Bounded turning circles are weak-quasicircles

We show that a metric Jordan curve $\Gamma$ is \emph{bounded turning} if and only if there exists a \emph{weak-quasisymmetric} homeomorphism $\phi\colon \mathsf{S}^1 \to \Gamma$.

Readers' resposes versus reader-response theories : An empirical study

This study examines both theoretically an empirically how well the theories of Norman Holland, David Bleich, Wolfgang Iser and Stanley Fish can explain readers' interpretations of literary texts. The theoretical analysis concentrates on their views on language from the point of view of Wittgenstein's Philosophical Investigations. This analysis shows that many of the assumptions related to language in these theories are problematic. The empirical data show that readers often form very similar interpretations. Thus the study challenges the common assumption that literary interpretations tend to be idiosyncratic. The empirical data consists of freely worded written answers to questions on three short stories. The interpretations were made by 27 Finnish university students. Some of the questions addressed issues that were discussed in large parts of the texts, some referred to issues that were mentioned only in passing or implied. The short stories were "The Witch à la Mode" by D. H. Lawrence, "Rain in the Heart" by Peter Taylor and "The Hitchhiking Game" by Milan Kundera. According to Fish, readers create both the formal features of a text and their interpretation of it according to an interpretive strategy. People who agree form an interpretive community. However, a typical answer usually contains ideas repeated by several readers as well as observations not mentioned by anyone else. Therefore it is very difficult to determine which readers belong to the same interpretive community. Moreover, readers with opposing opinions often seem to pay attention to the same textual features and even acknowledge the possibility of an opposing interpretation; therefore they do not seem to create the formal features of the text in different ways. Iser suggests that an interpretation emerges from the interaction between the text and the reader when the reader determines the implications of the text and in this way fills the "gaps" in the text. Iser believes that the text guides the reader, but as he also believes that meaning is on a level beyond words, he cannot explain how the text directs the reader. The similarity in the interpretations and the fact that the agreement is strongest when related to issues that are discussed broadly in the text do, however, support his assumption that readers are guided by the text. In Bleich's view, all interpretations have personal motives and each person has an idiosyncratic language system. The situation where a person learns a word determines the most important meaning it has for that person. In order to uncover the personal etymologies of words, Bleich asks his readers to associate freely on the basis of a text and note down all the personal memories and feelings that the reading experience evokes. Bleich's theory of the idiosyncratic language system seems to rely on a misconceived notion of the role that ostensive definitions have in language use. The readers' responses show that spontaneous associations to personal life seem to colour the readers' interpretations, but such instances are rather rare. According to Holland, an interpretation reflects the reader's identity theme. Language use is regulated by shared rules, but everyone follows the rules in his or her own way. Words mean different things to different people. The problem with this view is that if there is any basis for language use, it seems to be the shared way of following linguistic rules. Wittgenstein suggests that our understanding of words is related to the shared ways of using words and our understanding of human behaviour. This view seems to give better grounds for understanding similarity and differences in literary interpretations than the theories of Holland, Bleich, Fish and Iser.

