Numerical computation of the module of a quadrilateral

The module of a quadrilateral is a positive real number which divides quadrilaterals into conformal equivalence classes. This is an introductory text to the module of a quadrilateral with some historical background and some numerical aspects. This work discusses the following topics: 1. Preliminaries 2. The module of a quadrilateral 3. The Schwarz-Christoffel Mapping 4. Symmetry properties of the module 5. Computational results 6. Other numerical methods Appendices include: Numerical evaluation of the elliptic integrals of the first kind. Matlab programs and scripts and possible topics for future research. Numerical results section covers additive quadrilaterals and the module of a quadrilateral under the movement of one of its vertex.

Learning Nonlinear Visual Processing from Natural Images

The paradigm of computational vision hypothesizes that any visual function -- such as the recognition of your grandparent -- can be replicated by computational processing of the visual input. What are these computations that the brain performs? What should or could they be? Working on the latter question, this dissertation takes the statistical approach, where the suitable computations are attempted to be learned from the natural visual data itself. In particular, we empirically study the computational processing that emerges from the statistical properties of the visual world and the constraints and objectives specified for the learning process. This thesis consists of an introduction and 7 peer-reviewed publications, where the purpose of the introduction is to illustrate the area of study to a reader who is not familiar with computational vision research. In the scope of the introduction, we will briefly overview the primary challenges to visual processing, as well as recall some of the current opinions on visual processing in the early visual systems of animals. Next, we describe the methodology we have used in our research, and discuss the presented results. We have included some additional remarks, speculations and conclusions to this discussion that were not featured in the original publications. We present the following results in the publications of this thesis. First, we empirically demonstrate that luminance and contrast are strongly dependent in natural images, contradicting previous theories suggesting that luminance and contrast were processed separately in natural systems due to their independence in the visual data. Second, we show that simple cell -like receptive fields of the primary visual cortex can be learned in the nonlinear contrast domain by maximization of independence. Further, we provide first-time reports of the emergence of conjunctive (corner-detecting) and subtractive (opponent orientation) processing due to nonlinear projection pursuit with simple objective functions related to sparseness and response energy optimization. Then, we show that attempting to extract independent components of nonlinear histogram statistics of a biologically plausible representation leads to projection directions that appear to differentiate between visual contexts. Such processing might be applicable for priming, \ie the selection and tuning of later visual processing. We continue by showing that a different kind of thresholded low-frequency priming can be learned and used to make object detection faster with little loss in accuracy. Finally, we show that in a computational object detection setting, nonlinearly gain-controlled visual features of medium complexity can be acquired sequentially as images are encountered and discarded. We present two online algorithms to perform this feature selection, and propose the idea that for artificial systems, some processing mechanisms could be selectable from the environment without optimizing the mechanisms themselves. In summary, this thesis explores learning visual processing on several levels. The learning can be understood as interplay of input data, model structures, learning objectives, and estimation algorithms. The presented work adds to the growing body of evidence showing that statistical methods can be used to acquire intuitively meaningful visual processing mechanisms. The work also presents some predictions and ideas regarding biological visual processing.

Maintaining plant species richness by cattle grazing - mesic semi-natural grasslands as focal habitats

