Titanium Complexes for the Polymerisation of Ethene and Caprolactone

The literature part of the thesis mainly reviews the results of the use of titanium catalysts for ethene and caprolactone polymerisation. The behaviour of titanium catalysts bearing phenoxy-imino ligands has been the focus of more detailed investigations in ethene polymerisation. Reasons for the production of multimodal polyethene for a range of catalysts are also given. The experimental part of the thesis is divided into two sections based on the monomers used in the polymerisations: Part A (ethene) and part B (caprolactone). Part A: Titanium(IV) complexes bearing phenoxy-imino ligands are known to possess high ethene polymerisation activities after MAO activation. Depending on the ligand, the activities of the catalysts in polymerisation can vary between 1 and 44000 kgPE/(mol*cat*h*bar). Depending on the polymerisation temperature and the electronic and steric properties of the catalyst ligands, low to high molar mass values and uni- and multimodal polydispersity values can been observed. In order to discover the reasons for these differences, 22 titanium(IV) complexes containing differently substituted phenoxy-imino derivatives as di- and tetradentate ligands were synthesised with high yields and used as homogeneous catalysts in ethene polymerisations. Computational methods were used to predict the geometry of the synthesised complexes and their configuration after activation. Based on the results obtained, the geometry of the catalyst together with the ligand substituents seem to play a major role in defining the catalytic activity. Novel titanium(IV) complexes bearing malonate ligands were also synthesised. Malonates are considered to be suitable ligand pre-cursors since they can be produced by the simple reaction of any primary or secondary alcohol with malonylchloride, and thus they are easily modifiable. After treatment with MAO these complexes had polymerisation activities between 10 and 50 kgPE/(mol*cat*h*bar) and surprisingly low polydispersity values when compared with similar types of catalysts bearing the O?O chelate ligand. Part B: One of the synthesis routes in the preparation of the above mentioned phenoxy-imino titanium dichloride complexes involved the use of Ti(NMe2)4 with a range of salicylaldimine type compounds. On reaction, these two compounds formed an intermediate product selectively and quantitatively which was active in the ring-opening polymerisation of caprolactone. Several mono-anionic alcoholates were also combined with Ti(NMe2)4 in different molar ratios and used as catalysts. Full conversion of the monomer was achieved within 15 minutes with catalysts having a co-ordination number of 4 while after 22 hours full conversion was achieved with catalysts having a co-ordination number of 6.

Tailoring polyolefin properties by metallocene catalysis

This doctoral thesis deals with the syntheses of olefin homo- and copolymers using different kind of metallocene catalyst. Ethene, propene, 1-hexene, 1-hexadecene, vinylcyclohexane and phenylnorbornene were homo- or copolymerized with the catalysts. The unbridged benzyl substituted zirconium dichloride catalysts (1-4), ansa- bridged acenaphtyl substituted zirconium dichloride catalysts, ( 5, 6), rac- and meso-ethylene-bis(1-indenyl)zirconium dichlorides, (rac- and meso-8), rac-ethylene-bis(1-indenyl)hafnium dichloride, ( 12), bis(9-fluorenyl)hafnium dichloride (14 ) enantiomerically pure (R)- phenylethyl[(9-fluorenyl-1-indenyl)]ZrCl2, (11), 14 and asymmetric dimethylsilyl[(3-benzylindenyl-(2-methylbenzen[e]indenyl)] zirconium dichloride, (13), were prepared in our laboratory. Dimethylsilyl-bis(1-indenyl)zirconium dichloride, (9), isopropylidene(9-fluorenyl-cyclopentadienyl)zirconium dichloride, (10), and were obtained commercially. The solid-state structures of the catalysts rac- and meso-1 were determined by X-ray crystallography. Computational methods were used for the structure optimization of the catalyst rac- and meso-1 in order to compare the theoretical calculations with the experimental results. Polymerization experiments were conducted in a highly purified autoclave system using low pressures (< 5 bar) of gaseous monomers. The experiments were designed to attain the optimal catalytic activity and a uniform copolymer composition. The prepared homo- and copolymers were characterized by the gel permeation chromatography, GPC, differential scanning calorimetry, DSC, nuclear magnetic resonance, NMR, and Fourier transform infrared spectrometry, FTIR . Molar mass (Mw, Mn), molar mass distribution (Mw/Mn), tacticity, comonomer content, melting temperature, glass transition temperature, and end group structures and content were determined. A special attention was paid on the correlation of the polymer properties with the catalyst structures and polymerization conditions. An intramolecular phenyl coordination was found in phenyl substituted benzyl zirconocenes 1-3 explaining the decreased activity of the catalysts. Novel copolymers poly(propene-co-phenylnorbornene) and poly(propene co-vinylcyclohexane), were synthesized and high molar mass poly(ethene-co-1-hexene) and poly(ethene-co-1-hexadecene) copolymers with elastic properties were prepared. Activation of a hafnocene catalyst was studied with UV-Vis spectrometry and activation process for the synthesis of ultra high molar mass poly(1-hexene) was found out.

