This thesis treats inequalities of Carlson type, i.e. inequalities of the form <mml:math><mml:semantics><mml:mrow><mml:mrow><mml:msub><mml:mi>∥f∥</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo mml:stretchy="false">≤</mml:mo><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:munderover><mml:mo mml:stretchy="false">∏</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msubsup><mml:mi>∥f∥</mml:mi><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mo mml:stretchy="false">θ</mml:mo><mml:mi>i</mml:mi></mml:msub></mml:msubsup></mml:mrow></mml:mrow></mml:semantics></mml:math> where <mml:math><mml:semantics><mml:mrow><mml:mrow><mml:munderover><mml:mo mml:stretchy="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msub><mml:mo mml:stretchy="false">θ</mml:mo><mml:mn>i </mml:mn></mml:msub></mml:mrow><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:semantics></mml:math> and K is some constant, independent of the function f. X and <mml:math><mml:semantics><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:semantics></mml:math> are normed spaces, embedded in some Hausdorff topological vector space. In most cases, we have <mml:math><mml:semantics><mml:mrow><mml:mi>m</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:semantics></mml:math>, and the spaces involved are weighted Lebesgue spaces on some measure space. For example, the inequality <mml:math><mml:semantics><mml:mrow><mml:mrow><mml:munderover><mml:mo mml:stretchy="false">∫</mml:mo><mml:mn>0</mml:mn><mml:mo mml:stretchy="false">∞</mml:mo></mml:munderover><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi mml:fontstyle="italic">dx</mml:mi><mml:mo mml:stretchy="false">≤</mml:mo><mml:msqrt><mml:mo mml:stretchy="false">π</mml:mo></mml:msqrt></mml:mrow><mml:msup><mml:mfenced mml:open="(" mml:close=")"><mml:mrow><mml:mrow><mml:munderover><mml:mo mml:stretchy="false">∫</mml:mo><mml:mn>0</mml:mn><mml:mo mml:stretchy="false">∞</mml:mo></mml:munderover><mml:msup><mml:mi>f</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow><mml:mi mml:fontstyle="italic">dx</mml:mi></mml:mrow></mml:mfenced><mml:mrow><mml:mn>1</mml:mn><mml:mo mml:stretchy="false">/</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mfenced mml:open="(" mml:close=")"><mml:mrow><mml:mrow><mml:munderover><mml:mo mml:stretchy="false">∫</mml:mo><mml:mn>0</mml:mn><mml:mo mml:stretchy="false">∞</mml:mo></mml:munderover><mml:msup><mml:mi>x</mml:mi><mml:mn>2 </mml:mn></mml:msup></mml:mrow><mml:msup><mml:mi>f</mml:mi><mml:mn>2 </mml:mn></mml:msup><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow><mml:mi mml:fontstyle="italic">dx</mml:mi></mml:mrow></mml:mfenced><mml:mrow><mml:mn>1</mml:mn><mml:mo mml:stretchy="false">/</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:semantics></mml:math> first proved by F. Carlson, is the above inequality with <mml:math><mml:semantics><mml:mrow><mml:mi>m</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:semantics></mml:math>, <mml:math><mml:semantics><mml:mrow><mml:mrow><mml:msub><mml:mo mml:stretchy="false">θ</mml:mo><mml:mn>1 </mml:mn></mml:msub><mml:mo mml:stretchy="false">=</mml:mo><mml:msub><mml:mo mml:stretchy="false">θ</mml:mo><mml:mn>2 </mml:mn></mml:msub></mml:mrow><mml:mo mml:stretchy="false">=</mml:mo><mml:mfrac><mml:mn>1 </mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:semantics></mml:math>, <mml:math><mml:semantics><mml:mrow><mml:mrow><mml:mi>X</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mo mml:stretchy="false">ℝ</mml:mo><mml:mrow><mml:mo mml:stretchy="false">+</mml:mo><mml:mn>, </mml:mn></mml:mrow></mml:msub><mml:mi mml:fontstyle="italic">dx</mml:mi></mml:mrow><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow><mml:mn>, </mml:mn><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn>1 </mml:mn></mml:msub><mml:mo mml:stretchy="false">=</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn>2 </mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mo mml:stretchy="false">ℝ</mml:mo><mml:mrow><mml:mo mml:stretchy="false">+</mml:mo><mml:mn>, </mml:mn></mml:mrow></mml:msub><mml:mi mml:fontstyle="italic">dx</mml:mi></mml:mrow><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:semantics></mml:math> and <mml:math><mml:semantics><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn>2 </mml:mn></mml:msub><mml:mo mml:stretchy="false">=</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn>2 </mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mo mml:stretchy="false">ℝ</mml:mo><mml:mrow><mml:mo mml:stretchy="false">+</mml:mo><mml:mn>, </mml:mn></mml:mrow></mml:msub><mml:msup><mml:mi>x</mml:mi><mml:mn>2 </mml:mn></mml:msup><mml:mi mml:fontstyle="italic">dx</mml:mi></mml:mrow><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:semantics></mml:math>. In different situations, suffcient, and sometimes necessary, conditions are given on the weights in order for a Carlson type inequality to hold for some constant K. Carlson type inequalities have applications to e.g. moment problems, Fourier analysis, optimal sampling, and interpolation theory.