Semi-natural grasslands are the most important agricultural areas for biodiversity. The present study investigates the effects of traditional livestock grazing and mowing on plant species richness, the main emphasis being on cattle grazing in mesic semi-natural grasslands. The two reviews provide a thorough assessment of the multifaceted impacts and importance of grazing and mowing management to plant species richness. It is emphasized that livestock grazing and mowing have partially compensated the suppression of major natural disturbances by humans and mitigated the negative effects of eutrophication. This hypothesis has important consequences for nature conservation: A large proportion of European species originally adapted to natural disturbances may be at present dependent on livestock grazing and / or mowing. Furthermore, grazing and mowing are key management methods to mitigate effects of nutrient-enrichment. The species composition and richness in old (continuously grazed), new (grazing restarting 3-8 years ago) and abandoned (over 10 years) pastures differed consistently across a range of spatial scales, and was intermediate in new pastures compared to old and abandoned pastures. In mesic grasslands most plant species were shown to benefit from cattle grazing. Indicator species of biologically valuable grasslands and rare species were more abundant in grazed than in abandoned grasslands. Steep S-SW-facing slopes are the most suitable sites for many grassland plants and should be prioritized in grassland restoration. The proportion of species trait groups benefiting from grazing was higher in mesic semi-natural grasslands than in dry and wet grasslands. Consequently, species trait responses to grazing and the effectiveness of the natural factors limiting plant growth may be intimately linked High plant species richness of traditionally mowed and grazed areas is explained by numerous factors which operate on different spatial scales. Particularly important for maintaining large scale plant species richness are evolutionary and mitigation factors. Grazing and mowing cause a shift towards the conditions that have occurred during the evolutionary history of European plant species by modifying key ecological factors (nutrients, pH and light). The results of this Dissertation suggest that restoration of semi-natural grasslands by private farmers is potentially a useful method to manage biodiversity in the agricultural landscape. However, the quality of management is commonly improper, particularly due to financial constraints. For enhanced success of restoration, management regulations in the agri-environment scheme need to be defined more explicitly and the scheme should be revised to encourage management of biodiversity.

Human genetic variation in the Baltic Sea region: Features of population history and natural selection

In this thesis, the genetic variation of human populations from the Baltic Sea region was studied in order to elucidate population history as well as evolutionary adaptation in this region. The study provided novel understanding of how the complex population level processes of migration, genetic drift, and natural selection have shaped genetic variation in North European populations. Results from genome-wide, mitochondrial DNA and Y-chromosomal analyses suggested that the genetic background of the populations of the Baltic Sea region lies predominantly in Continental Europe, which is consistent with earlier studies and archaeological evidence. The late settlement of Fennoscandia after the Ice Age and the subsequent small population size have led to pronounced genetic drift, especially in Finland and Karelia but also in Sweden, evident especially in genome-wide and Y-chromosomal analyses. Consequently, these populations show striking genetic differentiation, as opposed to much more homogeneous pattern of variation in Central European populations. Additionally, the eastern side of the Baltic Sea was observed to have experienced eastern influence in the genome-wide data as well as in mitochondrial DNA and Y-chromosomal variation – consistent with linguistic connections. However, Slavic influence in the Baltic Sea populations appears minor on genetic level. While the genetic diversity of the Finnish population overall was low, genome-wide and Y-chromosomal results showed pronounced regional differences. The genetic distance between Western and Eastern Finland was larger than for many geographically distant population pairs, and provinces also showed genetic differences. This is probably mainly due to the late settlement of Eastern Finland and local isolation, although differences in ancestral migration waves may contribute to this, too. In contrast, mitochondrial DNA and Y-chromosomal analyses of the contemporary Swedish population revealed a much less pronounced population structure and a fusion of the traces of ancient admixture, genetic drift, and recent immigration. Genome-wide datasets also provide a resource for studying the adaptive evolution of human populations. This study revealed tens of loci with strong signs of recent positive selection in Northern Europe. These results provide interesting targets for future research on evolutionary adaptation, and may be important for understanding the background of disease-causing variants in human populations.

