A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

The European Union and Assembling Biofuel Development – topological investigations concerning the associations between law, policy and space

Biofuels for transport are a renewable source of energy that were once heralded as a solution to multiple problems associated with poor urban air quality, the overproduction of agricultural commodities, the energy security of the European Union (EU) and climate change. It was only after the Union had implemented an incentivizing framework of legal and political instruments for the production, trade and consumption of biofuels that the problems of weakening food security, environmental degradation and increasing greenhouse gases through land-use changes began to unfold. In other words, the difference between political aims for why biofuels are promoted and their consequences has grown – which is also recognized by the EU policy-makers. Therefore, the global networks of producing, trading and consuming biofuels may face a complete restructure if the European Commission accomplishes its pursuit to sideline crop-based biofuels after 2020. My aim with this dissertation is not only to trace the manifold evolutions of the instruments used by the Union to govern biofuels but also to reveal how this evolution has influenced the dynamics of biofuel development. Therefore, I study the ways the EU’s legal and political instruments of steering biofuels are coconstitutive with the globalized spaces of biofuel development. My analytical strategy can be outlined through three concepts. I use the term ‘assemblage’ to approach the operations of the loose entity of actors and non-human elements that are the constituents of multi-scalar and -sectorial biofuel development. ‘Topology’ refers to the spatiality of this European biofuel assemblage and its parts whose evolving relations are treated as the active constituents of space, instead of simply being located in space. I apply the concept of ‘nomosphere’ to characterize the framework of policies, laws and other instruments that the EU applies and construes while attempting to govern biofuels. Even though both the materials and methods vary in the independent articles, these three concepts characterize my analytical strategy that allows me to study law, policy and space associated with each other. The results of my examinations underscore the importance of the instruments of governance of the EU constituting and stabilizing the spaces of producing and, on the other hand, how topological ruptures in biofuel development have enforced the need to reform policies. This analysis maps the vast scope of actors that are influenced by the mechanism of EU biofuel governance and, what is more, shows how they are actively engaging in the Union’s institutional policy formulation. By examining the consequences of fast biofuel development that are spatially dislocated from the established spaces of producing, trading and consuming biofuels such as indirect land use changes, I unfold the processes not tackled by the instruments of the EU. Indeed, it is these spatially dislocated processes that have pushed the Commission construing a new type of governing biofuels: transferring the instruments of climate change mitigation to land-use policies. Although efficient in mitigating these dislocated consequences, these instruments have also created peculiar ontological scaffolding for governing biofuels. According to this mode of governance, the spatiality of biofuel development appears to be already determined and the agency that could dampen the negative consequences originating from land-use practices is treated as irrelevant.

Spinor Bose-Einstein Condensates and Topological Defects

This thesis concentrates on the topological defects of spin-1 and spin-2 Bose-Einstein condensates, the ground states of spin-3 condensates, and the inert states of spinor condensates with arbitrary spin. Our work is based on the description of a spinor condensate of spin-S atoms in terms of a state vector of a spin-S particle. The results of the homotopy theory are used to study the existence and structure of the topological defects in spinor condensates. We construct examples of defects, study their energetics, and examine how their stability is affected by the presence of an external magnetic field. The ground states of spin-3 condensates are calculated using analytical and numerical means. Special emphasis is put on the ground states of a chromium condensate, whose dependence on the magnetic dipole-dipole interaction is studied. A simple geometrical method for the calculation of inert states of spinor condensates is presented. This method is used to find candidates for the ground states of spin-S condensates.

Kollektiivista muistia etsimässä : How Collectivities Remember : Structures and Spaces of Social and Cultural Memory

Ajankohtaista

Mediating the Immediate – Endogenous meanings and simulated narratives in ludic spaces

The thesis discusses games and the gaming experience. It is divided into two main sections; the first examines games in general, while the second concentrates exclusively on electronic games. The text approaches games from two distinct directions by looking at both their spatiality and their narrativity at the same time. These two points of view are combined right from the beginning of the text as they are used in conceptualising the nature of the gaming experience. The purpose of the thesis is to investigate two closely related issues concerning both the field of game studies and the nature of games. In regard to studying games, the focus is placed on the juxtaposition of ludology and narratology, which acts as a framework for looking at gaming. In addition to aiming to find out whether or not it is possible to undermine the said state of affairs through the spatiality of games, the text looks at the interrelationships of games and their spaces as well as the role of narratives in those spaces. The thesis is characterised by discussing alternative points of view and its hypothetical nature. During the text, it becomes apparent that the relationship between games and narratives is strongly twofold: on one hand, the player continuously narrativizes the states the game is in while playing, while the narratives residing within the game space form their own partially separate narrative spaces, on the other. These spaces affect the conception the player has of the game states and the events taking place in the game space itself.

