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This thesis centers around dimensionality reduction and its usage on landmark-type data which are often used in anthropology and morphometrics. In particular we focus on non-linear dimensionality reduction methods - locally linear embedding and multidimensional scaling. We introduce a new approach to dimensionality reduction called multipass dimensionality reduction and show that improves the quality of classification as well as requiring less dimensions for successful classification than the traditional singlepass methods.

O objetivo principal de estudo deste trabalho são as estruturas localmente integráveis L e a fórmula de aproximação de Baouendi-Treves, segundo a qual qualquer solução homogênea de Lu = 0, pode, localmente, ser aproximada por polinômios nas suas integrais primeiras. A realização deste projeto requer um estudo rigoroso de alguns aspectos da teoria das estruturas involutivas e da teoria das distribuições. As principais referências são [2], [4] e [1]. / The main goal of this project is to study a locally integrable structures L and the Baouendi-Treves approximation formula, which states that every homogeneous solution of Lu = 0, can be, locally, approximated by polynomials in their first integrals. This result requires the rigorous study of some aspects of the involutive structures theory and of the distributions theory. The main references are [2], [4] e [1].

O principal objetivo desta dissertação é estudar um contraexemplo para o Décimo Quarto Problema de Hilbert no caso de dimensão n = 5, que foi apresentado por Arno van den Essen ([6]) em 2006 e que é baseado em um contraexemplo de D. Daigle e G. Freudenburg ([4]). Para isso, serão estudados os conceitos fundamentais da teoria de derivações e os princípios básicos das derivações localmente nilpotentes, bem como seus respectivos corolários. Dentre esses princípios encontra-se o Princípio 13, que garante que, se B é uma k- álgebra polinomial, digamos B = k[x1; ..., xn], (onde k é um corpo de característica zero) e D é uma derivação localmente nilpotente sobre B, então seu núcleo A = ker D satisfaz A = B &cap: Frac(A). Assim encontramos o contraexemplo esperado, ao mostrar que A não é finitamente gerado sobre k. Além disso, no apêndice deste trabalho, é dada uma prova para o caso de dimensão 1 do Décimo Quarto Problema de Hilbert. / The main objective of this thesis is to study a counterexample to the Hilberts Fourteenth Problem in dimension n = 5, which was presented by Arno van den Essen ([6]) in 2006 and that is based on a counterexample of D. Daigle and G. Freudenburg ([4]). For these purpose, we study the fundamental concepts of the theory of derivations and the basic principles of locally nilpotent derivations and their corollaries. Among these principles, Principle 13 ensures that if B is a k-algebra polynomial, say B = k[x1; ..., xn], (where k is a field of characteristic zero) and D is a locally nilpotent derivation on B, then its kernel A = ker D satisfies A = B ∩ Frac(A). Once we have proved that A is not finitely generated over k, we find the expected counterexample. In addition, in the appendix of this work is given a proof for the Hilberts Fourteenth Problemin dimension n = 1.

