On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

Lukemisen vaikeuden kuntoutus ensiluokkalaisilla : Kolme pedagogista interventiota

Remediation of Reading Difficulties in Grade 1. Three Pedagogical Interventions Keywords: initial teaching, learning to read, reading difficulties, intervention, dyslexia, remediation of dyslexia, home reading, computerized training In this study three different reading interventions were tested for first-graders at risk of reading difficulties at school commencement. The intervention groups were compared together and with a control group receiving special education provided by the school. First intervention was a new approach called syllable rhythmics in which syllabic rhythm, phonological knowledge and letter-phoneme correspondence are emphasized. Syllable rhythmics is based on multi-sensory training elements aimed at finding the most functional modality for every child. The second intervention was computerized training of letter-sound correspondence with the Ekapeli learning game. The third intervention was home-based shared book reading, where every family was given a story book, and dialogic reading style reading and writing exercises were prepared for each chapter of the book. The participants were 80 first-graders in 19 classes in nine schools. The children were matched in four groups according to pre-test results: three intervention and one control. The interventions took ten weeks starting from September in grade 1. The first post-test including several measures of reading abilities was administered in December. The first delayed post-test was administered in March, the second in September in grade 2, and the third, “ALLU” test (reading test for primary school) was administered in March in grade 2. The intervention and control groups differed only slightly from each other in grade 1. However, girls progressed significantly more than boys in both word reading and reading comprehension in December and this difference remained in March. The children who had been cited as inattentive by their teachers also lagged behind the others in the post-tests in December and March. When participants were divided into two groups according to their initial letter knowledge at school entry, the weaker group (maximum 17 correctly named letters in pre-test) progressed more slowly in both word reading and reading comprehension in grade 1. Intervention group and gender had no interaction effect in grade 1. Instead, intervention group and attentiveness had an interaction effect on most test measures the inattentive students in the syllable rhythmic group doing worst and attentive students in the control group doing best in grade 1. The smallest difference between results of attentive and inattentive students was in the Ekapeli group. In grade 2 still only minor differences were found between the intervention groups and control group. The only significant difference was in non-word reading, with the syllable rhythmics group outperforming the other groups in the fall. The difference between girls’ and boys’ performances in both technical reading and text comprehension disappeared in grade 2. The difference between the inattentive and attentive students cold no longer be found in technical reading, and the difference became smaller in text comprehension as well. The difference between two groups divided according to their initial letter knowledge disappeared in technical reading but remained significant in text comprehension measures in the ALLU test in the spring of grade 2. In all, the children in the study did better in the ALLU test than expected according to ALLU test norms. Being the weakest readers in their classes in the pre-test, 52.3 % reached the normal reading ability level. In the norm group 72.3 % of all students attained normal reading ability. The results of this study indicate that different types of remediation programs can be effective, and that special education has been apparently useful. The results suggest careful consideration of first-graders’ initial reading abilities (especially letter knowledge) and possible failure of attention; remediation should be individually targeted while flexibly using different methods.

Synthesis, Reactivity and Biological Activity of 17β-HSD1 Inhibitors Based on a Thieno[2,3-d]pryrimidin-4(3H)-one Core

