Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

Living Poetically in the Modern Age : The Situational Aspects of Kierkegaard's Thought

How did Søren Kierkegaard (1813 1855) situate the human subject into historical and social actuality? How did he take into consideration his own situatedness? As key for understanding these questions the research takes the ideal of living poetically that Kierkegaard outlined in his dissertation. In The Concept of Irony (1841) Kierkegaard took up this ideal of the Romantic ironists and made it into an ethical-religious ideal. For him the ideal of living poetically came to mean 1) becoming brought up by God, while 2) assuming ethical-religiously one s role and place in the historical actuality. Through an exegesis of Kierkegaard s texts from 1843 to 1851 it is shown how this ideal governed Kierkegaard s thought and action throughout his work. The analysis of Kierkegaard s ideal of living poetically not only a) shows how the Kierkegaardian subject is situated in its historical context. It also b) sheds light on Kierkegaard s social and political thought, c) helps to understand Kierkegaard s character as a religious thinker, and d) pits his ethical-religious orientation in life against its scientific and commonsense alternatives. The research evaluates the rationality of the way of life championed by Kierkegaard by comparing it with ways of life dominated by reflection and reasoning. It uses Kierkegaard s ideal of living poetically in trying to understand the tensions between religious and unreligious ways of life.

Dietary aspects of cow's milk allergy in young children

Cow s milk allergy (CMA) affects about 2-6% of infants and young children. Environmental factors during early life are suggested to play a role in the development of allergic diseases. One of these factors is likely to be maternal diet during pregnancy and lactation. The association between maternal diet and development of CMA in offspring is not well known, but diet could contain factors that facilitate development of tolerance. After an established food allergy, another issue is gaining tolerance towards an antigen that causes symptoms. The strictness of the elimination depends on the individual level of tolerance. This study aimed at validating a questionnaire used to inquire about food allergies in children, at researching associations between maternal diet during pregnancy and lactation and subsequent development of cow s milk allergy in the offspring, and at evaluating the degree of adherence to a therapeutic elimination diet of children with CMA and factors associated with the adherence and age of recovery. These research questions were addressed in a prospective birth cohort born between 1997 and 2004 at the Tampere and Oulu University Hospitals. Altogether 6753 children of the Diabetes Prediction and Prevention (DIPP) Nutrition cohort were investigated. Questionnaires regarding allergic diseases are often used in studies without validation. High-quality valid tools are therefore needed. Two validation studies were conducted here: one by comparing parentally reported food allergies with information gathered from patient records of 1122 children, and the other one by comparing parentally reported CMA with information in the reimbursement records of special infant formulae in the registers of the Social Insurance Institution for 6753 children. Both of these studies showed that the questionnaire works well and is a valid tool for measuring food allergies in children. In the first validation study, Cohen s kappa values were within 0.71-0.88 for CMA, 0.74-0.82 for cereal allergy, and 0.66-0.86 for any reported food allergy. In the second validation study, the kappa value was 0.79, sensitivity 0.958, and specificity 0.965 for reported and diagnosed CMA. To investigate the associations between maternal diet during pregnancy and lactation and CMA in offspring, 6288 children were studied. Maternal diet during pregnancy (8th month) and lactation (3rd month) was assessed by a validated, 181-item semi-quantitative food frequency questionnaire (FFQ), and as an endpoint register-based information on diagnosed CMA was obtained from the Social Insurance Institution and complemented with parental reports of CMA in their children. The associations between maternal food consumption and CMA in offspring were analyzed by logistic regression comparing the highest and lowest quarters with two middle quarters of consumption and adjusted for several potential confounding factors. High maternal intake of milk products (OR 0.56, 95% CI 0.37-0.86 p = 0.002) was associated with a lower risk of CMA in offspring. When stratified according to maternal allergic rhinitis or asthma, a protective association of high use of milk products with CMA was seen in children of allergy-free mothers (OR 0.30, 95% CI 0.13 - 0.69, p < 0.001), but not in children of allergic mothers. Moreover, low maternal consumption of fish during pregnancy was associated with a higher risk of CMA in children of mothers with allergic rhinitis or asthma (OR 1.47, 95% CI 0.96 - 2.27 for the lowest quarter, p = 0.043). In children of nonallergic mothers, this association was not seen. Maternal diet during lactation was not associated with CMA in offspring, apart from an inverse association between citrus and kiwi fruit consumption and CMA. These results imply that maternal diet during pregnancy may contain factors protective against CMA in offspring, more so than maternal diet during lactation. These results need to be confirmed in other studies before giving recommendations to the public. To evaluate the degree of adherence to a therapeutic elimination diet in children with diagnosed CMA, food records of 267 children were studied. Subsequent food records were examined to assess the age at reintroduction of milk products to the child s diet. Nine of ten families adhered to the elimination diet of the child with extreme accuracy. Older and monosensitized children had more often small amounts of cow s milk protein in their diet (p < 0.001 for both). Adherence to the diet was not related to any other sociodemographic factor studied or to the age at reintroduction of milk products to the diet. Low intakes of vitamin D, calcium, and riboflavin are of concern in children following a cow s milk-free diet. In summary, we found that the questionnaires used in the DIPP study are valid in investigating CMA in young children; that there are associations between maternal diet during pregnancy and lactation and the development of CMA in offspring; and that the therapeutic elimination diet in children with diagnosed CMA is rigorously adhered to.

