On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Search for Maximal Flavor Violating Scalars in Same-Charge Lepton Pairs in pp̅ Collisions at √s=1.96 TeV

Models of Maximal Flavor Violation (MxFV) in elementary particle physics may contain at least one new scalar SU$(2)$ doublet field $\Phi_{FV} = (\eta^0,\eta^+)$ that couples the first and third generation quarks ($q_1,q_3$) via a Lagrangian term $\mathcal{L}_{FV} = \xi_{13} \Phi_{FV} q_1 q_3$. These models have a distinctive signature of same-charge top-quark pairs and evade flavor-changing limits from meson mixing measurements. Data corresponding to 2 fb$^{-1}$ collected by the CDF II detector in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV are analyzed for evidence of the MxFV signature. For a neutral scalar $\eta^0$ with $m_{\eta^0} = 200$ GeV/$c^2$ and coupling $\xi_{13}=1$, $\sim$ 11 signal events are expected over a background of $2.1 \pm 1.8$ events. Three events are observed in the data, consistent with background expectations, and limits are set on the coupling $\xi_{13}$ for $m_{\eta^0} = 180-300$ GeV/$c^2$.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

Sensory auditory processing and intuitive sound detection : an investigation of musical experts and nonexperts

The auditory system can detect occasional changes (deviants) in acoustic regularities without the need for subjects to focus their attention on the sound material. Deviant detection is reflected in the elicitation of the mismatch negativity component (MMN) of the event-related potentials. In the studies presented in this thesis, the MMN is used to investigate the auditory abilities for detecting similarities and regularities in sound streams. To investigate the limits of these processes, professional musicians have been tested in some of the studies. The results show that auditory grouping is already more advanced in musicians than in nonmusicians and that the auditory system of musicians can, unlike that of nonmusicians, detect a numerical regularity of always four tones in a series. These results suggest that sensory auditory processing in musicians is not only a fine tuning of universal abilities, but is also qualitatively more advanced than in nonmusicians. In addition, the relationship between the auditory change-detection function and perception is examined. It is shown that, contrary to the generally accepted view, MMN elicitation does not necessarily correlate with perception. The outcome of the auditory change-detection function can be implicit and the implicit knowledge of the sound structure can, after training, be utilized for behaviorally correct intuitive sound detection. These results illustrate the automatic character of the sensory change detection function.

Feature integration in human vision

The earliest stages of human cortical visual processing can be conceived as extraction of local stimulus features. However, more complex visual functions, such as object recognition, require integration of multiple features. Recently, neural processes underlying feature integration in the visual system have been under intensive study. A specialized mid-level stage preceding the object recognition stage has been proposed to account for the processing of contours, surfaces and shapes as well as configuration. This thesis consists of four experimental, psychophysical studies on human visual feature integration. In two studies, classification image a recently developed psychophysical reverse correlation method was used. In this method visual noise is added to near-threshold stimuli. By investigating the relationship between random features in the noise and observer s perceptual decision in each trial, it is possible to estimate what features of the stimuli are critical for the task. The method allows visualizing the critical features that are used in a psychophysical task directly as a spatial correlation map, yielding an effective "behavioral receptive field". Visual context is known to modulate the perception of stimulus features. Some of these interactions are quite complex, and it is not known whether they reflect early or late stages of perceptual processing. The first study investigated the mechanisms of collinear facilitation, where nearby collinear Gabor flankers increase the detectability of a central Gabor. The behavioral receptive field of the mechanism mediating the detection of the central Gabor stimulus was measured by the classification image method. The results show that collinear flankers increase the extent of the behavioral receptive field for the central Gabor, in the direction of the flankers. The increased sensitivity at the ends of the receptive field suggests a low-level explanation for the facilitation. The second study investigated how visual features are integrated into percepts of surface brightness. A novel variant of the classification image method with brightness matching task was used. Many theories assume that perceived brightness is based on the analysis of luminance border features. Here, for the first time this assumption was directly tested. The classification images show that the perceived brightness of both an illusory Craik-O Brien-Cornsweet stimulus and a real uniform step stimulus depends solely on the border. Moreover, the spatial tuning of the features remains almost constant when the stimulus size is changed, suggesting that brightness perception is based on the output of a single spatial frequency channel. The third and fourth studies investigated global form integration in random-dot Glass patterns. In these patterns, a global form can be immediately perceived, if even a small proportion of random dots are paired to dipoles according to a geometrical rule. In the third study the discrimination of orientation structure in highly coherent concentric and Cartesian (straight) Glass patterns was measured. The results showed that the global form was more efficiently discriminated in concentric patterns. The fourth study investigated how form detectability depends on the global regularity of the Glass pattern. The local structure was either Cartesian or curved. It was shown that randomizing the local orientation deteriorated the performance only with the curved pattern. The results give support for the idea that curved and Cartesian patterns are processed in at least partially separate neural systems.

