36 resultados para galaxies: star clusters: general


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Mass occurrences (blooms) of cyanobacteria are common in aquatic environments worldwide. These blooms are often toxic, due to the presence of hepatotoxins or neurotoxins. The most common cyanobacterial toxins are hepatotoxins: microcystins and nodularins. In freshwaters, the main producers of microcystins are Microcystis, Anabaena, and Planktothrix. Nodularins are produced by strains of Nodularia spumigena in brackish waters. Toxic and nontoxic strains of cyanobacteria co-occur and cannot be differentiated by conventional microscopy. Molecular biological methods based on microcystin and nodularin synthetase genes enable detection of potentially hepatotoxic cyanobacteria. In the present study, molecular detection methods for hepatotoxin-producing cyanobacteria were developed, based on microcystin synthetase gene E (mcyE) and the orthologous nodularin synthetase gene F (ndaF) sequences. General primers were designed to amplify the mcyE/ndaF gene region from microcystin-producing Anabaena, Microcystis, Planktothrix, and Nostoc, and nodularin-producing Nodularia strains. The sequences were used for phylogenetic analyses to study how cyanobacterial mcy genes have evolved. The results showed that mcy genes and microcystin are very old and were already present in the ancestor of many modern cyanobacterial genera. The results also suggested that the sporadic distribution of biosynthetic genes in modern cyanobacteria is caused by repeated gene losses in the more derived lineages of cyanobacteria and not by horizontal gene transfer. Phylogenetic analysis also proposed that nda genes evolved from mcy genes. The frequency and composition of the microcystin producers in 70 lakes in Finland were studied by conventional polymerase chain reaction (PCR). Potential microcystin producers were detected in 84% of the lakes, using general mcyE primers, and in 91% of the lakes with the three genus-specific mcyE primers. Potential microcystin-producing Microcystis were detected in 70%, Planktothrix in 63%, and Anabaena in 37% of the lakes. The presence and co-occurrence of potential microcystin producers were more frequent in eutrophic lakes, where the total phosphorus concentration was high. The PCR results could also be associated with various environmental factors by correlation and regression analyses. In these analyses, the total nitrogen concentration and pH were both associated with the presence of multiple microcystin-producing genera and partly explained the probability of occurrence of mcyE genes. In general, the results showed that higher nutrient concentrations increased the occurrence of potential microcystin producers and the risk for toxic bloom formation. Genus-specific probe pairs for microcystin-producing Anabaena, Microcystis, Planktothrix, and Nostoc, and nodularin-producing Nodularia were designed to be used in a DNA-chip assay. The DNA-chip can be used to simultaneously detect all these potential microcystin/nodularin producers in environmental water samples. The probe pairs detected the mcyE/ndaF genes specifically and sensitively when tested with cyanobacterial strains. In addition, potential microcystin/nodularin producers were identified in lake and Baltic Sea samples by the DNA-chip almost as sensitively as by quantitative real-time PCR (qPCR), which was used to validate the DNA-chip results. Further improvement of the DNA-chip assay was achieved by optimization of the PCR, the first step in the assay. Analysis of the mcy and nda gene clusters from various hepatotoxin-producing cyanobacteria was rewarding; it revealed that the genes were ancient. In addition, new methods detecting all the main producers of hepatotoxins could be developed. Interestingly, potential microcystin-producing cyanobacterial strains of Microcystis, Planktothrix, and Anabaena, co-occurred especially in eutrophic and hypertrophic lakes. Protecting waters from eutrophication and restoration of lakes may thus decrease the prevalence of toxic cyanobacteria and the frequency of toxic blooms.

