Browsing by Subject "Singular value decomposition"
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Item Analyzing photochemical and physical processes for organic materials(2010-12) Cone, Craig William; Vanden Bout, David A.; Stevenson, Keith J.; Rossky, Peter J.; Truskett, Thomas M.; Webb, Lauren J.Since their discovery, organic electronic materials have been of great interest as an alternative active layer material for active area materials in electronic applications. Initially studied as probes or lasing material the field has progressed to the point where both conjugated polymers and small organics have become fashionable objects of current device oriented solid state research. Organic electronic materials are liquid crystalline materials, packing into well-ordered domains when annealed thermally or via solvent annealing. The macromolecular orientation of the molecules in the solid state causes a shift in the electronic properties due to coupling of the dipoles. The amount of interaction between molecules can be correlated to different nanoscale morphologies. Such morphologies can be measured using microscopy techniques and compared to the spectroscopic results. This can then be extrapolated out to infer how the charges move within a film. Cyanine dyes represent an interesting form class of dyes as the molecular packing is strongly affected by hydrophilic and hydrophobic pendent groups, which cause the dye to arrange into a tubular bilayer. Spectroelectrochemistry is used to monitor and controllably oxidize the samples. Using singular value decomposition (SVD) it is possible to extract each electronic species formed during electrochemical oxidation and model the proposed species using semi empirical quantum mechanical calculations. Polyfluorene is a blue luminescent polymer of interest for its high quantum yield. The solution and solid-state conformation has shown two distinct phases. The formation of the secondary phase shows a dependence on the molecular weight. In a poor solvent, as the molecular weight increases, the secondary phase forms easier. In the solid state, the highly efficient blue emission from polyfluorene is degraded by ketone defects. The energy transfer to preexisting ketone defects is increased as the filmed is thermally ordered. Glass transitions of block copolymers are studied using synthetically novel polymers where an environmentally sensitive fluorescent reporter is placed within various regions of a self-assembled film. Different dynamics are observed within the block of the film then specifically at the interface of two blocks.Item Numerical algorithms for inverse problems in acoustics and optics(2014-05) Ding, Tian, 1986-; Ren, Kui; Engquist, Bjorn; Gamba, Irene Martínez; Ghattas, Omar; Gonzalez, Oscar; Wheeler, Mary FanettThe objective of this dissertation is to develop computational algorithms for solving inverse coefficient problems for partial differential equations that appear in two medical imaging modalities. The aim of these inverse problems is to reconstruct optical properties of scattering media, such as biological tissues, from measured data collected on the surface of the media. In the first part of the dissertation, we study an inverse boundary value problems for the radiative transport equation. This inverse problem plays important roles in optics-based medical imaging techniques such as diffuse optical tomography and fluorescence optical tomography. We propose a robust reconstruction method that is based on subspace minimization techniques. The method splits the unknowns, both the unknown coefficient and the corresponding transport solutions (or a functional of it) into low-frequency and high-frequency components, and uses singular value decomposition to analytically recover part of low-frequency information. Minimization is then applied to recover part of the high-frequency components of the unknowns. We present some numerical simulations with synthetic data to demonstrate the performance of the proposed algorithm. In the second part of the dissertation, we develop a three-dimensional reconstruction algorithm for photoacoustic tomography in isotropic elastic media. There have been extensive study of photoacoustic tomography in recent years. However, all existing numerical reconstructions are developed for acoustic media in which case the model for wave propagation is the acoustic wave equation. We develop here a two-step reconstruction algorithm to reconstruct quantitatively optical properties, mainly the absorption coefficient and the Gr\"uneisen coefficient using measured elastic wave data. The algorithm consists of an inverse source step where we reconstruct the source function in the elastic wave equation from boundary data and an inverse coefficient step where we reconstruct the coefficients of the diffusion equation using the result of the previous step as interior data. We present some numerical reconstruction results with synthetic data to demonstrate the performance of our algorithm. This is, to the best of our knowledge, the first reconstruction algorithm developed for quantitative photoacoustic imaging in elastic media. Despite the fact that we separate the dissertation into these two different parts to make each part more focused, the algorithms we developed in the two parts are closely related. In fact, if we replace the diffusion model for light propagation in photoacoustic imaging by the radiative transport model, which is often done in the literature, the algorithm we developed in the first part can be integrated into the algorithm in the second part after some minor modifications.Item System identification of dynamic patterns of genome-wide gene expression(2011-12) Wang, Daifeng; Markey, Mia Kathleen; Arapostathis, Ari, 1954-; Vishwanath, Sriram; Aziz, Adnan; Wilke, Claus O.High-throughput methods systematically measure the internal state of the entire cell, but powerful computational tools are needed to infer dynamics from their raw data. Therefore, we have developed a new computational method, Eigen-genomic System Dynamic-pattern Analysis (ESDA), which uses systems theory to infer dynamic parameters from a time series of gene expression measurements. As many genes are measured at a modest number of time points, estimation of the system matrix is underdetermined and traditional approaches for estimating dynamic parameters are ineffective; thus, ESDA uses the principle of dimensionality reduction to overcome the data imbalance. We identify degradation dynamic patterns of a genomic system using ESDA. We also combine ESDA and Principal-oscillation-pattern (POP) analysis, which has been widely used in geosciences, to identify oscillation patterns. We demonstrate the first application of POP analysis to genome-wide time-series gene-expression data. Both simulation data and real-world data are used in this study to demonstrate the applicability of ESDA to genomic data. The biological interpretations of dynamic patterns are provided. We also show that ESDA not only compares favorably with previous experimental methods and existing computational methods, but that it also provides complementary information relative to other approaches.