Compressive sensing in Clifford analysis

Compressed sensing is a new paradigm in signal processing which states that for certain matrices sparse representations can be obtained by a simple l1-minimization. In this thesis we explore this paradigm for higher-dimensional signal. In particular three cases are being studied: signals taking values in a bicomplex algebra, quaternionic signals, and complex signals which are representable by a nonlinear Fourier basis, a so-called Takenaka-Malmquist system.

Hybrid formulation solution for stress analysis of curved pipes with welded bending joints

A method is presented for evaluating the stress intensity factor of part-through cracks in a thin pipe elbow. A hybrid formulation solution is used to evaluate the stress field close to the crack area. The stress field values are then inputted into a previously developed method published in the literature to evaluate the stress intensity factor in cylindrical shells. Results from cylindrical shells with part-through cracks are extended to double-curvature pipe configurations that contain the same kind of flaw.

FTIR, a potential tool to dementia diagnosis trough analysis of plasma

Nowadays it is still difficult to perform an early and accurate diagnosis of dementia, therefore many research focus on the finding of new dementia biomarkers that can aid in that purpose. So scientists try to find a noninvasive, rapid, and relatively inexpensive procedures for early diagnosis purpose. Several studies demonstrated that the utilization of spectroscopic techniques, such as Fourier Transform Infrared Spectroscopy (FTIR) and Raman spectroscopy could be an useful and accurate procedure to diagnose dementia. As several biochemical mechanisms related to neurodegeneration and dementia can lead to changes in plasma components and others peripheral body fluids, blood-based samples and spectroscopic analyses can be used as a more simple and less invasive technique. This work is intended to confirm some of the hypotheses of previous studies in which FTIR was used in the study of plasma samples of possible patient with AD and respective controls and verify the reproducibility of this spectroscopic technique in the analysis of such samples. Through the spectroscopic analysis combined with multivariate analysis it is possible to discriminate controls and demented samples and identify key spectroscopic differences between these two groups of samples which allows the identification of metabolites altered in this disease. It can be concluded that there are three spectral regions, 3500-2700 cm -1, 1800-1400 cm-1 and 1200-900 cm-1 where it can be extracted relevant spectroscopic information. In the first region, the main conclusion that is possible to take is that there is an unbalance between the content of saturated and unsaturated lipids. In the 1800-1400 cm-1 region it is possible to see the presence of protein aggregates and the change in protein conformation for highly stable parallel β-sheet. The last region showed the presence of products of lipid peroxidation related to impairment of membranes, and nucleic acids oxidative damage. FTIR technique and the information gathered in this work can be used in the construction of classification models that may be used for the diagnosis of cognitive dysfunction.