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Uusien polymeeripohjaisten teknologioiden ja materiaalien myötä räätälöityjen polymeerien tarve on kasvanut. Viime vuosituhannen lopussa kehitetyt kontrolloidut polymerointimenetelmät ovat avanneet uusia mahdollisuuksia paitsi monimutkaisten polymeerien synteesiin, myös itsejärjestyvyyteen perustuvien funktionaalisten nanorakenteiden suunnitteluun ja valmistukseen. Nämä voivat jäljitellä luonnossa esiintyviä rakenteita, joita muodostavat esimerkiksi lipidit ja proteiinit. Itsejärjestyvät molekyylit ovat usein amfifiilisiä eli ne koostuvat hydrofiilisistä ja hydrofobisista osista ja polymeereissä nämä osat voivat olla omina lohkoinaan, jolloin puhutaan amfifiilisistä lohko- tai blokkikopolymeereistä. Riippuen järjestyneiden rakenteiden koostumuksesta ja muodosta, amfifiilisiä blokkikopolymeerejä on tutkittu tai jo käytetty nanoteknologiassa, elastomeereissä, voiteluaineissa, pinta-aktiivisina aineina, lääkkeenannostelussa, maaleissa, sekä elektroniikka-, kosmetiikka- ja elintarviketeollisuudessa. Tavallisimmin käytetyt amfifiiliset blokkikopolymeerit ovat olleet lineaarisia, mutta viime aikoina tutkimus on suuntautunut kohti monimutkaisempia rakenteita. Tällaisia ovat esimerkiksi tähtipolymeerit. Tähtimäisissä polymeereissä miselleille tyypillinen ydin-kuori-rakenne säilyy hyvin alhaisissakin polymeerikonsentraatioissa, koska polymeeriketjut ovat kiinni toisissaan yhdessä pisteessä. Siten ne ovat erityisen kiinnostavia tutkimuskohteita erilaisten hydrofobisten orgaanisten yhdisteiden sitomiseksi ja vapauttamiseksi. Tässä työssä on tarkasteltu amfifiilisten tähtipolymeerien itsejärjestymistä vesiliuoksissa sekä kokeellisesti ja tietokonesimulaatioin. Työ koostuu kahdesta osasta: tähtipolymeerien synteesistä makrosyklisillä initiaattoreilla ja amfifiilisten tähtimäisten blokkikopolymeerien ominaisuuksien tutkimisesta.

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Microbial degradation pathways play a key role in the detoxification and the mineralization of polyaromatic hydrocarbons (PAHs), which are widespread pollutants in soil and constituents of petroleum hydrocarbons. In microbiology the aromatic degradation pathways are traditionally studied from single bacterial strains with capacity to degrade certain pollutant. In soil the degradation of aromatics is performed by a diverse community of micro-organisms. The aim of this thesis was to study biodegradation on different levels starting from a versatile aromatic degrader Sphingobium sp. HV3 and its megaplasmid, extending to revelation of diversity of key catabolic enzymes in the environment and finally studying birch rhizoremediation in PAH-polluted soil. To understand biodegradation of aromatics on bacterial species level, the aromatic degradation capacity of Sphingobium sp. HV3 and the role of the plasmid pSKY4, was studied. Toluene, m-xylene, biphenyl, fluorene, phenanthrene were detected as carbon and energy sources of the HV3 strain. Tn5 transposon mutagenesis linked the degradation capacity of toluene, m-xylene, biphenyl and naphthalene to the pSKY4 plasmid and qPCR expression analysis showed that plasmid extradiol dioxygenases genes (bphC and xylE) are inducted by phenanthrene, m-xylene and biphenyl whereas the 2,4-dichlorophenoxyacetic acid herbicide induced the chlorocatechol 1,2-dioxygenase gene (tfdC) from the ortho-pathway. A method to study upper meta-pathway extradiol dioxygenase gene diversity in soil was developed. The extradiol dioxygenases catalyse cleavage of the aromatic ring between a hydroxylated carbon and an adjacent non-hydroxylated carbon (meta-cleavage). A high diversity of extradiol dioxygenases were detected from polluted soils. The detected extradiol dioxygenases showed sequence similarity to known catabolic genes of Alpha-, Beta-, and Gammaproteobacteria. Five groups of extradiol dioxygenases contained sequences with no close homologues in the database, representing novel genes. In rhizoremediation experiment with birch (Betula pendula) treatment specific changes of extradiol dioxygenase communities were shown. PAH pollution changed the bulk soil extradiol dioxygenase community structure and birch rhizosphere contained a more diverse extradiol dioxygenase community than the bulk soil showing a rhizosphere effect. The degradation of pyrene in soil was enhanced with birch seedlings compared to soil without birch. The complete 280,923 kb nucleotide sequence of pSKY4 plasmid was determined. The open reading frames of pSKY4 were divided into putative conjugative transfer, aromatic degradation, replication/maintaining and transposition/integration function-encoding proteins. Aromatic degradation orfs shared high similarity to corresponding genes in pNL1, a plasmid from the deep subsurface strain Novosphingobium aromaticivorans F199. The plasmid backbones were considerably more divergent with lower similarity, which suggests that the aromatic pathway has functioned as a plasmid independent mobile genetic element. The functional diversity of microbial communities in soil is still largely unknown. Several novel clusters of extradiol dioxygenases representing catabolic bacteria, whose function, biodegradation pathways and phylogenetic position is not known were amplified with single primer pair from polluted soils. These extradiol dioxygenase communities were shown to change upon PAH pollution, which indicates that their hosts function in PAH biodegradation in soil. Although the degradation pathways of specific bacterial species are substantially better depicted than pathways in situ, the evolution of degradation pathways for the xenobiotic compounds is largely unknown. The pSKY4 plasmid contains aromatic degradation genes in putative mobile genetic element causing flexibility/instability to the pathway. The localisation of the aromatic biodegradation pathway in mobile genetic elements suggests that gene transfer and rearrangements are a competetive advantage for Sphingomonas bacteria in the environment.