Keltaista ja kimaltavaa : kodin ja koulun yhteistyöstä koulun ja kodin yhteyteen

Through this study I aim to portray connections between home and school through the patterns of thought and action shared in everyday life in a certain community. My observations are primarily based upon interviews, writings and artwork by people from home (N=32) and school (N=13) contexts. Through the stories told, I depict the characters and characteristic features of the home-school interaction by generations. According to the material, in the school days of the grandparents the focus was on discipline and order. For the parents, the focus had shifted towards knowledge, while for the pupils today, the focus lies on evaluation, through which the upbringing of the child is steered towards favourable outcomes. Teachers and those people at home hold partially different understandings of home-school interaction, both of its manifested forms and potentials. The forms of contact in use today are largely seen as one-sided. Yearning for openness and regularity is shared by both sides, yet understood differently. Common causes for failure are said to lie in plain human difficulties in communication and social interaction, but deeply rooted traditions regarding forms of contact also cast a shadow on the route to successful co-operation. This study started around the idea, that home-school interaction should be steered towards the ex-change of constructive ideas between both the home and school environments. Combining the dif-ferent views gives to something to build upon. To test this idea, I drafted a practice period, which was implemented in a small pre-school environment in the fall of 1997. My focus of interest in this project was on the handling of ordinary life information in the schools. So I combined individual views, patterns of knowledge and understanding of the world into the process of teaching. Works of art and writings by the informants worked as tools for information processing and as practical forms of building home-school interaction. Experiences from the pre-school environ-ment were later on echoed in constructing home-school interaction in five other schools. In both these projects, the teaching in the school was based on stories, thoughts and performances put to-gether by the parents, grandparents and children at home. During these processes, the material used in this study, consisting of artwork, writings and interviews (N=501), was collected. The data shows that information originating from the home environments was both a motivating and interesting addition to the teaching. There even was a sense of pride when assessing the seeds of knowledge from one’s own roots. In most cases and subjects, the homegrown information content was seamlessly connected to the functions of school and the curriculum. This project initiated thought processes between pupils and teachers, adults, children and parents, teachers and parents, and also between generations. It appeared that many of the subjects covered had not been raised before between the various participant groups. I have a special interest here in visual expression and its various contextual meanings. There art material portrays how content matter and characteristic features of the adult and parent contexts reflect in the works of the children. Another clearly noticeable factor in the art material is the impact of time-related traditions and functions on the means of visual expression. Comparing the visual material to the written material reveals variances of meaning and possibilities between these forms of expression. The visual material appears to be related especially to portraying objects, action and usage. Processing through that making of images was noted to bring back memories of concrete structures, details and also emotions. This process offered the child an intensive social connection with the adults. In some cases, with children and adults alike, this project brought forth an ongoing relation to visual expression. During this study I end up changing the concept to ‘home-school collaboration’. This widely used concept guides and outlines the interaction between schools and homes. In order to broaden the field of possibilities, I choose to use the concept ‘school-home interconnection’. This concept forms better grounds for forming varying impressions and practices when building interactive contexts. This concept places the responsibility of bridging the connection-gap in the schools. Through the experiences and innovations of thought gained from these projects, I form a model of pedagogy that embraces the idea of school-home interconnection and builds on the various impres-sions and expressions contained in it. In this model, school makes use of the experiences, thoughts and conceptions from the home environment. Various forms of expression are used to portray and process this information. This joint evaluation and observation evolves thought patterns both in school and at home. Keywords: percieving, visuality, visual culture, art and text, visual expression, art education, growth in interaction, home-school collaboration, school-home interconnection, school-home interaction model.