Environmental change and human history in the Jabal Harun area, Jordan

The research is related to the Finnish Jabal Harun Project (FJHP), which is part of the research unit directed by Professor Jaakko Frösén. The project consists of two interrelated parts: the excavation of a Byzantine monastery/pilgrimage centre on Jabal Harun, and a multiperiod archaeological survey of the surrounding landscape. It is generally held that the Near Eastern landscape has been modified by millennia of human habitation and activity. Past climatic changes and human activities could be expected to have significantly changed also the landscape of the Jabal Harun area. Therefore it was considered that a study of erosion in the Jabal Harun area could shed light on the environmental and human history of the area. It was hoped that it would be possible to connect the results of the sedimentological studies either to wider climatic changes in the Near East, or to archaeologically observable periods of human activity and land use. As evidence of some archaeological periods is completely missing from the Jabal Harun area, it was also of interest whether catastrophic erosion or unfavourable environmental change, caused either by natural forces or by human agency, could explain the gaps in the archaeological record. Changes in climate and/or land-use were expected to be reflected in the sedimentary record. The field research, carried out as part of the FJHP survey fieldwork, included the mapping of wadi terraces and cleaning of sediment profiles which were recorded and sampled for laboratory analyses of facies and lithology. To obtain a chronology for the sedimentation and erosion phases also OSL (optically stimulated luminescence) dating samples were collected. The results were compared to the record of the Near Eastern palaeoclimate, and to data from geoarchaeological studies in central and southern Jordan. The picture of the environmental development was then compared to the human history in the area, based on archaeological evidence from the FJHP survey and the published archaeological research in the Petra region, and the question of the relationship between human activity and environmental change was critically discussed. Using the palaeoclimatic data and the results from geoarchaeological studies it was possible to outline the environmental development in the Jabal Harun area from the Pleistocene to the present.It is appears that there was a phase of accumulation of sediment before the Middle Palaeolithic period, possibly related to tectonic movement. This phase was later followed by erosion, tentatively suggested to have taken place during the Upper Palaeolithic. A period of wadi aggradation probably occurred during the Late Glacial and continued until the end of the Pleistocene, followed by significant channel degradation, attributed to increased rainfall during the Early Holocene. It seems that during the later Holocene channel incision has been dominant in the Jabal Harûn area although there have been also small-scale channel aggradation phases, two of which were OSL-dated to around 4000-3000 BP and 2400-2000 BP. As there is no evidence of tectonic movements in the Jabal Harun area after the early Pleistocene, it is suggested that climate change and human activity have been the major causes of environmental change in the area. At a brief glance it seems that many of the changes in the settlement and land use in the Jabal Harun area can be explained by climatic and environmental conditions. However, the responses of human societies to environmental change are dependent on many factors. Therefore an evaluation of the significance of environmental, cultural, socio-economic and political factors is needed to decide whether certain phenomena are environmentally induced. Comparison with the wider Petra region is also needed to judge whether the phenomena are characteristic of the Jabal Harun area only, or can they be connected to social, political and economic development over a wider area.

Visual completion in an illusory figure

The visual systems of humans and animals represent physical reality in a modified way, depending on the specific demands that the species in question has for survival. The ability to perceive visual illusions is found in independently evolved visual systems, from honeybees to humans. In humans, the ability emerges early, at the age of four months. Thus the perception of illusion is likely to reflect visual processes of fundamental importance for object perception in natural vision. The experiments reported in this thesis employed various modifications of the Kanizsa triangle, a drawn configuration composed of three black disks with missing sectors on a white background. The sectors appear to form the tips of a triangle. The visual system completes the physically empty area between the disks, generally called inducers, with giving the perception of an illusory triangle. The illusory triangle consists of an illusory surface bounded by illusory contours; the triangle appears brighter than and to lie above the background. If the sectors are coloured, the colour fills the illusory area, a phenomenon known as neon colour spreading . We investigated spatial limitations on the perception of Kanizsa-type illusions and how other stimuli and viewing parameters affected these limitations. We also studied complex configurations thick, bent, mobile and chromatic inducers - to determine whether illusions combining several attributes can be perceived. The results suggest that the visual system is highly effective in completing a percept. The perception of an illusory figure is spatially scale invariant when perceived at threshold. The processing time and the number of fixations modify the percept, making the perception of the illusion more probable in various viewing conditions. Furthermore, the fact that the illusion can be perceived when only one inducer is physically present at any given moment indicates the potential of single inducers. Apparently, modelling illusory figure perception will require a combination of low-level, local processes and higher-level integrative processes. Our studies with stimuli combining several attributes relevant to object perception demonstrate that the perception of an illusory figure is flexible and is maintained also when it contains colour and volume and when shown in movement. All in all, the results confirm the assumed importance of the visual processes related with the perception of illusory figures in everyday viewing. This is indicated by the variety of inducer modifications that can be made without destroying the percept. Furthermore, the illusion can acquire additional attributes from such modifications. Due to individual differences in the perception of illusory figures, universal values for absolute performance are not always meaningful, but stable trends and general relations do exist.