Algorithms for 13C metabolic flux analysis

The metabolism of an organism consists of a network of biochemical reactions that transform small molecules, or metabolites, into others in order to produce energy and building blocks for essential macromolecules. The goal of metabolic flux analysis is to uncover the rates, or the fluxes, of those biochemical reactions. In a steady state, the sum of the fluxes that produce an internal metabolite is equal to the sum of the fluxes that consume the same molecule. Thus the steady state imposes linear balance constraints to the fluxes. In general, the balance constraints imposed by the steady state are not sufficient to uncover all the fluxes of a metabolic network. The fluxes through cycles and alternative pathways between the same source and target metabolites remain unknown. More information about the fluxes can be obtained from isotopic labelling experiments, where a cell population is fed with labelled nutrients, such as glucose that contains 13C atoms. Labels are then transferred by biochemical reactions to other metabolites. The relative abundances of different labelling patterns in internal metabolites depend on the fluxes of pathways producing them. Thus, the relative abundances of different labelling patterns contain information about the fluxes that cannot be uncovered from the balance constraints derived from the steady state. The field of research that estimates the fluxes utilizing the measured constraints to the relative abundances of different labelling patterns induced by 13C labelled nutrients is called 13C metabolic flux analysis. There exist two approaches of 13C metabolic flux analysis. In the optimization approach, a non-linear optimization task, where candidate fluxes are iteratively generated until they fit to the measured abundances of different labelling patterns, is constructed. In the direct approach, linear balance constraints given by the steady state are augmented with linear constraints derived from the abundances of different labelling patterns of metabolites. Thus, mathematically involved non-linear optimization methods that can get stuck to the local optima can be avoided. On the other hand, the direct approach may require more measurement data than the optimization approach to obtain the same flux information. Furthermore, the optimization framework can easily be applied regardless of the labelling measurement technology and with all network topologies. In this thesis we present a formal computational framework for direct 13C metabolic flux analysis. The aim of our study is to construct as many linear constraints to the fluxes from the 13C labelling measurements using only computational methods that avoid non-linear techniques and are independent from the type of measurement data, the labelling of external nutrients and the topology of the metabolic network. The presented framework is the first representative of the direct approach for 13C metabolic flux analysis that is free from restricting assumptions made about these parameters.In our framework, measurement data is first propagated from the measured metabolites to other metabolites. The propagation is facilitated by the flow analysis of metabolite fragments in the network. Then new linear constraints to the fluxes are derived from the propagated data by applying the techniques of linear algebra.Based on the results of the fragment flow analysis, we also present an experiment planning method that selects sets of metabolites whose relative abundances of different labelling patterns are most useful for 13C metabolic flux analysis. Furthermore, we give computational tools to process raw 13C labelling data produced by tandem mass spectrometry to a form suitable for 13C metabolic flux analysis.