On Topological Solitons in The Faddeev-Skyrme Model and its Extensions

The topological solitons of two classical field theories, the Faddeev-Skyrme model and the Ginzburg-Landau model are studied numerically and analytically in this work. The aim is to gain information on the existence and properties of these topological solitons, their structure and behaviour under relaxation. First, the conditions and mechanisms leading to the possibility of topological solitons are explored from the field theoretical point of view. This leads one to consider continuous deformations of the solutions of the equations of motion. The results of algebraic topology necessary for the systematic treatment of such deformations are reviewed and methods of determining the homotopy classes of topological solitons are presented. The Faddeev-Skyrme and Ginzburg-Landau models are presented, some earlier results reviewed and the numerical methods used in this work are described. The topological solitons of the Faddeev-Skyrme model, Hopfions, are found to follow the same mechanisms of relaxation in three different domains with three different topological classifications. For two of the domains, the necessary but unusual topological classification is presented. Finite size topological solitons are not found in the Ginzburg-Landau model and a scaling argument is used to suggest that there are indeed none unless a certain modification to the model, due to R. S. Ward, is made. In that case, the Hopfions of the Faddeev-Skyrme model are seen to be present for some parameter values. A boundary in the parameter space separating the region where the Hopfions exist and the area where they do not exist is found and the behaviour of the Hopfion energy on this boundary is studied.

Muuttuvat tilat lasten- ja nuortenkirjallisuuden tutkijoiden pohdittavana : : metamorphic spaces in children's literature and culture 17.-19.1.2008 Jyväskylä

Ajankohtaista

Towards combining interactive mobile TV and smart spaces : architectures, tools and application development

Technological developments in microprocessors and ICT landscape have made a shift to a new era where computing power is embedded in numerous small distributed objects and devices in our everyday lives. These small computing devices are ne-tuned to perform a particular task and are increasingly reaching our society at every level. For example, home appliances such as programmable washing machines, microwave ovens etc., employ several sensors to improve performance and convenience. Similarly, cars have on-board computers that use information from many di erent sensors to control things such as fuel injectors, spark plug etc., to perform their tasks e ciently. These individual devices make life easy by helping in taking decisions and removing the burden from their users. All these objects and devices obtain some piece of information about the physical environment. Each of these devices is an island with no proper connectivity and information sharing between each other. Sharing of information between these heterogeneous devices could enable a whole new universe of innovative and intelligent applications. The information sharing between the devices is a diffcult task due to the heterogeneity and interoperability of devices. Smart Space vision is to overcome these issues of heterogeneity and interoperability so that the devices can understand each other and utilize services of each other by information sharing. This enables innovative local mashup applications based on shared data between heterogeneous devices. Smart homes are one such example of Smart Spaces which facilitate to bring the health care system to the patient, by intelligent interconnection of resources and their collective behavior, as opposed to bringing the patient into the health system. In addition, the use of mobile handheld devices has risen at a tremendous rate during the last few years and they have become an essential part of everyday life. Mobile phones o er a wide range of different services to their users including text and multimedia messages, Internet, audio, video, email applications and most recently TV services. The interactive TV provides a variety of applications for the viewers. The combination of interactive TV and the Smart Spaces could give innovative applications that are personalized, context-aware, ubiquitous and intelligent by enabling heterogeneous systems to collaborate each other by sharing information between them. There are many challenges in designing the frameworks and application development tools for rapid and easy development of these applications. The research work presented in this thesis addresses these issues. The original publications presented in the second part of this thesis propose architectures and methodologies for interactive and context-aware applications, and tools for the development of these applications. We demonstrated the suitability of our ontology-driven application development tools and rule basedapproach for the development of dynamic, context-aware ubiquitous iTV applications.

Lebesgue and Sobolev spaces with variable exponents

Kirjallisuusarvostelu

Semantic and fuzzy modelling for human behaviour recognition in smart spaces : a case study on ambient assisted living.

