Kotitaloustaidon ulottuvuuksia : Analyysi kotitaloustaidosta eksistentialistis-hermeneuttisen fenomenologian valossa

DOMESTIC SKILLS AS THE ART OF EVERYDAY LIFE. An inquiry about domestic skills as a way of being-in-the-world in the light of existentialist-hermeneutics phenomenology. This study focuses on analyzing domestic skills in a phenomenological manner. The description phenomenological emerges from the interpretation process, which originates from the ontological question of domestic skills. The ontological question of how domestic skills are directs one s phenomenological gaze to the experiencing of domestic skills, rather than merely viewing their action or technical aspects. Along with the ontological question, the axiological question of what the meaning of domestic skills is drives the analysis. This study is both theoretical and philosophical. Phenomenology is the guiding philosophy, theory and methodology of the inquiry. Existentialist-hermeneutics is the emphasis which most appropriately describes the phenomenological attitude adopted within the analysis. Martin Heidegger s philosophy of being and Maurice Merleau-Ponty s philosophy of the lived body essentially form the theoretical base for the inquiry. The analysis reveals domestic skills within a core of Care and the Other. Care and the Other are anchored both in Heidegger s analysis of Dasein and in Merleau-Ponty s analysis of the reversible being-in-the-world. The social nature of being and the action-oriented intentionality of the lived body are embodied in Care and the Other. This ontological base of domestic skills enables us to see the extensions that inhabit in it. These extensions are redoing, emotional experiencing, adapting and emancipating. The analysis connects ability and action, which is why domestic skills and household activity must be seen as a united whole. This united whole is not the matter of the two components of the phenomenon, but is rather the matter of domestic skills as a way of being-in-the-world. Domestic skills are a channel for the phenomenon Home Economics to manifest in our lives. This is the gaze that presents domestic skills as to be like the poetry of everyday life. The main result of the study is the elucidation of the ontology of domestic skills and the naming of its extensions. This growth of philosophical understanding makes it possible to strengthen the science of home economics.

Idealähtöistä koulualgebraa : IDEAA-opetusmallin kehittäminen algebran opetukseen peruskoulun 7. luokalla

This research is based on the problems in secondary school algebra I have noticed in my own work as a teacher of mathematics. Algebra does not touch the pupil, it remains knowledge that is not used or tested. Furthermore the performance level in algebra is quite low. This study presents a model for 7th grade algebra instruction in order to make algebra more natural and useful to students. I refer to the instruction model as the Idea-based Algebra (IDEAA). The basic ideas of this IDEAA model are 1) to combine children's own informal mathematics with scientific mathematics ("math math") and 2) to structure algebra content as a "map of big ideas", not as a traditional sequence of powers, polynomials, equations, and word problems. This research project is a kind of design process or design research. As such, this project has three, intertwined goals: research, design and pedagogical practice. I also assume three roles. As a researcher, I want to learn about learning and school algebra, its problems and possibilities. As a designer, I use research in the intervention to develop a shared artefact, the instruction model. In addition, I want to improve the practice through intervention and research. A design research like this is quite challenging. Its goals and means are intertwined and change in the research process. Theory emerges from the inquiry; it is not given a priori. The aim to improve instruction is normative, as one should take into account what "good" means in school algebra. An important part of my study is to work out these paradigmatic questions. The result of the study is threefold. The main result is the instruction model designed in the study. The second result is the theory that is developed of the teaching, learning and algebra. The third result is knowledge of the design process. The instruction model (IDEAA) is connected to four main features of good algebra education: 1) the situationality of learning, 2) learning as knowledge building, in which natural language and intuitive thinking work as "intermediaries", 3) the emergence and diversity of algebra, and 4) the development of high performance skills at any stage of instruction.

Aritmetiikasta algebraan : Muutoksia osaamisessa peruskoulun päättöluokalla 20 vuoden aikana