Maltose and maltotriose transport into ale and lager brewer's yeast strains

Maltose and maltotriose are the two most abundant sugars in brewer s wort, and thus brewer s yeast s ability to utilize them efficiently is of major importance in the brewing process. The increasing tendency to utilize high and very-high-gravity worts containing increased concentrations of maltose and maltotriose renders the need for efficient transport of these sugars even more pronounced. Residual maltose and especially maltotriose are quite often present especially after high and very-high-gravity fermentations. Sugar uptake capacity has been shown to be the rate limiting factor for maltose and maltotriose utilization. The main aim of the present study was to find novel ways to improve maltose and maltotriose utilization during the main fermentation. Maltose and maltotriose uptake characteristics of several ale and lager strains were studied. Genotype determination of the genes needed for maltose and maltotriose utilization was performed. Maltose uptake inhibition studies were performed to reveal the dominant transporter types actually functioning in each of the strains. Temperature-dependence of maltose transport was studied for ale and for lager strains as well as for each of the single sugar transporter proteins Agt1p, Malx1p and Mtt1p. The AGT1 promoter regions of one ale and two lager strains were sequenced by chromosome walking and the promoter elements were searched for using computational methods. The results showed that ale and lager strains predominantly use different maltose and maltotriose transporter types for maltose and maltotriose uptake. Agt1 transporter was found to be the dominant maltose/maltotriose transporter in the ale strains whereas Malx1 and Mtt1- type transporters dominated in the lager strains. All lager strains studied were found to possess a non-functional Agt1 transporter. The ale strains were observed to be more sensitive to temperature decrease in their maltose uptake compared to the lager strains. Single transporters were observed to differ in their sensitivity to temperature decrease and their temperature-dependence was shown to decrease in the order Agt1≥Malx1>Mtt1. The different temperature-dependence between the ale and lager strains was observed to be due to the different dominant maltose/maltotriose transporters ale and lager strains possessed. The AGT1 promoter regions of ale and lager strains were found to differ markedly from the corresponding regions of laboratory strains. The ale strain was found to possess an extra MAL-activator binding site compared to the lager strains. Improved maltose and maltotriose uptake capacity was obtained with a modified lager strain where the AGT1 gene was repaired and put under the control of a strong promoter. Modified strains fermented wort faster and more completely, producing beers containing more ethanol and less residual maltose and maltotriose. Significant savings in the main fermentation time were obtained when modified strains were used. In high-gravity wort fermentations 8 20% and in very-high-gravity wort fermentations even 11 37% time savings were obtained. These are economically significant changes and would cause a marked increase in annual output from the same-size of brewhouse and fermentor facilities.

Scattering and Refraction as Contrast Mechanisms in X-Ray Imaging

Differentiation of various types of soft tissues is of high importance in medical imaging, because changes in soft tissue structure are often associated with pathologies, such as cancer. However, the densities of different soft tissues may be very similar, making it difficult to distinguish them in absorption images. This is especially true when the consideration of patient dose limits the available signal-to-noise ratio. Refraction is more sensitive than absorption to changes in the density, and small angle x-ray scattering on the other hand contains information about the macromolecular structure of the tissues. Both of these can be used as potential sources of contrast when soft tissues are imaged, but little is known about the visibility of the signals in realistic imaging situations. In this work the visibility of small-angle scattering and refraction in the context of medical imaging has been studied using computational methods. The work focuses on the study of analyzer based imaging, where the information about the sample is recorded in the rocking curve of the analyzer crystal. Computational phantoms based on simple geometrical shapes with differing material properties are used. The objects have realistic dimensions and attenuation properties that could be encountered in real imaging situations. The scattering properties mimic various features of measured small-angle scattering curves. Ray-tracing methods are used to calculate the refraction and attenuation of the beam, and a scattering halo is accumulated, including the effect of multiple scattering. The changes in the shape of the rocking curve are analyzed with different methods, including diffraction enhanced imaging (DEI), extended DEI (E-DEI) and multiple image radiography (MIR). A wide angle DEI, called W-DEI, is introduced and its performance is compared with that of the established methods. The results indicate that the differences in scattered intensities from healthy and malignant breast tissues are distinguishable to some extent with reasonable dose. Especially the fraction of total scattering has large enough differences that it can serve as a useful source of contrast. The peaks related to the macromolecular structure come to angles that are rather large, and have intensities that are only a small fraction of the total scattered intensity. It is found that such peaks seem to have only limited usefulness in medical imaging. It is also found that W-DEI performs rather well when most of the intensity remains in the direct beam, indicating that dark field imaging methods may produce the best results when scattering is weak. Altogether, it is found that the analysis of scattered intensity is a viable option even in medical imaging where the patient dose is the limiting factor.