The unifying theme of this dissertation is the development of new solutions for decoding and inference problems based on convex optimization methods. Th first part considers the joint detection and decoding problem for low-density parity-check (LDPC) codes on finite-state channels (FSCs). Hard-disk drives (or magnetic recording systems), where the required error rate (after decoding) is too low to be verifiable by simulation, are most important applications of this research. Recently, LDPC codes have attracted a lot of attention in the magnetic storage industry and some hard-disk drives have started using iterative decoding. Despite progress in the area of reduced-complexity detection and decoding algorithms, there has been some resistance to the deployment of turbo-equalization (TE) structures (with iterative detectors/decoders) in magnetic-recording systems because of error floors and the difficulty of accurately predicting performance at very low error rates. To address this problem for channels with memory, such as FSCs, we propose a new decoding algorithms based on a well-defined convex optimization problem. In particular, it is based on the linear-programing (LP) formulation of the joint decoding problem for LDPC codes over FSCs. It exhibits two favorable properties: provable convergence and predictable error-floors (via pseudo-codeword analysis). Since general-purpose LP solvers are too complex to make the joint LP decoder feasible for practical purposes, we develop an efficient iterative solver for the joint LP decoder by taking advantage of its dual-domain structure. The main advantage of this approach is that it combines the predictability and superior performance of joint LP decoding with the computational complexity of TE. The second part of this dissertation considers the matrix completion problem for the recovery of a data matrix from incomplete, or even corrupted entries of an unknown matrix. Recommender systems are good representatives of this problem, and this research is important for the design of information retrieval systems which require very high scalability. We show that our IMP algorithm reduces the well-known cold-start problem associated with collaborative filtering systems in practice.

Background The Swedish Association of local authorities and regions in collaboration with the national board of health and welfare produces the yearly “Swedish Health Care Report” in order to provide evaluations of the hospitals and counties in Sweden for both the politicians and the general public. Method We describe several standard methods which have been used to present the performance of each hospital or county: Forest plot (FL), League Table (LT), League Plot (LP) and Funnel Plot (FP). Using simulation technique to produce the League Plot of rank is also presented in order to illustrate the unreliable of the ranking principle. Results The league plot with confidence interval is easily understood by people, but it should provide the total number of operations (sample size) as well. The resulting multiple-indicators system gives a clear overview of the whole system, but the cut-off points used in the traffic light method is not the best choice. Several possible improved methodologies are: A league plot traffic light method and a standard funnel plot traffic light method is recommended when aiming at finding the outliers; A p=0.67 funnel plot traffic light method is suggested when wishing to divide the units into approximately equally large groups; A one-side traffic light method seems to be a wonderful choice when focusing on the bad performance units.

The Drosophila Lipoprotein particles bear lipid-linked morphogens on their surface and are required for long-range signaling activity of Wingless and Hedgehog. They also bind a wide variety of gpi-linked proteins. Whether any of these proteins affect morphogen signaling is unknown. Here, I show that the gpi-linked heparan sulfate proteoglycan Dally is released from cell membranes and binds to lipoprotein particles both with and without its lipid anchor. Hedgehog signaling efficiency is reduced in Dally mutant discs, but can be rescued non-autonomously by expression of non-gpi-modified Dally. This Dally isoform colocalizes with Hedgehog, Patched and Lipophorin in endosomes and increases Hedgehog signaling efficiency without affecting Hedgehog distribution. These data show that Hedgehog signaling activity can be influenced by other Lipophorin-associated proteins, and suggest Lipoproteins provide a platform for regulation of morphogen signaling.

