The class of POP (Polynomial Optimization Problems) covers a wide rang of optimization problems such as 0 - 1 integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. In this paper, we review some methods on solving the unconstraint case: minimize a real-valued polynomial p(x) : Rn → R, as well the constraint case: minimize p(x) on a semialgebraic set K, i.e., a set defined by polynomial equalities and inequalities. We also summarize some questions that we are currently considering. / Singapore-MIT Alliance (SMA)

Many optimization problems can be formulated as second order cone programming (SOCP) problems. Theoretical results show that applying interior-point method (IPM) to SOCP has global polynomial convergence. However, various stability issues arise in the implementation of IPM. The standard normal equation based implementation of IPM encounters stability problems in the computation of search direction. In this paper, an augmented system approach is proposed to overcome the stability problems. Numerical experiments show that the new approach can improve the stability. / Singapore-MIT Alliance (SMA)

A new approach for the control of the size of particles fabricated using the Electrohydrodynamic Atomization (EHDA) method is being developed. In short, the EHDA process produces solution droplets in a controlled manner, and as the solvent evaporates from the surface of the droplets, polymeric particles are formed. By varying the voltage applied, the size of the droplets can be changed, and consequently, the size of the particles can also be controlled. By using both a nozzle electrode and a ring electrode placed axisymmetrically and slightly above the nozzle electrode, we are able to produce a Single Taylor Cone Single Jet for a wide range of voltages, contrary to just using a single nozzle electrode where the range of permissible voltage for the creation of the Single Taylor Cone Single Jet is usually very small. Phase Doppler Particle Analyzer (PDPA) test results have shown that the droplet size increases with increasing voltage applied. This trend is predicted by the electrohydrodynamic theory of the Single Taylor Cone Single Jet based on a perfect dielectric fluid model. Particles fabricated using different voltages do not show much change in the particles size, and this may be attributed to the solvent evaporation process. Nevertheless, these preliminary results do show that this method has the potential of providing us with a way of fine controlling the particles size using relatively simple method with trends predictable by existing theories. / Singapore-MIT Alliance (SMA)

Megavoltage computed tomography (MVCT) and megavoltage cone beam computed tomography can be used for visualizing anatomical structures prior to radiation therapy treatments to assist in patient setup and target localization. These systems provide images using the same beam used for patient treatment, however their image contrast is limited by the low detective quantum efficiency (DQE) of the detectors currently available. By using higher DQE thick, segmented cadmium tungstate detectors we can improve the system contrast. This in turn would permit enhanced soft tissue visualization, allowing MVCT to be more useful. This thesis describes the evaluation of a prototype MVCT system that uses thick, segmented detectors. The system was found to be able to easily visualize a 15 mm diameter 1.5% contrast target with 2 cGy of radiation dose delivered. This system could become the basis for improved commercial MVCT systems. / Medical Physics

Dans ce travail, nous proposons des procédures de test paramétriques et nonparamétriques localement et asymptotiquement optimales au sens de Hajek et Le Cam, pour deux modèles de données de panel. Notre approche est fondée sur la théorie de Le Cam d'une part, pour obtenir les propriétés de normalité asymptotique, bases de la construction des tests paramétriques optimaux, et la théorie de Hajek d'autre part, qui, via un principe d'invariance, permet d'obtenir les procédures nonparamétriques. Dans le premier chapitre, nous considérons un modèle à erreurs composées et nous nous intéressons au problème qui consiste à tester l'absence de l'effet individuel aléatoire. Nous établissons la propriété de normalité locale asymptotique (LAN), ce qui nous permet de construire des procédures paramétriques localement et asymptotiquement optimales (“les plus stringentes”) pour le problème considéré. L'optimalité de ces procédures est liée à la densité-cible f1. Ces propriétés d'optimalité sont hautement paramétriques puisqu'elles requièrent que la densité sous-jacente soit f1. De plus, ces procédures ne seront valides que si la densité-cible f1 et la densité sous-jacent g1 coincïdent. Or, en pratique, une spécification correcte de la densité sous-jacente g1 est non réaliste, et g1 doit être considérée comme un paramètre de nuissance. Pour éliminer cette nuisance, nous adoptons l'argument d'invariance et nous nous restreignons aux procédures fondées sur des statistiques qui sont mesurables par rapport au vecteur des rangs. Les tests que nous obtenons restent valide quelle que soit la densité sous-jacente et sont localement et asymptotiquement les plus stringents. Afin d'avoir des renseignements sur l'efficacité des tests fondés sur les rangs sous différentes lois, nous calculons les efficacités asymptotiques relatives de ces tests par rapport aux tests pseudo-gaussiens, sous des densités g1 quelconques. Enfin, nous proposons quelques simulations pour comparer les performances des procédures proposées. Dans le deuxième chapitre, nous considérons un modèle à erreurs composées avec autocorrélation d'ordre 1 et nous montrons que ce modèle jouit de la propriété LAN. A partir de ce résultat, nous construisons des tests optimaux, au sens local et asymptotique, pour trois problèmes de tests importants dans ce contexte : (a) test de l'absence d'effet individuel et d'autocorrélation; (b) test de l'absence d'effet individuel en présence d'une autocorrélation non spécifiée; et (c) test de l'absence d'autocorrélation en présence d'un effet individuel non spécifié. Enfin, nous proposons quelques simulations pour comparer les performances des tests pseudogaussiens et des tests classiques.

We study pseudodifferential operators on a cylinder IR x B with cross section B that conical singularities. Configurations of that kind are the local model of cornere singularities with base spaces B. Operators A in our calculus are assumed to have symbols α which are meromorphic in the complex covariable with values in the space of all cone operators on B. In case α is dependent of the axial variable t ∈ IR, we show an explicit formula for solutions of the homogeneous equation. Each non-bjectivity point of the symbol in the complex plane corresponds to a finite-dimensional space of solutions. Moreover, we give a relative index formula.