From Arithmetic to Algebra. Changes in the skills in comprehensive school over 20 years. In recent decades we have emphasized the understanding of calculation in mathematics teaching. Many studies have found that better understanding helps to apply skills in new conditions and that the ability to think on an abstract level increases the transfer to new contexts. In my research I take into consideration competence as a matrix where content is in a horizontal line and levels of thinking are in a vertical line. The know-how is intellectual and strategic flexibility and understanding. The resources and limitations of memory have their effects on learning in different ways in different phases. Therefore both flexible conceptual thinking and automatization must be considered in learning. The research questions that I examine are what kind of changes have occurred in mathematical skills in comprehensive school over the last 20 years and what kind of conceptual thinking is demonstrated by students in this decade. The study consists of two parts. The first part is a statistical analysis of the mathematical skills and their changes over the last 20 years in comprehensive school. In the test the pupils did not use calculators. The second part is a qualitative analysis of the conceptual thinking of pupils in comprehensive school in this decade. The study shows significant differences in algebra and in some parts of arithmetic. The largest differences were detected in the calculation skills of fractions. In the 1980s two out of three pupils were able to complete tasks with fractions, but in the 2000s only one out of three pupils were able to do the same tasks. Also remarkable is that out of the students who could complete the tasks with fractions, only one out of three pupils was on the conceptual level in his/her thinking. This means that about 10% of pupils are able to understand the algebraic expression, which has the same isomorphic structure as the arithmetical expression. This finding is important because the ability to think innovatively is created when learning the basic concepts. Keywords: arithmetic, algebra, competence

Rab8 and Rab8-interacting proteins as players in cell polarization

Rab8 and its interacting proteins as regulators of cell polarization During the development of a multi-cellular organism, progenitor cells have to divide and migrate appropriately as well as organize their differentiation with one another, in order to produce a viable embryo. To divide, differentiate and migrate cells have to undergo polarization, a process where internal and external components such as actin, microtubules and adhesion receptors are reorganized to produce a cell that is asymmetric, with functionally different surfaces. Also in the adult organism there is a continuous need for these processes, as cells need to migrate in response to tissue damage and to fight infection. Improper regulation of cell proliferation and migration can conversely lead to disease such as cancer. GTP-binding proteins function as molecular switches by cycling between a GTP-bound (active) conformation and a GDP-bound (inactive) conformation. The Ras super-family of small GTPases are found in all eukaryotic cells. They can be functionally divided into five subfamilies. The Ras family members mainly regulate gene expression, controlling cell proliferation and differentiation. Ras was in fact the first human oncogene to be characterized, and as much as 30% of all human tumors may be directly or indirectly caused by mutations of Ras molecules The Rho family members mainly regulate cytoskeletal reorganization. Arf proteins are known to regulate vesicle budding and Rab proteins regulate vesicular transport. Ran regulates nuclear transport as well as microtubule organization during mitosis. The focus of the thesis of Katarina Hattula, is on Rab8, a small GTPase of the Rab family. Activated Rab8 has previously been shown to induce the formation of new surface extensions, reorganizing both actin and microtubules, and to have a role in directed membrane transport to cell surfaces. However, the exact membrane route it regulates has remained elusive. In the thesis three novel interactors of Rab8 are presented. Rabin8 is a Rab8-specific GEF that localizes to vesicles where it presumably recruits and activates its target Rab8. Its expression in cells leads to remodelling of actin and the formation of polarized cell surface domains. Optineurin, known to be associated with a leading cause of blindness in humans (open-angle glaucoma), is shown to interact specifically with GTP-bound Rab8. Rab8 binds to an amino-terminal region and interestingly, the Huntingtin protein binds a carboxy-terminal region of optineurin. (Aberrant Huntingtin protein is known to be the cause Huntington s disease in humans.) Co-expression of Huntingtin and optineurin enhanced the recruitment of Huntingtin to Rab8-positive vesicular structures. Furthermore, optineurin promoted cell polarization in a similar way to Rab8. A third novel interactor of Rab8 presented in this thesis is JFC1, a member of the synaptogamin-like protein (Slp) family. JFC1 interacts with Rab8 specifically in its GTP-bound form, co-localizes with endogenous Rab8 on tubular and vesicular structures, and is probably involved in controlling Rab8 membrane dynamics. Rab8 is in this thesis work clearly shown to have a strong effect on cell shape. Blocking Rab8 activity by expression of Rab8 RNAi, or by expressing the dominant negative Rab8 (T22N) mutant leads to loss of cell polarity. Conversely, cells expressing the constitutively active Rab8 (Q67L) mutant exhibit a strongly polarized phenotype. Experiments in live cells show that Rab8 is associated with macropinosomes generated at ruffling areas of the membrane. These macropinosomes fuse with or transform into tubules that move toward the cell centre, from where they are recycled back to the leading edge to participate in protrusion formation. The biogenesis of these tubules is shown to be dependent on both actin and microtubule dynamics. The Rab8-specific membrane route studied contained several markers known to be internalized and recycled (1 integrin, transferrin, transferrin receptor, cholera toxin B subunit (CTxB), and major histocompatibility complex class I protein (MHCI)). Co-expression studies revealed that Rab8 localization overlaps with that of Rab11 and Arf6. Rab8 is furthermore clearly functionally linked to Arf6. The data presented in this thesis strongly suggests a role for Rab8 as a regulator for a recycling compartment, which is involved in providing structural and regulatory components to the leading edge to participate in protrusion formation.