Dynamic nature of proteins - interpretation of residual dipolar couplings

Protein conformations and dynamics can be studied by nuclear magnetic resonance spectroscopy using dilute liquid crystalline samples. This work clarifies the interpretation of residual dipolar coupling data yielded by the experiments. It was discovered that unfolded proteins without any additional structure beyond that of a mere polypeptide chain exhibit residual dipolar couplings. Also, it was found that molecular dynamics induce fluctuations in the molecular alignment and doing so affect residual dipolar couplings. The finding clarified the origins of low order parameter values observed earlier. The work required the development of new analytical and computational methods for the prediction of intrinsic residual dipolar coupling profiles for unfolded proteins. The presented characteristic chain model is able to reproduce the general trend of experimental residual dipolar couplings for denatured proteins. The details of experimental residual dipolar coupling profiles are beyond the analytical model, but improvements are proposed to achieve greater accuracy. A computational method for rapid prediction of unfolded protein residual dipolar couplings was also developed. Protein dynamics were shown to modulate the effective molecular alignment in a dilute liquid crystalline medium. The effects were investigated from experimental and molecular dynamics generated conformational ensembles of folded proteins. It was noted that dynamics induced alignment is significant especially for the interpretation of molecular dynamics in small, globular proteins. A method of correction was presented. Residual dipolar couplings offer an attractive possibility for the direct observation of protein conformational preferences and dynamics. The presented models and methods of analysis provide significant advances in the interpretation of residual dipolar coupling data from proteins.

Multiscale study on hydrogen mobility in metallic fusion divertor material

For achieving efficient fusion energy production, the plasma-facing wall materials of the fusion reactor should ensure long time operation. In the next step fusion device, ITER, the first wall region facing the highest heat and particle load, i.e. the divertor area, will mainly consist of tiles based on tungsten. During the reactor operation, the tungsten material is slowly but inevitably saturated with tritium. Tritium is the relatively short-lived hydrogen isotope used in the fusion reaction. The amount of tritium retained in the wall materials should be minimized and its recycling back to the plasma must be unrestrained, otherwise it cannot be used for fueling the plasma. A very expensive and thus economically not viable solution is to replace the first walls quite often. A better solution is to heat the walls to temperatures where tritium is released. Unfortunately, the exact mechanisms of hydrogen release in tungsten are not known. In this thesis both experimental and computational methods have been used for studying the release and retention of hydrogen in tungsten. The experimental work consists of hydrogen implantations into pure polycrystalline tungsten, the determination of the hydrogen concentrations using ion beam analyses (IBA) and monitoring the out-diffused hydrogen gas with thermodesorption spectrometry (TDS) as the tungsten samples are heated at elevated temperatures. Combining IBA methods with TDS, the retained amount of hydrogen is obtained as well as the temperatures needed for the hydrogen release. With computational methods the hydrogen-defect interactions and implantation-induced irradiation damage can be examined at the atomic level. The method of multiscale modelling combines the results obtained from computational methodologies applicable at different length and time scales. Electron density functional theory calculations were used for determining the energetics of the elementary processes of hydrogen in tungsten, such as diffusivity and trapping to vacancies and surfaces. Results from the energetics of pure tungsten defects were used in the development of an classical bond-order potential for describing the tungsten defects to be used in molecular dynamics simulations. The developed potential was utilized in determination of the defect clustering and annihilation properties. These results were further employed in binary collision and rate theory calculations to determine the evolution of large defect clusters that trap hydrogen in the course of implantation. The computational results for the defect and trapped hydrogen concentrations were successfully compared with the experimental results. With the aforedescribed multiscale analysis the experimental results within this thesis and found in the literature were explained both quantitatively and qualitatively.