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Spirometry is the most widely used lung function test in the world. It is fundamental in diagnostic and functional evaluation of various pulmonary diseases. In the studies described in this thesis, the spirometric assessment of reversibility of bronchial obstruction, its determinants, and variation features are described in a general population sample from Helsinki, Finland. This study is a part of the FinEsS study, which is a collaborative study of clinical epidemiology of respiratory health between Finland (Fin), Estonia (Es), and Sweden (S). Asthma and chronic obstructive pulmonary disease (COPD) constitute the two major obstructive airways diseases. The prevalence of asthma has increased, with around 6% of the population in Helsinki reporting physician-diagnosed asthma. The main cause of COPD is smoking with changes in smoking habits in the population affecting its prevalence with a delay. Whereas airway obstruction in asthma is by definition reversible, COPD is characterized by fixed obstruction. Cough and sputum production, the first symptoms of COPD, are often misinterpreted for smokers cough and not recognized as first signs of a chronic illness. Therefore COPD is widely underdiagnosed. More extensive use of spirometry in primary care is advocated to focus smoking cessation interventions on populations at risk. The use of forced expiratory volume in six seconds (FEV6) instead of forced vital capacity (FVC) has been suggested to enable office spirometry to be used in earlier detection of airflow limitation. Despite being a widely accepted standard method of assessment of lung function, the methodology and interpretation of spirometry are constantly developing. In 2005, the ATS/ERS Task Force issued a joint statement which endorsed the 12% and 200 ml thresholds for significant change in forced expiratory volume in one second (FEV1) or FVC during bronchodilation testing, but included the notion that in cases where only FVC improves it should be verified that this is not caused by a longer exhalation time in post-bronchodilator spirometry. This elicited new interest in the assessment of forced expiratory time (FET), a spirometric variable not usually reported or used in assessment. In this population sample, we examined FET and found it to be on average 10.7 (SD 4.3) s and to increase with ageing and airflow limitation in spirometry. The intrasession repeatability of FET was the poorest of the spirometric variables assessed. Based on the intrasession repeatability, a limit for significant change of 3 s was suggested for FET during bronchodilation testing. FEV6 was found to perform equally well as FVC in the population and in a subgroup of subjects with airways obstruction. In the bronchodilation test, decreases were frequently observed in FEV1 and particularly in FVC. The limit of significant increase based on the 95th percentile of the population sample was 9% for FEV1 and 6% for FEV6 and FVC; these are slightly lower than the current limits for single bronchodilation tests (ATS/ERS guidelines). FEV6 was proven as a valid alternative to FVC also in the bronchodilation test and would remove the need to control duration of exhalation during the spirometric bronchodilation test.