Current and emerging threats to trees and forest ecosystems require a re-evaluation of the way forest genetic resources are managed. Governments in the United Kingdom and elsewhere are committed to the restoration, expansion and creation of new woodlands. Tree populations are often adaptively differentiated from one another, so a key question underpinning the success of planting schemes is the choice of seed origin. A long held understanding is that locally sourced seeds will have the best opportunity to tolerate conditions of the planting site (local provenancing). However, the rate at which the environment is changing introduces a great deal of uncertainty into decision making and there is concern that climate change is proceeding at rates faster than those with which locally adapted trees would be able to cope. As such, there are suggestions that seed collected from areas already experiencing the anticipated future conditions will improve the adaptability of forests (predictive provenancing). This thesis investigated outstanding questions relating to the merits of the local provenancing and predictive provenancing approaches, and the practical implementation of seed sourcing policy in British forestry. The validity of existing seed zone boundaries used under local provenancing was analysed for ancient semi-natural Scots pine Pinus sylvestris L. forests of Scotland. Vegetation description and analyses of climatic covariates revealed that the existing series of seed zones used to guide selection of planting stock for restoration do not necessarily environmentally match seed sources to planting sites under current conditions. Additional disparity is introduced when edaphic variation (or proxies for this) is considered. To determine whether future adaptation under local provenancing may be restricted by limited pollen flow among populations of native Scots pine in Scotland, the timing of pollen production in five populations was estimated by repeatedly measuring strobilus development on a series of twenty trees over three consecutive springs. Differences in the mean predicted date of pollen production were found, with populations in the warmer west shedding pollen earliest each year, although the timing and differences in timing among populations varied from year to year, with shedding taking place earliest in the warmest of the three years and latest in the coolest year. A theoretical multi-patch, ecological genetic individual-based model (IBM) was developed to investigate the utility of different seed sourcing strategies (local versus non local provenance) and their capacity to help populations adapt to directional climate change. As well as being adapted to climate, which varied in a clinal pattern, individuals also had to be well adapted to the habitat conditions of the planting site in order to survive hard selection at the seedling stage. The model showed that population size of a new planting was reduced when planting stock adapted to the future conditions but not to current conditions was deployed. The differences were most severe when selection acted simultaneously on both the climate-related and the habitat-related phenotype. Finally, a series of in-depth qualitative surveys conducted with members of the domestic forest nursery and seed supply sector in Great Britain found that there are many difficulties associated with seed sourcing and the supply of trees. These problems arise due to a very limited ability to predict demand at the time of seed sowing, and lead to waste when demand is overestimated and importation of planting stock when demand is underestimated. Confidence and competitiveness in the domestic sector could be greatly improved by updating seed sourcing guidelines and by simplifying certain aspects of the process by which forest planting projects are funded.

Title: Methods of dynamical analysis of portfolio composition Author: Ivana Meňhartová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Tomáš Hanzák, KPMS, MFF UK Abstract: In the presented thesis we study methods used for dynamic analysis of portfolio based on it's revenues. The thesis focuses on Kalman filter and local- ly weighted regression as two basic methods for dynamic analysis. It describes in detail theory for these methods as well as their utilization and it discusses their proper settings. Practical applications of both methods on artificial data and real data from Prague stock-exchange are presented. Using artificial data we demonstrate practical importance of Kalman filter's assumptions. Afterwards we introduce term multicolinearity as a possible complication to real data applicati- ons. At the end of the thesis we compare results and usage of both methods and we introduce possibility of enhancing Kalman filter by projection of estimations or by CUSUM tests (change detection tests). Keywords: Kalman filter, locally weighted regression, multicollinearity, CUSUM test

For many types of learners one can compute the statistically 'optimal' way to select data. We review how these techniques have been used with feedforward neural networks. We then show how the same principles may be used to select data for two alternative, statistically-based learning architectures: mixtures of Gaussians and locally weighted regression. While the techniques for neural networks are expensive and approximate, the techniques for mixtures of Gaussians and locally weighted regression are both efficient and accurate.

The study examines the phenomenon of purchasing locally produced foods in retail grocery stores. Theoretical foundations from the theory of planned behavior and from the stimulus-organism-response framework were used to support and test a model that hypothesized relationships between attitude, subjective norms, perceived consumer effectiveness, perceived product availability, intention to purchase, store atmospheric responsiveness, price consciousness, and extent of purchase behavior in a retail grocery setting. An online survey methodology was used to collect 600 responses across the United States. A two-step approach to structural equation modeling was used to test the relationships. Confirmatory factor analysis with measurement model development supported the hypotheses of store atmospheric responsiveness as a multidimensional construct reflected in four specific dimensions (1) product assortment responsiveness, (2) display factors responsiveness, (3) customer service responsiveness, and (4) store promotions responsiveness. The construct of perceived consumer effectiveness (PCE) was found to highly correlate with attitude and PCE was subsequently dropped as an independent latent construct. Results from analysis of the fitted structural model indicated that attitude and perceived product availability were significant positive indicators of intention to purchase, while subjective norms indicated a significant negative relationship to intention to purchase. A significant positive direct effect between intention to purchase and extent of purchase and a significant positive indirect effect through that of store atmospheric responsiveness was found, suggesting that store atmospheric responsiveness partially mediates the relationship. Consumer price consciousness was found to not significantly moderate the relationship between intention to purchase and extent of purchase. From the results, academic and managerial implications were suggested. For future research directions, four distinct categories emerged; they included (1) a focus on store atmospherics, specifically store atmospheric responsiveness when shopping for locally produced foods, (2) analysis of group differences between shoppers of locally produced foods, (3) category analysis of locally produced food items, and (4) research on the pricing of locally produced foods.

