Tannakian Formalism Applied to the Category of Mixed Hodge Structures

Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

Problems of Proto-Slavic Historical Nominal Morphology : On the Basis of Old Church Slavic

In this study I offer a diachronic solution for a number of difficult inflectional endings in Old Church Slavic nominal declensions. In this context I address the perhaps most disputed and the most important question of the Slavic nominal inflectional morphology: whether there was in Proto-Slavic an Auslautgesetz (ALG), a law of final syllables, that narrowed the Proto-Indo-European vowel */o/ to */u/ in closed word-final syllables. In addition, the work contains an exhaustive morphological classification of the nouns and adjectives that occur in canonical Old Church Slavic. I argue that Proto-Indo-European */o/ became Proto-Slavic */u/ before word-final */s/ and */N/. This conclusion is based on the impossibility of finding credible analogical (as opposed to phonological) explanations for the forms supporting the ALG hypothesis, and on the survival of the neuter gender in Slavic. It is not likely that the */o/-stem nominative singular ending */-u/ was borrowed from the accusative singular, because the latter would have been the only paradigmatic form with the stem vowel */-u-/. It is equally unlikely that the ending */-u/ was borrowed from the */u/-stems, because the latter constituted a moribund class. The usually stated motivation for such an analogical borrowing, i.e. a need to prevent the merger of */o/-stem masculines with neuters of the same class, is not tenable. Extra-Slavic, as well as intra-Slavic evidence suggests that phonologically-triggered mergers between two semantically opaque genders do not tend to be prevented, but rather that such mergers lead to the loss of the gender opposition in question. On the other hand, if */-os/ had not become */-us/, most nouns and, most importantly, all adjectives and pronouns would have lost the formal distinction between masculines and neuters. This would have necessarily resulted in the loss of the neuter gender. A new explanation is given for the most apparent piece of evidence against the ALG hypothesis, the nominative-accusative singular of the */es/-stem neuters, e.g. nebo 'sky'. I argue that it arose in late Proto-Slavic dialects, replacing regular nebe, under the influence of the */o/- and */yo/-stems where a correlation had emerged between a hard root-final consonant and the termination -o, on the one hand, and a soft root-final consonant and the termination -e, on the other.

Cancer survivors at work : Work-related problems and factors associated with their employment, work ability and social support from the work community

Due to the improved prognosis of many forms of cancer, an increasing number of cancer survivors are willing to return to work after their treatment. It is generally believed, however, that people with cancer are either unemployed, stay at home, or retire more often than people without cancer. This study investigated the problems that cancer survivors experience on the labour market, as well as the disease-related, sociodemographic and psychosocial factors at work that are associated with the employment and work ability of cancer survivors. The impact of cancer on employment was studied combining the data of Finnish Cancer Registry and census data of the years 1985, 1990, 1995 or 1997 of Statistics Finland. There were two data sets containing 46 312 and 12 542 people with cancer. The results showed that cancer survivors were slightly less often employed than their referents. Two to three years after the diagnosis the employment rate of the cancer survivors was 9% lower than that of their referents (64% vs. 73%), whereas the employment rate was the same before the diagnosis (78%). The employment rate varied greatly according to the cancer type and education. The probability of being employed was greater in the lower than in the higher educational groups. People with cancer were less often employed than people without cancer mainly because of their higher retirement rate (34% vs. 27%). As well as employment, retirement varied by cancer type. The risk of retirement was twofold for people having cancer of the nervous system or people with leukaemia compared to their referents, whereas people with skin cancer, for example, did not have an increased risk of retirement. The aim of the questionnaire study was to investigate whether the work ability of cancer survivors differs from that of people without cancer and whether cancer had impaired their work ability. There were 591 cancer survivors and 757 referents in the data. Even though current work ability of cancer survivors did not differ between the survivors and their referents, 26% of cancer survivors reported that their physical work ability, and 19% that their mental work ability had deteriorated due to cancer. The survivors who had other diseases or had had chemotherapy, most often reported impaired work ability, whereas survivors with a strong commitment to their work organization, or a good social climate at work, reported impairment less frequently. The aim of the other questionnaire study containing 640 people with the history of cancer was to examine extent of social support that cancer survivors needed, and had received from their work community. The cancer survivors had received most support from their co-workers, and they hoped for more support especially from the occupational health care personnel (39% of women and 29% of men). More support was especially needed by men who had lymphoma, had received chemotherapy or had a low education level. The results of this study show that the majority of the survivors are able to return to work. There is, however, a group of cancer survivors who leave work life early, have impaired work ability due to their illness, and suffer from lack of support from their work place and the occupational health services. Treatment-related, as well as sociodemographic factors play an important role in survivors' work-related problems, and presumably their possibilities to continue working.