Target Cell Topography and Cytoskeletal Reorganization in Natural Killer Cell Activity

The immune system has to recognize and destroy abnormal or infected cells to maintain homeostasis. Natural killer (NK) cells directly recognize and kill transformed or virus-infected cells without prior sensitization. We have studied both virus-infected and tumor cells in order to identify the target structures involved in triggering NK activity. Mouse/human cell hybrids containing various human chromosomes were used as targets. The human chromosome responsible for activating NK cell killing was identified to chromosome number 6. The results suggest that activated NK cells recognize ligands that are encoded on human chromosome 6. We showed that the ligand on the target cell side was intercellular adhesion molecule 2 (ICAM-2). There was no difference in the level of expression of ICAM-2, however, but a drastic difference was seen in the distribution of the molecule: ICAM-2 was evenly distributed on the surface of the NK-resistant cells, but almost totally redistributed to the tip of uropods, bud-like extensions, which were absent from the parental cells. Interestingly, the gene coding for cytoskeletal linker protein ezrin has been localized to human chromosome 6, and there was a colocalization of ezrin and ICAM-2 in the uropods. Furthermore, the transfected human ezrin into NK cell-resistant cells induced uropod formation, ICAM-2 and ezrin redistribution to newly formed uropods, and sensitized target cells to NK cell killing. These data reveal a novel form of NK cell recognition: target structures are already present on normal cells; they become detectable only after abnormal redistribution into hot spots on the target cell membrane. NK cells are central players in the defence against virus infections. They inhibit the spread of infection, allowing time for specific immune responses to develop. The virus-proteins that directly activate human NK cell killing are largely unknown. We studied the sensitivity of virus-specific early proteins of Semliki Forest virus (SFV) to NK killing. The viral non-structural proteins (nsP1-4) translated early in the virus cycle were transfected in NK-resistant cells. Viral early gene nsP1 alone efficiently sensitized target cells to NK activity, and the tight membrane association of nsP1 seems to be critical in the triggering of NK killing. NsP1 protein colocalized with (redistributed) ezrin in filopodia-like structures to which the NK cells were bound. The results suggest that also in viral infections NK cells react to rapid changes in membrane topography. Based on the results of this thesis, a new model of target cell recognition of NK cells can be suggested: reorganization of the cytoskeleton induces alterations in cell surface topography, and this new pattern of surface molecules is recognized as "altered-self".

Topological Quantum Computation - An Analysis of an Anyon Model Based on Quantum Double Symmetries

There exists various suggestions for building a functional and a fault-tolerant large-scale quantum computer. Topological quantum computation is a more exotic suggestion, which makes use of the properties of quasiparticles manifest only in certain two-dimensional systems. These so called anyons exhibit topological degrees of freedom, which, in principle, can be used to execute quantum computation with intrinsic fault-tolerance. This feature is the main incentive to study topological quantum computation. The objective of this thesis is to provide an accessible introduction to the theory. In this thesis one has considered the theory of anyons arising in two-dimensional quantum mechanical systems, which are described by gauge theories based on so called quantum double symmetries. The quasiparticles are shown to exhibit interactions and carry quantum numbers, which are both of topological nature. Particularly, it is found that the addition of the quantum numbers is not unique, but that the fusion of the quasiparticles is described by a non-trivial fusion algebra. It is discussed how this property can be used to encode quantum information in a manner which is intrinsically protected from decoherence and how one could, in principle, perform quantum computation by braiding the quasiparticles. As an example of the presented general discussion, the particle spectrum and the fusion algebra of an anyon model based on the gauge group S_3 are explicitly derived. The fusion algebra is found to branch into multiple proper subalgebras and the simplest one of them is chosen as a model for an illustrative demonstration. The different steps of a topological quantum computation are outlined and the computational power of the model is assessed. It turns out that the chosen model is not universal for quantum computation. However, because the objective was a demonstration of the theory with explicit calculations, none of the other more complicated fusion subalgebras were considered. Studying their applicability for quantum computation could be a topic of further research.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Luonnollisten lukujen joukon määriteltävyys funktioalgebroissa