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Background and aims. Type 1 diabetes (T1D), an autoimmune disease in which the insulin producing beta cells are gradually destroyed, is preceded by a prodromal phase characterized by appearance of diabetes-associated autoantibodies in circulation. Both the timing of the appearance of autoantibodies and their quality have been used in the prediction of T1D among first-degree relatives of diabetic patients (FDRs). So far, no general strategies for identifying individuals at increased disease risk in the general population have been established, although the majority of new cases originate in this population. The current work aimed at assessing the predictive role of diabetes-associated immunologic and metabolic risk factors in the general population, and comparing these factors with data obtained from studies on FDRs. Subjects and methods. Study subjects in the current work were subcohorts of participants of the Childhood Diabetes in Finland Study (DiMe; n=755), the Cardiovascular Risk in Young Finns Study (LASERI; n=3475), and the Finnish Type 1 Diabetes Prediction and Prevention Study (DIPP) Study subjects (n=7410). These children were observed for signs of beta-cell autoimmunity and progression to T1D, and the results obtained were compared between the FDRs and the general population cohorts. --- Results and conclusions. By combining HLA and autoantibody screening, T1D risks similar to those reported for autoantibody-positive FDRs are observed in the pediatric general population. Progression rate to T1D is high in genetically susceptible children with persistent multipositivity. Measurement of IAA affinity failed in stratifying the risk assessment in young IAA-positive children with HLA-conferred disease susceptibility, among whom affinity of IAA did not increase during the prediabetic period. Young age at seroconversion, increased weight-for-height, decreased early insulin response, and increased IAA and IA-2A levels predict T1D in young children with genetic disease susceptibility and signs of advanced beta-cell autoimmunity. Since the incidence of T1D continues to increase, efforts aimed at preventing T1D are important, and reliable disease prediction is needed both for intervention trials and for effective and safe preventive therapies in the future. Our observations confirmed that combined HLA-based screening and regular autoantibody measurements reveal similar disease risks in pediatric general population as those seen in prediabetic FDRs, and that risk assessment can be stratified further by studying glucose metabolism of prediabetic subjects. As these screening efforts are feasible in practice, the knowledge now obtained can be exploited while designing intervention trials aimed at secondary prevention of T1D.