Atomic Layer Deposition and Photocatalytic Properties of Titanium Dioxide Thin Films

Photocatalytic TiO2 thin films can be highly useful in many environments and applications. They can be used as self-cleaning coatings on top of glass, tiles and steel to reduce the amount of fouling on these surfaces. Photocatalytic TiO2 surfaces have antimicrobial properties making them potentially useful in hospitals, bathrooms and many other places where microbes may cause problems. TiO2 photocatalysts can also be used to clean contaminated water and air. Photocatalytic oxidation and reduction reactions proceed on TiO2 surfaces under irradiation of UV light meaning that sunlight and even normal indoor lighting can be utilized. In order to improve the photocatalytic properties of TiO2 materials even further, various modification methods have been explored. Doping with elements such as nitrogen, sulfur and fluorine, and preparation of different kinds of composites are typical approaches that have been employed. Photocatalytic TiO2 nanotubes and other nanostructures are gaining interest as well. Atomic Layer Deposition (ALD) is a chemical gas phase thin film deposition method with strong roots in Finland. This unique modification of the common Chemical Vapor Deposition (CVD) method is based on alternate supply of precursor vapors to the substrate which forces the film growth reactions to proceed only on the surface in a highly controlled manner. ALD gives easy and accurate film thickness control, excellent large area uniformity and unparalleled conformality on complex shaped substrates. These characteristics have recently led to several breakthroughs in microelectronics, nanotechnology and many other areas. In this work, the utilization of ALD to prepare photocatalytic TiO2 thin films was studied in detail. Undoped as well as nitrogen, sulfur and fluorine doped TiO2 thin films were prepared and thoroughly characterized. ALD prepared undoped TiO2 films were shown to exhibit good photocatalytic activities. Of the studied dopants, sulfur and fluorine were identified as much better choices than nitrogen. Nanostructured TiO2 photocatalysts were prepared through template directed deposition on various complex shaped substrates by exploiting the good qualities of ALD. A clear enhancement in the photocatalytic activity was achieved with these nanostructures. Several new ALD processes were also developed in this work. TiO2 processes based on two new titanium precursors, Ti(OMe)4 and TiF4, were shown to exhibit saturative ALD-type of growth when water was used as the other precursor. In addition, TiS2 thin films were prepared for the first time by ALD using TiCl4 and H2S as precursors. Ti1-xNbxOy and Ti1-xTaxOy transparent conducting oxide films were prepared successfully by ALD and post-deposition annealing. Highly unusual, explosive crystallization behaviour occurred in these mixed oxides which resulted in anatase crystals with lateral dimensions over 1000 times the film thickness.

Problems and Algorithms for Sequence Segmentations

The analysis of sequential data is required in many diverse areas such as telecommunications, stock market analysis, and bioinformatics. A basic problem related to the analysis of sequential data is the sequence segmentation problem. A sequence segmentation is a partition of the sequence into a number of non-overlapping segments that cover all data points, such that each segment is as homogeneous as possible. This problem can be solved optimally using a standard dynamic programming algorithm. In the first part of the thesis, we present a new approximation algorithm for the sequence segmentation problem. This algorithm has smaller running time than the optimal dynamic programming algorithm, while it has bounded approximation ratio. The basic idea is to divide the input sequence into subsequences, solve the problem optimally in each subsequence, and then appropriately combine the solutions to the subproblems into one final solution. In the second part of the thesis, we study alternative segmentation models that are devised to better fit the data. More specifically, we focus on clustered segmentations and segmentations with rearrangements. While in the standard segmentation of a multidimensional sequence all dimensions share the same segment boundaries, in a clustered segmentation the multidimensional sequence is segmented in such a way that dimensions are allowed to form clusters. Each cluster of dimensions is then segmented separately. We formally define the problem of clustered segmentations and we experimentally show that segmenting sequences using this segmentation model, leads to solutions with smaller error for the same model cost. Segmentation with rearrangements is a novel variation to the segmentation problem: in addition to partitioning the sequence we also seek to apply a limited amount of reordering, so that the overall representation error is minimized. We formulate the problem of segmentation with rearrangements and we show that it is an NP-hard problem to solve or even to approximate. We devise effective algorithms for the proposed problem, combining ideas from dynamic programming and outlier detection algorithms in sequences. In the final part of the thesis, we discuss the problem of aggregating results of segmentation algorithms on the same set of data points. In this case, we are interested in producing a partitioning of the data that agrees as much as possible with the input partitions. We show that this problem can be solved optimally in polynomial time using dynamic programming. Furthermore, we show that not all data points are candidates for segment boundaries in the optimal solution.

