In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang (Math. Comp. 54(1990)190, 483--493) are discussed. The modified operators are defined for non-smooth functions and are suited for the application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges.

The thesis introduces several methods of real estate price modelling suitable either for prediction of the housing prices or for exploring the relationships between the price and its determinants. We compared the conventional linear regression approach to the tree-based methods of machine learning. The comparison analysis on the dataset of 28 019 apartments in Prague suggests that regression trees (especially the Random forest) yield a higher accuracy in the price prediction. Another objective was to examine the effects of location attributes (especially its accessibility and environmental quality) on the prices of nearby apartments. To address the spatial interactions in the geographical data, we employed three spatially conscious models to achieve more reliable results. The local analysis performed with the geographically weighted regression confirmed the presence of spatial heterogeneity and described the price effects relative to the location. In some areas, an increase of 100 meters in distance from the nearest metro station and the nearest park are associated with a decrease in the apartment prices by 644 CZK/m2 and 916 CZK/m2 , respectively. These findings are especially important for the apartments near the stations of the new metro line, which is currently in construction.

Tree series transformations computed by bottom-up and top-down tree series transducers are called bottom-up and top-down tree series transformations, respectively. (Functional) compositions of such transformations are investigated. It turns out that the class of bottomup tree series transformations over a commutative and complete semiring is closed under left-composition with linear bottom-up tree series transformations and right-composition with boolean deterministic bottom-up tree series transformations. Moreover, it is shown that the class of top-down tree series transformations over a commutative and complete semiring is closed under right-composition with linear, nondeleting top-down tree series transformations. Finally, the composition of a boolean, deterministic, total top-down tree series transformation with a linear top-down tree series transformation is shown to be a top-down tree series transformation.

This thesis discusses properties arising when finite differences are implemented forsolving the two dimensional wave equation on media with various properties. Both homogeneous and heterogeneous surfaces are considered. The time derivative of the wave equation is discretised using a weighted central difference scheme, dependenton a variable parameter gamma. Stability and convergence properties are studied forsome different values of gamma. The report furthermore features an introduction to solving large sparse linear systems of equations, using so-called multigrid methods.The linear systems emerge from the finite difference discretisation scheme. Aconclusion is drawn stating that values of gamma in the unconditionally stable region provides the best computational efficiency. This holds true as the multigrid based numerical solver exhibits optimal or near optimal scaling properties.

Biologists and physicians study complex biologic phenomena in which they use advanced imaging methods. They acquire images containing a lot of information which must be extracted in a correct way. This requires computer skills and knowledge in image processing methods which they seldom have. To overcome the problem, this master thesis aimed to develop a routine for artefact correction and information extraction from images acquired in a research project at the Karolinska Institutet in Stockholm. By developing the routine, the thesis showed how software developed for images of human can be applied to images of rats. The routine handles formatting issues and artefact corrections, calculates diffusion metrics, and performs statistical tests on spatially aligned magnetic resonance images of rats acquired with diffusion weighted echo planar imaging. The routine was verified by analysing the images that it had processed and was considered to create reliable images. Future studies within the field should focus on developing atlases of rats and continue the work with identifying how software developed for images of human can be applied to images of rats. / Biologer och läkare studerar komplexa biologiska processer för vilket de använder avancerade bildgivande metoder. De samlar bilder som innehåller mycket information vilken måste extraheras på ett korrekt sätt. Detta kräver god datorvana och kunskaper inom bildprocessning, vilket de sällan har. För att komma runt problemet, syftade den här masteruppsattsen till att utveckla en rutin för artefaktkorrigering och informationsextrahering från bilder tagna i ett forskningsprojekt vid Karolinska Institutet i Stockholm. Genom att utveckla rutinen, visar uppsattsen hur mjukvaror utvecklade för bilder av människa kan appliceras på bilder av råtta. Rutinen hanterar formatteringsproblem och artefaktkorrigering, beräknar diffusionsmått, och utför statistiska tester på spatiellt matchade magnetresonansavbildningar tagna med diffusionsviktade ekoplana metoder. Rutinen verifierades genom att analysera bilder som den processat och det konstaterades att den skapar korrekta bilder. Framtida studier inom området bör fokusera på att utveckla atlaser av råttor och fortsätta identifieringen av hur mjukvaror utvecklade för bilder av människa kan appliceras på bilder av råtta.