11β-Hydroxysteroid dehydrogenase inhibitors and selectivity modeling of 11β-HSDs

11β-hydroksisteroididehydrogenaasientsyymit (11β-HSD) 1 ja 2 säätelevät kortisonin ja kortisolin määrää kudoksissa. 11β-HSD1 -entsyymin ylimäärä erityisesti viskeraalisessa rasvakudoksessa aiheuttaa metaboliseen oireyhtymän klassisia oireita, mikä tarjoaa mahdollisuuden metabolisen oireyhtymän hoitoon 11β-HSD1 -entsyymin selektiivisellä estämisellä. 11β-HSD2 -entsyymin inhibitio aiheuttaa kortisonivälitteisen mineralokortikoidireseptorien aktivoitumisen, mikä puolestaan johtaa hypertensiivisiin haittavaikutuksiin. Haittavaikutuksista huolimatta 11β-HSD2 -entsyymin estäminen saattaa olla hyödyllistä tilanteissa, joissa halutaan nostaa kortisolin määrä elimistössä. Lukuisia selektiivisiä 11β-HSD1 inhibiittoreita on kehitetty, mutta 11β-HSD2-inhibiittoreita on raportoitu vähemmän. Ero näiden kahden isotsyymin aktiivisen kohdan välillä on myös tuntematon, mikä vaikeuttaa selektiivisten inhibiittoreiden kehittämistä kummallekin entsyymille. Tällä työllä oli kaksi tarkoitusta: (1) löytää ero 11β-HSD entsyymien välillä ja (2) kehittää farmakoforimalli, jota voitaisiin käyttää selektiivisten 11β-HSD2 -inhibiittoreiden virtuaaliseulontaan. Ongelmaa lähestyttiin tietokoneavusteisesti: homologimallinnuksella, pienmolekyylien telakoinnilla proteiiniin, ligandipohjaisella farmakoforimallinnuksella ja virtuaaliseulonnalla. Homologimallinnukseen käytettiin SwissModeler -ohjelmaa, ja luotu malli oli hyvin päällekäinaseteltavissa niin templaattinsa (17β-HSD1) kuin 11β-HSD1 -entsyymin kanssa. Eroa entsyymien välillä ei löytynyt tarkastelemalla päällekäinaseteltuja entsyymejä. Seitsemän yhdistettä, joista kuusi on 11β-HSD2 -selektiivisiä, telakoitiin molempiin entsyymeihin käyttäen ohjelmaa GOLD. 11β-HSD1 -entsyymiin yhdisteet kiinnittyivät kuten suurin osa 11β-HSD1 -selektiivisistä tai epäselektiivisistä inhibiittoreista, kun taas 11β-HSD2 -entsyymiin kaikki yhdisteet olivat telakoituneet käänteisesti. Tällainen sitoutumistapa mahdollistaa vetysidokset Ser310:een ja Asn171:een, aminohappoihin, jotka olivat nähtävissä vain 11β-HSD2 -entsyymissä. Farmakoforimallinnukseen käytettiin ohjelmaa LigandScout3.0, jolla ajettiin myös virtuaaliseulonnat. Luodut kaksi farmakoforimallia, jotka perustuivat aiemmin telakointiinkin käytettyihin kuuteen 11β-HSD2 -selektiiviseen yhdisteeseen, koostuivat kuudesta ominaisuudesta (vetysidosakseptori, vetysidosdonori ja hydrofobinen), ja kieltoalueista. 11β-HSD2 -selektiivisyyden kannalta tärkeimmät ominaisuudet ovat vetysidosakseptori, joka voi muodostaa sidoksen Ser310 kanssa ja vetysidosdonori sen vieressä. Tälle vetysidosdonorille ei löytynyt vuorovaikutusparia 11β-HSD2-mallista. Sopivasti proteiiniin orientoitunut vesimolekyyli voisi kuitenkin olla sopiva ratkaisu puuttuvalle vuorovaikutusparille. Koska molemmat farmakoforimallit löysivät 11β-HSD2 -selektiivisiä yhdisteitä ja jättivät epäselektiivisiä pois testiseulonnassa, käytettiin molempia malleja Innsbruckin yliopistossa säilytettävistä yhdisteistä (2700 kappaletta) koostetun tietokannan seulontaan. Molemmista seulonnoista löytyneistä hiteistä valittiin yhteensä kymmenen kappaletta, jotka lähetettiin biologisiin testeihin. Biologisien testien tulokset vahvistavat lopullisesti sen kuinka hyvin luodut mallit edustavat todellisuudessa 11β-HSD2 -selektiivisyyttä.

