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 $\phi\colon \mathsf{S}^1 \to \Gamma$.

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.

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.

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.

Convex-transitive Banach spaces and their hyperplanes

The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.

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.

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.

Exotic superfluid states of ultra-cold Fermi gases

This is a study of ultra-cold Fermi gases in different systems. This thesis is focused on exotic superfluid states, for an example on the three component Fermi gas and the FFLO phase in optical lattices. In the two-components case, superfluidity is studied mainly in the case of the spin population imbalanced Fermi gases and the phase diagrams are calculated from the mean-field theory. Different methods to detect different phases in optical lattices are suggested. In the three-component case, we studied also the uniform gas and harmonically trapped system. In this case, the BCS theory is generalized to three-component gases. It is also discussed how to achieve the conditions to get an SU(3)-symmetric Hamiltonian in optical lattices. The thesis is divided in chapters as follows: Chapter 1 is an introduction to the field of cold quantum gases. In chapter 2 optical lattices and their experimental characteristics are discussed. Chapter 3 deals with two-components Fermi gases in optical lattices and the paired states in lattices. In chapter 4 three-component Fermi gases with and without a harmonic trap are explored, and the pairing mechanisms are studied. In this chapter, we also discuss three-component Fermi gases in optical lattices. Chapter 5 devoted to the higher order correlations, and what they can tell about the paired states. Chapter 6 concludes the thesis.

Suomalaisten yritysten vapaaehtoinen sosiaalinen vastuu : Sidosryhmäviitekehys yritysten ja ulkoisten sidosryhmien edustajien näkemyksissä

Corporate social responsibility (CSR) is no longer only an issue of companies but a concern shared by e.g. the European Union, the International Labour Organization, labour market organizations and many others. This thesis examines what kind of voluntary corporate social responsibility exceeding the minimum level set in the legislation can be expected from the Finnish companies. The research was based on the interviews of some representatives of Finnish companies and of external stakeholders. Earlier Finnish empirical research on the topic has solely analysed the stakeholder thinking and the ethics of the views of the company representatives. The views of the external stakeholders brought ht up a much more versatile perspective on the voluntary corporate social responsibility of the companies. That is the particular surplus value of this research. This research, founded on stakeholder thinking, evaluated what kind of starting points and ideas on responsibility the views of the representatives of the companies and the external stakeholders were based on the voluntary social responsibility. Furthermore, the research also investigated how their views about the corporate social responsibility indicated the benefits achieved on the cooperative actions with different partners - for example companies, communities and public administration. To fulfil the aims of the research, the following questions were used as part tasks in mapping the basic foundations and starting points expressed by the representatives of the companies and the external stakeholders: 1) How do laws, directions concerning social responsibility of companies, and opinions and demands of the stakeholders guide and affect the voluntary corporate social responsibility? 2) How can companies assume voluntary corporate social responsibility in addition to their core functions and without compromising their profitability, and how does, for example, the tightening competition affect the possibility of taking responsibility? 3) What kind of ethic and moral foundations is the corporate social responsibility based on? 4) What kind of roles can companies have in securing and promoting the well-being of citizens in Finland and on the global market as one subsystem of the society? The views on the voluntary corporate social responsibility of nine big companies, one medium-sized company and one small company, all considered responsible pioneer companies, were studied with surveys and half-structured theme interviews between 2003 and 2004. The research proceeded as a theory-bounded study. The empirical material and the previous stakeholder thinking theories (Takala 2000b, Vehkaperä 2003) guided the thesis and worked abductively in interplay with each other during the research process. (Tuomi, Sarajärvi 2002.) The aims and the methods of the research and the themes of the interviews were defined on the basis of that information. The aims of the research were surveyed qualitatively with the strategy of a multiple case study. Representatives from nine big peer companies and nine external stakeholders were interviewed with half-structured themes between 2004 and 2005. The external stakeholders and the peer companies were chosen with the "thinking" of theoretical replication by Yin, according to which the views of the representatives of those groups would differ from those of the pioneer companies and also from those of each others. The multiple case study supports analysing the internal cohesion of the views of different groups and comparing their differences, and it supports theoretical evaluation and theory-building as well. (Yin 2003.) Another reason for choosing the external stakeholders was their known cooperation with companies. The spoken argumentations of the company and stakeholder representatives on the voluntary social responsibility of the companies were analysed and interpreted in the first place with an analytic discourse analysis, and the argumentations were classified allusively into the stakeholder discourses in three of the part tasks. In the discourse analysis, argumentations of the speech is seen to be intervowen with cultural meanings. (Jokinen, Juhila 1999.) The views of the representatives of the pioneer companies and the external stakeholders were more stakeholder-orientated than the views of the representatives of the peer companies. For the most part, the voluntary corporate social responsibility was seemingly targeted on single, small cooperation projects of the companies and external stakeholders. The pioneer companies had more of those projects, and they were participating in the projects more actively than the peer companies were. The significant result in this research was the notion that, in particular, the representatives of the pioneer companies and external stakeholders did not consider employing and paying taxes to be enough of reciprocal corporate social responsibility. However, they still wanted to preserve the Finnish welfare model, and the interviewees did not wish major changes in the present legislation or the social agreements. According to this study, the voluntary corporate social responsibility is motivated by ethical utilitarianism which varied from very narrow to very wide in relation to benefits achieved by companies and stakeholders (Velasquez 2002, Lagerspetz 2004). Compared with the peer companies, more of the representatives of the pioneer companies and of external stakeholders estimated that companies in their decision-making and operations considered not only the advantages and the benefits of the owners and other internal stakeholders, but also those of the external stakeholders and of the whole society. However, all interviewees expressed more or less strongly that the economic responsibility guides the voluntary responsible actions of the companies in the first place. This kind of utilitarian foundation of behaviour appeared from this research was named as business-orientated company moral. This thesis also presents a new voluntary corporate social responsibility model with four variables on the stakeholder discourses and their distinctive characteristics. The utilitarian motivation of a company s behaviour on their operations has been criticized on the grounds that the end justifies the means. It has also been stated that it is impossible to evaluate the benefits of the utilitarian type of actions to the individuals and the society. It is expected however that companies for their part promote the material and immaterial well-being of the individuals on the global, national and local markets. The expectations are so strong that if companies do not take into account the ethical and moral values, they can possibly suffer significant financial losses. All stakeholders, especially consumers, can with their own choices promote the responsible behaviour of the companies. Key words: voluntary corporate social responsibility, external stakeholders, corporate citizenship, ethics and morality, utilitarianism, stakeholder discourses, welfare society, globalisation

