22 resultados para Locally Compact Group

em Helda - Digital Repository of University of Helsinki


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Glaucoma is a group of progressive optic neuropathies causing irreversible blindness if not diagnosed and treated in the early state of progression. Disease is often, but not always, associated with increased intraocular pressure (IOP), which is also the most important risk factor for glaucoma. Ophthlamic timolol preparations have been used for decades to lower increased intraocular pressure (IOP). Timolol is locally well tolerated but may cause e.g. cardiovascular and pulmonary adverse effects due to systemic absorption. It has been reported that approximately 80% of a topically administered eye drop is systemically absorbed. However, only limited information is available on timolol metabolism in the liver or especially in the human eye. The aim of this work was to investigate metabolism of timolol in human liver and human ocular tissues. The expression of drug metabolizing cytochrome P450 (CYP) enzymes in the human ciliary epithelial cells was studied. The metabolism of timolol and the interaction potential of timolol with other commercially available medicines were investigated in vitro using different liver preparations. The absorption of timolol to the aqueous humor from two commercially available products: 0.1% eye gel and 0.5% eye drops and the presence of timolol metabolites in the aqueous humor were investigated in a clinical trial. Timolol was confirmed to be metabolized mainly by CYP2D6 as previously suggested. Potent CYP2D6 inhibitors especially fluoxetine, paroxetine and quinidine inhibited the metabolism of timolol. The inhibition may be of clinical significance in patients using ophthalmic timolol products. CYP1A1 and CYP1B1 mRNAs were expressed in the human ciliary epithelial cells. CYP1B1 was also expressed at protein level and the expression was strongly induced by a known potent CYP1B1 inducer 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). The CYP1B1 induction is suggested to be mediated by aryl hydrocarbon receptor (AHR). Low levels of CYP2D6 mRNA splice variants were expressed in the human ciliary epithelial cells and very low levels of timolol metabolites were detected in the human aqueous humor. It seems that negligible amount of CYP2D6 protein is expressed in the human ocular tissues. Timolol 0.1% eye gel leads to aqueous humor concentration high enough to achieve therapeutic effect. Inter-individual variation in concentrations is low and intraocular as well as systemic safety can be increased when using this product with lower timolol concentration instead of timolol 0.5% eye drops.

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Sindbis virus (SINV) (genus Alphavirus, family Togaviridae) is an enveloped virus with a genome of single-stranded, positive-polarity RNA of 11.7 kilobases. SINV is widespread in Eurasia, Africa, and Australia, but clinical infection only occurs in a few geographically restricted areas, mainly in Northern Europe. In Europe, antibodies to SINV were detected from patients with fever, rash, and arthritis for the first time in the early 1980s in Finland. It became evident that the causative agent of this syndrome, named Pogosta disease, was closely related to SINV. The disease is also found in Sweden (Ockelbo disease) and in Russia (Karelian fever). Since 1974, for unknown reason, the disease has occurred as large outbreaks every seven years in Finland. This study is to a large degree based on the material collected during the 2002 Pogosta disease outbreak in Finland. We first developed SINV IgM and IgG enzyme immunoassays (EIA), based on highly purified SINV, to be used in serodiagnostics. The EIAs correlated well with the hemagglutination inhibition (HI) test, and all individuals showed neutralizing antibodies. The sensitivities of the IgM and IgG EIAs were 97.6% and 100%, and specificities 95.2% and 97.6%, respectively. E1 and E2 envelope glycoproteins of SINV were shown to be recognized by IgM and IgG in the immunoblot early in infection. We isolated SINV from five patients with acute Pogosta disease; one virus strain was recovered from whole blood, and four other strains from skin lesions. The etiology of Pogosta disease was confirmed by these first Finnish SINV strains, also representing the first human SINV isolates from Europe. Phylogenetic analysis indicated that the Finnish SINV strains clustered with the strains previously isolated from mosquitoes in Sweden and Russia, and seemed to have a common ancestor with South-African strains. Northern European SINV strains could be maintained locally in disease-endemic regions, but the phylogenetic analysis also suggests that redistribution of SINV tends to occur in a longitudinal direction, possibly with migratory birds. We searched for SINV antibodies in resident grouse (N=621), whose population crashes have previously coincided with human SINV outbreaks, and in migratory birds (N=836). SINV HI antibodies were found for the first time in birds during their spring migration to Northern Europe, from three individuals: red-backed shrike, robin, and song thrush. Of the grouse, 27.4% were seropositive in 2003, one year after a human outbreak, but only 1.4% of the grouse were seropositive in 2004. Thus, grouse might contribute to the human epidemiology of SINV. A total of 86 patients with verified SINV infection were recruited to the study in 2002. SINV RNA detection or virus isolation from blood and/or skin lesions was successful in eight patients. IgM antibodies became detectable within the first eight days of illness, and IgG within 11 days. The acute phase of Pogosta disease was characterized by arthritis, itching rash, fatigue, mild fever, headache, and muscle pain. Half of the patients reported in self-administered questionnaires joint symptoms to last > 12 months. Physical examination in 49 of these patients three years after infection revealed persistent joint manifestations. Arthritis (swelling and tenderness in physical examination) was diagnosed in 4.1% (2/49) of the patients. Tenderness in palpation or in movement of a joint was found in 14.3% of the patients in the rheumatologic examination, and additional 10.2% complained persisting arthralgia at the interview. Thus, 24.5% of the patients had joint manifestations attributable to the infection three years earlier. A positive IgM antibody response persisted in 3/49 of the patients; both two patients with arthritis were in this group. Persistent symptoms of SINV infection might have considerable public health implications in areas with high seroprevalence. The age-standardized seroprevalence of SINV (1999-2003, N=2529) in the human population in Finland was 5.2%. The seroprevalence was high in North Karelia, Kainuu, and Central Ostrobothnia. The incidence was highest in North Karelia. Seroprevalence in men (6.0%) was significantly higher than in women (4.1%), however, the average annualized incidence in the non-epidemic years was higher in women than in men, possibly indicating that infected men are more frequently asymptomatic. The seroprevalence increased with age, reaching 15.4% in persons aged 60-69 years. The incidence was highest in persons aged 50-59 years.

