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.

Sensemaking in the Third Space - Essays on French-Finnish Bicultural Experiences in Organizations and Their Narratives (summary section only)

Research on cross-cultural and intercultural aspects in organizations has been traditionally conducted from an objectivist, functionalist perspective, with culture treated as an independent variable, and often the key explanatory factor. In order to do justice to the ontological relativity of the phenomena studied, more subjectivist research on intercultural interactions, and especially on their relationships with the dynamics of cultural identity construction, is needed. The present research seeks to address this gap by focusing on bicultural interactions in organizations, as they are experienced by the involved individuals. It is argued that such bicultural situations see the emergence of a space of hybridity, which is here called a ‘third space’, and which can be understood as providing ‘occasions for sensemaking’: it is this individual sensemaking that is of particular interest in the empirical narrative study. A first overall aim of the study is to reach an understanding of the dynamics of bicultural interactions in organizations; an understanding not only of the potential for learning and emancipatory sensemaking, but also of the possibility of conflict and alienatory ordering (this is mainly addressed in the theoretical essays 1 and 2). Further, a second overall aim of the study is to analyze the reflexive identity construction of four young French expatriates involved in such bicultural interactions in organizations in Finland, in order to examine the extent to which their expatriation experiences have allowed for an emancipatory opportunity in their cases (in essays 3 and 4). The primary theoretical contribution in this study lies in its new articulation of the dynamics of bicultural interactions in organizations. The ways in which the empirical material is analyzed bring about methodological contributions: since the expatriates’ accounts are bound to be some kind of construction, the analysis is made from angles that point to how the self-narratives construct reality. There are two such angles here: a ‘performative’ one and a ‘spatial’ one. The most important empirical contributions lie in the analysis of, on the one hand, the alternative uses that the young expatriates made of the notion of ‘national culture’ in their self-narratives, and, on the other hand, their ‘narrative practices of the third space’: their politics of escape or stabilization, their exploration of space or search for place, their emancipation from their origin or return to home as only horizon.

Irradiation effects in graphene and related materials

Nanomaterials with a hexagonally ordered atomic structure, e.g., graphene, carbon and boron nitride nanotubes, and white graphene (a monolayer of hexagonal boron nitride) possess many impressive properties. For example, the mechanical stiffness and strength of these materials are unprecedented. Also, the extraordinary electronic properties of graphene and carbon nanotubes suggest that these materials may serve as building blocks of next generation electronics. However, the properties of pristine materials are not always what is needed in applications, but careful manipulation of their atomic structure, e.g., via particle irradiation can be used to tailor the properties. On the other hand, inadvertently introduced defects can deteriorate the useful properties of these materials in radiation hostile environments, such as outer space. In this thesis, defect production via energetic particle bombardment in the aforementioned materials is investigated. The effects of ion irradiation on multi-walled carbon and boron nitride nanotubes are studied experimentally by first conducting controlled irradiation treatments of the samples using an ion accelerator and subsequently characterizing the induced changes by transmission electron microscopy and Raman spectroscopy. The usefulness of the characterization methods is critically evaluated and a damage grading scale is proposed, based on transmission electron microscopy images. Theoretical predictions are made on defect production in graphene and white graphene under particle bombardment. A stochastic model based on first-principles molecular dynamics simulations is used together with electron irradiation experiments for understanding the formation of peculiar triangular defect structures in white graphene. An extensive set of classical molecular dynamics simulations is conducted, in order to study defect production under ion irradiation in graphene and white graphene. In the experimental studies the response of carbon and boron nitride multi-walled nanotubes to irradiation with a wide range of ion types, energies and fluences is explored. The stabilities of these structures under ion irradiation are investigated, as well as the issue of how the mechanism of energy transfer affects the irradiation-induced damage. An irradiation fluence of 5.5x10^15 ions/cm^2 with 40 keV Ar+ ions is established to be sufficient to amorphize a multi-walled nanotube. In the case of 350 keV He+ ion irradiation, where most of the energy transfer happens through inelastic collisions between the ion and the target electrons, an irradiation fluence of 1.4x10^17 ions/cm^2 heavily damages carbon nanotubes, whereas a larger irradiation fluence of 1.2x10^18 ions/cm^2 leaves a boron nitride nanotube in much better condition, indicating that carbon nanotubes might be more susceptible to damage via electronic excitations than their boron nitride counterparts. An elevated temperature was discovered to considerably reduce the accumulated damage created by energetic ions in both carbon and boron nitride nanotubes, attributed to enhanced defect mobility and efficient recombination at high temperatures. Additionally, cobalt nanorods encapsulated inside multi-walled carbon nanotubes were observed to transform into spherical nanoparticles after ion irradiation at an elevated temperature, which can be explained by the inverse Ostwald ripening effect. The simulation studies on ion irradiation of the hexagonal monolayers yielded quantitative estimates on types and abundances of defects produced within a large range of irradiation parameters. He, Ne, Ar, Kr, Xe, and Ga ions were considered in the simulations with kinetic energies ranging from 35 eV to 10 MeV, and the role of the angle of incidence of the ions was studied in detail. A stochastic model was developed for utilizing the large amount of data produced by the molecular dynamics simulations. It was discovered that a high degree of selectivity over the types and abundances of defects can be achieved by carefully selecting the irradiation parameters, which can be of great use when precise pattering of graphene or white graphene using focused ion beams is planned.

