Principles of Pitch Organization in Béla Bartók's 'Duke Bluebeard's Castle'

The topic of my doctoral thesis is to demonstrate the usefulness of incorporating tonal and modal elements into a pitch-web square analysis of Béla Bartók's (1881-1945) opera, 'A kékszakállú herceg vára' ('Duke Bluebeard's Castle'). My specific goal is to demonstrate that different musical materials, which exist as foreground melodies or long-term key progressions, are unified by the unordered pitch set {0,1,4}, which becomes prominent in different sections of Bartók's opera. In Bluebeard's Castle, the set {0,1,4} is also found as a subset of several tetrachords: {0,1,4,7}, {0,1,4,8}, and {0,3,4,7}. My claim is that {0,1,4} serves to link music materials between themes, between sections, and also between scenes. This study develops an analytical method, drawn from various theoretical perspectives, for conceiving superposed diatonic spaces within a hybrid pitch-space comprised of diatonic and chromatic features. The integrity of diatonic melodic lines is retained, which allows for a non-reductive understanding of diatonic superposition, without appealing to pitch centers or specifying complete diatonic collections. Through combining various theoretical insights of the Hungarian scholar Ernő Lendvai, and the American theorists Elliott Antokoletz, Paul Wilson and Allen Forte, as well as the composer himself, this study gives a detailed analysis of the opera's pitch material in a way that combines, complements, and expands upon the studies of those scholars. The analyzed pitch sets are represented on Aarre Joutsenvirta's note-web square, which adds a new aspect to the field of Bartók analysis. Keywords: Bartók, Duke Bluebeard's Castle (Op. 11), Ernő Lendvai, axis system, Elliott Antokoletz, intervallic cycles, intervallic cells, Allen Forte, set theory, interval classes, interval vectors, Aarre Joutsenvirta, pitch-web square, pitch-web analysis.

Devolution of forest-related rights: Comparative analyses of six developing countries

The study focused on the different ways that forest-related rights can be devolved to the local level according to the current legal frameworks in Laos, Nepal, Vietnam, Kenya, Mozambique and Tanzania. The eleven case studies represented the main ways in which forest-related rights can be devolved to communities or households in these countries. The objectives of this study were to 1) analyse the contents and extent of forest-related rights that can be devolved to the local level, 2) develop an empirical typology that represents the main types of devolution, and 3) compare the cases against a theoretical ideal type to assess in what way and to what extent the cases are similar to or differ from the theoretical construct. Fuzzy set theory, Qualitative Comparative Analysis and ideal type analysis were used in analysing the case studies and in developing an empirical typology. The theoretical framework, which guided data collection and analyses, was based on institutional economics and theories on property rights, common pool resources and collective action. On the basis of the theoretical and empirical knowledge, the most important attributes of rights were defined as use rights, management rights, exclusion rights, transfer rights and the duration and security of the rights. The ideal type was defined as one where local actors have been devolved comprehensive use rights, extensive management rights, rights to exclude others from the resource and rights to transfer these rights. In addition, the rights are to be secure and held perpetually. The ideal type was used to structure the analysis and as a tool against which the cases were analysed. The contents, extent and duration of the devolved rights varied greatly. In general, the results show that devolution has mainly meant the transfer of use rights to the local level, and has not really changed the overall state control over forest resources. In most cases the right holders participate, or have a limited role in the decision making regarding the harvesting and management of the resource. There was a clear tendency to devolve the rights to enforce rules and to monitor resource use and condition more extensively than the powers to decide on the management and development of the resource. The empirical typology of the cases differentiated between five different types of devolution. The types can be characterised by the devolution of 1) restricted use and control rights, 2) extensive use rights but restricted control rights, 3) extensive rights, 4) insecure, short term use and restricted control rights, and 5) insecure extensive rights. Overall, the case studies conformity to the ideal type was very low: only two cases were similar to the ideal type, all other cases differed considerably from the ideal type. The restricted management rights were the most common reason for the low conformity to the ideal type (eight cases). In three cases, the short term of the rights, restricted transfer rights, restricted use rights or restricted exclusion rights were the reason or one of the reasons for the low conformity to the ideal type. In two cases the rights were not secure.

On linear order and computation : The expressiveness of interactive computations on linear orders and computations indexed by ordinals

We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.