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The commodity plastics that are used in our everyday lives are based on polyolefin resins and they find wide variety of applications in several areas. Most of the production is carried out in catalyzed low pressure processes. As a consequence polymerization of ethene and α-olefins has been one of the focus areas for catalyst research both in industry and academia. Enormous amount of effort have been dedicated to fine tune the processes and to obtain better control of the polymerization and to produce tailored polymer structures The literature review of the thesis concentrates on the use of Group IV metal complexes as catalysts for polymerization of ethene and branched α-olefins. More precisely the review is focused on the use of complexes bearing [O,O] and [O,N] type ligands which have gained considerable interest. Effects of the ligand framework as well as mechanical and fluxional behaviour of the complexes are discussed. The experimental part consists mainly of development of new Group IV metal complexes bearing [O,O] and [O,N] ligands and their use as catalysts precursors in ethene polymerization. Part of the experimental work deals with usage of high-throughput techniques in tailoring properties of new polymer materials which are synthesized using Group IV complexes as catalysts. It is known that the by changing the steric and electronic properties of the ligand framework it is possible to fine tune the catalyst and to gain control over the polymerization reaction. This is why in this thesis the complex structures were designed so that the ligand frameworks could be fairly easily modified. All together 14 complexes were synthesised and used as catalysts in ethene polymerizations. It was found that the ligand framework did have an impact within the studied catalyst families. The activities of the catalysts were affected by the changes in complex structure and also effects on the produced polymers were observed: molecular weights and molecular weight distributions were depended on the used catalyst structure. Some catalysts also produced bi- or multi-modal polymers. During last decade high-throughput techniques developed in pharmaceutical industries have been adopted into polyolefin research in order to speed-up and optimize the catalyst candidates. These methods can now be regarded as established method suitable for both academia and industry alike. These high-throughput techniques were used in tailoring poly(4-methyl-1-pentene) polymers which were synthesized using Group IV metal complexes as catalysts. This work done in this thesis represents the first successful example where the high-throughput synthesis techniques are combined with high-throughput mechanical testing techniques to speed-up the discovery process for new polymer materials.