Physical activity, fitness, abdominal obesity, and cardiovascular risk factors in Finnish men and women : The National FINRISK 2002 Study

Physical inactivity, low cardiorespiratory fitness, and abdominal obesity are direct and mediating risk factors for cardiovascular disease (CVD). The results of recent studies suggest that individuals with higher levels of physical activity or cardiorespiratory fitness have lower CVD and all-cause mortality than those with lower activity or fitness levels regardless of their level of obesity. The interrelationships of physical activity, fitness, and abdominal obesity with cardiovascular risk factors have not been studied in detail. The aim of this study was to investigate the associations of different types of leisure time physical activity and aerobic fitness with cardiovascular risk factors in a large population of Finnish adults. In addition, a novel aerobic fitness test was implemented and the distribution of aerobic fitness was explored in men and women across age groups. The interrelationships of physical activity, aerobic fitness and abdominal obesity were examined in relation to cardiovascular risk factors. This study was part of the National FINRISK Study 2002, which monitors cardiovascular risk factors in a Finnish adult population. The sample comprised 13 437 men and women aged 25 to 74 years and was drawn from the Population Register as a stratified random sample according to 10-year age groups, gender and area. A separate physical activity study included 9179 subjects, of whom 5 980 participated (65%) in the study. At the study site, weight, height, waist and hip circumferences, and blood pressure were measured, a blood sample was drawn, and an aerobic fitness test was performed. The fitness test estimated maximal oxygen uptake (VO2max) and was based on a non-exercise method by using a heart rate monitor at rest. Waist-to-hip ratio (WHR) was calculated by dividing waist circumference with hip circumference and was used as a measure of abdominal obesity. Participants filled in a questionnaire on health behavior, a history of diseases, and current health status, and a detailed 12-month leisure time physical activity recall. Based on the recall data, relative energy expenditure was calculated using metabolic equivalents, and physical activity was divided into conditioning, non-conditioning, and commuting physical activity. Participants aged 45 to 74 years were later invited to take part in a 2-hour oral glucose tolerance test with fasting insulin and glucose measurements. Based on the oral glucose tolerance test, undiagnosed impaired glucose tolerance and type 2 diabetes were defined. The estimated aerobic fitness was lower among women and decreased with age. A higher estimated aerobic fitness and a lower WHR were independently associated with lower systolic and diastolic blood pressure, lower total cholesterol and triglyceride levels, and with higher high-density lipoprotein (HDL) cholesterol and HDL to total cholesterol ratio. The associations of the estimated aerobic fitness with diastolic blood pressure, triglycerides, and HDL to total cholesterol ratio were stronger in men with a higher WHR. High levels of conditioning and non-conditioning physical activity were associated with lower high-sensitivity C-reactive protein (CRP) levels. High levels of conditioning and overall physical activities were associated with lower insulin and glucose levels. The associations were stronger among women than men. A better self-rated physical fitness was associated with a higher estimated aerobic fitness, lower CRP levels, and lower insulin and glucose levels in men and women. In each WHR third, the risk of impaired glucose tolerance and type 2 diabetes was higher among physically inactive individuals who did not undertake at least 30 minutes of moderate-intensity physical activity on five days per week. These cross-sectional data show that higher levels of estimated aerobic fitness and regular leisure time physical activity are associated with a favorable cardiovascular risk factor profile and that these associations are present at all levels of abdominal obesity. Most of the associations followed a dose-response manner, suggesting that already low levels of physical activity or fitness are beneficial to health and that larger improvements in risk factor levels may be gained from higher activity and fitness levels. The present findings support the recommendation to engage regularly in leisure time physical activity, to pursue a high level of aerobic fitness, and to prevent abdominal obesity.