Characterization of Alloy-Spinel-Corundum Equilibrium in the System Fe-Ni-Al-O

The three phase equilibrium between alloy, spinel solid solution and α-alumina in the Fe-Ni-Al-O system has been fully characterized at 1823K as a function of alloy composition using both experimental and computational methods. The oxygen potential was measured using a solid state cell incorporating yttria-doped thoria as the electrolyte and Cr+ Cr2O3 as the reference electrode. Oxygen concentration of the alloy was determined by an inert gas fusion technique. The composition of the spinel solid solution, formed at the interface between the alloy and an alumina crucible, was determined by EPMA. The variation of the oxygen concentration and potential and composition of the spinel solid solution with mole fraction of nickel in the alloy have been computed using activities in binary Fe-Ni system, free energies of formation of end member spinels FeO•(1+x)Al2O3 and NiO•(1+x)Al2O3 and free energies of solution of oxygen in liquid iron and nickel, available in the literature. Activities in the spinel solid solution were computed using a cation distribution model. The variation of the activity coefficient of oxygen with alloy composition in Fe-Ni-O system was calculated using both the quasichemical model of Jacob and Alcock and the Wagner's model, with the correlation of Chiang and Chang. The computed results for the oxygen potential and the composition of the spinel solid solution are in good agreement with the measurements. The measured oxygen concentration lies between the values computed using models of Wagner and Jacob and Alcock. The results of the study indicate that the deoxidation hyper-surface in multicomponent systems can be computed with useful accuracy using data for end member systems and thermodynamic models.