Human activity recognition in everyday environments is a critical, but challenging task in Ambient Intelligence applications to achieve proper Ambient Assisted Living, and key challenges still remain to be dealt with to realize robust methods. One of the major limitations of the Ambient Intelligence systems today is the lack of semantic models of those activities on the environment, so that the system can recognize the speci c activity being performed by the user(s) and act accordingly. In this context, this thesis addresses the general problem of knowledge representation in Smart Spaces. The main objective is to develop knowledge-based models, equipped with semantics to learn, infer and monitor human behaviours in Smart Spaces. Moreover, it is easy to recognize that some aspects of this problem have a high degree of uncertainty, and therefore, the developed models must be equipped with mechanisms to manage this type of information. A fuzzy ontology and a semantic hybrid system are presented to allow modelling and recognition of a set of complex real-life scenarios where vagueness and uncertainty are inherent to the human nature of the users that perform it. The handling of uncertain, incomplete and vague data (i.e., missing sensor readings and activity execution variations, since human behaviour is non-deterministic) is approached for the rst time through a fuzzy ontology validated on real-time settings within a hybrid data-driven and knowledgebased architecture. The semantics of activities, sub-activities and real-time object interaction are taken into consideration. The proposed framework consists of two main modules: the low-level sub-activity recognizer and the high-level activity recognizer. The rst module detects sub-activities (i.e., actions or basic activities) that take input data directly from a depth sensor (Kinect). The main contribution of this thesis tackles the second component of the hybrid system, which lays on top of the previous one, in a superior level of abstraction, and acquires the input data from the rst module's output, and executes ontological inference to provide users, activities and their in uence in the environment, with semantics. This component is thus knowledge-based, and a fuzzy ontology was designed to model the high-level activities. Since activity recognition requires context-awareness and the ability to discriminate among activities in di erent environments, the semantic framework allows for modelling common-sense knowledge in the form of a rule-based system that supports expressions close to natural language in the form of fuzzy linguistic labels. The framework advantages have been evaluated with a challenging and new public dataset, CAD-120, achieving an accuracy of 90.1% and 91.1% respectively for low and high-level activities. This entails an improvement over both, entirely data-driven approaches, and merely ontology-based approaches. As an added value, for the system to be su ciently simple and exible to be managed by non-expert users, and thus, facilitate the transfer of research to industry, a development framework composed by a programming toolbox, a hybrid crisp and fuzzy architecture, and graphical models to represent and con gure human behaviour in Smart Spaces, were developed in order to provide the framework with more usability in the nal application. As a result, human behaviour recognition can help assisting people with special needs such as in healthcare, independent elderly living, in remote rehabilitation monitoring, industrial process guideline control, and many other cases. This thesis shows use cases in these areas.

Remote Observation of Radioactive Permit-Required Confined Spaces – Case: Posiva Oy’s Fuel Handling Cell

Posiva Oy’s final disposal facility’s encapsulation plant will start to operate in the 2020s. Once the operation starts, the facility is designed to run more than a hundred years. The encapsulation plant will be first of its kind in the world, being part of the solution to solve a global issue of final disposal of nuclear waste. In the encapsulation plant’s fuel handling cell the spent nuclear fuel will be processed to be deposited into the Finnish bedrock, into ONKALO. In the fuel handling cell, the environment is highly radioactive forming a permit-required enclosed space. Remote observation is needed in order to monitor the fuel handling process. The purpose of this thesis is to map (Part I) and compare (Part II) remote observation methods to observe Posiva Oy’s fuel handling cell’s process, and provide a possible theoretical solution for this case. Secondary purpose for this thesis is to provide resources for other remote observation cases, as well as to inform about possible future technology to enable readiness in the design of the encapsulation plant. The approach was to theoretically analyze the mapped remote observation methods. Firstly, the methods were filtered by three environmental challenges. These are the high levels of radiation, the permit-required confined space and the hundred year timespan. Secondly, the most promising methods were selected by the experts designing the facility. Thirdly, a customized feasibility analysis was created and performed on the selected methods to rank the methods with scores. The results are the mapped methods and the feasibility analysis scores. The three highest scoring methods were radiation tolerant camera, fiberscope and audio feed. A combination of these three methods was given as a possible theoretical solution for this case. As this case is first in the world, remote observation methods for it had not been thoroughly researched. The findings in this thesis will act as initial data for the design of the fuel handling cell’s remote observation systems and can potentially effect on the overall design of the facility by providing unique and case specific information. In addition, this thesis could provide resources for other remote observation cases.