Multiple socioeconomic circumstances and health : associations and explanations among Finnish and British public sector employees

Socioeconomic health inequalities have been widely documented, with a lower social position being associated with poorer physical and general health and higher mortality. For mental health the results have been more varied. However, the mechanisms by which the various dimensions of socioeconomic circumstances are associated with different domains of health are not yet fully understood. This is related to a lack of studies tackling the interrelations and pathways between multiple dimensions of socioeconomic circumstances and domains of health. In particular, evidence from comparative studies of populations from different national contexts that consider the complexity of the causes of socioeconomic health inequalities is needed. The aim of this study was to examine the associations of multiple socioeconomic circumstances with physical and mental health, more specifically physical functioning and common mental disorders. This was done in a comparative setting of two cohorts of white-collar public sector employees, one from Finland and one from Britain. The study also sought to find explanations for the observed associations between economic difficulties and health by analysing the contribution of health behaviours, living arrangements and work-family conflicts. The survey data were derived from the Finnish Helsinki Health Study baseline surveys in 2000-2002 among the City of Helsinki employees aged 40-60 years, and from the fifth phase of the London-based Whitehall II study (1997-9) which is a prospective study of civil servants aged 35-55 years at the time of recruitment. The data collection in the two countries was harmonised to safeguard maximal comparability. Physical functioning was measured with the Short Form (SF-36) physical component summary and common mental disorders with the General Health Questionnaire (GHQ-12). Socioeconomic circumstances were parental education, childhood economic difficulties, own education, occupational class, household income, housing tenure, and current economic difficulties. Further explanatory factors were health behaviours, living arrangements and work-family conflicts. The main statistical method used was logistic regression analysis. Analyses were conducted separately for the two sexes and two cohorts. Childhood and current economic difficulties were associated with poorer physical functioning and common mental disorders generally in both cohorts and sexes. Conventional dimensions of socioeconomic circumstances i.e. education, occupational class and income were associated with physical functioning and mediated each other’s effects, but in different ways in the two cohorts: education was more important in Helsinki and occupational class in London. The associations of economic difficulties with health were partly explained by work-family conflicts and other socioeconomic circumstances in both cohorts and sexes. In conclusion, this study on two country-specific cohorts confirms that different dimensions of socioeconomic circumstances are related but not interchangeable. They are also somewhat differently associated with physical and mental domains of health. In addition to conventionally measured dimensions of past and present socioeconomic circumstances, economic difficulties should be taken into account in studies and attempts to reduce health inequalities. Further explanatory factors, particularly conflicts between work and family, should also be considered when aiming to reduce inequalities and maintain the health of employees.

The structure of Norway spruce (Picea abies [L.] Karst.) stems in relation to wood properties of sawn timber

An important challenge in forest industry is to get the appropriate raw material out from the forests to the wood processing industry. Growth and stem reconstruction simulators are therefore increasingly integrated in industrial conversion simulators, for linking the properties of wooden products to the three-dimensional structure of stems and their growing conditions. Static simulators predict the wood properties from stem dimensions at the end of a growth simulation period, whereas in dynamic approaches, the structural components, e.g. branches, are incremented along with the growth processes. The dynamic approach can be applied to stem reconstruction by predicting the three-dimensional stem structure from external tree variables (i.e. age, height) as a result of growth to the current state. In this study, a dynamic growth simulator, PipeQual, and a stem reconstruction simulator, RetroSTEM, are adapted to Norway spruce (Picea abies [L.] Karst.) to predict the three-dimensional structure of stems (tapers, branchiness, wood basic density) over time such that both simulators can be integrated in a sawing simulator. The parameterisation of the PipeQual and RetroSTEM simulators for Norway spruce relied on the theoretically based description of tree structure developing in the growth process and following certain conservative structural regularities while allowing for plasticity in the crown development. The crown expressed both regularity and plasticity in its development, as the vertical foliage density peaked regularly at about 5 m from the stem apex, varying below that with tree age and dominance position (Study I). Conservative stem structure was characterized in terms of (1) the pipe ratios between foliage mass and branch and stem cross-sectional areas at crown base, (2) the allometric relationship between foliage mass and crown length, (3) mean branch length relative to crown length and (4) form coefficients in branches and stem (Study II). The pipe ratio between branch and stem cross-sectional area at crown base, and mean branch length relative to the crown length may differ in trees before and after canopy closure, but the variation should be further analysed in stands of different ages and densities with varying site fertilities and climates. The predictions of the PipeQual and RetroSTEM simulators were evaluated by comparing the simulated values to measured ones (Study III, IV). Both simulators predicted stem taper and branch diameter at the individual tree level with a small bias. RetroSTEM predictions of wood density were accurate. For focusing on even more accurate predictions of stem diameters and branchiness along the stem, both simulators should be further improved by revising the following aspects in the simulators: the relationship between foliage and stem sapwood area in the upper stem, the error source in branch sizes, the crown base development and the height growth models in RetroSTEM. In Study V, the RetroSTEM simulator was integrated in the InnoSIM sawing simulator, and according to the pilot simulations, this turned out to be an efficient tool for readily producing stand scale information about stem sizes and structure when approximating the available assortments of wood products.