Breast cancer is the most common cancer in women in Western countries. In the early stages of development most breast cancers are hormone-dependent, and estrogens, especially estradiol, have a pivotal role in their development and progression. One approach to the treatment of hormone-dependent breast cancers is to block the formation of the active estrogens by inhibiting the action of the steroid metabolising enzymes. 17beta-Hydroxysteroid dehydrogenase type 1 (17beta-HSD1) is a key enzyme in the biosynthesis of estradiol, the most potent female sex hormone. The 17beta-HSD1 enzyme catalyses the final step and converts estrone into the biologically active estradiol. Blocking 17beta-HSD1 activity with a specific enzyme inhibitor could provide a means to reduce circulating and tumour estradiol levels and thus promote tumour regression. In recent years 17beta-HSD1 has been recognised as an important drug target. Some inhibitors of 17beta-HSD1 have been reported, however, there are no inhibitors on the market nor have clinical trials been announced. The majority of known 17beta-HSD1 inhibitors are based on steroidal structures, while relatively little has been reported on non-steroidal inhibitors. As compared with 17beta-HSD1 inhibitors based on steroidal structures, non-steroidal compounds could have advantages of synthetic accessibility, drug-likeness, selectivity and non-estrogenicity. This study describes the synthesis of large group of novel 17beta-HSD1 inhibitors based on a non-steroidal thieno[2,3-d]pyrimidin-4(3H)-one core. An efficient synthesis route was developed for the lead compound and subsequently employed in the synthesis of thieno[2,3-d]pyrimidin-4(3H)-one based molecule library. The biological activities and binding of these inhibitors to 17beta-HSD1 and, finally, the quantitative structure activity relationship (QSAR) model are also reported. In this study, several potent and selective 17beta-HSD1 inhibitors without estrogenic activity were identified. This establishment of a novel class of inhibitors is a progressive achievement in 17beta-HSD1 inhibitor development. Furthermore, the 3D-QSAR model, constructed on the basis of this study, offers a powerful tool for future 17beta-HSD1 inhibitor development. As part of the fundamental science underpinning this research, the chemical reactivity of fused (di)cycloalkeno thieno[2,3-d]pyrimidin-4(3H)-ones with electrophilic reagents, i.e. Vilsmeier reagent and dimethylformamide dimethylacetal, was investigated. These findings resulted in a revision of the reaction mechanism of Vilsmeier haloformylation and further contributed to understanding the chemical reactivity of this compound class. This study revealed that the reactivity is dependent upon a stereoelectronic effect arising from different ring conformations.

Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

On the behaviour of some physical parameterization methods in high-resolution numerical weather prediction models

Modern-day weather forecasting is highly dependent on Numerical Weather Prediction (NWP) models as the main data source. The evolving state of the atmosphere with time can be numerically predicted by solving a set of hydrodynamic equations, if the initial state is known. However, such a modelling approach always contains approximations that by and large depend on the purpose of use and resolution of the models. Present-day NWP systems operate with horizontal model resolutions in the range from about 40 km to 10 km. Recently, the aim has been to reach operationally to scales of 1 4 km. This requires less approximations in the model equations, more complex treatment of physical processes and, furthermore, more computing power. This thesis concentrates on the physical parameterization methods used in high-resolution NWP models. The main emphasis is on the validation of the grid-size-dependent convection parameterization in the High Resolution Limited Area Model (HIRLAM) and on a comprehensive intercomparison of radiative-flux parameterizations. In addition, the problems related to wind prediction near the coastline are addressed with high-resolution meso-scale models. The grid-size-dependent convection parameterization is clearly beneficial for NWP models operating with a dense grid. Results show that the current convection scheme in HIRLAM is still applicable down to a 5.6 km grid size. However, with further improved model resolution, the tendency of the model to overestimate strong precipitation intensities increases in all the experiment runs. For the clear-sky longwave radiation parameterization, schemes used in NWP-models provide much better results in comparison with simple empirical schemes. On the other hand, for the shortwave part of the spectrum, the empirical schemes are more competitive for producing fairly accurate surface fluxes. Overall, even the complex radiation parameterization schemes used in NWP-models seem to be slightly too transparent for both long- and shortwave radiation in clear-sky conditions. For cloudy conditions, simple cloud correction functions are tested. In case of longwave radiation, the empirical cloud correction methods provide rather accurate results, whereas for shortwave radiation the benefit is only marginal. Idealised high-resolution two-dimensional meso-scale model experiments suggest that the reason for the observed formation of the afternoon low level jet (LLJ) over the Gulf of Finland is an inertial oscillation mechanism, when the large-scale flow is from the south-east or west directions. The LLJ is further enhanced by the sea-breeze circulation. A three-dimensional HIRLAM experiment, with a 7.7 km grid size, is able to generate a similar LLJ flow structure as suggested by the 2D-experiments and observations. It is also pointed out that improved model resolution does not necessary lead to better wind forecasts in the statistical sense. In nested systems, the quality of the large-scale host model is really important, especially if the inner meso-scale model domain is small.