Boundaries in Action : An Activity-theoretical Study of Development, Learning, and Change in Health Care Organization for Patients with Multiple and Chronic Illnesses

This study examines boundaries in health care organizations. Boundaries are sometimes considered things to be avoided in everyday living. This study suggests that boundaries can be important temporally and spatially emerging locations of development, learning, and change in inter-organizational activity. Boundaries can act as mediators of cultural and social formations and practices. The data of the study was gathered in an intervention project during the years 2000-2002 in Helsinki in which the care of 26 patients with multiple and chronic illnesses was improved. The project used the Change Laboratory method that represents a research assisted method for developing work. The research questions of the study are: (1) What are the boundary dynamics of development, learning, and change in health care for patients with multiple and chronic illnesses? (2) How do individual patients experience boundaries in their health care? (3) How are the boundaries of health care constructed and reconstructed in social interaction? (4) What are the dynamics of boundary crossing in the experimentation with the new tools and new practice? The methodology of the study, the ethnography of the multi-organizational field of activity, draws on cultural-historical activity theory and anthropological methods. The ethnographic fieldwork involves multiple research techniques and a collaborative strategy for raising research data. The data of this study consists of observations, interviews, transcribed intervention sessions, and patients' health documents. According to the findings, the care of patients with multiple and chronic illnesses emerges as fragmented by divisions of a patient and professionals, specialties of medicine and levels of health care organization. These boundaries have a historical origin in the Finnish health care system. As an implication of these boundaries, patients frequently experience uncertainty and neglect in their care. However, the boundaries of a single patient were transformed in the Change Laboratory discussions among patients, professionals and researchers. In these discussions, the questioning of the prevailing boundaries was triggered by the observation of gaps in inter-organizational care. Transformation of the prevailing boundaries was achieved in implementation of the collaborative care agreement tool and the practice of negotiated care. However, the new tool and practice did not expand into general use during the project. The study identifies two complementary models for the development of health care organization in Finland. The 'care package model', which is based on productivity and process models adopted from engineering and the 'model of negotiated care', which is based on co-configuration and the public good.

Matkalla suomalaiseksi ja hoiva-alan ammattilaiseksi? : Venäläis- ja virolaistaustaisten naisten ja suomalaisuuden kohtaamiset kuulumista rakentamassa

The research examines the process by which a sense of belonging to Finnish society is constructed among women of Russian and Estonian background who are multiply marginalised in Finnish society. It does so by analysing the encounters between their nationality and 'being Finnis'. Attention is focused on the question of what kind of "journey" they take after moving to Finland, how a sense of belonging is constructed especially along the paths followed in education and at work, and what kind of agency is available to them. The thesis is connected with post-colonial research and also draws from studies on citizenship and nationality as well as the social structures of interaction, when analysing careers. As the educational system forms the most central context of the research, the work is also focused on educational sociology. The research methodology includes life history and a narrative approach. The raw data is from thematic interviews concerning the life experiences of women of immigrant backgrounds. They were studying in Finland to be practical nurses or to complete Bachelor of Social Service degree. According to the study, the women had been encountered as alien, strange, and carrying a shade of "otherness". The experience of inclusion in Finnish communities and society turned out to be conditional, an inclusion based on the notion of a citizen worker, which is defined by national needs. The person from abroad is placed in the position of someone who fills gaps in the services of the welfare state. The choice of education in the care sector and the overall necessity of obtaining Finnish education turned out to be socially directed. Gendered structures of education and working life were found to act as a frame in which the decisions of the immigrant women were made. Although national education policy emphasis as an orientation to global labour markets, the immigrant student is placed above all in the position of an object to be made suitable for the Finnish labour market. Citizenship, a goal of education, requires consent to being "socialised" into Finnish society as well as learning to be Finnish. One s only option to negotiate appearing suitable as a member is to construct oneself into someone who adopts Finnish and Western cultural values, values which favour individuality. However, Finnish education is a resource to Finnishness. Finnish education enables a sense of being Finnish, and empowers the job applicant for example, and in addition to providing cultural, human and social capital strengthen inclusion as well. The study confirms the view that the encounter of an immigrant is still characterised by its colonial nature. It shows that encounters with Finns and Finnish society place the person of immigrant background, even one receiving a Finnish education, in the position of "the other". The journey as an immigrant continues. The immigrant has access only to certain predefined subject positions, which limits agency. When categorised as an immigrant, one becomes a per-son who is different and "other", while the sense of belonging as a member of Finnish society without conditions appears to be somewhat unreachable. Yet, new arrivals are capable of acting change. An immigrant woman can challenge the positions offered to her and present herself as strong. Her life story has often included struggle, and she has the fortitude strength to change her circumstances. Key words: life story, post-colonial encounter, nationality, citizenship, the career of immi-grant, position, agency