Suomen maatalouden tuottamat kasvihuonekaasujen päästöt eri politiikkaskenaarioissa

Climate change is the single biggest environmental problem in the world at the moment. Although the effects are still not fully understood and there is considerable amount of uncertainty, many na-tions have decided to mitigate the change. On the societal level, a planner who tries to find an eco-nomically optimal solution to an environmental pollution problem seeks to reduce pollution from the sources where reductions are most cost-effective. This study aims to find out how effective the instruments of the agricultural policy are in the case of climate change mitigation in Finland. The theoretical base of this study is the neoclassical economic theory that is based on the assumption of a rational economic agent who maximizes his own utility. This theoretical base has been widened towards the direction clearly essential to the matter: the theory of environmental eco-nomics. Deeply relevant to this problem and central in the theory of environmental economics are the concepts of externalities and public goods. What are also relevant are the problems of global pollution and non-point-source pollution. Econometric modelling was the method that was applied to this study. The Finnish part of the AGMEMOD-model, covering the whole EU, was used for the estimation of the development of pollution. This model is a seemingly recursive, partially dynamic partial-equilibrium model that was constructed to predict the development of Finnish agricultural production of the most important products. For the study, I personally updated the model and also widened its scope in some relevant matters. Also, I devised a table that can calculate the emissions of greenhouse gases according to the rules set by the IPCC. With the model I investigated five alternative scenarios in comparison to the base-line scenario of Agenda 2000 agricultural policy. The alternative scenarios were: 1) the CAP reform of 2003, 2) free trade on agricultural commodities, 3) technological change, 4) banning the cultivation of organic soils and 5) the combination of the last three scenarios as the maximal achievement in reduction. The maximal achievement in the alternative scenario 5 was 1/3 of the level achieved on the base-line scenario. CAP reform caused only a minor reduction when com-pared to the base-line scenario. Instead, the free trade scenario and the scenario of technological change alone caused a significant reduction. The biggest single reduction was achieved by banning the cultivation of organic land. However, this was also the most questionable scenario to be real-ized, the reasons for this are further elaborated in the paper. The maximal reduction that can be achieved in the Finnish agricultural sector is about 11 % of the emission reduction that is needed to comply with the Kyoto protocol.

Distortion of Dimension under Quasiconformal Mappings

Quasiconformal mappings are natural generalizations of conformal mappings. They are homeomorphisms with 'bounded distortion' of which there exist several approaches. In this work we study dimension distortion properties of quasiconformal mappings both in the plane and in higher dimensional Euclidean setting. The thesis consists of a summary and three research articles. A basic property of quasiconformal mappings is the local Hölder continuity. It has long been conjectured that this regularity holds at the Sobolev level (Gehring's higher integrabilty conjecture). Optimal regularity would also provide sharp bounds for the distortion of Hausdorff dimension. The higher integrability conjecture was solved in the plane by Astala in 1994 and it is still open in higher dimensions. Thus in the plane we have a precise description how Hausdorff dimension changes under quasiconformal deformations for general sets. The first two articles contribute to two remaining issues in the planar theory. The first one concerns distortion of more special sets, for rectifiable sets we expect improved bounds to hold. The second issue consists of understanding distortion of dimension on a finer level, namely on the level of Hausdorff measures. In the third article we study flatness properties of quasiconformal images of spheres in a quantitative way. These also lead to nontrivial bounds for their Hausdorff dimension even in the n-dimensional case.

Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

On the ecology of cold-water phytoplankton in the Baltic Sea

Increased anthropogenic loading of nitrogen (N) and phosphorus (P) has led to an eutrophication problem in the Baltic Sea, and the spring bloom is a key component in the biological uptake of increased nutrient concentrations. The spring bloom in the Baltic Sea is dominated by both diatoms and dinoflagellates. However, the sedimentation of these groups is different: diatoms tend to sink to the sea floor at the end of the bloom, while dinoflagellates to a large degree are been remineralized in the euphotic zone. Understanding phytoplankton competition and species specific ecological strategies is thus of importance for assessing indirect effects of phytoplankton community composition on eutrophication problems. The main objective of this thesis was to describe some basic physiological and ecological characteristics of the main cold-water diatoms and dinoflagellates in the Baltic Sea. This was achieved by specific studies of: (1) seasonal vertical positioning, (2) dinoflagellate life cycle, (3) mixotrophy, (4) primary production, respiration and growth and (5) diatom silicate uptake, using cultures of common cold-water diatoms: Chaetoceros wighamii, C. gracilis, Pauliella taeniata, Thalassiosira baltica, T. levanderi, Melosira arctica, Diatoma tenuis, Nitzschia frigida, and dinoflagellates: Peridiniella catenata, Woloszynskia halophila and Scrippsiella hangoei. The diatoms had higher primary production capacity and lower respiration rate compared with the dinoflagellates. This difference was reflected in the maximum growth rate, which for the examined diatoms range from 0.6 to 1.2 divisions d-1, compared with 0.2 to 0.3 divisions d-1 for the dinoflagellates. Among diatoms there were species specific differences in light utilization and uptake of silicate, and C. wighamii had the highest carbon assimilation capacity and maximum silicate uptake. The physiological properties of diatoms and dinoflagellates were used in a model of the onset of the spring bloom: for the diatoms the model could predict the initiation of the spring bloom; S. hangoei, on the other hand, could not compete successfully and did not obtain positive growth in the model. The other dinoflagellates did not have higher growth rates or carbon assimilation rates and would thus probably not perform better than S. hangoei in the model. The dinoflagellates do, however, have competitive advantages that were not included in the model: motility and mixotrophy. Previous investigations has revealed that the chain-forming P. catenata performs diurnal vertical migration (DVM), and the results presented here suggest that active positioning in the water column, in addition to DVM, is a key element in this species' life strategy. There was indication of mixotrophy in S. hangoei, as it produced and excreted the enzyme leucine aminopeptidase (LAP). Moreover, there was indirect evidence that W. halophila obtains carbon from other sources than photosynthesis when comparing increase in cell numbers with in situ carbon assimilation rates. The results indicate that mixotrophy is a part of the strategy of vernal dinoflagellates in the Baltic Sea. There were also indications that the seeding of the spring bloom is very important for the dinoflagellates to succeed. In mesocosm experiments dinoflagellates could not compete with diatoms when their initial numbers were low. In conclusion, this thesis has provided new information about the basic physiological and ecological properties of the main cold-water phytoplankton in the Baltic Sea. The main phytoplankton groups, diatoms and dinoflagellates, have different physiological properties, which clearly separate their life strategies. The information presented here could serve as further steps towards better prognostic models of the effects of eutrophication in the Baltic Sea.