Hard Custom, Hard Dance : Social Organisation, (Un)Differentiation and Notions of Power in a Tabiteuean Community, Southern Kiribati

Hard Custom, Hard Dance: Social Organisation, (Un)Differentiation and Notions of Power in a Tabiteuean Community, Southern Kiribati is an ethnographic study of a village community. This work analyses social organisation on the island of Tabiteuea in the Micronesian state of Kiribati, examining the intertwining of hierarchical and egalitarian traits, meanwhile bringing a new perspective to scholarly discussions of social differentiation by introducing the concept of undifferentiation to describe non-hierarchical social forms and practices. Particular attention is paid to local ideas concerning symbolic power, abstractly understood as the potency for social reproduction, but also examined in one of its forms; authority understood as the right to speak. The workings of social differentiation and undifferentiation in the village are specifically studied in two contexts connected by local notions of power: the meetinghouse institution (te maneaba) and traditional dancing (te mwaie). This dissertation is based on 11 months of anthropological fieldwork in 1999‒2000 in Kiribati and Fiji, with an emphasis on participant observation and the collection of oral tradition (narratives and songs). The questions are approached through three distinct but interrelated topics: (i) A key narrative of the community ‒ the story of an ancestor without descendants ‒ is presented and discussed, along with other narratives. (ii) The Kiribati meetinghouse institution, te maneaba, is considered in terms of oral tradition as well as present-day practices and customs. (iii) Kiribati dancing (te mwaie) is examined through a discussion of competing dance groups, followed by an extended case study of four dance events. In the course of this work the community of close to four hundred inhabitants is depicted as constructed primarily of clans and households, but also of churches, work co-operatives and dance groups, but also as a significant and valued social unit in itself, and a part of the wider island district. In these partly cross-cutting and overlapping social matrices, people are alternatingly organised by the distinct values and logic of differentiation and undifferentiation. At different levels of social integration and in different modes of social and discursive practice, there are heightened moments of differentiation, followed by active undifferentiation. The central notions concerning power and authority to emerge are, firstly, that in order to be valued and utilised, power needs to be controlled. Secondly, power is not allowed to centralize in the hands of one person or group for any long period of time. Thirdly, out of the permanent reach of people, power/authority is always, on the one hand, left outside the factual community and, on the other, vested in community, the social whole. Several forms of differentiation and undifferentiation emerge, but these appear to be systematically related. Social differentiation building on typically Austronesian complementary differences (such as male:female, elder:younger, autochtonous:allotochtonous) is valued, even if eventually restricted, whereas differentiation based on non-complementary differences (such as monetary wealth or level of education) is generally resisted, and/or is subsumed by the complementary distinctions. The concomitant forms of undifferentiation are likewise hierarchically organised. On the level of the society as a whole, undifferentiation means circumscribing and ultimately withholding social hierarchy. Potential hierarchy is both based on a combination of valued complementary differences between social groups and individuals, but also limited by virtue of the undoing of these differences; for example, in the dissolution of seniority (elder-younger) and gender (male-female) into sameness. Like the suspension of hierarchy, undifferentiation as transformation requires the recognition of pre-existing difference and does not mean devaluing the difference. This form of undifferentiation is ultimately encompassed by the first one, as the processes of the differentiation, whether transformed or not, are always halted. Finally, undifferentiation can mean the prevention of non-complementary differences between social groups or individuals. This form of undifferentiation, like the differentiation it works on, takes place on a lower level of societal ideology, as both the differences and their prevention are always encompassed by the complementary differences and their undoing. It is concluded that Southern Kiribati society be seen as a combination of a severely limited and decentralised hierarchy (differentiation) and of a tightly conditional and contextual (intra-category) equality (undifferentiation), and that it is distinctly characterised by an enduring tension between these contradicting social forms and cultural notions. With reference to the local notion of hardness used to characterise custom on this particular island as well as dance in general, it is argued in this work that in this Tabiteuean community some forms of differentiation are valued though strictly delimited or even undone, whereas other forms of differentiation are a perceived as a threat to community, necessitating pre-emptive imposition of undifferentiation. Power, though sought after and displayed - particularly in dancing - must always remain controlled.