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This study aims at improving understanding of the interactions of livelihoods and the environment focusing on both socio-economic and biodiversity implications of land use change in the context of population pressure, global and local markets, climate change, cultural and regional historical factors in the highlands of East Africa. The study is based on three components (1) two extensive livelihood surveys, one on Mt. Kilimanjaro in Tanzania and the other in the Taita Hills of Kenya, (2) a land use change study of the southern slopes of Mt. Kilimanjaro focusing on land use trends between 1960s and 1980s and 1980s and 2000 and (3) a bird diversity study focusing on the potential impacts of the future land use change on birds in the main land use types on the slopes and the adjacent plains of Mt. Kilimanjaro. In addition, information on the highlands in Embu and the adjacent lowlands in Mbeere of Kenya are added to the discussion. Some general patterns of livelihood, land use and environment interactions can be found in the three sites. However, the linkages are very complex. Various external factors at different times in history have influenced most of the major turning points. Farmers continually make small adaptations to their farming practices, but the locally conceived alternatives are too few. Farmers lack specific information and knowledge on the most suitable crops, market opportunities and the quality requirements for growing the crops for markets. Population growth emerges as the most forceful driver of land use and environmental change. The higher altitudes have become extremely crowded with population densities in some areas higher than typical urban population densities. Natural vegetation has almost totally been replaced by farmland. Decreasing farm size due to population pressure is currently threatening the viability of whole farming systems. In addition, capital-poor intensification has lead to soil fertility depletion. Agricultural expansion to the agriculturally marginal lowlands has created a new and distinct group of farmers struggling constantly with climate variability causing frequent crop failures. Extensification to the fragile drylands is the major cause of fragmentation and loss of wildlife habitat. The linkages between livelihoods, land use and the environment generally point to degradation of the environment leading to reduced environmental services and ecosystem functions. There is no indication that the system is self-regulating in this respect. Positive interventions will be needed to maintain ecosystem integrity.

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This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

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

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The parasitic wasps are one of the largest insect groups and their life histories are remarkably variable. Common to all parasitic wasps is that they kill their hosts, which are usually beetles, butterflies and sometimes spiders. Hosts are often at a larval or pupal stage and live in concealed conditions, such as in plant tissue. Parasitic wasps have two main ways of finding their host. 1) They can detect chemical compounds emitted by damaged plant material or released by larvae living in plant tissue, and 2) detect the larvae by sound vibrations. Even though pupae are immobile and silent, and therefore do not cause vibration, parasitoids have, however, adapted to find passive developmental stages by producing vibration themselves by knocking the substrate with their antennae, and then detecting the echoes with their legs. This echolocation allows a parasitoid to locate its potential hosts that are deeply buried in wood. This study focuses on the relationships of the subfamily Cryptinae (Hymenoptera: Ichneumonidae) and related taxa, and the evolution of host location mechanism. There are no earlier studies of the phylogeny of the Cryptinae, and the position of related taxa are unclear. According to the earlier classification, which is entirely intuitional, the Cryptinae is divided into three tribes: Cryptini, Hemigasterini and Phygadeuontini. Further, these tribes are subdiveded into numerous subtribes. This work, based on molecular characters, shows that the cryptine tribes Cryptini, Phygadeuon¬tini and Hemigasterini come out largely as monophyletic groups, thus agreeing with the earlier classification. The earlier subtribal classification had no support. In addition, it is shown that modified antennal structures are associated with host usage of wood-boring coleopteran hosts. The cryptines have a clear modification series on their antennal tips from a simply tip to a hammer-like structure. The species with strongly modified antennae belong mostly to the tribe Cryptini and they utilise wood-boring beetles as hosts. Also, field observations on insect behaviour support this result.

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Sjögren s syndrome (SS) is a common autoimmune disease affecting the lacrimal and salivary glands. SS is characterized by a considerable female predominance and a late age of onset, commonly at the time of adreno- and menopause. The levels of the androgen prohormone dehydroepiandrosterone-sulphate (DHEA-S) in the serum are lower in patients with SS than in age- and sex-matched healthy control subjects. The eventual systemic effects of low androgen levels in SS are not currently well understood. Basement membranes (BM) are specialized layers of extracellular matrix and are composed of laminin (LM) and type IV collagen matrix networks. BMs deliver messages to epithelial cells via cellular LM-receptors including integrins (Int) and Lutheran blood group antigen (Lu). The composition of BMs and distribution of LM-receptors in labial salivary glands (LSGs) of normal healthy controls and patients with SS was assessed. LMs have complex and highly regulated distribution in LSGs. LMs seem to have specific tasks in the dynamic regulation of acinar cell function. LM-111 is important for the normal acinar cell differentiation and its expression is diminished in SS. Also LM-211 and -411 seem to have some acinar specific functional tasks in LSGs. LM-311, -332 and -511 seem to have more general structure maintaining and supporting roles in LSGs and are relatively intact also in SS. Ints α3β1, α6β1, α6β4 and Lu seem to supply structural basis for the firm attachment of epithelial cells to the BM in LSGs. The expression of Ints α1β1 and α2β1 differed clearly from other LM-receptors in that they were found almost exclusively around the acini and intercalated duct cells in salivons suggesting some type of acinar cell compartment-specific or dominant function. Expression of these integrins was lower in SS compared to healthy controls suggesting that the LM-111 and -211-to-Int α1β1 and α2β1 interactions are defective in SS and are crucial to the maintenance of the acini in LSGs. DHEA/DHEA-S concentration in serum and locally in saliva of patients with SS seems to have effects on the salivary glands. These effects were first detected using the androgen-dependent CRISP-3 protein, the production and secretion of which were clearly diminished in SS. This might be due to the impaired function of the intracrine DHEA prohormone metabolizing machinery, which fails to successfully convert DHEA into its active metabolites in LSGs. The progenitor epithelial cells from the intercalated ductal area of LSGs migrate to the acinar compartment and then undergo a phenotype change into secretory acinar cells. This migration and phenotype change seem to be regulated by the LM-111-to-Int α1β1/Int α2β1 interactions. Lack of these interactions could be one factor limiting the normal remodelling process. Androgens are effective stimulators of Int α1β1 and α2β1 expression in physiologic concentrations. Addition of DHEA to the culture medium had effective stimulating effect on the Int α1β1 and α2β1 expression and its effect may be deficient in the LSGs of patients with SS.

