Tensor Completion for Multidimensional Inverse Problems with Applications to Magnetic Resonance Relaxometry

This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed. We derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property (RIP) based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by non-uniform sampling from a Parseval tight frame. We show how tensor completion can be used to solve multidimensional inverse problems arising in NMR relaxometry. Algorithms are developed for regularization parameter selection, including accelerated k-fold cross-validation and generalized cross-validation. These methods are validated on experimental and simulated data. We also derive condition number estimates for nonnegative least squares problems. Tensor recovery promises to significantly accelerate N-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments. Our methods could also be applied to other inverse problems arising in machine learning, image processing, signal processing, computer vision, and other fields.

Nuclear relaxation in low fields and the study of ultraslow atomic motions in solids

U of I Only

Chiroptical spectroscopy of biomolecules using chiral plasmonic nanostructures

This thesis explores the potential of chiral plasmonic nanostructures for the ultrasensitive detection of protein structure. These nanostructures support the generation of fields with enhanced chirality relative to circularly polarised light and are an extremely incisive probe of protein structure. In chapter 4 we introduce a nanopatterned Au film (Templated Plasmonic Substrate, TPS) fabricated using a high through-put injection moulding technique which is a viable alternative to expensive lithographically fabricated nanostructures. The optical and chiroptical properties of TPS nanostructures are found to be highly dependent on the coupling between the electric and magnetic modes of the constituent solid and inverse structures. Significantly, refractive index based measurements of strongly coupled TPSs display a similar sensitivity to protein structure as previous lithographic nanostructures. We subsequently endeavour to improve the sensing properties of TPS nanostructures by developing a high through-put nanoscale chemical functionalisation technique. This process involves a chemical protection/deprotection strategy. The protection step generates a self-assembled monolayer (SAM) of a thermally responsive polymer on the TPS surface which inhibits protein binding. The deprotection step exploits the presence of nanolocalised thermal gradients in the water surrounding the TPS upon irradiation with an 8ns pulsed laser to modify the SAM conformation on surfaces with high net chirality. This allows binding of biomaterial in these regions and subsequently enhances the TPS sensitivity levels. In chapter 6 an alternative method for the detection of protein structure using TPS nanostructures is introduced. This technique relies on mediation of the electric/magnetic coupling in the TPS by the adsorbed protein. This phenomenon is probed through both linear reflectance and nonlinear second harmonic generation (SHG) measurements. Detection of protein structure using this method does not require the presence of fields of enhanced chirality whilst it is also sensitive to a larger array of secondary structure motifs than the measurements in chapters 4 and 5. Finally, a preliminary investigation into the detection of mesoscale biological structure is presented. Sensitivity to the mesoscale helical pitch of insulin amyloid fibrils is displayed through the asymmetry in the circular dichroism (CD) of lithographic gammadions of varying thickness upon adsorption of insulin amyloid fibril spherulites and fragmented fibrils. The proposed model for this sensitivity to the helical pitch relies on the vertical height of the nanostructures relative to this structural property as well as the binding orientation of the fibrils.

Heat-transfer enhancement with pulsed jets in turbulent pipe flow at high-Reynolds number

Improving heat transfer is a critical area of ​​research in various fields such as thermal engineering, energy conversion and aeronautical engineering. The aim of this thesis is to present the design, construction and testing of an experimental setup for the study of heat transfer enhancement in a turbulent boundary layer using cross-flow pulsed jets. The set-up is designed to generate and control pulsed jets, measure heat transfer and acquire all parameters related to wind tunnel flow and is also capable of varying the parameters of the pulsed jets, such as frequency, amplitude and the duty cycle, in order to study the effects on the increase in heat transfer. The thesis describes the design phases, the construction process and the final successful testing of the plant. The test results verify the functionality and accuracy of the set-up and ensure that it can be used to perform a full experimental campaign to investigate heat transfer enhancement using cross-flow pulsed jets in a turbulent layer boundary.

Cardiac Magnetic Resonance Assessment Of Interstitial Myocardial Fibrosis And Cardiomyocyte Hypertrophy In Hypertensive Mice Treated With Spironolactone.