Nous présentons quelques contributions à l'estimation fonctionnelle par méthodes d'ondelettes.<br />Deux axes de recherches orientent notre travail. Premier axe: étude de modèles statistiques complexes. Le point de départ de notre étude est le modèle de bruit blanc gaussien généralisé et le modèle de régression à pas aléatoires.<br />Ceux-ci font intervenir une fonction perturbant l'estimation de la fonction inconnue.<br />Notre objectif est de montrer l'influence exacte de cette fonction parasite via l'approche minimax sous le risque Lp. Dans un premier temps,<br />nous utilisons des méthodes en ondelettes pour cerner les limites de cette approche lorsque l'on se place sur des boules de Besov standards. Dans un deuxième temps, nous étudions l'alternative des boules de Besov pondérées et des méthodes en ondelettes déformées.<br />Deuxième axe: estimation adaptative. Nous étudions les performances de plusieurs estimateurs de seuillage par blocs en ondelettes sous le risque Lp.<br />Nous montrons leurs excellentes propriétés minimax et maxisets pour un large panel de modèles statistiques. En guise d'applications, nous traitons le modèle de régression à pas aléatoires et le modèle de convolution en bruit blanc gaussien.

Linear programming (LP) decoding of low-density parity-check codes was introduced by Feldman et al. in [1]. In his formulation it is assumed that communication takes place over a memoryless channel and that the source is uniform. Here, we extend the LP decoding paradigm by studying its application to scenarios with source non-uniformity and to decoding over channels with memory. We develop two decoders for the scenario of non-uniform memoryless sources transmitted over memoryless channels. The first decoder uses a modified linear cost function which incorporates the a-priori source information and works with systematic codes. The second decoder differs by using non-systematic codes obtained by puncturing lower rate systematic codes and using an “extended decoding polytope.” Simulations show that the modified decoders yield gains over the standard LP decoder. Next, LP decoding is considered for two channels with memory: the binary additive Markov noise channel and the infinite-memory non-ergodic Polya-contagion channel. For the Markov channel, no linear cost function corresponding to maximum likelihood (ML) decoding could be obtained and hence it is unclear how to proceed. For the Polya channel, two LP-based decoders are developed. The first is derived in a straightforward manner from the ML decoding rule of [2]. The second decoder relies on a simplification of the same ML decoding rule which holds for codes containing the all-ones codeword. Simulations are performed for both decoders with regular and irregular LDPC codes and demonstrate relatively good performance with respect to the channel epsilon-capacity. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2008-12-08 16:24:43.358

We consider a family of generalized Procrustes problems. In this class of problems, one aims at aligning a set of vectors to a given second set of vectors. The distance between both sets is measured in the q norm, and for the alignment, isometries with respect to the p norm are allowed. In contrast to the classical Procrustes problem with p = q = 2, we allow p and q to differ. We will see that it makes a difference whether the problem is real or cast over the complex field. Therefore, we discuss the solutions for p = 2 separately for these cases. We show that all the real cases can be solved efficiently. Most of the complex cases can up to now only be solved approximately in polynomial time, but we show the existence of polynomial time algorithms for q ∈ {2, 4, ∞}. Computational experiments illustrate the suggested algorithms.

We consider a family of generalized Procrustes problems. In this class of problems, one aims at aligning a set of vectors to a given second set of vectors. The distance between both sets is measured in the q norm, and for the alignment, isometries with respect to the p norm are allowed. In contrast to the classical Procrustes problem with p = q = 2, we allow p and q to differ. We will see that it makes a difference whether the problem is real or cast over the complex field. Therefore, we discuss the solutions for p = 2 separately for these cases. We show that all the real cases can be solved efficiently. Most of the complex cases can up to now only be solved approximately in polynomial time, but we show the existence of polynomial time algorithms for q ∈ {2, 4, ∞}. Computational experiments illustrate the suggested algorithms.

