DNA-based detection and characterisation of strictly anaerobic beer-spoilage bacteria

Megasphaera cerevisiae, Pectinatus cerevisiiphilus, Pectinatus frisingensis, Selenomonas lacticifex, Zymophilus paucivorans and Zymophilus raffinosivorans are strictly anaerobic Gram-stain-negative bacteria that are able to spoil beer by producing off-flavours and turbidity. They have only been isolated from the beer production chain. The species are phylogenetically affiliated to the Sporomusa sub-branch in the class "Clostridia". Routine cultivation methods for detection of strictly anaerobic bacteria in breweries are time-consuming and do not allow species identification. The main aim of this study was to utilise DNA-based techniques in order to improve detection and identification of the Sporomusa sub-branch beer-spoilage bacteria and to increase understanding of their biodiversity, evolution and natural sources. Practical PCR-based assays were developed for monitoring of M. cerevisiae, Pectinatus species and the group of Sporomusa sub-branch beer spoilers throughout the beer production process. The developed assays reliably differentiated the target bacteria from other brewery-related microbes. The contaminant detection in process samples (10 1,000 cfu/ml) could be accomplished in 2 8 h. Low levels of viable cells in finished beer (≤10 cfu/100 ml) were usually detected after 1 3 d culture enrichment. Time saving compared to cultivation methods was up to 6 d. Based on a polyphasic approach, this study revealed the existence of three new anaerobic spoilage species in the beer production chain, i.e. Megasphaera paucivorans, Megasphaera sueciensis and Pectinatus haikarae. The description of these species enabled establishment of phenotypic and DNA-based methods for their detection and identification. The 16S rRNA gene based phylogenetic analysis of the Sporomusa sub-branch showed that the genus Selenomonas originates from several ancestors and will require reclassification. Moreover, Z. paucivorans and Z. raffinosivorans were found to be in fact members of the genus Propionispira. This relationship implies that they were carried to breweries along with plant material. The brewery-related Megasphaera species formed a distinct sub-group that did not include any sequences from other sources, suggesting that M. cerevisiae, M. paucivorans and M. sueciensis may be uniquely adapted to the brewery ecosystem. M. cerevisiae was also shown to exhibit remarkable resistance against many brewery-related stress conditions. This may partly explain why it is a brewery contaminant. This study showed that DNA-based techniques provide useful tools for obtaining more rapid and specific information about the presence and identity of the strictly anaerobic spoilage bacteria in the beer production chain than is possible using cultivation methods. This should ensure financial benefits to the industry and better product quality to customers. In addition, DNA-based analyses provided new insight into the biodiversity as well as natural sources and relations of the Sporomusa sub-branch bacteria. The data can be exploited for taxonomic classification of these bacteria and for surveillance and control of contaminations.

But if you desire God and His Messenger : The concept of choice in Sahih al-Bukhari

The aim of this dissertation is to discuss the concept of choice in the most important collection of Islamic traditions, Sahih al-Bukhari. The author of the collection, Muhammad ibn Isma'il al-Bukhari, lived between 810-870. My starting point is the collection of texts as it is now in its normative, established form. I read the hadiths as pieces of reality, not as statements about reality. The historicity of the texts has no role at all in my analysis. Part I sketches out the hagiography of the life and work of the author and provides a short history of the development of hadith literature and the processes of collecting and classifying the texts are discussed briefly. Part one ends with the presentation of my way of using rhetorical analysis as a methodological tool. Part II introduces my analysis of the concept of choice. It is divided into ten chapters, each concentrating on one hadith cluster. Part II ends with a discussion of the philosophy of free will and predestination in early Islam. Hadith literature is often considered as a representative of predestinarian theology compared to the Qur'an which emphasises the reponsibility of people of their own acts. In my conclusions I suggest that accoding to the texts in Sahih al-Bukhari, people do deal with real choices in their lives. The collection includes both strictly predestinarian texts but it also compises texts which claim that people are demanded to make real choices, even choices concerning life and death.