The main goal of this thesis is a contribution to the classification of all incidence geometries of rank two on which some group PSL(2,q), q a prime power, acts flag-transitively. Actually we require that the action be RWPRI (residually weakly primitive) and (2T)1 (doubly transitive on every residue of rank one). In fact our definition of RWPRI requires the geometry to be firm (each residue of rank one has at least two elements) and RC (residually connected). The main goal is achieved in this thesis. It is stated in our "Main Theorem". The proof of this theorem requires more than 60pages. Quite surprisingly, our proof in the direction of the main goal uses essentially the classification of all subgroups of PSL(2,q), a famous result provided in Dickson’s book "Linear groups: With an exposition of the Galois field theory", section 260, in which the group is called Linear Fractional Group LF(n, pn). Our proof requires to work with all ordered pairs of subgroups up to conjugacy. The restrictions such as RWPRI and (2T)1 allow for a complete analysis. The geometries obtained in our "Main Theorem" are bipartite graphs; and also locally 2-arc-transitive graphs in the sense of Giudici, Li and Cheryl Praeger. These graphs are interesting in their own right because of the numerous connections they have with other fields of mathematics.

Rectal cancer is the eight most common cancer diagnosis in Sweden in both men and women, with almost 2000 new cases per year. Radiotherapy, which is an important treatment modality for rectal cancer, has evolved during the past decades. Diagnostic tools have also improved, allowing better staging and offering information used to make well-founded decisions in multidisciplinary team conferences. In a retrospective study (n=46) with locally advanced rectal cancer (LARC) patients, unfit for chemoradiotherapy, patients were treated with short-course radiotherapy. Delayed surgery was done when possible. Radical surgery was possible in 89% of the patients who underwent surgery (80%). Grade IV diarrhoea affected three elderly patients. Target radiation volume should be reduced in elderly or metastatic patients. In a prospective study (n=68) with LARC patients, magnetic resonance imaging (MRI) and 2-18F-fluoro-2-D-deoxyglucose (FDG) positron emission tomography (PET) were used to determine if FDG-PET could provide extra treatment information. Information from FDG-PET changed the stage of 10 patients. Delineation with FDG-PET generally resulted in smaller target volumes than MRI only. Seven of the most advanced LARC patients in the above cohort were used for a methodological study to determine if dose escalation to peripheral, non-resectable regions was feasible. Simultaneous integrated boost plans with photons and protons were evaluated. While toxicity was acceptable in five patients with both protons and photons, two patients with very large tumours had unacceptable risk for intestinal toxicity regardless of modality. In the interim analysis of the Stockholm III Trial (n=303, studying radiotherapy-fractionation and timing of surgery in relation to radiotherapy) compliance was acceptable and severe acute toxicity was infrequent, irrespective of fractionation. Short-course radiotherapy with immediate surgery tended to give more postoperative complications, but only if surgery was delayed more than 10 days after the start of radiotherapy. Quality-of-life in the Stockholm III Trial was studied before, during and shortly after treatment using the EORTC QLQ-C30 and CR38 questionnaires. Surgery accounted for more adverse effects than radiotherapy in all groups. Postoperatively, the poorest quality-of-life was seen in patients given short-course radiotherapy followed by immediate surgery. No postoperative differences were seen between the two groups with delayed surgery.