Nearly 50% of patients with heart failure (HF) have preserved LV ejection fraction, with interstitial fibrosis and cardiomyocyte hypertrophy as early manifestations of pressure overload. However, methods to assess both tissue characteristics dynamically and noninvasively with therapy are lacking. We measured the effects of mineralocorticoid receptor blockade on tissue phenotypes in LV pressure overload using cardiac magnetic resonance (CMR). Mice were randomized to l-nitro-ω-methyl ester (l-NAME, 3 mg/mL in water; n=22), or l-NAME with spironolactone (50 mg/kg/day in subcutaneous pellets; n=21). Myocardial extracellular volume (ECV; marker of diffuse interstitial fibrosis) and the intracellular lifetime of water (τic; marker of cardiomyocyte hypertrophy) were determined by CMR T1 imaging at baseline and after 7 weeks of therapy alongside histological assessments. Administration of l-NAME induced hypertensive heart disease in mice, with increases in mean arterial pressure, LV mass, ECV, and τic compared with placebo-treated controls, while LV ejection fraction was preserved (>50%). In comparison, animals receiving both spironolactone and l-NAME (l-NAME+S) showed less concentric remodeling, and a lower myocardial ECV and τic, indicating decreased interstitial fibrosis and cardiomyocyte hypertrophy (ECV: 0.43 ± 0.09 for l-NAME versus 0.25 ± 0.03 for l-NAME+S, P<0.001; τic: 0.42 ± 0.11 for l-NAME groups versus 0.12 ± 0.05 for l-NAME+S group). Mice treated with a combination of l-NAME and spironolactone were similar to placebo-treated controls at 7 weeks. Spironolactone attenuates interstitial fibrosis and cardiomyocyte hypertrophy in hypertensive heart disease. CMR can phenotype myocardial tissue remodeling in pressure-overload, furthering our understanding of HF progression.

Feasibility And Reproducibility Of Diffusion-weighted Magnetic Resonance Imaging Of The Fetal Brain In Twin-twin Transfusion Syndrome.

The aim of this study is to test the feasibility and reproducibility of diffusion-weighted magnetic resonance imaging (DW-MRI) evaluations of the fetal brains in cases of twin-twin transfusion syndrome (TTTS). From May 2011 to June 2012, 24 patients with severe TTTS underwent MRI scans for evaluation of the fetal brains. Datasets were analyzed offline on axial DW images and apparent diffusion coefficient (ADC) maps by two radiologists. The subjective evaluation was described as the absence or presence of water diffusion restriction. The objective evaluation was performed by the placement of 20-mm(2) circular regions of interest on the DW image and ADC maps. Subjective interobserver agreement was assessed by the kappa correlation coefficient. Objective intraobserver and interobserver agreements were assessed by proportionate Bland-Altman tests. Seventy-four DW-MRI scans were performed. Sixty of them (81.1%) were considered to be of good quality. Agreement between the radiologists was 100% for the absence or presence of diffusion restriction of water. For both intraobserver and interobserver agreement of ADC measurements, proportionate Bland-Altman tests showed average percentage differences of less than 1.5% and 95% CI of less than 18% for all sites evaluated. Our data demonstrate that DW-MRI evaluation of the fetal brain in TTTS is feasible and reproducible.

Beam-energy Dependence Of Charge Separation Along The Magnetic Field In Au+au Collisions At Rhic.

Local parity-odd domains are theorized to form inside a quark-gluon plasma which has been produced in high-energy heavy-ion collisions. The local parity-odd domains manifest themselves as charge separation along the magnetic field axis via the chiral magnetic effect. The experimental observation of charge separation has previously been reported for heavy-ion collisions at the top RHIC energies. In this Letter, we present the results of the beam-energy dependence of the charge correlations in Au+Au collisions at midrapidity for center-of-mass energies of 7.7, 11.5, 19.6, 27, 39, and 62.4 GeV from the STAR experiment. After background subtraction, the signal gradually reduces with decreased beam energy and tends to vanish by 7.7 GeV. This implies the dominance of hadronic interactions over partonic ones at lower collision energies.

Possible Unconventional Superconductivity In Substituted Bafe2as2 Revealed By Magnetic Pair-breaking Studies.

The possible existence of a sign-changing gap symmetry in BaFe2As2-derived superconductors (SC) has been an exciting topic of research in the last few years. To further investigate this subject we combine Electron Spin Resonance (ESR) and pressure-dependent transport measurements to investigate magnetic pair-breaking effects on BaFe1.9M0.1As2 (M = Mn, Co, Cu, and Ni) single crystals. An ESR signal, indicative of the presence of localized magnetic moments, is observed only for M = Cu and Mn compounds, which display very low SC transition temperature (Tc) and no SC, respectively. From the ESR analysis assuming the absence of bottleneck effects, the microscopic parameters are extracted to show that this reduction of Tc cannot be accounted by the Abrikosov-Gorkov pair-breaking expression for a sign-preserving gap function. Our results reveal an unconventional spin- and pressure-dependent pair-breaking effect and impose strong constraints on the pairing symmetry of these materials.

Intraventricular Mass Lesions At Magnetic Resonance Imaging: Iconographic Essay - Part 1.

The present essay is illustrated with magnetic resonance images obtained at the authors' institution over the past 15 years and discusses the main imaging findings of intraventricular tumor-like lesions (ependymoma, pilocytic astrocytoma, central neurocytoma, ganglioglioma, choroid plexus papilloma, primitive neuroectodermal tumors, meningioma, epidermoid tumor). Such lesions represent a subgroup of intracranial lesions with unique characteristics and some image patterns that may facilitate the differential diagnosis.