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Paikallisesti levinnyttä (T3-4 M0) ja luustoon levinnyttä (T1-4 M1) eturauhassyöpää sairastaneet potilaat satunnaistettiin kirurgiseen kastraatioon (orkiektomia) tai lääkkeelliseen kastraatioon lihaksensisäisellä polyestradiolifosfaatilla (PEP) annoksella 240 mg/kk. Verrattiin hoitojen kliinistä tehoa sekä sydän- ja verisuonikomplikaatioita (SV-komplikaatioita). Verrattiin myös hoitoa edeltäviä plasman testosteroni (T) ja estradioli (E2) pitoisuuksia T3-4 M0 ja T1-4 M1 potilaiden välillä sekä selvitettiin potilaiden yleistilan vaikutusta näihin hormonitasoihin. Lopuksi luotiin T1-4 M1 potilaille eturauhassyövän aiheuttaman kuoleman ennusteellinen riskiluokittelu kolmeen riskiryhmään käyttämällä hoitoa edeltäviä ennustetekijöitä. Kliinisessä tehossa ei orkiektomian ja PEP-hoidon välillä todettu tilastollisesti merkitsevää eroa. Odotetusti T1-4 M1 potilaiden ennuste oli huonompi kuin T3-4 M0 potilaiden. T1-4 M1 potilailla ei ollut SV-kuolemissa hoitoryhmien välillä tilastollista eroa, mutta ei-tappavia SV-komplikaatioita oli PEP ryhmässä (5.9%) enemmän kuin orkiektomia ryhmässä (2.0%). T3-4 M0 potilailla PEP-hoitoon liittyi tilastollisesti merkitsevä SV-kuolleisuus riski orkiektomiaan verrattuna (p = 0.001). PEP ryhmässä 67% kuolemista oli akuutteja sydäninfarkteja. Tämä PEP hoitoon liittyvä sydäninfarktiriski (mukaan lukien myös ei-tappavat sydäninfarktit) oli merkitsevästi pienempi potilailla, joiden hoitoa edeltävä E2 taso oli vähintään 93 pmol/l (p = 0.022). E2 taso oli merkitsevästi matalampi T1-4 M1 potilailla (74.7 pmol/l) kuin T3-4 M0 potilailla (87.9 pmol/l), mutta vastaavaa eroa ei ollut T tasoissa. Sekä T3-4 M0 että T1-4 M1 potilailla yleistilan lasku osittain selitti yksilöllisen T ja E2 tasojen laskun. Eturauhassyövän aiheuttaman kuoleman riskiryhmäluokittelu (Rg) kolmeen ryhmään luotiin käyttämällä alkalista fosfataasia (AFOS), prostata spesifistä antigeenia (PSA), laskoa (La) ja potilaan ikää. Yksi riskipiste annettiin, jos AFOS > 180 U/l (tällä hetkellä käytössä olevalla menetelmällä AFOS > 83 U/l), PSA > 35 µg/l, La > 80 mm/h ja ikä < 60 vuotta. Lopuksi pisteet laskettiin yhteen. Muodostettiin seuraavat ryhmät: Rg-a (0 -1 riskipistettä), Rg-b (2 riskipistettä) ja Rg-c (3 – 4 riskipistettä). Eturauhassyövän aiheuttama kuoleman riski lisääntyi merkitsevästi siirryttäessä riskiryhmästä seuraavaan (p < 0.001). Rg-luokittelu oli kliinisesti käytännöllinen ja hyvä havaitsemaan huonon ennusteen potilaat.