Nitrous oxide emissions from selected natural and managed northern ecosystems

Microbial activity in soils is the main source of nitrous oxide (N2O) to the atmosphere. Nitrous oxide is a strong greenhouse gas in the troposphere and participates in ozone destructive reactions in the stratosphere. The constant increase in the atmospheric concentration, as well as uncertainties in the known sources and sinks of N2O underline the need to better understand the processes and pathways of N2O in terrestrial ecosystems. This study aimed at quantifying N2O emissions from soils in northern Europe and at investigating the processes and pathways of N2O from agricultural and forest ecosystems. Emissions were measured in forest ecosystems, agricultural soils and a landfill, using the soil gradient, chamber and eddy covariance methods. Processes responsible for N2O production, and the pathways of N2O from the soil to the atmosphere, were studied in the laboratory and in the field. These ecosystems were chosen for their potential importance to the national and global budget of N2O. Laboratory experiments with boreal agricultural soils revealed that N2O production increases drastically with soil moisture content, and that the contribution of the nitrification and denitrification processes to N2O emissions depends on soil type. Laboratory study with beech (Fagus sylvatica) seedlings demonstrated that trees can serve as conduits for N2O from the soil to the atmosphere. If this mechanism is important in forest ecosystems, the current emission estimates from forest soils may underestimate the total N2O emissions from forest ecosystems. Further field and laboratory studies are needed to evaluate the importance of this mechanism in forest ecosystems. The emissions of N2O from northern forest ecosystems and a municipal landfill were highly variable in time and space. The emissions of N2O from boreal upland forest soil were among the smallest reported in the world. Despite the low emission rates, the soil gradient method revealed a clear seasonal variation in N2O production. The organic topsoil was responsible for most of the N2O production and consumption in this forest soil. Emissions from the municipal landfill were one to two orders of magnitude higher than those from agricultural soils, which are the most important source of N2O to the atmosphere. Due to their small areal coverage, landfills only contribute minimally to national N2O emissions in Finland. The eddy covariance technique was demonstrated to be useful for measuring ecosystem-scale emissions of N2O in forest and landfill ecosystems. Overall, more measurements and integration between different measurement techniques are needed to capture the large variability in N2O emissions from natural and managed northern ecosystems.

Management of semi-natural grasslands for butterfly and moth communities

This work focuses on the factors affecting species richness, abundance and species composition of butterflies and moths in Finnish semi-natural grasslands, with a special interest in the effects of grazing management. In addition, an aim was set at evaluating the effectiveness of the support for livestock grazing in semi-natural grasslands, which is included in the Finnish agri-environment scheme. In the first field study, butterfly and moth communities in resumed semi-natural pastures were com-pared to old, annually grazed and abandoned previous pastures. Butterfly and moth species compo-sition in restored pastures resembled the compositions observed in old pastures after circa five years of resumed cattle grazing, but diversity of butterflies and moths in resumed pastures remained at a lower level compared with old pastures. None of the butterfly and moth species typical of old pas-tures had become more abundant in restored pastures compared with abandoned pastures. There-fore, it appears that restoration of butterfly and moth communities inhabiting semi-natural grass-lands requires a longer time that was available for monitoring in this study. In the second study, it was shown that local habitat quality has the largest impact on the occurrence and abundance of butterflies and moths compared to the effects of grassland patch area and connec-tivity of the regional grassland network. This emphasizes the importance of current and historical management of semi-natural grasslands on butterfly and moth communities. A positive effect of habitat connectivity was observed on total abundance of the declining butterflies and moths, sug-gesting that these species have strongest populations in well-connected habitat networks. Highest species richness and peak abundance of most individual species of butterflies and moths were generally observed in taller grassland vegetation compared with vascular plants, suggesting a preference towards less intensive management in insects. These differences between plants and their insect herbivores may be understood in the light of both (1) the higher structural diversity of tall vegetation and (2) weaker tolerance of disturbances by herbivorous insects due to their higher trophic level compared to plants. The ecological requirements of all species and species groups inhabiting semi-natural grasslands are probably never met at single restricted sites. Therefore, regional implementation of management to create differently managed areas is imperative for the conservation of different species and species groups dependent on semi-natural grasslands. With limited resources it might be reasonable to focus much of the management efforts in the densest networks of suitable habitat to minimise the risk of extinction of the declining species.

