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.

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.

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.

Comparison of Local Feature Detectors and Descriptors for Visual Object Categorization

Local features are used in many computer vision tasks including visual object categorization, content-based image retrieval and object recognition to mention a few. Local features are points, blobs or regions in images that are extracted using a local feature detector. To make use of extracted local features the localized interest points are described using a local feature descriptor. A descriptor histogram vector is a compact representation of an image and can be used for searching and matching images in databases. In this thesis the performance of local feature detectors and descriptors is evaluated for object class detection task. Features are extracted from image samples belonging to several object classes. Matching features are then searched using random image pairs of a same class. The goal of this thesis is to find out what are the best detector and descriptor methods for such task in terms of detector repeatability and descriptor matching rate.

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.

On the Properties and Cosmology of Q-balls

The properties and cosmological importance of a class of non-topological solitons, Q-balls, are studied. Aspects of Q-ball solutions and Q-ball cosmology discussed in the literature are reviewed. Q-balls are particularly considered in the Minimal Supersymmetric Standard Model with supersymmetry broken by a hidden sector mechanism mediated by either gravity or gauge interactions. Q-ball profiles, charge-energy relations and evaporation rates for realistic Q-ball profiles are calculated for general polynomial potentials and for the gravity mediated scenario. In all of the cases, the evaporation rates are found to increase with decreasing charge. Q-ball collisions are studied by numerical means in the two supersymmetry breaking scenarios. It is noted that the collision processes can be divided into three types: fusion, charge transfer and elastic scattering. Cross-sections are calculated for the different types of processes in the different scenarios. The formation of Q-balls from the fragmentation of the Aflieck-Dine -condensate is studied by numerical and analytical means. The charge distribution is found to depend strongly on the initial energy-charge ratio of the condensate. The final state is typically noted to consist of Q- and anti-Q-balls in a state of maximum entropy. By studying the relaxation of excited Q-balls the rate at which excess energy can be emitted is calculated in the gravity mediated scenario. The Q-ball is also found to withstand excess energy well without significant charge loss. The possible cosmological consequences of these Q-ball properties are discussed.

Coarse Global Visual Localization of a Mobile Robot

Localization, which is the ability of a mobile robot to estimate its position within its environment, is a key capability for autonomous operation of any mobile robot. This thesis presents a system for indoor coarse and global localization of a mobile robot based on visual information. The system is based on image matching and uses SIFT features as natural landmarks. Features extracted from training images arestored in a database for use in localization later. During localization an image of the scene is captured using the on-board camera of the robot, features are extracted from the image and the best match is searched from the database. Feature matching is done using the k-d tree algorithm. Experimental results showed that localization accuracy increases with the number of training features used in the training database, while, on the other hand, increasing number of features tended to have a negative impact on the computational time. For some parts of the environment the error rate was relatively high due to a strong correlation of features taken from those places across the environment.

Supervised localimage feature detection

This thesis is about detection of local image features. The research topic belongs to the wider area of object detection, which is a machine vision and pattern recognition problem where an object must be detected (located) in an image. State-of-the-art object detection methods often divide the problem into separate interest point detection and local image description steps, but in this thesis a different technique is used, leading to higher quality image features which enable more precise localization. Instead of using interest point detection the landmark positions are marked manually. Therefore, the quality of the image features is not limited by the interest point detection phase and the learning of image features is simplified. The approach combines both interest point detection and local description into one phase for detection. Computational efficiency of the descriptor is therefore important, leaving out many of the commonly used descriptors as unsuitably heavy. Multiresolution Gabor features has been the main descriptor in this thesis and improving their efficiency is a significant part. Actual image features are formed from descriptors by using a classifierwhich can then recognize similar looking patches in new images. The main classifier is based on Gaussian mixture models. Classifiers are used in one-class classifier configuration where there are only positive training samples without explicit background class. The local image feature detection method has been tested with two freely available face detection databases and a proprietary license plate database. The localization performance was very good in these experiments. Other applications applying the same under-lying techniques are also presented, including object categorization and fault detection.

