Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

Integral Transformations of Volterra Gaussian Processes

We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.

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.

Semantic Classes in Topic Detection and Tracking

Topic detection and tracking (TDT) is an area of information retrieval research the focus of which revolves around news events. The problems TDT deals with relate to segmenting news text into cohesive stories, detecting something new, previously unreported, tracking the development of a previously reported event, and grouping together news that discuss the same event. The performance of the traditional information retrieval techniques based on full-text similarity has remained inadequate for online production systems. It has been difficult to make the distinction between same and similar events. In this work, we explore ways of representing and comparing news documents in order to detect new events and track their development. First, however, we put forward a conceptual analysis of the notions of topic and event. The purpose is to clarify the terminology and align it with the process of news-making and the tradition of story-telling. Second, we present a framework for document similarity that is based on semantic classes, i.e., groups of words with similar meaning. We adopt people, organizations, and locations as semantic classes in addition to general terms. As each semantic class can be assigned its own similarity measure, document similarity can make use of ontologies, e.g., geographical taxonomies. The documents are compared class-wise, and the outcome is a weighted combination of class-wise similarities. Third, we incorporate temporal information into document similarity. We formalize the natural language temporal expressions occurring in the text, and use them to anchor the rest of the terms onto the time-line. Upon comparing documents for event-based similarity, we look not only at matching terms, but also how near their anchors are on the time-line. Fourth, we experiment with an adaptive variant of the semantic class similarity system. The news reflect changes in the real world, and in order to keep up, the system has to change its behavior based on the contents of the news stream. We put forward two strategies for rebuilding the topic representations and report experiment results. We run experiments with three annotated TDT corpora. The use of semantic classes increased the effectiveness of topic tracking by 10-30\% depending on the experimental setup. The gain in spotting new events remained lower, around 3-4\%. The anchoring the text to a time-line based on the temporal expressions gave a further 10\% increase the effectiveness of topic tracking. The gains in detecting new events, again, remained smaller. The adaptive systems did not improve the tracking results.

Mining Sequential Data – in Search of Segmental Structures

Segmentation is a data mining technique yielding simplified representations of sequences of ordered points. A sequence is divided into some number of homogeneous blocks, and all points within a segment are described by a single value. The focus in this thesis is on piecewise-constant segments, where the most likely description for each segment and the most likely segmentation into some number of blocks can be computed efficiently. Representing sequences as segmentations is useful in, e.g., storage and indexing tasks in sequence databases, and segmentation can be used as a tool in learning about the structure of a given sequence. The discussion in this thesis begins with basic questions related to segmentation analysis, such as choosing the number of segments, and evaluating the obtained segmentations. Standard model selection techniques are shown to perform well for the sequence segmentation task. Segmentation evaluation is proposed with respect to a known segmentation structure. Applying segmentation on certain features of a sequence is shown to yield segmentations that are significantly close to the known underlying structure. Two extensions to the basic segmentation framework are introduced: unimodal segmentation and basis segmentation. The former is concerned with segmentations where the segment descriptions first increase and then decrease, and the latter with the interplay between different dimensions and segments in the sequence. These problems are formally defined and algorithms for solving them are provided and analyzed. Practical applications for segmentation techniques include time series and data stream analysis, text analysis, and biological sequence analysis. In this thesis segmentation applications are demonstrated in analyzing genomic sequences.

Religion Explained? : A Philosophical Appraisal of the Cognitive Science of Religion

