Now showing items 18-37 of 37

    • 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. ...
    • 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 ...
    • 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 ...
    • 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. ...
    • Modulation of Orthographic Decoding by Frontal Cortex 

      Whaley, Meagan Lee; Kadipasaoglu, Cihan Mehmet; Cox, Steven James; Tandon, Nitin (2016)
      Opinions are divided on whether word reading processes occur in a hierarchical, feedforward fashion or within an interactive framework. To critically evaluate these competing theories, we recorded electrocorticographic ...
    • A New Compressive Video Sensing Framework for Mobile Broadcast 

      Li, Chengbo; Jiang, Hong; Wilford, Paul; Zhang, Yin; Scheutzow, Mike (2013-03)
      A new video coding method based on compressive sampling is proposed. In this method, a video is coded using compressive measurements on video cubes. Video reconstruction is performed by minimization of total variation ...
    • Numerical method of characteristics for one-dimensional blood flow 

      Acosta, Sebastian; Puelz, Charles; Riviére, Béatrice; Penny, Daniel J.; Rusin, Craig G. (2015)
      Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often ...
    • Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces 

      Albani, V.; Elbau, P.; de Hoop, M.V.; Scherzer, O. (2016)
      In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on ...
    • 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 ...
    • Predicting solvation free energies and thermodynamics in polar solvents and mixtures using a solvation-layer interface condition 

      Tabrizi, Amirhossein Molavi; Goossens, Spencer; Rahimi, Ali Mehdizadeh; Knepley, Matthew; Bardhan, Jaydeep P. (2017)
      We demonstrate that with two small modifications, the popular dielectric continuum model is capable of predicting, with high accuracy, ion solvation thermodynamics (Gibbs free energies, entropies, and heat capacities) in ...
    • Reconstruction of Lamé Moduli and Density at the Boundary Enabling Directional Elastic Wavefield Decomposition 

      de Hoop, Maarten V.; Nakamura, Gen; Zhai, Jian (2017)
      We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data are the dynamical ...
    • Residual-Based Adaptivity and PWDG Methods for the Helmholtz Equation 

      Kapita, Shelvean; Monk, Peter; Warburton, Timothy (2015)
      We present a study of two residual a posteriori error indicators for the plane wave discontinuous Galerkin (PWDG) method for the Helmholtz equation. In particular, we study the $h$-version of PWDG in which the number of ...
    • 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 ...
    • Scattering and dip angle decomposition based on subsurface offset extended wave-equation migration 

      Dafni, Raanan; Symes, William W. (2016)
      An angle-dependent reflection coefficient is recovered by seismic migration in the angle domain. We have developed a postmigration technique for computing scattering and dip angle common-image gathers (CIGs) from seismic ...
    • 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 ...
    • Synthetic Aperture Radar Imaging and Motion Estimation via Robust Principal Component Analysis 

      Borcea, Liliana; Callaghan, Thomas; Papanicolaou, George (2012-08-22)
      We consider the problem of synthetic aperture radar (SAR) imaging and motion estimation of complex scenes. By complex we mean scenes with multiple targets, stationary and in motion. We use the usual setup with one moving ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...