Thermal modelling of semiconductor switches in three-level Neutral Point Clamped Medium Voltage DTC-inverter

The aim of this thesis is to investigate the thermal loading of medium voltage three-level NPC inverter’s semiconductor IGCT switches in different operation points. The objective is to reach both a fairly accurate off-line simulation program and also so simple a simulation model that its implementation into an embedded system could be reasonable in practice and a real time use should become feasible. Active loading limitation of the inverter can be realized with a thermal model which is practical in a real time use. Determining of the component heating has been divided into two parts; defining of component losses and establishing the structure of a thermal network. Basics of both parts are clarified. The simulation environment is Matlab-Simulink. Two different models are constructed – a more accurate one and a simplified one. Potential simplifications are clarified with the help of the first one. Simplifications are included in the latter model and the functionalities of both models are compared. When increasing the calculation time step a decreased number of considered components and time constants of the thermal network can be used in the simplified model. Heating of a switching component is dependent on its topological position and inverter’s operation point. The output frequency of the converter defines mainly which one of the switching components is – because of its losses and heating – the performance limiting component of the converter. Comparison of results given by different thermal models demonstrates that with larger time steps, describing of fast occurring switching losses becomes difficult. Generally articles and papers dealing with this subject are written for two-level inverters. Also inverters which apply direct torque control (DTC) are investigated rarely from the heating point of view. Hence, this thesis completes the former material.

On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.

Pencil grip : a descriptive model and four empirical studies

Previous studies on pencil grip have typically dealt with the developmental aspects in young children while handwriting research is mainly concerned with speed and legibility. Studies linking these areas are few. Evaluation of the existing pencil grip studies is hampered by methodological inconsistencies. The operational definitions of pencil grip arerational but tend to be oversimplified while detailed descriptors tend to be impractical due to their multiplicity. The present study introduces a descriptive two-dimensional model for the categorisation of pencil grip suitable for research applications in a classroom setting. The model is used in four empirical studies of children during the first six years of writing instruction. Study 1 describes the pencil grips observed in a large group of pupils in Finland (n = 504). The results indicate that in Finland the majority of grips resemble the traditional dynamic tripod grip. Significant genderrelated differences in pencil grip were observed. Study 2 is a longitudinal exploration of grip stability vs. change (n = 117). Both expected and unexpected changes were observed in about 25 per cent of the children's grips over four years. A new finding emerged using the present model for categorisation: whereas pencil grips would change, either in terms of ease of grip manipulation or grip configuration, no instances were found where a grip would have changed concurrently on both dimensions. Study 3 is a cross-cultural comparison of grips observed in Finland and the USA (n = 793). The distribution of the pencil grips observed in the American pupils was significantly different from those found in Finland. The cross-cultural disparity is most likely related to the differences in the onset of writing instruction. The differences between the boys' and girls' grips in the American group were non-significant.An implication of Studies 2 and 3 is that the initial pencil grip is of foremost importance since pencil grips are largely stable over time. Study 4 connects the pencil grips to assessment of the mechanics of writing (n = 61). It seems that certain previously not recommended pencil grips might nevertheless be includedamong those accepted since they did not appear to hamper either fluency or legibility.

Lärande som text : en dramapedagogiskt förankrad läsning av det kroppsliga, rumsliga och retoriska i kunskapsbildande processer