Yhteinen käsityö peruskoulun 7. luokalla : Opettajien kokemuksia yhteisen käsityön opetuksesta ja organisoinnista

Finnish education politics presume that basic education should be equal to all students. While organising craft education equality can be understood as similarity or as possibility to choose. The possibility to be able to choose whether textile or technical craft despite of one´s gender has been the aim of laws and curriculums already over 30 years. In practice it´s almost impossible to students to ignore feminine and masculine roles that go deep into our culture. Choosing craft has been divided by gender, which is the reason why possibility to choose has not been good enough to educationalists of equality. The latest guidelines for the National core curriculum for bacis education were issued in 2004. According to curriculum craft education consists parts of both technical and textile craft. All students should take part in both sectors of crafts. Furthermore, one can be given a possibility to consentrate his studies in whether textile or technical craft. The curriculum does not set the rules how the education should be organised, which means that it can be organised in many ways depending on city, school or teacher. Teachers and other specialists have contradictory feelings towards shared craft education, because traditional way to see craft in Finland is to separate textile craft from technical craft. Both crafts have some common features that are introduced in curriculum. Besides there is many equal things in craft theories that bind textile and technical craft to each other. The main purpose of this research was to find out, how shared craft education has been organised at the 7.th grade in Finnish comprehensive school, and which things affect in the settlements. Second goal was to describe and compare teachers´ experiences in teaching shared craft education. Third aim of this study was how shared craft has changed craft education. I collected the research material in May 2006 by interviewing both textile and technical craft teachers who teach shared craft. The material consists of fourteen theme interviews. In the analysis of the material I used theoretic bounded document analysis. According to the research there are three different ways to organise shared craft education: 50 50-arrangement, exchanging period and project week. In the schools that carried out 50 50-arrangement teaching was realised mainly in heterogenous groups. Principals had usual a lot of authorization on how to arrange craft education, which means that their views on equality, laws and curriculum affected in the settlemets more than teachers´ opinions. Teachers´ attitudes to shared craft were mainly positive. The changing of craft education can be divided in two parts: the aims and the containings of the curriculum have changed, as well as the meaning of the craft as core subject. Teachers have been forced to decrease the containings of both textile and technical crafts. Despite of eliminations both crafts still have comprehensive containings. Teachers decided what to teach by these argumets: Students should learn some basic things or produce a certain product. Usually teachers had also a lot of experience and special intrests in crafts. According to this research there is four significant meanings for shared craft education: 1) developing readiness for doing things, 2) developing skills of thinking, 3) delight of doing things and 4) teaching attitude.