The social patterning of health, smoking and drinking in Estonia, Latvia, Lithuania and Finland in 1994-2004

The Baltic countries share public health problems typical of most Eastern European transition economies: morbidity and mortality from non-communicable diseases is higher than in Western European countries. This situation has many similarities compared to a neighbouring country, Finland during the late 1960s. There are reasons to expect that health disadvantage may be increasing among the less advantaged population groups in the Baltic countries. The evidence on social differences in health in the Baltic countries is, however, scattered to studies using different methodologies making comparisons difficult. This study aims to bridge the evidence gap by providing comparable standardized cross-sectional and time trend analyses to the social patterning of variation in health and two key health behaviours i.e. smoking and drinking in Estonia, Latvia, Lithuania and Finland in 1994-2004 representing Eastern European transition countries and a stable Western European country. The data consisted of similar cross-sectional postal surveys conducted in 1994, 1996, 1998, 2000, 2002 and 2004 on adult populations (aged 20 64 years) in Estonia (n=9049), Latvia (n=7685), Lithuania (n=11634) and Finland (n=18821) in connection with the Finbalt Health Monitor project. The main statistical method was logistic regression analysis. Perceived health was found to be worse among both men and women in the Baltic countries than in Finland. Poor health was associated with older age and lower education in all countries studied. Urbanization and marital status were not consistently related to health. The existing educational inequalities in health remained generally stable over time from 1994 to 2004. In the Baltic countries, however, improvement in perceived health was mainly found among the better educated men and women. Daily smoking was associated with young age, lower education and psychological distress in all countries. Among women smoking was also associated with urbanisation in all countries except Estonia. Among Lithuanian women, the educational gradient in smoking was weakest, and the overall prevalence of smoking increased over time. Drinking was generally associated with young age among men and women, and with education among women. Better educated women were more often frequent drinkers and less educated binge drinkers. The exception was that in Latvian men and women both frequent drinking and binge drinking were associated with low education. In conclusion, the Baltic countries are likely to resemble Western European countries rather than other transition societies. While health inequalities did not markedly change, substantial inequalities do remain, and there were indications of favourable developments mainly among the better educated. Pressures towards increasing health inequalities may therefore be visible in the future, which would be in accordance with the results on smoking and drinking in this study.

Molecular and epidemiological aspects of Streptococcus pyogenes disease in Finland: Severe infections and bacterial, non-necrotizing cellulitis

Streptococcus pyogenes (group A streptococcus) is an important human pathogen, causing a wide array of infections ranging in severity. The majority of S. pyogenes infections are mild upper respiratory tract or skin infections. Severe, invasive infections, such as bacteraemia, are relatively rare, but constitute a major global burden with a high mortality. Certain streptococcal types are associated with a more severe disease and higher mortality. Bacterial, non-necrotizing cellulitis and erysipelas are localised infections of the skin, and although they are usually not life-threatening, they have a tendency to recur and therefore cause substantial morbidity. Despite several efforts aimed at developing an effective and safe vaccine against S. pyogenes infections, no vaccine is yet available. In this study, the epidemiology of invasive S. pyogenes infections in Finland was described over a decade of national, population-based surveillance. Recent trends in incidence, outcome and bacterial types were investigated. The beta-haemolytic streptococci causing cellulitis and erysipelas infections in Finland were studied in a case-control study. Bacterial isolates were characterised using both conventional and molecular typing methods, such as the emm typing, which is the most widely used typing method for beta-haemolytic streptococci. The incidence of invasive S. pyogenes disease has had an increasing trend during the past ten years in Finland, especially from 2006 onwards. Age- and sex-specific differences in the incidence rate were identified, with men having a higher incidence than women, especially among persons aged 45-64 years. In contrast, more infections occurred in women aged 25-34 years than men. Seasonal patterns with occasional peaks during the midsummer and midwinter were observed. Differences in the predisposing factors and underlying conditions of patients may contribute to these distinctions. Case fatality associated with invasive S. pyogenes infections peaked in 2005 (12%) but remained at a reasonably low level (8% overall during 2004-2007) compared to that of other developed countries (mostly exceeding 10%). Changes in the prevalent emm types were associated with the observed increases in incidence and case fatality. In the case-control study, acute bacterial non-necrotizing cellulitis was caused predominantly by Streptococcus dysgalactiae subsp. equisimilis, instead of S. pyogenes. The recurrent nature of cellulitis became evident. This study adds to our understanding of S. pyogenes infections in Finland and provides a basis for comparison to other countries and future trends. emm type surveillance and outcome analyses remain important for detecting such changes in type distribution that might lead to increases in incidence and case fatality. Bacterial characterisation serves as a basis for disease pathogenesis studies and vaccine development.