This study examines philosophically the main theories and methodological assumptions of the field known as the cognitive science of religion (CSR). The study makes a philosophically informed reconstruction of the methodological principles of the CSR, indicates problems with them, and examines possible solutions to these problems. The study focuses on several different CSR writers, namely, Scott Atran, Justin Barrett, Pascal Boyer and Dan Sperber. CSR theorising is done in the intersection between cognitive sciences, anthropology and evolutionary psychology. This multidisciplinary nature makes CSR a fertile ground for philosophical considerations coming from philosophy of psychology, philosophy of mind and philosophy of science. The study begins by spelling out the methodological assumptions and auxiliary theories of CSR writers by situating these theories and assumptions in the nexus of existing approaches to religion. The distinctive feature of CSR is its emphasis on information processing: CSR writers claim that contemporary cognitive sciences can inform anthropological theorising about the human mind and offer tools for producing causal explanations. Further, they claim to explain the prevalence and persistence of religion by cognitive systems that undergird religious thinking. I also examine the core theoretical contributions of the field focusing mainly on the (1) “minimally counter-intuitiveness hypothesis” and (2) the different ways in which supernatural agent representations activate our cognitive systems. Generally speaking, CSR writers argue for the naturalness of religion: religious ideas and practices are widespread and pervasive because human cognition operates in such a way that religious ideas are easy to acquire and transmit. The study raises two philosophical problems, namely, the “problem of scope” and the “problem of religious relevance”. The problem of scope is created by the insistence of several critics of the CSR that CSR explanations are mostly irrelevant for explaining religion. Most CSR writers themselves hold that cognitive explanations can answer most of our questions about religion. I argue that the problem of scope is created by differences in explanation-begging questions: the former group is interested in explaining different things than the latter group. I propose that we should not stick too rigidly to one set of methodological assumptions, but rather acknowledge that different assumptions might help us to answer different questions about religion. Instead of adhering to some robust metaphysics as some strongly naturalistic writers argue, we should adopt a pragmatic and explanatory pluralist approach which would allow different kinds of methodological presuppositions in the study of religion provided that they attempt to answer different kinds of why-questions, since religion appears to be a multi-faceted phenomenon that spans over a variety of fields of special sciences. The problem of religious relevance is created by the insistence of some writers that CSR theories show religious beliefs to be false or irrational, whereas others invoke CSR theories to defend certain religious ideas. The problem is interesting because it reveals the more general philosophical assumptions of those who make such interpretations. CSR theories can (and have been) interpreted in terms of three different philosophical frameworks: strict naturalism, broad naturalism and theism. I argue that CSR theories can be interpreted inside all three frameworks without doing violence to the theories and that these frameworks give different kinds of results regarding the religious relevance of CSR theories.

A role to play: Investigating concepts of masculinity in Australia through theatre

Health professionals, academics, social commentators and the media are increasingly sending the same message – Australian men are in crisis. This message has been supported by documented rises in alcoholism, violence, depression, suicide and crime amongst men in Australia. A major cause of this crisis, it can be argued, is an over-reliance on the out-dated and limited model of hegemonic masculinity that all men are encouraged to imitate in their own behaviour. This paper, as part of a larger study, explores representations of masculinity in selected works of contemporary Australian theatre in order to investigate the concept of hegemonic masculinity and any influence it may have on the perceived ‘crisis of masculinity’. Theatre is but one of the artistic modes that can be used to investigate masculinity and issues associated with identity. The Australia Council for the Arts recognises theatre, along with literature, dance, film, television, inter-arts, music and visual arts, as critical to the understanding and expression of Australian culture and identity. Theatre has been chosen in this instance because of the opportunities available to this study for direct access to specific theatre performances and creators and, also, because of the researcher’s experience, as a theatre director, with the dramatic arts. Through interviews with writers, directors and actors, combined with the analysis of scripts, academic writings, reviews, articles, programmes, play rehearsals and workshops, this research utilises theatre as a medium to explore masculinity in Australia.

(Re)presenting Masculinity: A theatre director's critical observations of, and theatrical experimentation with, (re)presentations of masculinity in selected works of contemporary Australian theatre