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This three-phase design research describes the modelling processes for DC-circuit phenomena. The first phase presents an analysis of the development of the DC-circuit historical models in the context of constructing Volta s pile at the turn of the 18th century. The second phase involves the designing of a teaching experiment for comprehensive school third graders. Among other considerations, the design work utilises the results of the first phase and research literature of pupils mental models for DC-circuit phenomena. The third phase of the research was concerned with the realisation of the planned teaching experiment. The aim of this phase was to study the development of the external representations of DC-circuit phenomena in a small group of third graders. The aim of the study has been to search for new ways to guide pupils to learn DC-circuit phenomena while emphasing understanding at the qualitative level. Thus, electricity, which has been perceived as a difficult and abstract subject, could be learnt more comprehensively. Especially, the research of younger pupils learning of electricity concepts has not been of great interest at the international level, although DC-circuit phenomena are also taught in the lower classes of comprehensive schools. The results of this study are important, because there has tended to be more teaching of natural sciences in the lower classes of comprehensive schools, and attempts are being made to develop this trend in Finland. In the theoretical part of the research an Experimental-centred representation approach, which emphasises the role of experimentalism in the development of pupil s representations, is created. According to this approach learning at the qualitative level consists of empirical operations like experimenting, observations, perception, and prequantification of nature phenomena, and modelling operations like explaining and reasoning. Besides planning teaching, the new approach can be used as an analysis tool in describing both historical modelling and the development of pupils representations. In the first phase of the study, the research question was: How did the historical models of DC-circuit phenomena develop in Volta s time? The analysis uncovered three qualitative historical models associated with the historical concept formation process. The models include conceptions of the electric circuit as a scene in the DC-circuit phenomena, the comparative electric-current phenomenon as a cause of different observable effect phenomena, and the strength of the battery as a cause of the electric-current phenomenon. These models describe the concept formation process and its phases in Volta s time. The models are portrayed in the analysis using fragments of the models, where observation-based fragments and theoretical fragements are distinguished from each other. The results emphasise the significance of the qualitative concept formation and the meaning of language in the historical modelling of DC-circuit phenomena. For this reason these viewpoints are stressed in planning the teaching experiment in the second phase of the research. In addition, the design process utilised the experimentation behind the historical models of DC-circuit phenomena In the third phase of the study the research question is as follows: How will the small group s external representations of DC-circuit phenomena develop during the teaching experiment? The main question is divided into the following two sub questions: What kind of talk exists in the small group s learning? What kinds of external representations for DC-circuit phenomena exist in the small group discourse during the teaching experiment? The analysis revealed that the teaching experiment of the small group succeeded in its aim to activate talk in the small group. The designed connection cards proved especially successful in activating talk. The connection cards are cards that represent the components of the electric circuit. In the teaching experiment the pupils constructed different connections with the connection cards and discussed, what kinds of DC-circuit phenomena would take place in the corresponding real connections. The talk of the small group was analysed by comparing two situations, firstly, when the small group discussed using connections made with the connection cards and secondly with the same connections using real components. According to the results the talk of the small group included more higher-order thinking when using the connection cards than with similar real components. In order to answer the second sub question concerning the small group s external representations that appeared in the talk during the teaching experiment; student talk was visualised by the fragment maps which incorporate the electric circuit, the electric current and the source voltage. The fragment maps represent the gradual development of the external representations of DC-circuit phenomena in the small group during the teaching experiment. The results of the study challenge the results of previous research into the abstractness and difficulty of electricity concepts. According to this research, the external representations of DC-circuit phenomena clearly developed in the small group of third graders. Furthermore, the fragment maps uncover that although the theoretical explanations of DC-circuit phenomena, which have been obtained as results of typical mental model studies, remain undeveloped, learning at the qualitative level of understanding does take place.

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This thesis studies the nature and logic of collective doxastic attitudes, or what is referred to in ordinary language as "group beliefs". Beliefs and other intentional attitudes are attributed to groups and collections of people, and such attributions are used to explain and predict the actions of groups. The thesis develops an understanding of group beliefs as voluntarily adopted views or acceptances rather than as ordinary beliefs. Such an understanding can provide new answers to questions concerning collective knowledge and justification of group beliefs, and it allows developing modal logics with collective doxastic and epistemic notions. The thesis consists of six articles. The first three articles are philosophical studies concerned with the nature of group beliefs. The last three articles are logical studies that aim at developing proof-theoretical calculi for reasoning about collective doxastic attitudes.