New aspects of the diagnosis of Helicobacter pylori infection

Aims: Helicobacter pylori infection, although the prevalence is declining in Western world, is still responsible for several clinically important diseases. None of the diagnostic tests is perfect and in this study, the performance of three stool antigen tests was assessed. In areas of high H. pylori prevalence, the definition of patients with the greatest benefit from eradication therapy may be a problem; the role of duodenal gastric metaplasia in categorizing patients at risk for duodenal ulcer was evaluated in this respect. Whether persistent chronic inflammation and elevated H. pylori antibodies after successful eradication are associated with each other or with atrophic gastritis, a long term sequelae of H. pylori infection, were also studied. Patients and methods: The three stool antigen tests were assessed in pre- and post-eradication settings among 364 subjects in two studies as compared to the rapid urease test (RUT), histology, culture, the 13C-urea breath test (UBT) and enzyme immunoassay (EIA) based H. pylori serology. The association between duodenal gastric metaplasia with duodenal ulcer was evaluated in a retrospective study including 1054 patients gastroscopied due to clinical indications and 154 patients previously operated for duodenal ulcer. The extent of duodenal gastric metaplasia was assessed from histological specimens in different patient groups formed on the basis of gastroscopy findings and H. pylori infection. Chronic gastric inflammation (108 patients) and H. pylori antibodies and serum markers for atrophy (77 patients) were assessed in patients earlier treated for H. pylori. Results: Of the stool antigen tests studied, the monoclonal antibody-based EIA-test showed the highest sensitivity and specificity both in the pre-treatment setting (96.9% and 95.9%) and after therapy (96.9% and 97.8%). The polyclonal stool antigen test and the in-office test had at baseline a sensitivity of 91% and 94%, and a specificity of 96% and 89%, respectively and in a post-treatment setting, a sensitivity of 78% and 91%, and a specificity of 97%, respectively. Duodenal gastric metaplasia was strongly associated with H. pylori positive duodenal ulcer (odds ratio 42). Although common still five years after eradication, persistent chronic gastric inflammation (21%) and elevated H. pylori antibodies (33%) were neither associated with each other nor with atrophic gastritis. Conclusions: Current H. pylori infection can feasibly be diagnosed by a monoclonal antibody-based EIA test with the accuracy comparable to that of reference methods. The performance of the polyclonal test as compared to the monoclonal test was inferior especially in the post-treatment setting. The in-office test had a low specificity for primary diagnosis and hence positive test results should probably be confirmed with another test before eradication therapy is prescribed. The presence of widespread duodenal gastric metaplasia showed promising results in detecting patients who should be treated for H. pylori due to an increased risk of duodenal ulcer. If serology is used later on in patients with earlier successfully treated for H. pylori, it should be taken into account that H. pylori antibodies may persist elevated for years for unknown reason. However, this phenomenon was not found to be associated with persistent chronic inflammation or atrophic changes.

Bioavailability aspects of hydrophobic contaminant degradation in soils

This thesis concentrates on bioavailability of organic soil contaminants in the context of bioremediation of soil contaminated with volatile or non-volatile hydrophobic pollutants. Bioavailability and biodegradation was studied from four viewpoints: (i) Improvement of bioavailability and biodegradation of volatile hydrocarbons in contained bioremediation systems at laboratory - and pilot-scale. (ii) Improvement of bioavailability of non-volatile, hydrophobic compounds in such systems. (iii) Biodegradation of a non-volatile hydrophobic compound in soil organic matter in microcosms. (iiii) Bioavailability of nitrogen in an open, full-scale bioremediation system. It was demonstrated that volatility of organic compounds can be controlled by amending the soil with adsorbents. The sorbed hydrocarbons were shown to be available to soil microbiota. As the result, biodegradation of the volatile hydrocarbons was greatly favored at the expense of volatilization. PAH compounds were shown to be mobilized and their bioavailability improved by a hydrophobic, non-toxic additive, vegetable oil. Bioavailability of the PAHs was recorded as an increased toxicity of the soil. In spite of the increased bioavailability, biodegradation of the PAHs decreased. In microcosms simulating boreal forest organic surface soil, PAH-compound (pyrene) was shown to be removed from soil biologically. Therefore hydrophobicity of the substrate does not necessarily mean low availability and biodegradation in organic soil. Finally, in this thesis it was demonstrated that an unsuitable source of nitrogen or its overdose resulted in wasteful spending of this nutrient and even harmful effects on soil microbes. Such events may inhibit rather than promote the bioremediation process in soil.

Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.