Essays on the Modeling and Prediction of Volatility and Higher Moments of Stock Returns (summary section only)

One of the most fundamental and widely accepted ideas in finance is that investors are compensated through higher returns for taking on non-diversifiable risk. Hence the quantification, modeling and prediction of risk have been, and still are one of the most prolific research areas in financial economics. It was recognized early on that there are predictable patterns in the variance of speculative prices. Later research has shown that there may also be systematic variation in the skewness and kurtosis of financial returns. Lacking in the literature so far, is an out-of-sample forecast evaluation of the potential benefits of these new more complicated models with time-varying higher moments. Such an evaluation is the topic of this dissertation. Essay 1 investigates the forecast performance of the GARCH (1,1) model when estimated with 9 different error distributions on Standard and Poor’s 500 Index Future returns. By utilizing the theory of realized variance to construct an appropriate ex post measure of variance from intra-day data it is shown that allowing for a leptokurtic error distribution leads to significant improvements in variance forecasts compared to using the normal distribution. This result holds for daily, weekly as well as monthly forecast horizons. It is also found that allowing for skewness and time variation in the higher moments of the distribution does not further improve forecasts. In Essay 2, by using 20 years of daily Standard and Poor 500 index returns, it is found that density forecasts are much improved by allowing for constant excess kurtosis but not improved by allowing for skewness. By allowing the kurtosis and skewness to be time varying the density forecasts are not further improved but on the contrary made slightly worse. In Essay 3 a new model incorporating conditional variance, skewness and kurtosis based on the Normal Inverse Gaussian (NIG) distribution is proposed. The new model and two previously used NIG models are evaluated by their Value at Risk (VaR) forecasts on a long series of daily Standard and Poor’s 500 returns. The results show that only the new model produces satisfactory VaR forecasts for both 1% and 5% VaR Taken together the results of the thesis show that kurtosis appears not to exhibit predictable time variation, whereas there is found some predictability in the skewness. However, the dynamic properties of the skewness are not completely captured by any of the models.

Computational Methods for Studies of Quantum Dots and Boson Condensates

This thesis presents ab initio studies of two kinds of physical systems, quantum dots and bosons, using two program packages of which the bosonic one has mainly been developed by the author. The implemented models, \emph{i.e.}, configuration interaction (CI) and coupled cluster (CC) take the correlated motion of the particles into account, and provide a hierarchy of computational schemes, on top of which the exact solution, within the limit of the single-particle basis set, is obtained. The theory underlying the models is presented in some detail, in order to provide insight into the approximations made and the circumstances under which they hold. Some of the computational methods are also highlighted. In the final sections the results are summarized. The CI and CC calculations on multiexciton complexes in self-assembled semiconductor quantum dots are presented and compared, along with radiative and non-radiative transition rates. Full CI calculations on quantum rings and double quantum rings are also presented. In the latter case, experimental and theoretical results from the literature are re-examined and an alternative explanation for the reported photoluminescence spectra is found. The boson program is first applied on a fictitious model system consisting of bosonic electrons in a central Coulomb field for which CI at the singles and doubles level is found to account for almost all of the correlation energy. Finally, the boson program is employed to study Bose-Einstein condensates confined in different anisotropic trap potentials. The effects of the anisotropy on the relative correlation energy is examined, as well as the effect of varying the interaction potential.}