Actin Dynamics in Muscle Cells

In every cell, actin is a key component involved in migration, cytokinesis, endocytosis and generation of contraction. In non-muscle cells, actin filaments are very dynamic and regulated by an array of proteins that interact with actin filaments and/or monomeric actin. Interestingly, in non-muscle cells the barbed ends of the filaments are the predominant assembly place, whereas in muscle cells actin dynamics was reported to predominate at the pointed ends of thin filaments. The actin-based thin filament pointed (slow growing) ends extend towards the middle of the sarcomere's M-line where they interact with the thick filaments to generate contraction. The actin filaments in muscle cells are organized into a nearly crystalline array and are believed to be significantly less dynamic than the ones in other cell types. However, the exact mechanisms of the sarcomere assembly and turnover are largely unknown. Interestingly, although sarcomeric actin structures are believed to be relatively non-dynamic, many proteins promoting actin dynamics are expressed also in muscle cells (e.g ADF/cofilin, cyclase-associated protein and twinfilin). Thus, it is possible that the muscle-specific isoforms of these proteins promote actin dynamics differently from their non-muscle counterparts, or that actin filaments in muscle cells are more dynamic than previously thought. To study protein dynamics in live muscle cells, I used primary cell cultures of rat cardiomyocytes. My studies revealed that a subset of actin filaments in cardiomyocyte sarcomeres displays rapid turnover. Importantly, I discovered that the turnover of actin filaments depends on contractility of the cardiomyocytes and that the contractility-induced actin dynamics plays an important role in sarcomere maturation. Together with previous studies those findings suggest that sarcomeres undergo two types of actin dynamics: (1) contractility-dependent turnover of whole filaments and (2) regulatory pointed end monomer exchange to maintain correct thin filament length. Studies involving an actin polymerization inhibitor suggest that the dynamic actin filament pool identified here is composed of filaments that do not contribute to contractility. Additionally, I provided evidence that ADF/cofilins, together with myosin-induced contractility, are required to disassemble non-productive filaments in developing cardiomyocytes. In addition, during these studies we learned that isoforms of actin monomer binding protein twinfilin, Twf-1 and Twf-2a localise to myofibrils in cardiomyocytes and may thus contribute to actin dynamics in myofibrils. Finally, in collaboration with Roberto Dominguez s laboratory we characterized a new actin nucleator in muscle cells - leiomodin (Lmod). Lmod localises towards actin filament pointed ends and its depletion by siRNA leads to severe sarcomere abnormalities in cardiomyocytes. The actin filament nucleation activity of Lmod is enhanced by interactions with tropomyosin. We also revealed that Lmod expression correlates with the maturation of myofibrils, and that it associates with sarcomeres only at relatively late stages of myofibrillogenesis. Thus, Lmod is unlikely to play an important role in myofibril formation, but rather might be involved in the second step of the filament arrangement and/or maintenance through its ability to promote tropomyosin-induced actin filament nucleation occurring at the filament pointed ends. The results of these studies provide valuable new information about the molecular mechanisms underlying muscle sarcomere assembly and turnover. These data offer important clues to understanding certain physiological and pathological behaviours of muscle cells. Better understanding of the processes occurring in muscles might help to find strategies for determining, diagnosis, prognosis and therapy in heart and skeletal muscles diseases.

Dynamics of Finnish starlings in 1951-2005 : from monitoring to population modelling

Farmland bird species have been declining in Europe. Many declines have coincided with general intensification of farming practices. In Finland, replacement of mixed farming, including rotational pastures, with specialized cultivation has been one of the most drastic changes from the 1960s to the 1990s. This kind of habitat deterioration limits the persistence of populations, as has been previously indicated from local populations. Integrated population monitoring, which gathers species-specific information of population size and demography, can be used to assess the response of a population to environment changes also at a large spatial scale. I targeted my analysis at the Finnish starling (Sturnus vulgaris). Starlings are common breeders in farmland habitats, but severe declines of local populations have been reported from Finland in the 1970s and 1980s and later from other parts of Europe. Habitat deterioration (replacement of pasture and grassland habitats with specialized cultivation areas) limits reproductive success of the species. I analysed regional population data in order to exemplify the importance of agricultural change to bird population dynamics. I used nestling ringing and nest-card data from 1951 to 2005 in order to quantify population trends and per capita reproductive success within several geographical regions (south/north and west/east aspects). I used matrix modelling, acknowledging age-specific survival and fecundity parameters and density-dependence, to model population dynamics. Finnish starlings declined by 80% from the end of the 1960s up to the end of the 1980s. The observed patterns and the model indicated that the population decline was due to the decline of the carrying capacity of farmland habitats. The decline was most severe in north Finland where populations largely become extinct. However, habitat deterioration was most severe in the southern breeding areas. The deteriorations in habitat quality decreased reproduction, which finally caused the decline. I suggest that poorly-productive northern populations have been partly maintained by immigration from the highly-productive southern populations. As the southern populations declined, ceasing emigration caused the population extinction in north. This phenomenon was explained with source sink population dynamics, which I structured and verified on the basis of a spatially explicit simulation model. I found that southern Finnish starling population exhibits ten-year cyclic regularity, a phenomenon that can be explained with delayed density-dependence in reproduction.