On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Patient exposure monitoring and radiation qualities in two-dimensional digital x-ray imaging

The methods for estimating patient exposure in x-ray imaging are based on the measurement of radiation incident on the patient. In digital imaging, the useful dose range of the detector is large and excessive doses may remain undetected. Therefore, real-time monitoring of radiation exposure is important. According to international recommendations, the measurement uncertainty should be lower than 7% (confidence level 95%). The kerma-area product (KAP) is a measurement quantity used for monitoring patient exposure to radiation. A field KAP meter is typically attached to an x-ray device, and it is important to recognize the effect of this measurement geometry on the response of the meter. In a tandem calibration method, introduced in this study, a field KAP meter is used in its clinical position and calibration is performed with a reference KAP meter. This method provides a practical way to calibrate field KAP meters. However, the reference KAP meters require comprehensive calibration. In the calibration laboratory it is recommended to use standard radiation qualities. These qualities do not entirely correspond to the large range of clinical radiation qualities. In this work, the energy dependence of the response of different KAP meter types was examined. According to our findings, the recommended accuracy in KAP measurements is difficult to achieve with conventional KAP meters because of their strong energy dependence. The energy dependence of the response of a novel large KAP meter was found out to be much lower than with a conventional KAP meter. The accuracy of the tandem method can be improved by using this meter type as a reference meter. A KAP meter cannot be used to determine the radiation exposure of patients in mammography, in which part of the radiation beam is always aimed directly at the detector without attenuation produced by the tissue. This work assessed whether pixel values from this detector area could be used to monitor the radiation beam incident on the patient. The results were congruent with the tube output calculation, which is the method generally used for this purpose. The recommended accuracy can be achieved with the studied method. New optimization of radiation qualities and dose level is needed when other detector types are introduced. In this work, the optimal selections were examined with one direct digital detector type. For this device, the use of radiation qualities with higher energies was recommended and appropriate image quality was achieved by increasing the low dose level of the system.

Characterisation of properties of coniferous wood tracheids by x-ray diffraction, laser scattering and microscopy

In recent years there has been growing interest in selecting suitable wood raw material to increase end product quality and to increase the efficiency of industrial processes. Genetic background and growing conditions are known to affect properties of growing trees, but only a few parameters reflecting wood quality, such as volume and density can be measured on an industrial scale. Therefore research on cellular level structures of trees grown in different conditions is needed to increase understanding of the growth process of trees leading to desired wood properties. In this work the cellular and cell wall structures of wood were studied. Parameters, such as the mean microfibril angle (MFA), the spiral grain angles, the fibre length, the tracheid cell wall thickness and the cross-sectional shape of the tracheid, were determined as a function of distance from the pith towards the bark and mutual dependencies of these parameters were discussed. Samples from fast-grown trees, which belong to a same clone, grown in fertile soil and also from fertilised trees were measured. It was found that in fast-grown trees the mean MFA decreased more gradually from the pith to the bark than in reference stems. In fast-grown samples cells were shorter, more thin-walled and their cross-sections were rounder than in slower-grown reference trees. Increased growth rate was found to cause an increase in spiral grain variation both within and between annual rings. Furthermore, methods for determination of the mean MFA using x-ray diffraction were evaluated. Several experimental arrangements including the synchrotron radiation based microdiffraction were compared. For evaluation of the data analysis procedures a general form for diffraction conditions in terms of angles describing the fibre orientation and the shape of the cell was derived. The effects of these parameters on the obtained microfibril angles were discussed. The use of symmetrical transmission geometry and tangentially cut samples gave the most reliable MFA values.

External signal-activated liposomal drug delivery systems

Modern drug discovery gives rise to a great number of potential new therapeutic agents, but in some cases the efficient treatment of patient may not be achieved because the delivery of active compounds to the target site is insufficient. Thus, drug delivery is one of the major challenges in current pharmaceutical research. Numerous nanoparticle-based drug carriers, e.g. liposomes, have been developed for enhanced drug delivery and targeting. Drug targeting may enhance the efficiency of the treatment and, importantly, reduce unwanted side effects by decreasing drug distribution to non-target tissues. Liposomes are biocompatible lipid-based carriers that have been studied for drug delivery during the last 40 years. They can be functionalized with targeting ligands and sensing materials for triggered activation. In this study, various external signal-assisted liposomal delivery systems were developed. Signals can be used to modulate drug permeation or release from the liposome formulation, and they provide accurate control of time, place and rate of activation. The study involved three types of signals that were used to trigger drug permeation and release: electricity, heat and light. Electrical stimulus was utilized to enhance the permeation of liposomal DNA across the skin. Liposome/DNA complex-mediated transfections were performed in tight rat epidermal cell model. Various transfection media and current intensities were tested, and transfection efficiency was evaluated non-invasively by monitoring the concentration of secreted reporter protein in cell culture medium. Liposome/DNA complexes produced gene expression, but electrical stimulus did not enhance the transfection efficiency significantly. Heat-sensitive liposomal drug delivery system was developed by coating liposomes with biodegradable and thermosensitive poly(N-(2-hydroxypropyl) methacrylamide-mono/dilactate polymer. Temperature-triggered liposome aggregation and contents release from liposomes were evaluated. The cloud point temperature (CP) of the polymer was set to 42 °C. Polymer-coated liposome aggregation and contents release were observed above CP of the polymer, while non-coated liposomes remained intact. Polymer precipitates above its CP and interacts with liposomal bilayers. It is likely that this induces permeabilization of the liposomal membrane and contents release. Light-sensitivity was introduced to liposomes by incorporation of small (< 5 nm) gold nanoparticles. Hydrophobic and hydrophilic gold nanoparticles were embedded in thermosensitive liposomes, and contents release was investigated upon UV light exposure. UV light-induced lipid phase transitions were examined with small angle X-ray scattering, and light-triggered contents release was shown also in human retinal pigment epithelial cell line. Gold nanoparticles absorb light energy and transfer it into heat, which induces phase transitions in liposomes and triggers the contents release. In conclusion, external signal-activated liposomes offer an advanced platform for numerous applications in drug delivery, particularly in the localized drug delivery. Drug release may be localized to the target site with triggering stimulus that results in better therapeutic response and less adverse effects. Triggering signal and mechanism of activation can be selected according to a specific application.

