQP) method for the solution of smooth equality constrained optimization problems, which allows the inexact and hence iterative solution of linear ...
  • A mathematical framework for inverse wave problems in heterogeneous media 

    Blazek, Kirk D.; Stolk, Christiaan; Symes, William W. (2013)
    This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. ...
  • Convergence of a high order method in time and space for the miscible displacement equations 

    Li, Jizhou; Riviere, Beatrice; Walkington, Noel (2015)
    A numerical method is formulated and analyzed for solving the miscible displacement problem under low regularity assumptions. The scheme employs discontinuous Galerkin time stepping with mixed and interior penalty discontinuous ...
  • Genetic Suppression of Transgenic APP Rescues Hypersynchronous Network Activity in a Mouse Model of Alzeimer's Disease 

    Born, Heather A.; Kim, Ji-Yoen; Savjani, Ricky R.; Das, Pritam; Dabaghian, Yuri A.; Guo, Qinxi; Yoo, Jong W.; Schuler, Dorothy R.; Cirrito, John R.; Zheng, Hui; Golde, Todd E.; Noebels, Jeffrey L.; Jankowsky, Joanna L. (2014)
    Alzheimer's disease (AD) is associated with an elevated risk for seizures that may be fundamentally connected to cognitive dysfunction. Supporting this link, many mouse models for AD exhibit abnormal electroencephalogram ...
  • A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty 

    Kouri, D.P.; Heinkenschloss, M.; Ridzal, D.; van Bloemen Waanders, B.G. (2013)
    The numerical solution of optimization problems governed by partial differential equations (PDEs) with random coefficients is computationally challenging because of the large number of deterministic PDE solves required at ...
  • Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions 

    Liu, Xin; Wen, Zaiwen; Zhang, Yin (2013)
    In many data-intensive applications, the use of principal component analysis and other related techniques is ubiquitous for dimension reduction, data mining, or other transformational purposes. Such transformations often ...
  • A Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems 

    Wirtz, D.; Sorensen, D.C.; Haasdonk, B. (2014)
    In this work an efficient approach for a posteriori error estimation for POD-DEIM reduced nonlinear dynamical systems is introduced. The considered nonlinear systems may also include time- and parameter-affine linear terms ...
  • Horizontal contraction in image domain for velocity inversion 

    Shen, Peng; Symes, William W. (2015)
    A kinematically correct choice of velocity focuses subsurface offset image gathers at a zero offset. Infinitesimal warping from the current image toward its focus can be approximated by a horizontal contraction. The image ...
  • 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)
    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)
    A weak solution of the coupling of time-dependent incompressible NavierヨStokes equations with Darcy equations is defined. The interface conditions include the BeaversヨJosephヨSaffman condition. Existence and uniqueness of ...
  • An Algebraic Exploration of Dominating Sets and Vizing's Conjecture 

    Margulies, S.; Hicks, I.V. (2012)
    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)
    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 ...
  • Short-term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices 

    Embree, Mark; Sifuentes, Josef A.; Soodhalter, Kirk M.; Szyld, Daniel B.; Xue, Fei (2012)
    The progressive GMRES algorithm, introduced by Beckermann and Reichel in 2008, is a residual-minimizing short-recurrence Krylov subspace method for solving a linear system in which the coefficient matrix has a low-rank ...
  • Edge Guided Reconstruction for Compressive Imaging 

    Guo, Weihong; Yin, Wotao (2012-07-03)
    We propose EdgeCS—an edge guided compressive sensing reconstruction approach—to recover images of higher quality from fewer measurements than the current methods. Edges are important image features that are used in various ...

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