Health professionals, academics, social commentators and the media are increasingly sending the same message – Australian men are in crisis. This message has been supported by documented rises in alcoholism, violence, depression, suicide and crime amongst men in Australia. A major cause of this crisis, it can be argued, is an over-reliance on the out-dated and limited model of hegemonic masculinity that all men are encouraged to imitate in their own behaviour. This paper, as part of a larger study, explores representations of masculinity in selected works of contemporary Australian theatre in order to investigate the concept of hegemonic masculinity and any influence it may have on the perceived ‘crisis of masculinity’. Theatre is but one of the artistic modes that can be used to investigate masculinity and issues associated with identity. The Australia Council for the Arts recognises theatre, along with literature, dance, film, television, inter-arts, music and visual arts, as critical to the understanding and expression of Australian culture and identity. Theatre has been chosen in this instance because of the opportunities available to this study for direct access to specific theatre performances and creators and, also, because of the researcher’s experience, as a theatre director, with the dramatic arts. Through interviews with writers, directors and actors, combined with the analysis of scripts, academic writings, reviews, articles, programmes, play rehearsals and workshops, this research utilises theatre as a medium to explore masculinity in Australia.

Governing literacies: Securing literate subjects

This review of literacy research explores ways in which literacy has come to be understood as a problem about human populations. I describe connections between literacy education and the biopolitical government of population, especially the relationship between liberal forms of government and the administration of human freedom. The review takes into account ways in which literacy is implicated in the cultivation of civil society by attending to the interests, as well as to the conduct, of human subjects. I draw on research available in English from across the globe, which provides an overview of how literacy has been rethought and conceptualised through ethnographic, historical and classroom based studies. I discuss claims made for literacy, the way that human populations have been made visible in relation to their literacy practices and the social contexts of their use. The review informs research of representations of literacy as a tool for securing national interests.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

On the integration of self-tracking data amongst quantified self members

Self-tracking, the process of recording one's own behaviours, thoughts and feelings, is a popular approach to enhance one's self-knowledge. While dedicated self-tracking apps and devices support data collection, previous research highlights that the integration of data constitutes a barrier for users. In this study we investigated how members of the Quantified Self movement---early adopters of self-tracking tools---overcome these barriers. We conducted a qualitative analysis of 51 videos of Quantified Self presentations to explore intentions for collecting data, methods for integrating and representing data, and how intentions and methods shaped reflection. The findings highlight two different intentions---striving for self-improvement and curiosity in personal data---which shaped how these users integrated data, i.e. the effort required. Furthermore, we identified three methods for representing data---binary, structured and abstract---which influenced reflection. Binary representations supported reflection-in-action, whereas structured and abstract representations supported iterative processes of data collection, integration and reflection. For people tracking out of curiosity, this iterative engagement with personal data often became an end in itself, rather than a means to achieve a goal. We discuss how these findings contribute to our current understanding of self-tracking amongst Quantified Self members and beyond, and we conclude with directions for future work to support self-trackers with their aspirations.

Matrices of finite Lorentz transformations in a noncompact basis. III. Completeness relation for O(2, 1)

A parametrization of the elements of the three-dimensional Lorentz group O(2, 1), suited to the use of a noncompact O(1, 1) basis in its unitary representations, is derived and used to set up the representation matrices for the entire group. The Plancherel formula for O(2, 1) is then expressed in this basis.

Archaea, Bacteria, and methane production along environmental gradients in fens and bogs