Käsitteellisestä ruumiilliseen, sitaatiosta paikkaan - maalaustaide ja nykytaiteen historia

The dissertation "From Conceptual to Corporeal, from Quotation to Site: Painting and History of Contemporary Art" explores the state of painting in contemporary art and art theory since the 1960s. The purpose of the study is to re-consider the dominant "end of painting" -narrative in contemporary art history, which goes back to the modernist ideology of painting as a reductive, medium-specific form of art. Drawing on Michel Foucault´s concepts of discursive formation and archive, as well as Jean-Luc Nancy´s post-phenomenological philosophy on corporeality, I suggest that contemporary painting can be redefined as a discursive-sensuous practice. Instead of seeing painting as obsolete or over as an avantgarde art genre, I show that there have been alternative, neo-avantgardist ways of defining painting since the end of the 1960s, such as French artist Daniel Buren´s early writings on painting as "theoretical practice". Consequently, the tendency of the canonical Anglo-American contemporary art narratives to underestimate the historical and institutional codes of art can be questioned. This tendency can be seen, for example, in Rosalind Krauss´s influential theory on index. The study also reflects the relations between conceptual art and painting since the 1960s and maps recent theories of painting, which re-examine the genre´s possibilities after the modernist rhetoric. Concepts of "flatbed", "painting in the extended field", "as painting" and so on are compared critically with the idea of painting as discursive practice. It is also shown that the issues in painting arise from the contemporary critical art debate while the dematerialisation paradigm of conceptual art has dissolved. The study focuses on the corporeal-material-sensuous -cluster of meanings attached to painting and searches for its avantgardist possibilities as redefined by postfeminist and post-phenomenological discourse. The ideas of hierarchy of the senses and synesthesia are developed within the framework of Jean-Luc Nancy´s and Luce Irigaray´s thought. The parameters for the study have been Finnish painting from 1990 to 2002. On the Finnish art scene there has been no "end of painting" ideology, strictly speaking. The mythology and medium-specificity of modernism have been deconstructed since the mid-1980s, but "the archive" of painting, like themes of abstraction, formalism and synesthesia have been re-worked by the discursive practice of painting, for example, in the works of Nina Roos, Tarja Pitkänen-Walter and Jussi Niva.