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Background: Irritable bowel syndrome (IBS) is a common functional gastrointestinal (GI) disorder characterised by abdominal pain and abnormal bowel function. It is associated with a high rate of healthcare consumption and significant health care costs. The prevalence and economic burden of IBS in Finland has not been studied before. The aims of this study were to assess the prevalence of IBS according to various diagnostic criteria and to study the rates of psychiatric and somatic comorbidity in IBS. In addition, health care consumption and societal costs of IBS were to be evaluated. Methods: The study was a two-phase postal survey. Questionnaire I identifying IBS by Manning 2 (at least two of the six Manning symptoms), Manning 3 (at least three Manning symptoms), Rome I, and Rome II criteria, was mailed to a random sample of 5 000 working age subjects. It also covered extra-GI symptoms such as headache, back pain, and depression. Questionnaire II, covering rates of physician visits, and use of GI medication, was sent to subjects fulfilling Manning 2 or Rome II IBS criteria in Questionnaire I. Results: The response rate was 73% and 86% for questionnaires I and II. The prevalence of IBS was 15.9%, 9.6%, 5.6%, and 5.1% according to Manning 2, Manning 3, Rome I, and Rome II criteria. Of those meeting Rome II criteria, 97% also met Manning 2 criteria. Presence of severe abdominal pain was more often reported by subjects meeting either of the Rome criteria than those meeting either of the Manning criteria. Presence of depression, anxiety, and several somatic symptoms was more common among subjects meeting any IBS criterion than by controls. Of subjects with depressive symptoms, 11.6% met Rome II IBS criteria compared to 3.7% of those with no depressiveness. Subjects meeting any IBS criteria made more physician visits than controls. Intensity of GI symptoms and presence of dyspeptic symptoms were the strongest predictors of GI consultations. Presence of dyspeptic symptoms and a history of abdominal pain in childhood also predicted non-GI visits. Annual GI related individual costs were higher in the Rome II group (497 ) than in the Manning 2 group (295 ). Direct expenses of GI symptoms and non GI physician visits ranged between 98M for Rome II and 230M for Manning 2 criteria. Conclusions: The prevalence of IBS varies substantially depending on the criteria applied. Rome II criteria are more restrictive than Manning 2, and they identify an IBS population with more severe GI symptoms, more frequent health care use, and higher individual health care costs. Subjects with IBS demonstrate high rates of psychiatric and somatic comorbidity regardless of health care seeking status. Perceived symptom severity rather than psychiatric comorbidity predicts health care seeking for GI symptoms. IBS incurs considerable medical costs. The direct GI and non-GI costs are equivalent to up to 5% of outpatient health care and medicine costs in Finland. A more integral approach to IBS by physicians, accounting also for comorbid conditions, may produce a more favourable course in IBS patients and reduce health care expenditures.

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The cosmological observations of light from type Ia supernovae, the cosmic microwave background and the galaxy distribution seem to indicate that the expansion of the universe has accelerated during the latter half of its age. Within standard cosmology, this is ascribed to dark energy, a uniform fluid with large negative pressure that gives rise to repulsive gravity but also entails serious theoretical problems. Understanding the physical origin of the perceived accelerated expansion has been described as one of the greatest challenges in theoretical physics today. In this thesis, we discuss the possibility that, instead of dark energy, the acceleration would be caused by an effect of the nonlinear structure formation on light, ignored in the standard cosmology. A physical interpretation of the effect goes as follows: due to the clustering of the initially smooth matter with time as filaments of opaque galaxies, the regions where the detectable light travels get emptier and emptier relative to the average. As the developing voids begin to expand the faster the lower their matter density becomes, the expansion can then accelerate along our line of sight without local acceleration, potentially obviating the need for the mysterious dark energy. In addition to offering a natural physical interpretation to the acceleration, we have further shown that an inhomogeneous model is able to match the main cosmological observations without dark energy, resulting in a concordant picture of the universe with 90% dark matter, 10% baryonic matter and 15 billion years as the age of the universe. The model also provides a smart solution to the coincidence problem: if induced by the voids, the onset of the perceived acceleration naturally coincides with the formation of the voids. Additional future tests include quantitative predictions for angular deviations and a theoretical derivation of the model to reduce the required phenomenology. A spin-off of the research is a physical classification of the cosmic inhomogeneities according to how they could induce accelerated expansion along our line of sight. We have identified three physically distinct mechanisms: global acceleration due to spatial variations in the expansion rate, faster local expansion rate due to a large local void and biased light propagation through voids that expand faster than the average. A general conclusion is that the physical properties crucial to account for the perceived acceleration are the growth of the inhomogeneities and the inhomogeneities in the expansion rate. The existence of these properties in the real universe is supported by both observational data and theoretical calculations. However, better data and more sophisticated theoretical models are required to vindicate or disprove the conjecture that the inhomogeneities are responsible for the acceleration.

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A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.