On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

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

Proofs, Paradoxes, and Probabilities : The Logical Turn of Philosophy in Finland

This monograph describes the emergence of independent research on logic in Finland. The emphasis is placed on three well-known students of Eino Kaila: Georg Henrik von Wright (1916-2003), Erik Stenius (1911-1990), and Oiva Ketonen (1913-2000), and their research between the early 1930s and the early 1950s. The early academic work of these scholars laid the foundations for today's strong tradition in logic in Finland and also became internationally recognized. However, due attention has not been given to these works later, nor have they been comprehensively presented together. Each chapter of the book focuses on the life and work of one of Kaila's aforementioned students, with a fourth chapter discussing works on logic by authors who would later become known within other disciplines. Through an extensive use of correspondence and other archived material, some insight has been gained into the persons behind the academic personae. Unique and unpublished biographical material has been available for this task. The chapter on Oiva Ketonen focuses primarily on his work on what is today known as proof theory, especially on his proof theoretical system with invertible rules that permits a terminating root-first proof search. The independency of the parallel postulate is proved as an example of the strength of root-first proof search. Ketonen was to our knowledge Gerhard Gentzen's (the 'father' of proof theory) only student. Correspondence and a hitherto unavailable autobiographic manuscript, in addition to an unpublished article on the relationship between logic and epistemology, is presented. The chapter on Erik Stenius discusses his work on paradoxes and set theory, more specifically on how a rigid theory of definitions is employed to avoid these paradoxes. A presentation by Paul Bernays on Stenius' attempt at a proof of the consistency of arithmetic is reconstructed based on Bernays' lecture notes. Stenius correspondence with Paul Bernays, Evert Beth, and Georg Kreisel is discussed. The chapter on Georg Henrik von Wright presents his early work on probability and epistemology, along with his later work on modal logic that made him internationally famous. Correspondence from various archives (especially with Kaila and Charlie Dunbar Broad) further discusses his academic achievements and his experiences during the challenging circumstances of the 1940s.

Contributions to the Theory of Finite-State Based Grammars

This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIG) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs: (i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchyand the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction. (ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, left- and right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the Chomsky-Schützenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance-motivated approximations are linear time parseable. (iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite-state representations for parse forests is sketched. These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing. Avainsanat: syntactic parsing, finite-state automata, dependency grammar, first-order logic, linguistic performance, star-free regular approximations, mildly context-sensitive grammars

Space in Musical Semiosis : An Abductive Theory of the Musical Composition Process

Space in musical semiosis is a study of musical meaning, spatiality and composition. Earlier studies on musical composition have not adequately treated the problems of musical signification. Here, composition is considered an epitomic process of musical signification. Hence the core problems of composition theory are core problems of musical semiotics. The study employs a framework of naturalist pragmatism, based on C. S. Peirce’s philosophy. It operates on concepts such as subject, experience, mind and inquiry, and incorporates relevant ideas of Aristotle, Peirce and John Dewey into a synthetic view of esthetic, practic, and semiotic for the benefit of grasping musical signification process as a case of semiosis in general. Based on expert accounts, music is depicted as real, communicative, representational, useful, embodied and non-arbitrary. These describe how music and the musical composition process are mental processes. Peirce’s theories are combined with current morphological theories of cognition into a view of mind, in which space is central. This requires an analysis of space, and the acceptance of a relativist understanding of spatiality. This approach to signification suggests that mental processes are spatially embodied, by virtue of hard facts of the world, literal representations of objects, as well as primary and complex metaphors each sharing identities of spatial structures. Consequently, music and the musical composition process are spatially embodied. Composing music appears as a process of constructing metaphors—as a praxis of shaping and reshaping features of sound, representable from simple quality dimensions to complex domains. In principle, any conceptual space, metaphorical or literal, may set off and steer elaboration, depending on the practical bearings on the habits of feeling, thinking and action, induced in musical communication. In this sense, it is evident that music helps us to reorganize our habits of feeling, thinking, and action. These habits, in turn, constitute our existence. The combination of Peirce and morphological approaches to cognition serves well for understanding musical and general signification. It appears both possible and worthwhile to address a variety of issues central to musicological inquiry in the framework of naturalist pragmatism. The study may also contribute to the development of Peircean semiotics.

Widening Perspectives of Teacher Education : Studies on theory-practice relationship, reflection, research and professional development