The Miocene of Western Asia; Fossil mammals at the crossroads of faunal provinces and climate regimes

Being at the crossroads of the Old World continents, Western Asia has a unique position through which the dispersal and migration of mammals and the interaction of faunal bioprovinces occurred. Despite its critical position, the record of Miocene mammals in Western Asia is sporadic and there are large spatial and temporal gaps between the known fossil localities. Although the development of the mammalian faunas in the Miocene of the Old World is well known and there is ample evidence for environmental shifts in this epoch, efforts toward quantification of habitat changes and development of chronofaunas based on faunal compositions were mostly neglected. Advancement of chronological, paleoclimatological, and paleogeographical reconstruction tools and techniques and increased numbers of new discoveries in recent decades have brought the need for updating and modification of our level of understanding. We under took fieldwork and systematic study of mammalian trace and body fossils from the northwestern parts of Iran along with analysis of large mammal data from the NOW database. The data analysis was used to study the provinciality, relative abundance, and distribution history of the closed- and open-adapted taxa and chronofaunas in the Miocene of the Old World and Western Asia. The provinciality analysis was carried out, using locality clustering, and the relative abundance of the closed- and open-adapted taxa was surveyed at the family level. The distribution history of the chronofaunas was studied, using faunal resemblance indices and new mapping techniques, together with humidity analysis based on mean ordinated hypsodonty. Paleoichnological studies revealed the abundance of mammalian footprints in several parts of the basins studied, which are normally not fossiliferous in terms of body fossils. The systematic study and biochronology of the newly discovered mammalian fossils in northwestern Iran indicates their close affinities with middle Turolian faunas. Large cranial remains of hipparionine horses, previously unknown in Iran and Western Asia, are among the material studied. The initiation of a new field project in the famous Maragheh locality also brings new opportunities to address questions regarding the chronology and paleoenvironment of this classical site. Provinciality analysis modified our previous level of understandings, indicating the interaction of four provinces in Western Asia. The development of these provinces was apparently due to the presence of high mountain ranges in the area, which affected the dispersal of mammals and also climatic patterns. Higher temperatures and possibly higher co2 levels in the Middle Miocene Climatic Optimum apparently favored the development of the closed forested environments that supported the dominance of the closed-adapted taxa. The increased seasonality and the progressive cooling and drying of the midlatitudes toward the Late Miocene maintained the dominance of open-adapted faunas. It appears that the late Middle Miocene was the time of transition from a more forested to a less forested world. The distribution history of the closed- and open-adapted chronofaunas shows the presence of cosmopolitan and endemic faunas in Western Asia. The closed-adapted faunas, such as the Arabian chronofauna of the late Early‒early Middle Miocene, demonstrated a rapid buildup and gradual decline. The open-adapted chronofaunas, such as the Late Miocene Maraghean fauna, climaxed gradually by filling the opening environments and moving in response to changes in humidity patterns. They abruptly declined due to demise of their favored environments. The Siwalikan chronofauna of the early Late Miocene remained endemic and restricted through all its history. This study highlights the importance of field investigations and indicates that new surveys in the vast areas of Western Asia, which are poorly sampled in terms of fossil mammal localities, can still be promising. Clustering of the localities supports the consistency of formerly known patterns and augments them. Although the quantitative approach to relative abundance history of the closed- and open-adapted mammals harks back to more than half a century ago, it is a novel technique providing robust results. Tracking the history of the chronofaunas in space and time by means of new computational and illustration methods is also a new practice that can be expanded to new areas and time spans.

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

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.

Paleomagnetic and rock magnetic study with emphasis on the Precambrian intrusions and impact structures in Fennoscandia and South Africa