Biologists and physicians study complex biologic phenomena in which they use advanced imaging methods. They acquire images containing a lot of information which must be extracted in a correct way. This requires computer skills and knowledge in image processing methods which they seldom have. To overcome the problem, this master thesis aimed to develop a routine for artefact correction and information extraction from images acquired in a research project at the Karolinska Institutet in Stockholm. By developing the routine, the thesis showed how software developed for images of human can be applied to images of rats. The routine handles formatting issues and artefact corrections, calculates diffusion metrics, and performs statistical tests on spatially aligned magnetic resonance images of rats acquired with diffusion weighted echo planar imaging. The routine was verified by analysing the images that it had processed and was considered to create reliable images. Future studies within the field should focus on developing atlases of rats and continue the work with identifying how software developed for images of human can be applied to images of rats. / Biologer och läkare studerar komplexa biologiska processer för vilket de använder avancerade bildgivande metoder. De samlar bilder som innehåller mycket information vilken måste extraheras på ett korrekt sätt. Detta kräver god datorvana och kunskaper inom bildprocessning, vilket de sällan har. För att komma runt problemet, syftade den här masteruppsattsen till att utveckla en rutin för artefaktkorrigering och informationsextrahering från bilder tagna i ett forskningsprojekt vid Karolinska Institutet i Stockholm. Genom att utveckla rutinen, visar uppsattsen hur mjukvaror utvecklade för bilder av människa kan appliceras på bilder av råtta. Rutinen hanterar formatteringsproblem och artefaktkorrigering, beräknar diffusionsmått, och utför statistiska tester på spatiellt matchade magnetresonansavbildningar tagna med diffusionsviktade ekoplana metoder. Rutinen verifierades genom att analysera bilder som den processat och det konstaterades att den skapar korrekta bilder. Framtida studier inom området bör fokusera på att utveckla atlaser av råttor och fortsätta identifieringen av hur mjukvaror utvecklade för bilder av människa kan appliceras på bilder av råtta.

In this thesis, we study the notion of graph summarization, which is a fundamental task of finding a compact representation of the original graph called the summary. Graph summarization can be used for reducing the footprint of the input graph, better visualization, anonymizing the identity of users, and query answering. There are two different frameworks of graph summarization we consider in this thesis, the utility-based framework and the correction set-based framework. In the utility-based framework, the input graph is summarized until a utility threshold is not violated. In the correction set-based framework a set of correction edges is produced along with the summary graph. In this thesis we propose two algorithms for the utility-based framework and one for the correction set-based framework. All these three algorithms are for static graphs (i.e. graphs that do not change over time). Then, we propose two more utility-based algorithms for fully dynamic graphs (i.e. graphs with edge insertions and deletions). Algorithms for graph summarization can be lossless (summarizing the input graph without losing any information) or lossy (losing some information about the input graph in order to summarize it more). Some of our algorithms are lossless and some lossy, but with controlled utility loss. Our first utility-driven graph summarization algorithm, G-SCIS, is based on a clique and independent set decomposition, that produces optimal compression with zero loss of utility. The compression provided is significantly better than state-of-the-art in lossless graph summarization, while the runtime is two orders of magnitude lower. Our second algorithm is T-BUDS, a highly scalable, utility-driven algorithm for fully controlled lossy summarization. It achieves high scalability by combining memory reduction using Maximum Spanning Tree with a novel binary search procedure. T-BUDS outperforms state-of-the-art drastically in terms of the quality of summarization and is about two orders of magnitude better in terms of speed. In contrast to the competition, we are able to handle web-scale graphs in a single machine without performance impediment as the utility threshold (and size of summary) decreases. Also, we show that our graph summaries can be used as-is to answer several important classes of queries, such as triangle enumeration, Pagerank and shortest paths. We then propose algorithm LDME, a correction set-based graph summarization algorithm that produces compact output representations in a fast and scalable manner. To achieve this, we introduce (1) weighted locality sensitive hashing to drastically reduce the number of comparisons required to find good node merges, (2) an efficient way to compute the best quality merges that produces more compact outputs, and (3) a new sort-based encoding algorithm that is faster and more robust. More interestingly, our algorithm provides performance tuning settings to allow the option of trading compression for running time. On high compression settings, LDME achieves compression equal to or better than the state of the art with up to 53x speedup in running time. On high speed settings, LDME achieves up to two orders of magnitude speedup with only slightly lower compression. We also present two lossless summarization algorithms, Optimal and Scalable, for summarizing fully dynamic graphs. More concretely, we follow the framework of G-SCIS, which produces summaries that can be used as-is in several graph analytics tasks. Different from G-SCIS, which is a batch algorithm, Optimal and Scalable are fully dynamic and can respond rapidly to each change in the graph. Not only are Optimal and Scalable able to outperform G-SCIS and other batch algorithms by several orders of magnitude, but they also significantly outperform MoSSo, the state-of-the-art in lossless dynamic graph summarization. While Optimal produces always the most optimal summary, Scalable is able to trade the amount of node reduction for extra scalability. For reasonable values of the parameter $K$, Scalable is able to outperform Optimal by an order of magnitude in speed, while keeping the rate of node reduction close to that of Optimal. An interesting fact that we observed experimentally is that even if we were to run a batch algorithm, such as G-SCIS, once for every big batch of changes, still they would be much slower than Scalable. For instance, if 1 million changes occur in a graph, Scalable is two orders of magnitude faster than running G-SCIS just once at the end of the 1 million-edge sequence. / Graduate