We construct elliptic elements in the algebra of (classical pseudo-differential) operators on a manifold M with conical singularities. The ellipticity of any such operator A refers to a pair of principal symbols (σ0, σ1) where σ0 is the standard (degenerate) homogeneous principal symbol, and σ1 is the so-called conormal symbol, depending on the complex Mellin covariable z. The conormal symbol, responsible for the conical singularity, is operator-valued and acts in Sobolev spaces on the base X of the cone. The σ1-ellipticity is a bijectivity condition for all z of real part (n + 1)/2 − γ, n = dimX, for some weight γ. In general, we have to rule out a discrete set of exceptional weights that depends on A. We show that for every operator A which is elliptic with respect to σ0, and for any real weight γ there is a smoothing Mellin operator F in the cone algebra such that A + F is elliptic including σ1. Moreover, we apply the results to ellipticity and index of (operator-valued) edge symbols from the calculus on manifolds with edges.

Contemporary algorithms employed for reconstruction of 3D volumes from helical cone beam projections are so called non-exact algorithms. This means that the reconstructed volumes contain artifacts irrespective of the detector resolution and number of projection angles employed in the process. In this thesis, three iterative schemes for suppression of these so called cone artifacts are investigated. The first scheme, iterative weighted filtered backprojection (IWFBP), is based on iterative application of a non-exact algorithm. For this method, artifact reduction, as well as spatial resolution and noise properties are measured. During the first five iterations, cone artifacts are clearly reduced. As a side effect, spatial resolution and noise are increased. To avoid this side effect and improve the convergence properties, a regularization procedure is proposed and evaluated. In order to reduce the cost of the IWBP scheme, a second scheme is created by combining IWFBP with the so called ordered subsets technique, which we call OSIWFBP. This method divides the projection data set into subsets, and operates sequentially on each of these in a certain order, hence the name “ordered subsets”. We investigate two different ordering schemes and number of subsets, as well as the possibility to accelerate cone artifact suppression. The main conclusion is that the ordered subsets technique indeed reduces the number of iterations needed, but that it suffers from the drawback of noise amplification. The third scheme starts by dividing input data into high- and low-frequency data, followed by non-iterative reconstruction of the high-frequency part and IWFBP reconstruction of the low-frequency part. This could open for acceleration by reduction of data in the iterative part. The results show that a suppression of artifacts similar to that of the IWFBP method can be obtained, even if a significant part of high-frequency data is non-iteratively reconstructed.

FibMat2.0 is a fibrinogen multilayer developed by AddBIO. Other proteins such as immunoglobulin G (IgG) and human serum albumin (HSA) can also be used to build multilayers with the same technique. The aim of this study of FibMat2.0 was to investigate if the manufacturing of the protein multilayer would induce an immune or haemostatic response in the body. The multilayers of IgG and HSA were also studied. Methods such as null ellipsometry, imaging of coagulation and the cone-and-plate setup were used to study immune reactions, activation of the coagulation cascade, and stability of the multilayers. Small amounts of plasma proteins were adsorbed to fibrinogen multilayers, but complement proteins adsorbed only to the IgG matrix and high molecular weight kininogen (HMWK) adsorbed only to the HSA monolayer. The imaging of coagulation method indicated that the titanium surface and the HSA monolayer activate surface induced coagulation rapidly, whereas fibrinogen and IgG multilayers demonstrated longer coagulation times. Platelets and a few white blood cells were bound to titanium surfaces and fibrinogen multilayers, but not to IgG multilayers or HSA monolayers. A conclusion in this study is that the surface of an implant can be coated with FibMat2.0 without any risks, but more studies are needed to better understand the interactions between the surfaces prepared in the present study and the immune and the haemostatic systems of the human body.

In this project several tests were performed to evaluate the performance of an On-Board Imager® (OBI) mounted on a clinical linear accelerator. The measurements were divided into three parts; geometric accuracy, image registration and couch shift accuracy, and image quality. A cube phantom containing a radiation opaque marker was used to study the agreement with treatment isocenter for both kV-images and cone-beam CT (CBCT) images. The long term stability was investigated by acquiring frontal and lateral kV images twice a week over a 3 month period. Stability in vertical and longitudinal robotic arm motion as well as the stability of the center-of-rotation was evaluated. Further, the agreement of kV image and CBCT center with MV image center was examined. A marker seed phantom was used to evaluate and compare the three applications in image registration; 2D/2D, 2D/3D and 3D/3D. Image registration using kV-kV image sets were compared with MV MV and MV-kV image sets. Further, the accuracy in 2D/2D matches with images acquired at non-orthogonal gantry angles was evaluated. The image quality in CBCT images was evaluated using a Catphan® phantom. Hounsfield unit (HU) uniformity and linearity was compared with planning CT. HU accuracy is crucial for dose verification using CBCT data. The geometric measurements showed good long term stability and accurate position reproducibility after robotic arm motions. A systematic error of about 1 mm in lateral direction of the kV-image center was detected. A small difference between kV and CBCT center was observed and related to a lateral kV detector offset. The vector disagreement between kV- and MV-image centers was  2 mm at some gantry angles. Image registration with the different match applications worked sufficiently. 2D/3D match was seen to correct more accurately than 2D/2D match for large translational and rotational shifts. CBCT images acquired with full-fan mode showed good HU uniformity but half fan images were less uniform. In the soft tissue region the HU agreement with planning CT was reasonable while a larger disagreement was observed at higher densities. This work shows that the OBI is robust and stable in its performance. With regular QC and calibrations the geometric precision of the OBI can be maintained within 1 mm of treatment isocenter.