The importance of supercontinents in our understanding of the geological evolution of the planet Earth has been recently emphasized. The role of paleomagnetism in reconstructing lithospheric blocks in their ancient paleopositions is vital. Paleomagnetism is the only quantitative tool for providing ancient latitudes and azimuthal orientations of continents. It also yields information of content of the geomagnetic field in the past. In order to obtain a continuous record on the positions of continents, dated intrusive rocks are required in temporal progression. This is not always possible due to pulse-like occurrences of dykes. In this work we demonstrate that studies of meteorite impact-related rocks may fill some gaps in the paleomagnetic record. This dissertation is based on paleomagnetic and rock magnetic data obtained from samples of the Jänisjärvi impact structure (Russian Karelia, most recent 40Ar-39Ar age of 682 Ma), the Salla diabase dyke (North Finland, U-Pb 1122 Ma), the Valaam monzodioritic sill (Russian Karelia, U-Pb 1458 Ma), and the Vredefort impact structure (South Africa, 2023 Ma). The paleomagnetic study of Jänisjärvi samples was made in order to obtain a pole for Baltica, which lacks paleomagnetic data from 750 to ca. 600 Ma. The position of Baltica at ca. 700 Ma is relevant in order to verify whether the supercontinent Rodinia was already fragmented. The paleomagnetic study of the Salla dyke was conducted to examine the position of Baltica at the onset of supercontinent Rodinia's formation. The virtual geomagnetic pole (VGP) from Salla dyke provides hints that the Mesoproterozoic Baltica - Laurentia unity in the Hudsonland (Columbia, Nuna) supercontinent assembly may have lasted until 1.12 Ga. Moreover, the new VGP of Salla dyke provides new constraint on the timing of the rotation of Baltica relative to Laurentia (e.g. Gower et al., 1990). A paleomagnetic study of the Valaam sill was carried out in order to shed light into the question of existence of Baltica-Laurentia unity in the supercontinent Hudsonland. Combined with results from dyke complex of the Lake Ladoga region (Schehrbakova et al., 2008) a new robust paleomagnetic pole for Baltica is obtained. This pole places Baltica on a latitude of 10°. This low latitude location is supported also by Mesoproterozoic 1.5 1.3 Ga red-bed sedimentation (for example the Satakunta sandstone). The Vredefort impactite samples provide a well dated (2.02 Ga) pole for the Kaapvaal Craton. Rock magnetic data reveal unusually high Koenigsberger ratios (Q values) in all studied lithologies of the Vredefort dome. The high Q values are now first time also seen in samples from the Johannesburg Dome (ca. 120 km away) where there is no impact evidence. Thus, a direct causative link of high Q values to the Vredefort impact event can be ruled out.

Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

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.

Problems and Algorithms for Sequence Segmentations

The analysis of sequential data is required in many diverse areas such as telecommunications, stock market analysis, and bioinformatics. A basic problem related to the analysis of sequential data is the sequence segmentation problem. A sequence segmentation is a partition of the sequence into a number of non-overlapping segments that cover all data points, such that each segment is as homogeneous as possible. This problem can be solved optimally using a standard dynamic programming algorithm. In the first part of the thesis, we present a new approximation algorithm for the sequence segmentation problem. This algorithm has smaller running time than the optimal dynamic programming algorithm, while it has bounded approximation ratio. The basic idea is to divide the input sequence into subsequences, solve the problem optimally in each subsequence, and then appropriately combine the solutions to the subproblems into one final solution. In the second part of the thesis, we study alternative segmentation models that are devised to better fit the data. More specifically, we focus on clustered segmentations and segmentations with rearrangements. While in the standard segmentation of a multidimensional sequence all dimensions share the same segment boundaries, in a clustered segmentation the multidimensional sequence is segmented in such a way that dimensions are allowed to form clusters. Each cluster of dimensions is then segmented separately. We formally define the problem of clustered segmentations and we experimentally show that segmenting sequences using this segmentation model, leads to solutions with smaller error for the same model cost. Segmentation with rearrangements is a novel variation to the segmentation problem: in addition to partitioning the sequence we also seek to apply a limited amount of reordering, so that the overall representation error is minimized. We formulate the problem of segmentation with rearrangements and we show that it is an NP-hard problem to solve or even to approximate. We devise effective algorithms for the proposed problem, combining ideas from dynamic programming and outlier detection algorithms in sequences. In the final part of the thesis, we discuss the problem of aggregating results of segmentation algorithms on the same set of data points. In this case, we are interested in producing a partitioning of the data that agrees as much as possible with the input partitions. We show that this problem can be solved optimally in polynomial time using dynamic programming. Furthermore, we show that not all data points are candidates for segment boundaries in the optimal solution.