On cluster approximations of cellular automata

In this thesis I examine one commonly used class of methods for the analytic approximation of cellular automata, the so-called local cluster approximations. This class subsumes the well known mean-field and pair approximations, as well as higher order generalizations of these. While a straightforward method known as Bayesian extension exists for constructing cluster approximations of arbitrary order on one-dimensional lattices (and certain other cases), for higher-dimensional systems the construction of approximations beyond the pair level becomes more complicated due to the presence of loops. In this thesis I describe the one-dimensional construction as well as a number of approximations suggested for higher-dimensional lattices, comparing them against a number of consistency criteria that such approximations could be expected to satisfy. I also outline a general variational principle for constructing consistent cluster approximations of arbitrary order with minimal bias, and show that the one-dimensional construction indeed satisfies this principle. Finally, I apply this variational principle to derive a novel consistent expression for symmetric three cell cluster frequencies as estimated from pair frequencies, and use this expression to construct a quantitatively improved pair approximation of the well-known lattice contact process on a hexagonal lattice.

"Ei sitä ainakaan helpommaksi tehdä sairaan opiskelijan elämää" : Pitkäaikaissairaiden kokemuksia korkeakoulutuksen esteistä ja mahdollisuuksista

This study examines the experiences of students with chronic illnesses in higher education. I chose to study rheumatic and other musculoskeletal diseases because they are group of diseases that are nationally significant in Finland. From students experiences I do interpretation of their agency. My research problems are: What kind of obstacles and possibilities student with chronic illness experiences in studying? What kind of obstacles illness set up for the agency or does it set any? How agency of student with chronic illness shows in the context of the university? I collected the data by using interview and focus group method. Additionally I had different kinds of documents of accessibility and equality in the university. Interviews were like halfstructured theme and open interviews. Focus group method I have applied. All the people that participated in the study were students from the university of Helsinki. They all have rheumatic or other musculoskeletal diseases. I have five interviewees and the group consisted of two people and the researcher. In the data analysis I use categorizing by the themes. Students that participated in my study spoke about their pain related experiences of their illness which also connected to their experiences of the higher education. Students agencies were limited the more they experienced pain. Pain forces students to certain activity one actions avoidance and another s favouring. If part-time studying would have been possible economically, it would have made the life easier for a part of the students. Students were aware of the available resources of their body for some of the students illness and life control set challenge and for some it set conditions. Students thought that university education is more possible to them than vocational education. Students didn t feel their own body limited in the context of university that emphasize intellectual and knowledge connected values and some of the students had reversed their illness as a resource of studying. However students felt their illness as a private matter and they considered illness profit and disadvantage before telling about it, which I interpretated limiting students agencies. In the university terms of students agencies were bond to individuality that came up in positive and negative. Freedom of studying was positive but official and individual study accommodations made agency bounded. Majority of the students didn t see possibilities to do differently in the university s practice but some of the students had recognised values underneath the practices that made it possible to reflect them, do differently and made space for agency.

Aspiration-based utility functions in a planning model for timber flow management.

The study presents a theory of utility models based on aspiration levels, as well as the application of this theory to the planning of timber flow economics. The first part of the study comprises a derivation of the utility-theoretic basis for the application of aspiration levels. Two basic models are dealt with: the additive and the multiplicative. Applied here solely for partial utility functions, aspiration and reservation levels are interpreted as defining piecewisely linear functions. The standpoint of the choices of the decision-maker is emphasized by the use of indifference curves. The second part of the study introduces a model for the management of timber flows. The model is based on the assumption that the decision-maker is willing to specify a shape of income flow which is different from that of the capital-theoretic optimum. The utility model comprises four aspiration-based compound utility functions. The theory and the flow model are tested numerically by computations covering three forest holdings. The results show that the additive model is sensitive even to slight changes in relative importances and aspiration levels. This applies particularly to nearly linear production possibility boundaries of monetary variables. The multiplicative model, on the other hand, is stable because it generates strictly convex indifference curves. Due to a higher marginal rate of substitution, the multiplicative model implies a stronger dependence on forest management than the additive function. For income trajectory optimization, a method utilizing an income trajectory index is more efficient than one based on the use of aspiration levels per management period. Smooth trajectories can be attained by squaring the deviations of the feasible trajectories from the desired one.