Kirjan tie lukijalle : Kirjakauppojen vakiintuminen Suomessa 1740 - 1860

Books Paths to Readers describes the history of the origins and consolidation of modern and open book stores in Finland 1740 1860. The thesis approaches the book trade as a part of a print culture. Instead of literary studies choice to concentrate on texts and writers, book history seeks to describe the print culture of a society and how the literary activities and societies interconnect. For book historians, printed works are creations of various individuals and groups: writers, printers, editors, book sellers, censors, critics and finally, readers. They all take part in the creation, delivery and interpretation of printed works. The study reveals the ways selling and distributing books have influenced the printed works and the literary and print culture. The research period 1740 1860 covers the so-called second revolution of the book, or the modernisation of the print culture. The thesis describes the history of 60 book stores and their 96 owners. The study concentrates on three themes: firstly, how the particular book trade network became a central institution for printed works distribution, secondly what were the relations between cosmopolitan European book markets and the national cultural sphere, and thirdly how book stores functioned as cultural institutions and business enterprises. Book stores that have a varied assortment and are targeted to all readers became the main institution for book trade in Finland during 1740 1860. It happened because of three features. First, the book binders monopoly on selling bound copies in Sweden was abolished in 1740s. As a consequence entrepreneurs could concentrate solely to trade activities and offer copies from various publishers at their stores. Secondly the common business model of bartering was replaced by selling copies for cash, first in the German book trade centre Leipzig in 1770s. The change intensified book markets activities and Finnish book stores foreign connections. Thirdly, after Finland was annexed to the Russian empire in 1809, the Grand duchy s administration steered foreign book trade to book stores (because of censorship demands). Up to 1830 s book stores were available only in Helsinki and Turku. During next ten years book stores opened in six regional centres. The early entrepreneurs ran usually vertical businesses consisting of printing, publishing and distribution activities. This strategy lowered costs, eased the delivery of printed works and helped to create elaborated centres for all book activities. These book stores main clientele consisted of the Swedish speaking gentry. During late 1840s various opinion leaders called for the development of a national Finnish print culture, and also book stores. As a result, during the five years before the beginning of the Crimean war (1853 1856) book stores were opened in almost all Finnish towns: at the beginning of the war 36 book stores operated in 21 towns. The later book sellers, mainly functioning in small towns among Finnish speaking people, settled usually strictly for selling activities. Book stores received most of their revenues from selling foreign titles. Swedish, German, French and Belgian (pirate editions of popular French novels) books were widely available for the multilingual gentry. Foreign titles and copies brought in most of the revenues. Censorship inspections or unfavourable custom fees would not limit the imports. Even if the local Finnish print production steadily rose, many copies, even titles, were never delivered via book stores. Only during the 1840 s and 1850 s the most advanced publishers would concentrate on creating publishing programmes and delivering their titles via book stores. Book sellers regulated commissions were small. They got even smaller because of large amounts of unsold copies, various and usual misunderstandings of consignments and accounts or plain accidents that destroyed shipments and warehouses. Also, the cultural aim of a creating large and assortments and the tendency of short selling periods demanded professional entrepreneurship, which many small town book sellers however lacked. In the midst of troublesome business efforts, co-operation and mutual concern of the book market s entrepreneurs were the key elements of the trade, although on local level book sellers would compete, sometimes even ferociously. The difficult circumstances (new censorship decree of 1850, Crimean war) and lack of entrepreneurship, experience and customers meant that half of the book stores opened in 1845 1860 was shut in less than five years. In 1858 the few leading publishers established The Finnish Book Publishers Association. Its first task was to create new business rules and manners for the book trade. The association s activities began to professionalise the whole network, but at the same time the earlier independence of regional publishing and selling enterprises diminished greatly. The consolidation of modern and open book store network in Finland is a history of a slow and complex development without clear signs of a beginning or an end. The ideal book store model was rarely accomplished in its all features. Nevertheless, book stores became the norm of the book trade. They managed to offer larger selections, reached larger clienteles and maintained constant activity better than any other book distribution model. In essential, the book stores methods have not changed up to present times.

Molecular Mechanisms of Androgen Receptor Interactions

The androgen receptor (AR) mediates the effects of the male sex-steroid hormones (androgens), testosterone and 5?-dihydrotestosterone. Androgens are critical in the development and maintenance of male sexual characteristics. AR is a member of the steroid receptor ligand-inducible transcription factor family. The steroid receptor family is a subgroup of the nuclear receptor superfamily that also includes receptors for the active forms of vitamin A, vitamin D3, and thyroid hormones. Like all nuclear receptors, AR has a conserved modular structure consisting of a non-conserved amino-terminal domain (NTD), containing the intrinsic activation function 1, a highly conserved DNA-binding domain, and a conserved ligand-binding domain (LBD) that harbors the activation function 2. Each of these domains plays an important role in receptor function and signaling, either via intra- and inter-receptor interactions, interactions with specific DNA sequences, termed hormone response elements, or via functional interactions with domain-specific proteins, termed coregulators (coactivators and corepressors). Upon binding androgens, AR acquires a new conformational state, translocates to the nucleus, binds to androgen response elements, homodimerizes and recruits sequence-specific coregulatory factors and the basal transcription machinery. This set of events is required to activate gene transcription (expression). Gene transcription is a strictly modulated process that governs cell growth, cell homeostasis, cell function and cell death. Disruptions of AR transcriptional activity caused by receptor mutations and/or altered coregulator interactions are linked to a wide spectrum of androgen insensitivity syndromes, and to the pathogenesis of prostate cancer (CaP). The treatment of CaP usually involves androgen depletion therapy (ADT). ADT achieves significant clinical responses during the early stages of the disease. However, under the selective pressure of androgen withdrawal, androgen-dependent CaP can progress to an androgen-independent CaP. Androgen-independent CaP is invariably a more aggressive and untreatable form of the disease. Advancing our understanding of the molecular mechanisms behind the switch in androgen-dependency would improve our success of treating CaP and other AR related illnesses. This study evaluates how clinically identified AR mutations affect the receptor s transcriptional activity. We reveal that a potential molecular abnormality in androgen insensitivity syndrome and CaP patients is caused by disruptions of the important intra-receptor NTD/LBD interaction. We demonstrate that the same AR LBD mutations can also disrupt the recruitment of the p160 coactivator protein GRIP1. Our investigations reveal that 30% of patients with advanced, untreated local CaP have somatic mutations that may lead to increases in AR activity. We report that somatic mutations that activate AR may lead to early relapse in ADT. Our results demonstrate that the types of ADT a CaP patient receives may cause a clustering of mutations to a particular region of the receptor. Furthermore, the mutations that arise before and during ADT do not always result in a receptor that is more active, indicating that coregulator interactions play a pivotal role in the progression of androgen-independent CaP. To improve CaP therapy, it is necessary to identify critical coregulators of AR. We screened a HeLa cell cDNA library and identified small carboxyl-terminal domain phosphatase 2 (SCP2). SCP2 is a protein phosphatase that directly interacts with the AR NTD and represses AR activity. We demonstrated that reducing the endogenous cellular levels of SCP2 causes more AR to load on to the prostate specific antigen (PSA) gene promoter and enhancer regions. Additionally, under the same conditions, more RNA polymerase II was recruited to the PSA promoter region and overall there was an increase in androgen-dependent transcription of the PSA gene, revealing that SCP2 could play a role in the pathogenesis of CaP.