The strong emphasis placed on improving equality and well-being for all in the Sustainable Development Goals underscores the importance of tackling persistent within-country disparities in maternal mortality and poor health outcomes. Addressing maternal healthcare access barriers is, thus, crucial, particularly in low-resource settings. Numerous studies investigating determinants of maternal healthcare service use in Ethiopia exist but are limited by their focus on individual and household factors, and by methodological weaknesses. A nuanced understanding of the role of socioeconomic and geographic context in influencing access to care is needed to respond effectively. Maternity waiting homes (MWHs) are a potential strategy to address geographical barriers that delay women’s access to obstetric care. However, in addition to concerns about service quality, there is limited evidence on their effectiveness and on what models meet women’s needs. My research goals were, therefore, to contribute to the understanding of what contextual factors influence maternal healthcare service use in general; and to determine whether or not upgraded MWHs operating in an enabling environment could improve delivery care use in rural Ethiopia. My primary data sources were household surveys conducted as part of a cluster-randomized controlled trial evaluating MWHs and local leader training in Jimma Zone, Ethiopia. Random effects multivariable logistic regression analysis of survey data brought to light the social and financial resources that facilitate MWH use, highlighting the need for complementary interventions to make access more equitable. Spatial analyses identified subnational variation in service use at a finer scale than routinely reported and unmasked local variation in the relevance and magnitude of associations between individual-, interpersonal-, and health system factors and maternal healthcare use. These findings have implications for relying upon homogenous national responses to improve equality in access to care and health outcomes. Finally, analysis of trial data found a non-significant effect of interventions on delivery care use likely due to implementation issues and extraneous factors. The need to generate strong evidence of effectiveness of MWHs in improving maternal healthcare service use using sustainable and equitable MWH models using methods appropriate for complex intervention evaluation remains.

Recently implemented reform of the IMF was motivated by empowering smaller developing and emerging countries. My work has an ambition to assess the countries were empowered and whether there would be a more efficient way for IMF reform. I analyse of role and power of countries using well-established methodology of Voting Power Indices. Apart from the immediate change a longer perspective covering last 20 years would be implemented. My aim is not only assess the power of countries as isolated variables but also to assess them in context of other indicators such as economic development. Lastly, I would suggest a new way of reform proposal for the IMF. Currently countries are represented in the locus of executive power through constituencies. Constituencies are formed arbitrary often reflecting power-seeking behaviour of developed countries. The result is composition of constituencies that often further marginalize the developing countries. My proposal is to restructure these constituencies in line with regional international organizations, which can enhance the position of developing countries in two ways. By providing institutional capacity of already existing organizations the consensus within the constituency would be better facilitated. By formation constituencies in line with regional...

Diffusion weighted imaging (DWI) and dynamic susceptibility contrast-enhanced (DSC) perfusion-weighted imaging (PWI) are commonly employed in clinical practice and in research to give pathophysiological information for patients with acute ischemic stroke. DWI is thought to roughly reflect the severely damaged infarct core, while DSC-PWI reflects the area of hypoperfusion. The volumetric difference between DWI and DSC-PWI is termed the PWI/DWI-mismatch, and has been suggested as an MRI surrogate of the ischemic penumbra. However, due to the application of a contrast agent, which has potentially severe side-effects (e.g., nephrogenic systemic fibrosis), the DSC-PWI precludes repetitive examinations for monitoring purposes. New approaches are being sought to overcome this shortcoming. BOLD (blood oxygen-level dependent) signal can reflect the metabolism of blood oxygen in the brain and hemodynamics can be assessed with resting-state fMRI. The aim of this thesis was to use resting-state fMRI as a new approach to give similar information as DSC-PWI. This thesis comprises two studies: In the first study (see Chapter 2), two resting-state fMRI methods, local methods which compare low frequency amplitudes between two hemispheres and a k-means clustering approach, were applied to investigate the functional damage of patients with acute ischemic stroke both in the time domain and frequency domain. We found that the lesion areas had lower amplitudes than contralateral homotopic healthy tissues. We also differentiated the lesion areas from healthy tissues using a k-means clustering approach. In the second study (see Chapter 3), time-shift analysis (TSA), which assesses time delays of the spontaneous low frequency fluctuations of the resting-state BOLD signal, was applied to give similar pathophysiological information as DSC-PWI in the acute phase of stroke. We found that areas which showed a pronounced time delay to the respective mean time course were very similar to the hypoperfusion area. In summary, we suggest that the resting-state fMRI methods, especially the time-shift analysis (TSA), may provide comparable information to DSC-PWI and thus serve as a useful diagnostic tool for stroke MRI without the need for the application of a contrast agent.