Talking About Time in Russian and Finnish

In this study I look at what people want to express when they talk about time in Russian and Finnish, and why they use the means they use. The material consists of expressions of time: 1087 from Russian and 1141 from Finnish. They have been collected from dictionaries, usage guides, corpora, and the Internet. An expression means here an idiomatic set of words in a preset form, a collocation or construction. They are studied as lexical entities, without a context, and analysed and categorized according to various features. The theoretical background for the study includes two completely different approaches. Functional Syntax is used in order to find out what general meanings the speaker wishes to convey when talking about time and how these meanings are expressed in specific languages. Conceptual metaphor theory is used for explaining why the expressions are as they are, i.e. what kind of conceptual metaphors (transfers from one conceptual domain to another) they include. The study has resulted in a grammatically glossed list of time expressions in Russian and Finnish, a list of 56 general meanings involved in these time expressions and an account of the means (constructions) that these languages have for expressing the general meanings defined. It also includes an analysis of conceptual metaphors behind the expressions. The general meanings involved turned out to revolve around expressing duration, point in time, period of time, frequency, sequence, passing of time, suitable time and the right time, life as time, limitedness of time, and some other notions having less obvious semantic relations to the others. Conceptual metaphor analysis of the material has shown that time is conceptualized in Russian and Finnish according to the metaphors Time Is Space (Time Is Container, Time Has Direction, Time Is Cycle, and the Time Line Metaphor), Time Is Resource (and its submapping Time Is Substance), Time Is Actor; and some characteristics are added to these conceptualizations with the help of the secondary metaphors Time Is Nature and Time Is Life. The limits between different conceptual metaphors and the connections these metaphors have with one another are looked at with the help of the theory of conceptual integration (the blending theory) and its schemas. The results of the study show that although Russian and Finnish are typologically different, they are very similar both in the needs of expression their speakers have concerning time, and in the conceptualizations behind expressing time. This study introduces both theoretical and methodological novelties in the nature of material used, in developing empirical methodology for conceptual metaphor studies, in the exactness of defining the limits of different conceptual metaphors, and in seeking unity among the different facets of time. Keywords: time, metaphor, time expression, idiom, conceptual metaphor theory, functional syntax, blending theory

Kansakunnan parhaaksi. : Suomalaiset naisten- ja lastensairaalat 1920 1940-luvulla arkkitehtonisena, lääketieteellisenä ja yhteiskunnallisena suunnittelukohteena

This dissertation addresses the modernization process of Finnish hospital architecture between the First and Second World War, with focus on facilities explicitly designed for women and children, which as special hospitals reflect specialization, a distinct feature of the modern era. The facilities considered in the study are the Salus hospital, Dr. Länsimäki s women s hospital, the Folkhälsan in Svenska Finland association s child-care institute, the Helsinki Women s Clinic, the Viipuri Women s Hospital, the Helsinki Children s Clinic and the Children's Castle (Lastenlinna) in Helsinki. The study considers hospital architecture as an architectural, medical and social object of design. The theoretical starting point and perspective are the views of the French philosopher and historian Michel Foucault (1925 1983) concerning the relationship of bio-power and architecture. Underlying the construction of health-care facilities for women and children were not only the desire to help but also issues of population policy, social policies, training and professionalization. In this study, hospital architecture is interpreted as reflecting developments in medicine, while also producing and reinforcing discourses associated with the ideologies of the time of design and construction. The results of the present research provide new information on the field of hospital design. The design of hospitals was no longer the sole prerogative of architects. Instead, modern hospital design involved the collaboration and networking of experts in various fields. During the period studied, the pavilion system was incorporated in hospital architecture in the block system, which was regarded as a rational. Rationalization was implemented upon the conditions of medical work. This led to spatial design in accordance with medical practices, through which norms were reinforced and created. An important aspect of the material is that the requirements of light, air, openness and hygiene created architecture in glass of an x-ray character, strongly associated with the element of discipline. The alliance of hygiene and architecture became a strategy for controlling the behaviour and encounters of people, for producing pedagogical and moral hygiene, and for reinforcing class hygiene. The modern hospital building also had to meet the requirements of aesthetic hygiene. Health-care facilities designed for women and children became production-oriented machinery, instruments for producing a healthy population and for reinforcing medical discourses.