Regulation of tumor suppressor protein p53 in cellular stress and tumorigenesis

Functional loss of tumor suppressor protein p53 is a common feature in diverse human cancers. The ability of this protein to sense cellular damage and halt the progression of the cell cycle or direct the cells to apoptosis is essential in preventing tumorigenesis. Tumors having wild-type p53 also respond better to current chemotherapies. The loss of p53 function may arise from TP53 mutations or dysregulation of factors controlling its levels and activity. Probably the most significant inhibitor of p53 function is Mdm2, a protein mediating its degradation and inactivation. Clearly, the maintenance of a strictly controlled p53-Mdm2 route is of great importance in preventing neoplastic transformation. Moreover, impairing Mdm2 function could be a nongenotoxic way to increase p53 levels and activity. Understanding the precise molecular mechanisms behind p53-Mdm2 relationship is thus essential from a therapeutic point of view. The aim of this thesis study was to discover factors affecting the negative regulation of p53 by Mdm2, causing activation of p53 in stressed cells. As a model of cellular damage, we used UVC radiation, inducing a complex cellular stress pathway. Exposure to UVC, as well as to several chemotherapeutic drugs, causes robust transcriptional stress in the cells and leads to activation of p53. By using this model of cellular stress, our goal was to understand how and by which proteins p53 is regulated. Furthermore, we wanted to address whether these pathways affecting p53 function could be altered in human cancers. In the study, two different p53 pathway proteins, nucleophosmin (NPM) and promyelocytic leukemia protein (PML), were found to participate in the p53 stress response following UV stress. Subcellular translocations of these proteins were discovered rapidly after exposure to UV. The alterations in the cellular localizations were connected to transient interactions with p53 and Mdm2, implicating their significance in the regulation of p53 stress response. NPM was shown to control Mdm2-p53 interface and mediate p53 stabilization by blocking the ability of Mdm2 to promote p53 degradation. Furthermore, NPM mediated p53 stabilization upon viral insult. We further detected a connection between cellular pathways of NPM and PML, as PML was found to associate with NPM in UV-radiated cells. The observed temporal UV-induced interactions strongly imply existence of a multiprotein complex participating in the p53 response. In addition, PML controlled the UV response of NPM, its localization and complex formation with chromatin associated factors. The relevance of the UV-promoted interactions was demonstrated in studies in a human leukemia cell line, being under abnormal transcriptional repression due to expression of oncogenic PML-RARa fusion protein. Reversing the leukemic phenotype with a therapeutically significant drug was associated with similar complex formation between p53 and its partners as following UV. In conclusion, this thesis study identifies novel p53 pathway interactions associated with the recovery from UV-promoted as well as oncogenic transcriptional repression.