Intraventricular Mass Lesions At Magnetic Resonance Imaging: Iconographic Essay - Part 2.

The present essay is illustrated with magnetic resonance images obtained at the authors' institution over the past 15 years and discusses the main imaging findings of intraventricular tumor-like lesions (colloid cyst, oligodendroglioma, astroblastoma, lipoma, cavernoma) and of inflammatory/infectious lesions (neurocysticercosis and an atypical presentation of neurohistoplasmosis). Such lesions represent a subgroup of intracranial lesions with unique characteristics and some imaging patterns that may facilitate the differential diagnosis.

Megalencephalic Leukoencephalopathy With Subcortical Cysts (mlc) - A Case With Clinical And Magnetic Resonance Imaging (mri) Dissociation.

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Magnetic resonance imaging in the evaluation of patients with aseptic meningoencephalitis and connective tissue disorders

OBJECTIVE: To describe the role of magnetic resonance imaging (MRI) in the evaluation of patients with chronic and recurrent aseptic meningitis.METHOD: A retrospective study of five patients with aseptic meningoencefalitis diagnosed by clinical and CSF findings. CT scans showed without no relevant findings. RESULTS: MRI showed small multifocal lesions hyperintense on T2 weighted images and FLAIR, with mild or no gadolinium enhancement, mainly in periventricular and subcortical regions. Meningoencephalitis preceded the diagnosis of the underlying disease in four patients (Behçet´s disease or systemic lupus erythematosus). After the introduction of adequate treatment for the rheumatic disease, they did not present further symptoms of aseptic meningoencephalitis. CONCLUSION: Aseptic meningoencephalitis can be an early presentation of an autoimmune disease. It is important to emphasize the role of MRI in the diagnosis and follow-up of these patients.

Spatial pattern detection modeling of thrips (Thrips tabaci) on onion fields

Onion (Allium cepa) is one of the most cultivated and consumed vegetables in Brazil and its importance is due to the large laborforce involved. One of the main pests that affect this crop is the Onion Thrips (Thrips tabaci), but the spatial distribution of this insect, although important, has not been considered in crop management recommendations, experimental planning or sampling procedures. Our purpose here is to consider statistical tools to detect and model spatial patterns of the occurrence of the onion thrips. In order to characterize the spatial distribution pattern of the Onion Thrips a survey was carried out to record the number of insects in each development phase on onion plant leaves, on different dates and sample locations, in four rural properties with neighboring farms under different infestation levels and planting methods. The Mantel randomization test proved to be a useful tool to test for spatial correlation which, when detected, was described by a mixed spatial Poisson model with a geostatistical random component and parameters allowing for a characterization of the spatial pattern, as well as the production of prediction maps of susceptibility to levels of infestation throughout the area.

EPR and magnetic studies of a carboxylate-bridged dinuclear copper(II) compound: [cu2(flu)4(dmf)2]

We report magnetic and EPR (electron paramagnetic resonance) spectroscopy studies of [Cu2(flu)4(dmf)2] (flu = flufenamate and dmf = dimethylformamide), which has CuII ions in tetracarboxylate "paddle wheel" dinuclear units. Susceptibility measurements at 10 < T < 275 K allowed the evaluation of an antiferromagnetic intradinuclear exchange coupling J0 = -294 ± 5 cm-1 between CuII ions (Hex = "J0 S1·S2). EPR experiments at 300 K in powder and single-crystals at 9.5 and 34.4 GHz indicated g// = 2.373, g⊥ = 2.073 and zero field splitting parameters D = (-0.334 ± 0.001) cm"1 and E ca. 0. EPR signal intensity measurements at X-band in the range 4 < T < 295 K indicated that J0 = "283 ± 5 cm"1. A higher limit |J´| < 5×10-3 cm-1 for the interdinuclear exchange coupling between neighbor units at ca.14.24 Å was estimated from the angular variation of the single crystal spectra around the magic angles. The results are discussed in terms of the structure of the dinuclear unit and the bridges connecting CuII ions and compared with values reported for similar compounds.

Enzymatic kinetic resolution of (RS)-1-(Phenyl)ethanols by Burkholderia cepacia lipase immobilized on magnetic nanoparticles

Lipase from Burkholderia cepacia immobilized on superparamagnetic nanoparticles using adsorption and chemisorption methodologies was efficiently applied as recyclable biocatalyst in the enzymatic kinetic resolution of (RS)-1-(phenyl)ethanols via transesterification reactions. (R)-Esters and the remaining (S)-alcohols were obtained with excellent enantiomeric excess (> 99%), which corresponds to a perfect process of enzymatic kinetic resolution (conversion 50%, E > 200). The transesterification reactions catalysed with B. cepacia lipase immobilized by the glutaraldehyde method showed the best results in terms of reusability, preserving the enzyme activity (conversion 50%, E > 200) for at least 8 successive cycles.