CAAM Publications
CAAM Faculty Publications
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ResidualBased Adaptivity and PWDG Methods for the Helmholtz Equation
(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 ... 
A Comparison of High Order Interpolation Nodes for the Pyramid
(2015)The use of pyramid elements is crucial to the construction of efficient hexdominant meshes [M. Bergot, G. Cohen, and M. Duruflé, J. Sci. Comput., 42 (2010), pp. 345381]. For conforming nodal finite element methods with ... 
An Efficient GaussNewton Algorithm for Symmetric LowRank Product Matrix Approximations
(2015)We derive and study a GaussNewton method for computing a symmetric lowrank product $XX^{{T}}$, where $X \in{\mathbb{R}}^{n\times k}$ for $k<n$, that is the closest to a given symmetric matrix $A \in{\mathbb{R}}^{n\times ... 
Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
(2016)In this article, we prove optimal convergence rates results for regularization methods for solving linear illposed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on ... 
Inverse Boundary Value Problem For The Helmholtz Equation: Quantitative Conditional Lipschitz Stability Estimates
(2016)We study the inverse boundary value problem for the Helmholtz equation using the DirichlettoNeumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the ... 
A DEIM Induced CUR Factorization
(2016)We derive a CUR approximate matrix factorization based on the discrete empirical interpolation method (DEIM). For a given matrix ${\bf A}$, such a factorization provides a lowrank approximate decomposition of the form ... 
An approximate inverse to the extended Born modeling operator
(2015)Given a correct (dataconsistent) velocity model, reverse time migration (RTM) correctly positions reflectors but generally with incorrect amplitudes and wavelets. Iterative leastsquares migration (LSM) corrects the ... 
Numerical method of characteristics for onedimensional blood flow
(2015)Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a onedimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often ... 
Scattering and dip angle decomposition based on subsurface offset extended waveequation migration
(2016)An angledependent reflection coefficient is recovered by seismic migration in the angle domain. We have developed a postmigration technique for computing scattering and dip angle commonimage gathers (CIGs) from seismic ... 
An adaptive multiscale algorithm for efficient extended waveform inversion
(2017)Subsurfaceoffset extended fullwaveform inversion (FWI) may converge to kinematically accurate velocity models without the lowfrequency data accuracy required for standard datadomain FWI. However, this robust alternative ... 
Reconstruction of Lamé Moduli and Density at the Boundary Enabling Directional Elastic Wavefield Decomposition
(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 finitetime Laplace transform. The data are the dynamical ... 
Predicting solvation free energies and thermodynamics in polar solvents and mixtures using a solvationlayer interface condition
(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 ... 
Modulation of Orthographic Decoding by Frontal Cortex
(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 Topological Model of the Hippocampal Cell Assembly Network
(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 doxorubicininduced DNA and synaptic damage in neurons
(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
(2016)Spatial navigation in mammals is based on building a mental representation of their environmenta cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains ... 
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 ... 
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 ...