Department of Mathematics
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Multiscale Coupling of Transcranial Direct Current Stimulation to Neuron Electrodynamics: Modeling the Influence of the Transcranial Electric Field on Neuronal Depolarization
(Hindawi Publishing Corporation, 20141023)Transcranial direct current stimulation (tDCS) continues to demonstrate success as a medical intervention for neurodegenerative diseases, psychological conditions, and traumatic brain injury recovery. One aspect of tDCS ... 
JigCell Run Manager (JCRM): a tool for managing large sets of biochemical model parametrizations
(20151224)Abstract Background Most biomolecular reaction modeling tools allow users to build models with a single list of parameter values. However, a common scenario involves different ... 
A Network Biology Approach to Denitrification in Pseudomonas aeruginosa
(20150223)Pseudomonas aeruginosa is a metabolically flexible member of the Gammaproteobacteria. Under anaerobic conditions and the presence of nitrate, P. aeruginosa can perform (complete) denitrification, a respiratory process of ... 
Predicting the combined effect of multiple genetic variants
(20150730)Abstract Background Many genetic variants have been identified in the human genome. The functional effects of a single variant have been intensively studied. However, the joint effects of multiple variants in the same genes ... 
Cohomology of Finite Groups
(University of Essen, 1992)This is a short lecture course on the cohomology of finite groups. Topics include Künneth formula, cup products and cohomology ring, differential graded algebras, Evens norm map and the Steenrod operations. 
Pulse propagation in a randomly perturbed ocean: Single pulse statistics
(Acoustical Society of America, 198010)A statistical theory of broadband single pulse propagation in a random ocean is presented. The mutual coherence function of the received signal is derived using an analysis based upon coupled mode theory. As propagation ... 
Dynamics of selfdriven microcantilevers
(American Institute of Physics, 20020401)The small amplitude thermal vibrations of the microcantilever of an atomic force microscope can be enhanced via a delayed feedback system. This is verified experimentally for a triangular cantilever, and modeled theoretically ... 
Convergence theorems for intermediate problems. II
(Cambridge University Press, 2002)Convergence theorems for the practical eigenvector free methods of Gay and Goerisch are obtained under a variety of hypotheses, so that our theorems apply to both traditional boundaryvalue problems and atomic problems. ... 
Growth of functions in cercles de remplissage
(Cambridge University Press, 200202)Suppose that f is meromorphic in the plane, and that there is a sequence z(n) > infinity and a sequence of positive numbers epsilon(n) > 0, such that epsilon(n)\z(n)f(#)(z(n))/log\z(n)\ > infinity. It is shown that ... 
Deformation of a hydrophobic ferrofluid droplet suspended in a viscous medium under uniform magnetic fields
(Cambridge University Press, 201011)The effect of applied magnetic fields on the deformation of a biocompatible hydrophobic ferrofluid drop suspended in a viscous medium is investigated numerically and compared with experimental data. A numerical formulation ... 
Pyramidal and toroidal water drops after impact on a solid surface
(Cambridge University Press, 200306)Superhydrophobic surfaces generate very high contact angles as a result of their microstructure. The impact of a water drop on such a surface shows unusual features, such as total rebound at low impact speed. We report ... 
Fieldinduced motion of ferrofluid droplets through immiscible viscous media
(Cambridge University Press, 200809)The motion of a hydrophobic ferrofluid droplet placed in a viscous medium and driven by an externally applied magnetic field is investigated numerically in an axisymmetric geometry. Initially, the drop is spherical and ... 
Nonlinear integral inequalities in two independent variables and their applications
(Hindawi Publishing Corporation, 2007)This paper generalizes results of Cheung and Ma (2005) to more general inequalities with more than one distinct nonlinear term. From our results, some results of Cheung and Ma ( 2005) can be deduced as some special cases. ... 
A finite element splitting extrapolation for second order hyperbolic equations
(Siam Publications, 2009)Splitting extrapolation is an efficient technique for solving large scale scientific and engineering problems in parallel. This article discusses a finite element splitting extrapolation for second order hyperbolic equations ... 
Recycling Krylov subspaces for sequences of linear systems
(Siam Publications, 2006)Many problems in science and engineering require the solution of a long sequence of slowly changing linear systems. We propose and analyze two methods that significantly reduce the total number of matrixvector products ... 
Model reduction of descriptor systems by interpolatory projection methods
(Siam Publications, 2013)In this paper, we investigate an interpolatory projection framework for model reduction of descriptor systems. With a simple numerical example, we first illustrate that directly applying the subspace conditions from the ... 
A regularized GaussNewton trust region approach to imaging in diffuse optical tomography
(Siam Publications, 2011)We present a new algorithm for the solution of nonlinear least squares problems arising from parameterized imaging problems with diffuse optical tomographic data [D. Boas et al., IEEE Signal Process. Mag., 18 (2001), pp. ... 
Recycling BICG with an application to model reduction
(Siam Publications, 2012)Science and engineering problems frequently require solving a sequence of dual linear systems. Besides having to store only a few Lanczos vectors, using the biconjugate gradient method (BiCG) to solve dual linear systems ... 
Interpolatory projection methods for parameterized model reduction
(Siam Publications, 2011)We provide a unifying projectionbased framework for structurepreserving interpolatory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to ... 
An effective method for parameter estimation with pde constraints with multiple righthand sides
(Siam Publications, 2012)Often, parameter estimation problems of parameterdependent PDEs involve multiple righthand sides. The computational cost and memory requirements of such problems increase linearly with the number of righthand sides. For ...