Computational and Applied Mathematics
Recent Submissions

The MinimalﾠkCore Problem for Modelingﾠ kAssemblies
(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 sphingosine1phosphate pathway modulates neuronal autophagy
(2015)Autophagy is an important homeostatic mechanism that eliminates longlived proteins, protein aggregates and damaged organelles. Its dysregulation is involved in many neurodegenerative disorders. Autophagy is therefore a ... 
A MatrixFree TrustRegion SQP Method for Equality Constrained Optimization
(2014)We develop and analyze a trustregion 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 Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems
(2014)In this work an efficient approach for a posteriori error estimation for PODDEIM reduced nonlinear dynamical systems is introduced. The considered nonlinear systems may also include time and parameteraffine linear terms ... 
Genetic Suppression of Transgenic APP Rescues Hypersynchronous Network Activity in a Mouse Model of Alzeimer's Disease
(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 TrustRegion Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
(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
(2013)In many dataintensive 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 mathematical framework for inverse wave problems in heterogeneous media
(2013)This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integrodifferential equations with bounded and measurable coefficients. ... 
Convergence of a high order method in time and space for the miscible displacement equations
(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 ... 
Horizontal contraction in image domain for velocity inversion
(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 strongweak neurons
(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
(6/19/2014)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 ... 
TimeDependent Coupling of NavierStokes and Darcy Flows
(1/11/2013)A weak solution of the coupling of timedependent 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
(4/7/2012)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 NonHermitian Matrices
(12/12/2012)RayleighRitz 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 nonHermitian ... 
Shortterm Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices
(6/5/2012)The progressive GMRES algorithm, introduced by Beckermann and Reichel in 2008, is a residualminimizing shortrecurrence Krylov subspace method for solving a linear system in which the coefficient matrix has a lowrank ... 
Edge Guided Reconstruction for Compressive Imaging
(20120703)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 ... 
Local Error Analysis of Discontinuous Galerkin Methods for AdvectionDominated Elliptic LinearQuadratic Optimal Control Problems
(20120815)This paper analyzes the local properties of the symmetric interior penalty upwind discontinuous Galerkin (SIPG) method for the numerical solution of optimal control problems governed by linear reactionadvectiondiffusion ... 
Filtering Deterministic Layer Effects in Imaging
(2012)Sensor array imaging arises in applications such as nondestructive evaluation of materials with ultrasonic waves, seismic exploration, and radar. The sensors probe a medium with signals and record the resulting echoes, ... 
A New Compressive Video Sensing Framework for Mobile Broadcast
(201303)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 ...