This dissertation examined the research-based teacher education at the University of Helsinki from different theoretical and practical perspectives. Five studies focused on these perspectives separately as well as overlappingly. Study I focused on the reflection process of graduating teacher students. The data consisted of essays the students wrote as their last assignment before graduating, where their assignment was to examine their development as researchers during their MA thesis research process. The results indicated that the teacher students had analysed their own development thoroughly during the process and that they had reflected on theoretical as well as practical educational matters. The results also pointed out that, in the students’ opinion, personally conducted research is a significant learning process. -- Study II investigated teacher students’ workplace learning and the integration of theory and practice in teacher education. The students’ interviews focused on their learning of teacher’s work prior to education. The interviewees’ responses concerning their ‘surviving’ in teaching prior to teacher education were categorized into three categories: learning through experiences, school as a teacher learning environment, and case-specific learning. The survey part of the study focused on integration of theory and practice within the education process. The results showed that the students who worked while they studied took advantage of the studies and applied them to work. They set more demanding teaching goals and reflected on their work more theoretically. -- Study III examined practical aspects of the teacher students’ MA thesis research as well as the integration of theory and practice in teacher education. The participants were surveyed using a web-based survey which dealt with the participants’ teacher education experiences. According to the results, most of the students had chosen a practical topic for their MA thesis, one arising from their work environment, and most had chosen a research topic that would develop their own teaching. The results showed that the integration of theory and practice had taken place in much of the course work, but most obviously in the practicum periods, and also in the courses concerning the school subjects. The majority felt that the education had in some way been successful with regards to integration. -- Study IV explored the idea of considering teacher students’ MA thesis research as professional development. Twenty-three teachers were interviewed on the subject of their experiences of conducting research about their own work as teachers. The results of the interviews showed that the reasons for choosing the MA thesis research topic were multiple: practical, theoretical, personal, professional reasons, as well as outside effect. The objectives of the MA thesis research, besides graduating, were actual projects, developing the ability to work as teachers, conducting significant research, and sharing knowledge of the topic. The results indicated that an MA thesis can function as a tool for professional development, for example in finding ways for adjusting teaching, increasing interaction skills, gaining knowledge or improving reflection on theory and/or practice, strengthening self-confidence as a teacher, increasing researching skills or academic writing skills, as well as becoming critical and being able to read scientific and academic literature. -- Study V analysed teachers’ views of the impact of practitioner research. According to the results, the interviewees considered the benefits of practitioner research to be many, affecting teachers, pupils, parents, the working community, and the wider society. Most of the teachers indicated that they intended to continue to conduct research in the future. The results also showed that teachers often reflected personally and collectively, and viewed this as important. -- These five studies point out that MA thesis research is and can be a useful tool for increasing reflection doing with personal and professional development, as well as integrating theory and practice. The studies suggest that more advantage could be taken of the MA thesis research project. More integration of working and studying could and should be made possible for teacher students. This could be done in various ways within teacher education, but the MA thesis should be seen as a pedagogical possibility.

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.

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.

Climate change and agriculture: theory and application of mitigation policies

Agriculture’s contribution to climate change is controversial as it is a significant source of greenhouse gases but also a sink of carbon. Hence its economic and technological potential to mitigate climate change have been argued to be noteworthy. However, social profitability of emission mitigation is a result from factors among emission reductions such as surface water quality impact or profit from production. Consequently, to value comprehensive results of agricultural climate emission mitigation practices, these co-effects to environment and economics should be taken into account. The objective of this thesis was to develop an integrated economic and ecological model to analyse the social welfare of crop cultivation in Finland on distinctive cultivation technologies, conventional tillage and conservation tillage (no-till). Further, we ask whether it would be privately or socially profitable to allocate some of barley cultivation for alternative land use, such as green set-aside or afforestation, when production costs, GHG’s and water quality impacts are taken into account. In the theoretical framework we depict the optimal input use and land allocation choices in terms of environmental impacts and profit from production and derive the optimal tax and payment policies for climate and water quality friendly land allocation. The empirical application of the model uses Finnish data about production cost and profit structure and environmental impacts. According to our results, given emission mitigation practices are not self-evidently beneficial for farmers or society. On the contrary, in some cases alternative land allocation could even reduce social welfare, profiting conventional crop cultivation. This is the case regarding mineral soils such as clay and silt soils. On organic agricultural soils, climate mitigation practices, in this case afforestation and green fallow give more promising results, decreasing climate emissions and nutrient runoff to water systems. No-till technology does not seem to profit climate mitigation although it does decrease other environmental impacts. Nevertheless, the data behind climate emission mitigation practices impact to production and climate is limited and partly contradictory. More specific experiment studies on interaction of emission mitigation practices and environment would be needed. Further study would be important. Particularly area specific production and environmental factors and also food security and safety and socio-economic impacts should be taken into account.

Rough Justice or Zero Tolerance? - Reassessing the Nature of Copyright in Light of Collective Licensing (Part I)

Starting point in the European individualistic copyright ideology is that an individual author creates a work and controls the use of it. However, this paper argues that it is (and has always been) impossible to control the use of works after their publication. This has also been acknowledged by the legislator, who has introduced collective licensing agreements because of this impossibility. Since it is impossible to rigorously control the use of works this writing "Rough Justice or Zero Tolerance - Reassessing the Nature of Copyright in Light of Collective Licensing" examines what reality of copyright is actually about. Finding alternative (and hopefully more "true") ways to understand copyright helps us to create alternative solutions in order to solve possible problems we have as it comes e.g. to use of content in online environment. The paper makes a claim that copyright is actually about defining negotiation points for different stakeholders and that nothing in the copyright reality prevents us from defining e.g. a new negotiation point where representatives of consumers would meet representatives of right holders in order to agree on the terms of use for certain content types in online environment.