The effects of the 2004 reduction in the price of alcohol on alcohol-related harm in Finland : A natural experiment based on register data

Changes in alcohol pricing have been documented as inversely associated with changes in consumption and alcohol-related problems. Evidence of the association between price changes and health problems is nevertheless patchy and is based to a large extent on cross-sectional state-level data, or time series of such cross-sectional analyses. Natural experimental studies have been called for. There was a substantial reduction in the price of alcohol in Finland in 2004 due to a reduction in alcohol taxes of one third, on average, and the abolition of duty-free allowances for travellers from the EU. These changes in the Finnish alcohol policy could be considered a natural experiment, which offered a good opportunity to study what happens with regard to alcohol-related problems when prices go down. The present study investigated the effects of this reduction in alcohol prices on (1) alcohol-related and all-cause mortality, and mortality due to cardiovascular diseases, (2) alcohol-related morbidity in terms of hospitalisation, (3) socioeconomic differentials in alcohol-related mortality, and (4) small-area differences in interpersonal violence in the Helsinki Metropolitan area. Differential trends in alcohol-related mortality prior to the price reduction were also analysed. A variety of population-based register data was used in the study. Time-series intervention analysis modelling was applied to monthly aggregations of deaths and hospitalisation for the period 1996-2006. These and other mortality analyses were carried out for men and women aged 15 years and over. Socioeconomic differentials in alcohol-related mortality were assessed on a before/after basis, mortality being followed up in 2001-2003 (before the price reduction) and 2004-2005 (after). Alcohol-related mortality was defined in all the studies on mortality on the basis of information on both underlying and contributory causes of death. Hospitalisation related to alcohol meant that there was a reference to alcohol in the primary diagnosis. Data on interpersonal violence was gathered from 86 administrative small-areas in the Helsinki Metropolitan area and was also assessed on a before/after basis followed up in 2002-2003 and 2004-2005. The statistical methods employed to analyse these data sets included time-series analysis, and Poisson and linear regression. The results of the study indicate that alcohol-related deaths increased substantially among men aged 40-69 years and among women aged 50-69 after the price reduction when trends and seasonal variation were taken into account. The increase was mainly attributable to chronic causes, particularly liver diseases. Mortality due to cardiovascular diseases and all-cause mortality, on the other hand, decreased considerably among the-over-69-year-olds. The increase in alcohol-related mortality in absolute terms among the 30-59-year-olds was largest among the unemployed and early-age pensioners, and those with a low level of education, social class or income. The relative differences in change between the education and social class subgroups were small. The employed and those under the age of 35 did not suffer from increased alcohol-related mortality in the two years following the price reduction. The gap between the age and education groups, which was substantial in the 1980s, thus further broadened. With regard to alcohol-related hospitalisation, there was an increase in both chronic and acute causes among men under the age of 70, and among women in the 50-69-year age group when trends and seasonal variation were taken into account. Alcohol dependence and other alcohol-related mental and behavioural disorders were the largest category in both the total number of chronic hospitalisation and in the increase. There was no increase in the rate of interpersonal violence in the Helsinki Metropolitan area, and even a decrease in domestic violence. There was a significant relationship between the measures of social disadvantage on the area level and interpersonal violence, although the differences in the effects of the price reduction between the different areas were small. The findings of the present study suggest that that a reduction in alcohol prices may lead to a substantial increase in alcohol-related mortality and morbidity. However, large population group differences were observed regarding responsiveness to the price changes. In particular, the less privileged, such as the unemployed, were most sensitive. In contrast, at least in the Finnish context, the younger generations and the employed do not appear to be adversely affected, and those in the older age groups may even benefit from cheaper alcohol in terms of decreased rates of CVD mortality. The results also suggest that reductions in alcohol prices do not necessarily affect interpersonal violence. The population group differences in the effects of the price changes on alcohol-related harm should be acknowledged, and therefore the policy actions should focus on the population subgroups that are primarily responsive to the price reduction.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.