The need to construct optimal drape surfaces arises in airborne geophysical surveys where it is necessary to fly a safe distance above the ground and within the performance limits of the aircraft used, but as close as possible to the surface. The problem is formulated as an LP with constraints at every point of a grid covering the area concerned, yielding a very large problem. The objective of the LP is to create as "good" a surface as possible. This formulation is new, as previous methods did not aim to minimise an objective function. If the desired surface has only slope limitations, the resulting drape surface must be constrained in the first derivative. Such a drape surface is readily constructed using the Lifting Algoritlun. It is shown that the Litling Algorithm is both exact and has great speed advantages. Some numerical results confinning exacmcss and speed are presented, as is the algorithm's analogy to a flow network method. An enhanced lifting method with a better order of complexity is also proposed and tested numerically. In most practical situations a drape surface is required which has both first and second derivatives constrained. If only a cut through such a surface is considered, the problem can be solved with relative ease by exploiting its nctwork~Jike structure. This method fonns the basis of one of the preferred heuristics developed later. It was not possible to generalise this method to a full two~dimensional drape surface. A commercially available LP package fares better in finding the optimal solution. Several heuristic methods were examined. first a general heuristic method based on a lifting approach was developed. This was followed by a method using repeated application of the method used for sections (the Alternating One-dimensional Dual Algorithm ["AODA"]). Three heuristics based on thimbles were also designed. Thimbles are caps whose first and second derivatives are acceptable and which are placed over local infeasibilities in the topography The work ends with a chapter comparing the efficiency of various heuristics and comparing the results obtained using a number of test datasets. It was fOLmd that heuristic methods provide acceptable drape surfaces and that the choice lies between speed and accuracy, with a previously designed smoothing method being the fastesl and the AODA the most accurate and quick enough. / Operations Research / D.Phil.

Patients with rheumatoid arthritis (RA) have a shorter life span than the general population. An increased death due to cardiovascular disease (CVD) has been reported. RA is characterized by synovitis and joint destruction accompanied by an acute phase reaction and systemic features. The present work investigates the epidemiology of CVD in patients with RA in the county of Västerbotten and the influence of inflammation on lipid metabolism and haemostasis. In a retrospective cohort study on 606 RA patients, the overall mortality was significantly higher than in the general population, with an excess death rate for CVD and for ishemic heart diseae (IHD) in both sexes. Multiple Cox regression, showed that male sex, higher age at disease onset and cardiovascular event increased the risk for death. Male sex, high age at disease onset and hypertension increased the risk for cardiovascular event. Diabetes mellitus, treatment with corticosteroids, disease modifying antirheumatic drugs and postmenopausal estrogen neither influenced survival nor the risk of cardiovascular event. In 93 patients with active RA, the levels of cholesterol, high density- (HDL) and low density (LDL) lipoprotein cholesterol were significantly lower, and Lipoprotein(a) was significantly higher compared to controls. In a follow-up on 53 patients, a relation between the change of Lp(a) and acute phase proteins was found only in patients with high levels of Lp(a). Preheparin lipoprotein lipase (LPL) activity and mass were significantly decreased in 17 postmenopausal women with active RA. Preheparin LPL mass correlated inversely to several acute phase proteins and interleukin-6. Low levels of LPL mass may implicate increased hepatic clearence but also increased macrophage ingestion of lipoproteins via the LDL receptor-related protein (LRP). Haemostasis of the circulation was investigated in 74 of the 93 patients with active RA. In patients with extraarticular disease, the release of tissue plasminogen activator (tPA) was significantly decreased, and its inhibitor (PAI-1) was significantly increased compared to patients with nonsystemic disease, implicating hypofibrinolysis. In a two year follow-up, patients with thromboembolic events had significantly elevated levels of von Willebrand factor, PAI-1, triglycerides and haptoglobin compared to event-free patients. In 29 RA patients and 18 spondylarthropathy patients with gonarthritis, radiological joint destruction correlated to PAI-1 antigen in synovial fluid and, inversely, to plasminogen. A relationship between activation of fibrin degrading proteolytic enzymes and joint destruction was implicated. In conclusion, several processes involved in lipid metabolism and haemostasis are influenced in active RA. In view of the increased death rate due to CVD, an efficient control of inflammation should be important, not only for reducing joint destruction, but also for reducing systemical atherogenic and thrombogenic effects. / <p>s. 1-54: sammanfattning, s. 55-133: 6 uppsatser</p> / digitalisering@umu.se