Studies of the Human Transcriptome

Gene expression is one of the most critical factors influencing the phenotype of a cell. As a result of several technological advances, measuring gene expression levels has become one of the most common molecular biological measurements to study the behaviour of cells. The scientific community has produced enormous and constantly increasing collection of gene expression data from various human cells both from healthy and pathological conditions. However, while each of these studies is informative and enlighting in its own context and research setup, diverging methods and terminologies make it very challenging to integrate existing gene expression data to a more comprehensive view of human transcriptome function. On the other hand, bioinformatic science advances only through data integration and synthesis. The aim of this study was to develop biological and mathematical methods to overcome these challenges and to construct an integrated database of human transcriptome as well as to demonstrate its usage. Methods developed in this study can be divided in two distinct parts. First, the biological and medical annotation of the existing gene expression measurements needed to be encoded by systematic vocabularies. There was no single existing biomedical ontology or vocabulary suitable for this purpose. Thus, new annotation terminology was developed as a part of this work. Second part was to develop mathematical methods correcting the noise and systematic differences/errors in the data caused by various array generations. Additionally, there was a need to develop suitable computational methods for sample collection and archiving, unique sample identification, database structures, data retrieval and visualization. Bioinformatic methods were developed to analyze gene expression levels and putative functional associations of human genes by using the integrated gene expression data. Also a method to interpret individual gene expression profiles across all the healthy and pathological tissues of the reference database was developed. As a result of this work 9783 human gene expression samples measured by Affymetrix microarrays were integrated to form a unique human transcriptome resource GeneSapiens. This makes it possible to analyse expression levels of 17330 genes across 175 types of healthy and pathological human tissues. Application of this resource to interpret individual gene expression measurements allowed identification of tissue of origin with 92.0% accuracy among 44 healthy tissue types. Systematic analysis of transcriptional activity levels of 459 kinase genes was performed across 44 healthy and 55 pathological tissue types and a genome wide analysis of kinase gene co-expression networks was done. This analysis revealed biologically and medically interesting data on putative kinase gene functions in health and disease. Finally, we developed a method for alignment of gene expression profiles (AGEP) to perform analysis for individual patient samples to pinpoint gene- and pathway-specific changes in the test sample in relation to the reference transcriptome database. We also showed how large-scale gene expression data resources can be used to quantitatively characterize changes in the transcriptomic program of differentiating stem cells. Taken together, these studies indicate the power of systematic bioinformatic analyses to infer biological and medical insights from existing published datasets as well as to facilitate the interpretation of new molecular profiling data from individual patients.

Exact bounds for distributed graph colouring

A distributed system is a collection of networked autonomous processing units which must work in a cooperative manner. Currently, large-scale distributed systems, such as various telecommunication and computer networks, are abundant and used in a multitude of tasks. The field of distributed computing studies what can be computed efficiently in such systems. Distributed systems are usually modelled as graphs where nodes represent the processors and edges denote communication links between processors. This thesis concentrates on the computational complexity of the distributed graph colouring problem. The objective of the graph colouring problem is to assign a colour to each node in such a way that no two nodes connected by an edge share the same colour. In particular, it is often desirable to use only a small number of colours. This task is a fundamental symmetry-breaking primitive in various distributed algorithms. A graph that has been coloured in this manner using at most k different colours is said to be k-coloured. This work examines the synchronous message-passing model of distributed computation: every node runs the same algorithm, and the system operates in discrete synchronous communication rounds. During each round, a node can communicate with its neighbours and perform local computation. In this model, the time complexity of a problem is the number of synchronous communication rounds required to solve the problem. It is known that 3-colouring any k-coloured directed cycle requires at least ½(log* k - 3) communication rounds and is possible in ½(log* k + 7) communication rounds for all k ≥ 3. This work shows that for any k ≥ 3, colouring a k-coloured directed cycle with at most three colours is possible in ½(log* k + 3) rounds. In contrast, it is also shown that for some values of k, colouring a directed cycle with at most three colours requires at least ½(log* k + 1) communication rounds. Furthermore, in the case of directed rooted trees, reducing a k-colouring into a 3-colouring requires at least log* k + 1 rounds for some k and possible in log* k + 3 rounds for all k ≥ 3. The new positive and negative results are derived using computational methods, as the existence of distributed colouring algorithms corresponds to the colourability of so-called neighbourhood graphs. The colourability of these graphs is analysed using Boolean satisfiability (SAT) solvers. Finally, this thesis shows that similar methods are applicable in capturing the existence of distributed algorithms for other graph problems, such as the maximal matching problem.