Characterization of the TRIM37 gene and mutations underlying mulibrey nanism

Mulibrey nanism is a hereditary developmental disorder, characterized by prenatal onset growth failure without postnatal catch-up growth, distinctive craniofacial features, progressive cardiopathy and failure of sexual maturation. In addition, the patients develop insulin resistance syndrome and type 2 diabetes and they have an increased risk of developing tumors. The TRIM37 gene that underlies mulibrey nanism encodes for a member of the tripartite motif (TRIM) protein family. The physiological function of TRIM37 and the pathogenetic mechanisms leading from TRIM37 dysfunction to the mulibrey nanism phenotype are unknown. However, TRIM37 localizes at least partially to peroxisomes, and possesses ubiquitin E3-ligase activity. Thus, it may mediate ubiquitin dependent protein degradation, suggesting that accumulation of yet unknown substrate proteins may underlie the disease pathogenesis. In this study, the TRIM37 gene was characterized in detail. A transcription initiation window, with several separate transcription start sites, was identified and the putative promoter region immediately upstream from the transcription initiation window was shown to possess basal promoter activity. Further, several alternative splice variants of the gene were identified, including a highly expressed testis specific variant, encoding for an identical protein product with the main transcript. Expression of TRIM37 mRNA was detected in several different tissues, with highest expression seen in testis and in brain, when the expression patterns of the two major transcripts in different human tissues were studied by quantitative real-time PCR. Several mulibrey nanism patients were studied and thirteen novel mutations in TRIM37 were found, including three mutations (p.Gly322Val, p.Cys109Ser, p.Glu271_Ser287), that are likely to express mutant TRIM37 proteins. These mutations were further shown to alter the subcellular localization of the mutant proteins. Most of the mulibrey nanism associated mutations however, lead to premature termination codons and degradation of mRNA. All the TRIM37 mutations identified to date predict loss-of-function alleles, and thus no phenotype-genotype correlation is seen among the patients. In order to understand the pathogenetic mechanisms underlying mulibrey nanism, an animal model for the disorder is needed. For the development of a Trim37 knock-out mouse, the mouse Trim37 gene was characterized. Alternative splice variants, were identified, including a testis specific variant predicting a longer protein product. Further, a strictly tissue and cell-specific pattern of Trim37 expression was observed in developing and adult mouse tissues, when studied by immunohistochemical methods. This distribution of Trim37 expression in mouse tissues is in agreement with the clinical findings in human mulibrey nanism patients. This thesis work gives new tools for the diagnostics of mulibrey nanism as well as for studying the molecular pathogenesis behind this interesting disorder.

Technicolor

In technicolor theories the scalar sector of the Standard Model is replaced by a strongly interacting sector. Although the Standard Model has been exceptionally successful, the scalar sector causes theoretical problems that make these theories seem an attractive alternative. I begin my thesis by considering QCD, which is the known example of strong interactions. The theory exhibits two phenomena: confinement and chiral symmetry breaking. I find the low-energy dynamics to be similar to that of the sigma models. Then I analyze the problems of the Standard Model Higgs sector, mainly the unnaturalness and triviality. Motivated by the example of QCD, I introduce the minimal technicolor model to resolve these problems. I demonstrate the minimal model to be free of anomalies and then deduce the main elements of its low-energy particle spectrum. I find the particle spectrum contains massless or very light technipions, and also technibaryons and techni-vector mesons with a high mass of over 1 TeV. Standard Model fermions remain strictly massless at this stage. Thus I introduce the technicolor companion theory of flavor, called extended technicolor. I show that the Standard Model fermions and technihadrons receive masses, but that they remain too light. I also discuss flavor-changing neutral currents and precision electroweak measurements. I then show that walking technicolor models partly solve these problems. In these models, contrary to QCD, the coupling evolves slowly over a large energy scale. This behavior adds to the masses so that even the light technihadrons are too heavy to be detected at current particle accelerators. Also all observed masses of the Standard Model particles can be generated, except for the bottom and top quarks. Thus it is shown in this thesis that, excluding the masses of third generation quarks, theories based on walking technicolor can in principle produce the observed particle spectrum.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

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

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

Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.