Metanogeenit ovat hapettomissa oloissa eläviä arkkien pääryhmään kuuluvia mikrobeja, joiden ainutlaatuisen aineenvaihdunnan seurauksena syntyy metaania. Ilmakehässä metaani on voimakas kasvihuonekaasu. Yksi suurimmista luonnon metaanilähteistä ovat kosteikot. Pohjoisten soiden metaanipäästöt vaihtelevat voimakkaasti eri soiden välillä ja yhden suon sisälläkin, riippuen muun muassa vuodenajasta, suotyypistä ja kasvillisuudesta. Väitöskirjatyössä tutkittiin metaanipäästöjen vaihtelun mikrobiologista taustaa. Tutkimuksessa selvitettiin suotyypin, vuodenajan, tuhkalannoituksen ja turvesyvyyden vaikutusta metanogeeniyhteisöihin sekä metaanintuottoon kolmella suomalaisella suolla. Lisäksi tutkittiin ei-metanogeenisia arkkeja ja bakteereita, koska ne muodostavat metaanin tuoton lähtöaineet osana hapetonta hajotusta. Mikrobiyhteisöt analysoitiin DNA- ja RNA-lähtöisillä, polymeraasiketjureaktioon (PCR) perustuvilla menetelmillä. Merkkigeeneinä käytettiin metaanin tuottoon liittyvää mcrA-geeniä sekä arkkien ja bakteerien ribosomaalista 16S RNA-geeniä. Metanogeeniyhteisöt ja metaanintuotto erosivat huomattavasti happaman ja vähäravinteisen rahkasuon sekä ravinteikkaampien sarasoiden välillä. Rahkasuolta löytyi lähes yksinomaan Methanomicrobiales-lahkon metanogeeneja, jotka tuottavat metaania vedystä ja hiilidioksidista. Sarasoiden metanogeeniyhteisöt olivat monimuotoisempia, ja niillä esiintyi myös asetaattia käyttäviä metanogeeneja. Vuodenaika vaikutti merkittävästi metaanintuottoon. Talvella havaittiin odottamattoman suuri metaanintuottopotentiaali sekä viitteitä aktiivisista metanogeeneista. Arkkiyhteisön koostumus sen sijaan vaihteli vain vähän. Tuhkalannoitus, jonka tarkoituksena on edistää puiden kasvua ojitetuilla soilla, ei merkittävästi vaikuttanut metaanintuottoon tai -tuottajiin. Ojitetun suon yhteisöt kuitenkin muuttuivat turvesyvyyden mukaan. Vertailtaessa erilaisia PCR-menetelmiä todettiin, että kolmella mcrA-geeniin kohdistuvalla alukeparilla havaittiin pääosin samat ojitetun suon metanogeenit, mutta lajien runsaussuhteet riippuvat käytetyistä alukkeista. Soilla havaitut bakteerit kuuluivat pääjaksoihin Deltaproteobacteria, Acidobacteria ja Verrucomicrobia. Lisäksi löydettiin Crenarchaeota-pääjakson ryhmiin 1.1c ja 1.3 kuuluvia ei-metanogeenisia arkkeja. Tulokset ryhmien esiintymisestä hapettomassa turpeessa antavat lähtökohdan selvittää niiden mahdollisia vuorovaikutuksia metanogeenien kanssa. Tutkimuksen tulokset osoittivat, että metanogeeniyhteisön koostumus heijastaa metaanintuottoon vaikuttavia kemiallisia tai kasvillisuuden vaihteluita kuten suotyyppiä. Soiden metanogeenien ja niiden fysiologian parempi tuntemus voi auttaa ennustamaan ympäristömuutosten vaikutusta soiden metaanipäästöihin.

Mining topical relevant patterns for multi-document summarization

Multi-document summarization addressing the problem of information overload has been widely utilized in the various real-world applications. Most of existing approaches adopt term-based representation for documents which limit the performance of multi-document summarization systems. In this paper, we proposed a novel pattern-based topic model (PBTMSum) for the task of the multi-document summarization. PBTMSum combining pattern mining techniques with LDA topic modelling could generate discriminative and semantic rich representations for topics and documents so that the most representative and non-redundant sentences can be selected to form a succinct and informative summary. Extensive experiments are conducted on the data of document understanding conference (DUC) 2007. The results prove the effectiveness and efficiency of our proposed approach.

Using a glow graph to represent data flow and dependency in event logs

The idea of extracting knowledge in process mining is a descendant of data mining. Both mining disciplines emphasise data flow and relations among elements in the data. Unfortunately, challenges have been encountered when working with the data flow and relations. One of the challenges is that the representation of the data flow between a pair of elements or tasks is insufficiently simplified and formulated, as it considers only a one-to-one data flow relation. In this paper, we discuss how the effectiveness of knowledge representation can be extended in both disciplines. To this end, we introduce a new representation of the data flow and dependency formulation using a flow graph. The flow graph solves the issue of the insufficiency of presenting other relation types, such as many-to-one and one-to-many relations. As an experiment, a new evaluation framework is applied to the Teleclaim process in order to show how this method can provide us with more precise results when compared with other representations.