Browsing Computational and Applied Mathematics by Title
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Quantifying DNA Melting Transitions Using SingleMolecule Force Spectroscopy
(200809)We stretched a DNA molecule using atomic force microscope and quantified the mechanical properties associated withﾠBandﾠSﾠforms of doublestranded DNA (dsDNA), molten DNA, and singlestranded DNA (ssDNA). We also fit ... 
Quantifying Multiscale Noise Sources in SingleMolecule Time Series
(200809)When analyzing singlemolecule data, a lowdimensional set of system observables typically serve as the observational data. We calibrate stochastic dynamical models from time series that record such observables. Numerical ... 
Quantitative Object Reconstruction using Abel Transform XRay Tomography and Mixed Variable Optimization
(200702)This paper introduces a new approach to the problem of quantitatively reconstructing cylindrically symmetric objects from radiograph data obtained via xray tomography. Specifically, a mixed variable programming (MVP) ... 
QuasiNewton Methods and Galerkin Procedures for Nonlinear Elliptic Boundary Value Problems
(198312)Least change secant update strategies are derived that are compatible with algebraic systems of nonlinear equations arising when Galerkin procedures are applied to nonlinear elliptic boundary value problems. The resulting ... 
RankTwo Relaxation Heuristics for MaxCut and Other Binary Quadratic Programs
(200011)Semidefinite relaxation for certain discrete optimization problems involves replacing a vectorvalued variable by a matrixvalued one, producing a convex program while increasing the number of variables by an order of ... 
Reconstructing an Even Damping from a Single Spectrum
(201008)We consider the wave equation on a finite interval with fixed ends and nonuniform viscous damping. We prove that the spectrum of the associated damped wave operator uniquely determines an even damping. We then develop a ... 
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 ... 
Recovering an Optimal LP Basis from an Interior Point Solution
(199110)An important issue in the implementation of interior point algorithms for linear programming is the recovery of an optimal basic solution from an optimal interior point solution. In this paper we describe a method for ... 
Reduced order modeling for timedependent optimization problems with initial value controls
(2018)This paper presents a new reduced order model (ROM) Hessian approximation for linearquadratic optimal control problems where the optimal control is the initial value. Such problems arise in parameter identification and ... 
Reduced storage nodal discontinuous Galerkin methods on semistructured prismatic meshes
(2017)We present a high order timedomain nodal discontinuous Galerkin method for wave problems on hybrid meshes consisting of both wedge and tetrahedral elements. We allow for vertically mapped wedges which can be deformed along ... 
Reducible Nonlinear Programming Problems
(198505)In this thesis we are concerned with general nonlinear programming problems in which the variables can be naturally separated into two groups. This separation has the property that if the variables in one of the groups are ... 
Reoptimization in InteriorPoint Methods with Application to Integer Programming
(199905)This thesis examines current reoptimization techniques for interiorpoint methods available in the literature and studies their efficacy in a branchandbound framework for 0/1 mixed integer programming problems. This work ... 
Representation and Estimation of Seismic Sources via Multipoles
(201705)Accurate representation and estimation of seismic sources are essential to the seismic inversion problem. General sources can be approximated by a truncated series of multipoles depending on the source anisotropy. Most ... 
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 ... 
Resistor Networks and Optimal Grids for the Numerical Solution of Electrical Impedance Tomography with Partial Boundary Measurements
(201005)The problem of Electrical Impedance Tomography (EIT) with partial boundary measurements is to determine the electric conductivity inside a body from the simultaneous measurements of direct currents and voltages on a subset ... 
Resolving Degeneracy in Linear Programs: Steepest Edge, Steepest Ascent, and Closest Ascent
(199107)While variants of the steepest edge pivoting rule are commonly used in linear programming codes they are not known to have the theoretically attractive property of avoiding an infinite sequence of pivots at points of ... 
Restricted 2factors in Bipartite Graphs
(200010)The krestricted 2factor problem is that of finding a spanning subgraph consisting of disjoint cycles with no cycle of length less than or equal to k. It is a generalization of the well known Hamilton cycle problem and ... 
Reverse Time Migration with Optimal Checkpointing
(200611)The optimal checkpointing algorithm (Griewank and Walther, 2000) minimizes the computational complexity of the adjoint state method. Applied to reverse time migration, optimal checkpointing eliminates (or at least drastically ... 
Ritz Value for NonHermitian Matrices
(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 ... 
Ritz Value Localization for NonHermitian Matrices
(201201)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 ...