Let X be a topological space and K the real algebra of the reals, the complex numbers, the quaternions, or the octonions. The functions form X to K form an algebra T(X,K) with pointwise addition and multiplication. We study first-order definability of the constant function set N' corresponding to the set of the naturals in certain subalgebras of T(X,K). In the vocabulary the symbols Constant, +, *, 0', and 1' are used, where Constant denotes the predicate defining the constants, and 0' and 1' denote the constant functions with values 0 and 1 respectively. The most important result is the following. Let X be a topological space, K the real algebra of the reals, the compelex numbers, the quaternions, or the octonions, and R a subalgebra of the algebra of all functions from X to K containing all constants. Then N' is definable in , if at least one of the following conditions is true. (1) The algebra R is a subalgebra of the algebra of all continuous functions containing a piecewise open mapping from X to K. (2) The space X is sigma-compact, and R is a subalgebra of the algebra of all continuous functions containing a function whose range contains a nonempty open set of K. (3) The algebra K is the set of reals or the complex numbers, and R contains a piecewise open mapping from X to K and does not contain an everywhere unbounded function. (4) The algebra R contains a piecewise open mapping from X to the set of the reals and function whose range contains a nonempty open subset of K. Furthermore R does not contain an everywhere unbounded function.

On linear order and computation : The expressiveness of interactive computations on linear orders and computations indexed by ordinals

We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

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.

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.

A Decentralized Session Management Framework for Heterogeneous Ad-Hoc and Fixed Networks

Wireless technologies are continuously evolving. Second generation cellular networks have gained worldwide acceptance. Wireless LANs are commonly deployed in corporations or university campuses, and their diffusion in public hotspots is growing. Third generation cellular systems are yet to affirm everywhere; still, there is an impressive amount of research ongoing for deploying beyond 3G systems. These new wireless technologies combine the characteristics of WLAN based and cellular networks to provide increased bandwidth. The common direction where all the efforts in wireless technologies are headed is towards an IP-based communication. Telephony services have been the killer application for cellular systems; their evolution to packet-switched networks is a natural path. Effective IP telephony signaling protocols, such as the Session Initiation Protocol (SIP) and the H 323 protocol are needed to establish IP-based telephony sessions. However, IP telephony is just one service example of IP-based communication. IP-based multimedia sessions are expected to become popular and offer a wider range of communication capabilities than pure telephony. In order to conjoin the advances of the future wireless technologies with the potential of IP-based multimedia communication, the next step would be to obtain ubiquitous communication capabilities. According to this vision, people must be able to communicate also when no support from an infrastructured network is available, needed or desired. In order to achieve ubiquitous communication, end devices must integrate all the capabilities necessary for IP-based distributed and decentralized communication. Such capabilities are currently missing. For example, it is not possible to utilize native IP telephony signaling protocols in a totally decentralized way. This dissertation presents a solution for deploying the SIP protocol in a decentralized fashion without support of infrastructure servers. The proposed solution is mainly designed to fit the needs of decentralized mobile environments, and can be applied to small scale ad-hoc networks or also bigger networks with hundreds of nodes. A framework allowing discovery of SIP users in ad-hoc networks and the establishment of SIP sessions among them, in a fully distributed and secure way, is described and evaluated. Security support allows ad-hoc users to authenticate the sender of a message, and to verify the integrity of a received message. The distributed session management framework has been extended in order to achieve interoperability with the Internet, and the native Internet applications. With limited extensions to the SIP protocol, we have designed and experimentally validated a SIP gateway allowing SIP signaling between ad-hoc networks with private addressing space and native SIP applications in the Internet. The design is completed by an application level relay that permits instant messaging sessions to be established in heterogeneous environments. The resulting framework constitutes a flexible and effective approach for the pervasive deployment of real time applications.

Matrix Decomposition Methods for Data Mining : Computational Complexity and Algorithms

Matrix decompositions, where a given matrix is represented as a product of two other matrices, are regularly used in data mining. Most matrix decompositions have their roots in linear algebra, but the needs of data mining are not always those of linear algebra. In data mining one needs to have results that are interpretable -- and what is considered interpretable in data mining can be very different to what is considered interpretable in linear algebra. --- The purpose of this thesis is to study matrix decompositions that directly address the issue of interpretability. An example is a decomposition of binary matrices where the factor matrices are assumed to be binary and the matrix multiplication is Boolean. The restriction to binary factor matrices increases interpretability -- factor matrices are of the same type as the original matrix -- and allows the use of Boolean matrix multiplication, which is often more intuitive than normal matrix multiplication with binary matrices. Also several other decomposition methods are described, and the computational complexity of computing them is studied together with the hardness of approximating the related optimization problems. Based on these studies, algorithms for constructing the decompositions are proposed. Constructing the decompositions turns out to be computationally hard, and the proposed algorithms are mostly based on various heuristics. Nevertheless, the algorithms are shown to be capable of finding good results in empirical experiments conducted with both synthetic and real-world data.