Lower Gastrointestinal Microbiota in Health and Irritable Bowel Syndrome : Characterisation and Effect of Probiotic Intervention

The human gastrointestinal (GI) microbiota is a complex ecosystem that lives in symbiosis with its host. The growing awareness of the importance of the microbiota to the host as well as the development of culture-free laboratory techniques and computational methods has enormously expanded our knowledge of this microbial community. Irritable bowel syndrome (IBS) is a common functional bowel disorder affecting up to a fifth of the Western population. To date, IBS diagnosis has been based on GI symptoms and the exclusion of organic diseases. The GI microbiota has been found to be altered in this syndrome and probiotics can alleviate the symptoms, although clear links between the symptoms and the microbiota have not been demonstrated. The aim of the present work was to characterise IBS related alterations in the intestinal microbiota, their relation to IBS symptoms and their responsiveness to probiotic theraphy. In this thesis research, the healthy human microbiota was characterised by cloning and sequencing 16S rRNA genes from a faecal microbial community DNA pool that was first profiled and fractionated according to its guanine and cytosine content (%G+C). The most noticeable finding was that the high G+C Gram-positive bacteria (the phylum Actinobacteria) were more abundant compared to a corresponding library constructed from the unfractionated DNA pool sample. Previous molecular analyses of the gut microbiota have also shown comparatively low amounts of high G+C bacteria. Furthermore, the %G+C profiling approach was applied to a sample constructed of faecal DNA from diarrhea-predominant IBS (IBS-D) subjects. The phylogenetic microbial community comparison performed for healthy and IBS-D sequence libraries revealed that the IBS-D sample was rich in representatives of the phyla Firmicutes and Proteobacteria whereas Actinobacteria and Bacteroidetes were abundant in the healthy subjects. The family Lachnospiraceae within the Firmicutes was especially prevalent in the IBS-D sample. Moreover, associations of the GI microbiota with intestinal symptoms and the quality of life (QOL) were investigated, as well as the effect of probiotics on these factors. The microbial targets that were analysed with the quantitative real-time polymerase chain reaction (qPCR) in this study were phylotypes (species definition according to 16S rRNA gene sequence similarity) previously associated with either health or IBS. With a set of samples, the presence or abundance of a phylotype that had 94% 16S rRNA gene sequence similarity to Ruminococcus torques (R. torques 94%) was shown to be associated with the severity of IBS symptoms. The qPCR analyses for selected phylotypes were also applied to samples from a six-month probiotic intervention with a mixture of Lactobacillus rhamnosus GG, L. rhamnosus Lc705, Propionibacterium freudenreichii ssp. shermanii JS and Bifidobacterium breve Bb99. The intervention had been previously reported to alleviate IBS symptoms, but no associations with the analysed microbiota representatives were shown. However, with the phylotype-specific assays applied here, the abundance of the R. torques 94% -phylotype was shown to be lowered in the probiotic-receiving group during the probiotic supplementation, whereas a Clostridium thermosuccinogenes 85% phylotype, previously associated with a healthy microbiota, was found to be increased compared to the placebo group. To conclude, with the combination of methods applied, higher abundance of Actinobacteria was detected in the healthy gut than found in previous studies, and significant phylum-level microbiota alterations could be shown in IBS-D. Thus, the results of this study provide a detailed overview of the human GI microbiota in healthy subjects and in subjects with IBS. Furthermore, the IBS symptoms were linked to a particular clostridial phylotype, and probiotic supplementation was demonstrated to alter the GI microbiota towards a healthier state with regard to this and an additional bacterial phylotype. For the first time, distinct phylotype-level alterations in the microbiota were linked to IBS symptoms and shown to respond to probiotic therapy.

Multi-physics self-consistent modeling in nanotechnological applications: quantum dots and quantum-well lasers

This paper reports a self-consistent Poisson-Schr¨odinger scheme including the effects of the piezoelectricity, the spontaneous polarization and the charge density on the electronic states and the quasi-Fermi level energy in wurtzite type semiconductor heterojunction and quantum-laser.