My presupposition, that learning at some level deals with life praxis, is expressed in four metaphors: space, time, fable and figure. Relations between learning,knowledge building and meaning making are linked to the concept of personal knowledge. I present a two part study of learning as text in a drama pedagogical rooted reading where learning is framed as the ongoing event, and knowledge, as the product of previous processes, is framed as culturally formed utterances. A frame analysis model is constructed as a topological guide for relations between the two concepts learning and knowledge. It visualises an aesthetic understanding, rooted in drama pedagogical comprehension. Insight and perception are linked in an inner relationship that is neither external nor identical. This understanding expresses the movement "in between" connecting asymmetrical and nonlinear features of human endeavour and societal issues. The performability of bodily and oral participation in the learning event in a socio-cultural setting is analysed as a dialogised text. In an ethnographical case study I have gathered material with an interest for the particular. The empirical material is based on three problem based learning situations in a Polytechnic setting. The act of transformation in the polyphony of the event is considered as a turning point in the narrative employment. Negotiation and figuration in the situation form patterns of the space for improvisation (flow) and tensions at the boundaries (thresholds) which imply the logical structure of transformation. Learning as a dialogised text of "yes" and "no", of structure and play for the improvised, interrelate in that movement. It is related to both the syntagmic and the paradigmatic forms of thinking. In the philosophical study, forms of understanding are linked to the logical structure of transformation as a cultural issue. The classical rhetorical concepts of Logos, Pathos, Ethos and Mythos are connected to the multidimensional rationality of the human being. In the Aristotelian form of knowledge, phronesis,a logic structure of inquiry is recognised. The shifting of perspectives between approaches, the construction of knowledge as context and the human project of meaning making as a subtext, illuminates multiple layers of the learning text. In an argumentation that post-modern apprehension of knowledge, emphasising contextual and situational values, has an empowering impact on learning, I find pedagogical benefits. The dialogical perspective has opened lenses that manage to hold in aesthetic doubling the individual action of inquiry and the stage with its cultural tools in a three dimensional reading.

GIS assessing traditional and modern agricultural land use/land cover change. A case study 1959-2005: Rekijoki, Somero, SW-Finland

Finland’s rural landscape has gone through remarkable changes from the 1950’s, due to agricultural developments. Changed farming practices have influenced especially traditional landscape management, and modifications in the arable land structure and grasslands transitions are notable. The review of the previous studies reveal the importance of the rural landscape composition and structure to species and landscape diversity, whereas including the relevance in presence of the open ditches, size of the field and meadow patches, topology of the natural and agricultural landscape. This land-change study includes applying remote sensed data from two time series and empirical geospatial analysis in Geographic Information Systems (GIS). The aims of this retrospective research is to detect agricultural landscape use and land cover change (LULCC) dynamics and discuss the consequences of agricultural intensification to landscape structure covering from the aspects of landscape ecology. Measurements of LULC are derived directly from pre-processed aerial images by a variety of analytical procedures, including statistical methods and image interpretation. The methodological challenges are confronted in the process of landscape classification and combining change detection approaches with landscape indices. Particular importance is paid on detecting agricultural landscape features at a small scale, demanding comprehensive understanding of such agroecosystems. Topological properties of the classified arable land and valley are determined in order to provide insight and emphasize the aspect the field edges in the agricultural landscape as important habitat. Change detection dynamics are presented with change matrix and additional calculations of gain, loss, swap, net change, change rate and tendencies are made. Transition’s possibility is computed following Markov’s probability model and presented with matrix, as well. Thesis’s spatial aspect is revealed with illustrative maps providing knowledge of location of the classified landscape categories and location of the dynamics of the changes occurred. It was assured that in Rekijoki valley’s landscape, remarkable changes in landscape has occurred. Landscape diversity has been strongly influenced by modern agricultural landscape change, as NP of open ditches has decreased and the MPS of the arable plot has decreased. Overall change in the diversity of the landscape is determined with the decrease of SHDI. Valley landscape considered as traditional land use area has experienced major transitional changes, as meadows class has lost almost one third of the area due to afforestation. Also, remarkable transitions have occurred from forest to meadow and arable land to built area. Boundaries measurement between modern and traditional landscape has indicated noticeable proportional increase in arable land-forest edge type and decrease in arable land-meadow edge type. Probability calculations predict higher future changes for traditional landscape, but also for arable land turning into built area.