Kalman Filter Algorithm for Rating and Prediction in Basketball

The Thesis presents a state-space model for a basketball league and a Kalman filter algorithm for the estimation of the state of the league. In the state-space model, each of the basketball teams is associated with a rating that represents its strength compared to the other teams. The ratings are assumed to evolve in time following a stochastic process with independent Gaussian increments. The estimation of the team ratings is based on the observed game scores that are assumed to depend linearly on the true strengths of the teams and independent Gaussian noise. The team ratings are estimated using a recursive Kalman filter algorithm that produces least squares optimal estimates for the team strengths and predictions for the scores of the future games. Additionally, if the Gaussianity assumption holds, the predictions given by the Kalman filter maximize the likelihood of the observed scores. The team ratings allow probabilistic inference about the ranking of the teams and their relative strengths as well as about the teams’ winning probabilities in future games. The predictions about the winners of the games are correct 65-70% of the time. The team ratings explain 16% of the random variation observed in the game scores. Furthermore, the winning probabilities given by the model are concurrent with the observed scores. The state-space model includes four independent parameters that involve the variances of noise terms and the home court advantage observed in the scores. The Thesis presents the estimation of these parameters using the maximum likelihood method as well as using other techniques. The Thesis also gives various example analyses related to the American professional basketball league, i.e., National Basketball Association (NBA), and regular seasons played in year 2005 through 2010. Additionally, the season 2009-2010 is discussed in full detail, including the playoffs.

Playing Games on Sets and Models

The most prominent objective of the thesis is the development of the generalized descriptive set theory, as we call it. There, we study the space of all functions from a fixed uncountable cardinal to itself, or to a finite set of size two. These correspond to generalized notions of the universal Baire space (functions from natural numbers to themselves with the product topology) and the Cantor space (functions from natural numbers to the {0,1}-set) respectively. We generalize the notion of Borel sets in three different ways and study the corresponding Borel structures with the aims of generalizing classical theorems of descriptive set theory or providing counter examples. In particular we are interested in equivalence relations on these spaces and their Borel reducibility to each other. The last chapter shows, using game-theoretic techniques, that the order of Borel equivalence relations under Borel reduciblity has very high complexity. The techniques in the above described set theoretical side of the thesis include forcing, general topological notions such as meager sets and combinatorial games of infinite length. By coding uncountable models to functions, we are able to apply the understanding of the generalized descriptive set theory to the model theory of uncountable models. The links between the theorems of model theory (including Shelah's classification theory) and the theorems in pure set theory are provided using game theoretic techniques from Ehrenfeucht-Fraïssé games in model theory to cub-games in set theory. The bottom line of the research declairs that the descriptive (set theoretic) complexity of an isomorphism relation of a first-order definable model class goes in synch with the stability theoretical complexity of the corresponding first-order theory. The first chapter of the thesis has slightly different focus and is purely concerned with a certain modification of the well known Ehrenfeucht-Fraïssé games. There we (me and my supervisor Tapani Hyttinen) answer some natural questions about that game mainly concerning determinacy and its relation to the standard EF-game

Imagining Some Space

Some texts and a performance story. All motivated by the author’s interest in space, in this that surrounds, and that interest, in turn, originating from the author’s earlier studies in cultural anthropology, in observing and experiencing the surrounding animate and inanimate world. The texts in this thesis are alternating between academic and creative writing. They are texts written on a specific site on Suomenlinna island in Helsinki, Finland, as part of the performance ”Beyond the Wind in Front of Me / A Space Ship Journey” story or prologues to that, and the more academic ones supporting them or growing out of them, being accompanied also by the thoughts and practices of others. The main research questions and themes being How to perceive this that surrounds me? What is space, what does it consist of? Is it something that simply surrounds me? Am I a part of it or is it a part of me? How can a space be researched? How to activate a space? What kind of mental images do spaces/places create/uncover/open up in us? How to animate/make alive those images? Body giving meaning to space via actions created by the body. Physical environment contra emotional, imaginary, visionary one. Presence in a space/place. Physical and mental presence. Presence in memories.