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Black hole X-ray binaries, binary systems where matter from a companion star is accreted by a stellar mass black hole, thereby releasing enormous amounts of gravitational energy converted into radiation, are seen as strong X-ray sources in the sky. As a black hole can only be detected via its interaction with its surroundings, these binary systems provide important evidence for the existence of black holes. There are now at least twenty cases where the measured mass of the X-ray emitting compact object in a binary exceeds the upper limit for a neutron star, thus inferring the presence of a black hole. These binary systems serve as excellent laboratories not only to study the physics of accretion but also to test predictions of general relativity in strongly curved space time. An understanding of the accretion flow onto these, the most compact objects in our Universe, is therefore of great importance to physics. We are only now slowly beginning to understand the spectra and variability observed in these X-ray sources. During the last decade, a framework has developed that provides an interpretation of the spectral evolution as a function of changes in the physics and geometry of the accretion flow driven by a variable accretion rate. This doctoral thesis presents studies of two black hole binary systems, Cygnus~X-1 and GRS~1915+105, plus the possible black hole candidate Cygnus~X-3, and the results from an attempt to interpret their observed properties within this emerging framework. The main result presented in this thesis is an interpretation of the spectral variability in the enigmatic source Cygnus~X-3, including the nature and accretion geometry of its so-called hard spectral state. The results suggest that the compact object in this source, which has not been uniquely identified as a black hole on the basis of standard mass measurements, is most probably a massive, ~30 Msun, black hole, and thus the most massive black hole observed in a binary in our Galaxy so far. In addition, results concerning a possible observation of limit-cycle variability in the microquasar GRS~1915+105 are presented as well as evidence of `mini-hysteresis' in the extreme hard state of Cygnus X-1.

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Acceleration of the universe has been established but not explained. During the past few years precise cosmological experiments have confirmed the standard big bang scenario of a flat universe undergoing an inflationary expansion in its earliest stages, where the perturbations are generated that eventually form into galaxies and other structure in matter, most of which is non-baryonic dark matter. Curiously, the universe has presently entered into another period of acceleration. Such a result is inferred from observations of extra-galactic supernovae and is independently supported by the cosmic microwave background radiation and large scale structure data. It seems there is a positive cosmological constant speeding up the universal expansion of space. Then the vacuum energy density the constant describes should be about a dozen times the present energy density in visible matter, but particle physics scales are enormously larger than that. This is the cosmological constant problem, perhaps the greatest mystery of contemporary cosmology. In this thesis we will explore alternative agents of the acceleration. Generically, such are called dark energy. If some symmetry turns off vacuum energy, its value is not a problem but one needs some dark energy. Such could be a scalar field dynamically evolving in its potential, or some other exotic constituent exhibiting negative pressure. Another option is to assume that gravity at cosmological scales is not well described by general relativity. In a modified theory of gravity one might find the expansion rate increasing in a universe filled by just dark matter and baryons. Such possibilities are taken here under investigation. The main goal is to uncover observational consequences of different models of dark energy, the emphasis being on their implications for the formation of large-scale structure of the universe. Possible properties of dark energy are investigated using phenomenological paramaterizations, but several specific models are also considered in detail. Difficulties in unifying dark matter and dark energy into a single concept are pointed out. Considerable attention is on modifications of gravity resulting in second order field equations. It is shown that in a general class of such models the viable ones represent effectively the cosmological constant, while from another class one might find interesting modifications of the standard cosmological scenario yet allowed by observations. The thesis consists of seven research papers preceded by an introductory discussion.

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Koskenniemen Äärellistilaisen leikkauskieliopin (FSIG) lauseopilliset rajoitteet ovat loogisesti vähemmän kompleksisia kuin mihin niissä käytetty formalismi vittaisi. Osoittautuukin että vaikka Voutilaisen (1994) englannin kielelle laatima FSIG-kuvaus käyttää useita säännöllisten lausekkeiden laajennuksia, kieliopin kuvaus kokonaisuutenaan palautuu äärelliseen yhdistelmään unionia, komplementtia ja peräkkäinasettelua. Tämä on oleellinen parannus ENGFSIG:n descriptiiviseen kompleksisuuteen. Tulos avaa ovia FSIG-kuvauksen loogisten ominaisuuksien syvemmälle analyysille ja FSIG kuvausten mahdolliselle optimoinnillle. Todistus sisältää uuden kaavan, joka kääntää Koskenniemien rajoiteoperaation ilman markkerimerkkejä.