Optimisation Problems in Wireless Sensor Networks : Local Algorithms and Local Graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

Confronting Confucian Understandings of the Christian Doctrine of Salvation : A systematic theological analysis of the basic problems in the Confucian-Christian dialogue

The aim of the present study is to analyze Confucian understandings of the Christian doctrine of salvation in order to find the basic problems in the Confucian-Christian dialogue. I will approach the task via a systematic theological analysis of four issues in order to limit the thesis to an appropriate size. They are analyzed in three chapters as follows: 1. The Confucian concept concerning the existence of God. Here I discuss mainly the issue of assimilation of the Christian concept of God to the concepts of Sovereign on High (Shangdi) and Heaven (Tian) in Confucianism. 2. The Confucian understanding of the object of salvation and its status in Christianity. 3. The Confucian understanding of the means of salvation in Christianity. Before beginning this analysis it is necessary to clarify the vast variety of controversies, arguments, ideas, opinions and comments expressed in the name of Confucianism; thus, clear distinctions among different schools of Confucianism are given in chapter 2. In the last chapter I will discuss the results of my research in this study by pointing out the basic problems that will appear in the analysis. The results of the present study provide conclusions in three related areas: the tacit differences in the ways of thinking between Confucians and Christians, the basic problems of the Confucian-Christian dialogue, and the affirmative elements in the dialogue. In addition to a summary, a bibliography and an index, there are also eight appendices, where I have introduced important background information for readers to understand the present study.

Spirituality of Finnish peacekeepers

The previous academic research on Finnish peacekeeping has clarified the operative and historical aspects of Finnish peacekeeping lacking the view of an individual who does the actual peacekeeping work. This research is based on the underlying theoretical assumption of human beings possessing different kinds of talents and intelligences creating a holistic entity. In this broad perspective spirituality was explored as an umbrella concept, as a holistic ability or talent, that can be explored as the deepest aspect of defining what it means to be human. The theoretical framework incorporated the concept of an intelligence, which is defined in Gardner's theory of multiple intelligences as the ability to solve problems, or to create products, that are valued within one or more cultural settings (Gardner, 1993, x). The viability of this theory was studied in the sample of Finnish peacekeepers. Spirituality in the theoretical and conceptual horizon was viewed as an extension of Gardner's theory of intelligences as one potential Gardnerian intelligence candidate. In addition to Gardner's theory, spirituality was explored as sensitivity which includes capacities such as sensing awareness, sensing mystery and sensing value (Hay, 1998). Also the practical aspects of spirituality were taken in account as shown in our everyday lives giving us the direction and influencing our social responsibilities and concerns (Bradford, 1995). Spirituality was explored also involving the element of the peacekeepers' community, the element of personal moral orientations and in the domain of religion and coping. The purpose of this research aimed in two dimensions. First, the aim was to outline the intelligence profile and the spiritual sensitivity profile of peacekeepers. Second, the aim was to understand qualitatively the nature of peacekeepers' spirituality The research interests were studied with different kinds of peacekeepers. Applying the mixed methods approach the research was conducted in two phases: first the former SFOR peacekeepers (N=6) were interviewed and the data was analysed. Inspired by the primary findings of these interviews, the data for the case-study of one peacekeeper was collected in co-operation with one former SFOR peacekeeper (N=1). In the second phase the data was collected from KFOR peacekeepers through the quantitative MI-Survey and the spiritual sensitivity survey (N=195). The quantitative method was used to outline the intelligence profile and the spiritual sensitivity profile of peacekeepers (N=195). In the mixed methods approach this method highlighted the general overview of intelligence traits and spiritual sensitivity of peacekeepers. In the mixed methods approach the qualitative method including interviews (N=6) and a case-study of one peacekeeper (N=1) increased subjective, qualitative information of spirituality of peacekeepers. The intelligence profile of peacekeepers highlighted the bodily-kinesthetic and interpersonal dimensions as the practical and social aspects of peacekeepers. Strong inter-item dependencies in the intrapersonal intelligence profile meant that peacekeepers possess a self-reflection and self-knowledge component and they reflect on deep psychological and philosophical issues. Regarding the spiritual sensitivity, peacekeepers found awareness-sensing, mystery-sensing, value-sensing and community-sensing important. The community-sensing emphasised a strong will to advance peace and to help people who are in need: things that are close to the heart of the peacekeepers. These results depicted practicality, being socially capable, and reflecting one's inner world as essential to peacekeepers. Moreover, spirituality as peacekeepers' moral endeavour became clearer because the sub-model of their community-sensing described morally charged destinations: advancing peace and helping people in need. In the qualitative findings peacekeepers articulated justice orientation and rule-following characterising the nature of peacekeepers' moral attitude and moral call (Kohlberg, 1969). An ethic of care (Gilligan, 1982) describes mainly female moral orientation, but the findings revealed that an ethic of care is also an important agent supporting strongly male peacekeepers in their aim to carry out qualitatively good peacekeeping work. The moral endeavour was voiced, when the role of religion in coping meant the assessment of the a way of life, a way of conduct, a way of being truthful to one's own values in confusing surroundings. The practical level of spiritual and religious contemplation was voiced as morally charged inner motivation to fulfil one's duties and at the same time to cope with various peacekeeping challenges. The results of different data sets were combined and interpreted as the moral endeavour, which characterises peacekeepers' spirituality. As the combining result, the perspective of peacekeepers' spirituality is considered moral or at least morally charged.