A Possible and Necessary Consistency Proof

After Gödel's incompleteness theorems and the collapse of Hilbert's programme Gerhard Gentzen continued the quest for consistency proofs of Peano arithmetic. He considered a finitistic or constructive proof still possible and necessary for the foundations of mathematics. For a proof to be meaningful, the principles relied on should be considered more reliable than the doubtful elements of the theory concerned. He worked out a total of four proofs between 1934 and 1939. This thesis examines the consistency proofs for arithmetic by Gentzen from different angles. The consistency of Heyting arithmetic is shown both in a sequent calculus notation and in natural deduction. The former proof includes a cut elimination theorem for the calculus and a syntactical study of the purely arithmetical part of the system. The latter consistency proof in standard natural deduction has been an open problem since the publication of Gentzen's proofs. The solution to this problem for an intuitionistic calculus is based on a normalization proof by Howard. The proof is performed in the manner of Gentzen, by giving a reduction procedure for derivations of falsity. In contrast to Gentzen's proof, the procedure contains a vector assignment. The reduction reduces the first component of the vector and this component can be interpreted as an ordinal less than epsilon_0, thus ordering the derivations by complexity and proving termination of the process.

Tieteellinen ajattelu yliopisto-opinnoissa : haastattelututkimus psykologian, teologian ja farmasian opiskelijoista

The aim of this dissertation is to explore the academic thinking and personal epistemology of university students. More specifically, the aim is to understand and promote students’ research and academic skills as a central goal of academic studies in the research-intensive university of Helsinki. Two of the four studies examine the personal epistemology of psychology students in different study phases, and the variation in personal epistemology among final-year psychology, theology and pharmacy students. Furthermore, personal epistemology was explored as a phenomenon among the student groups. In the fourth study the individual answers of the students interviewed are investigated in more detail. The main focus is on examining students’ beliefs about the nature of knowledge and knowledge acquisition as a representation of their personal epistemology. Study I presents a model which describes the main elements and aspects of teaching and learning in pharmacy education. Firstly, the meaning of quality of teaching and learning is explored. On the basis of this information, the study concentrates on the pedagogical implications of changing pharmacy teaching to improve the quality of learning. Study II describes the results of a cross-sectional study of psychology students participating in undergraduate and master’s level psychology programmes. The students (N = 53) were interviewed concerning their beliefs about knowledge and knowing, the aim being to explore students’ responses about thinking and reasoning. The results are analysed using content analysis to create categories of personal epistemology and comparisons among the students according to the phase of their studies. Study III examines interdisciplinary differences in final-year psychology, pharmacy and theology students’ (N = 52) academic thinking and personal epistemology. The aims of study IV are to examine and compare the consistency of personal epistemology profiles among university students (N = 87) representing three academic disciplines. The individual answers are examined and rated on a scale from absolutist to evaluativist thinking. On the basis of this data, three personal epistemology profiles are identified: a) absolutist profiles; b) relativistic profiles; and c) evaluativist profiles consisting of the subgroups entitled “limited” and “sophisticated”. The results of the studies clearly demonstrate that personal epistemology varies between students in different age groups, study phases, and disciplines. Three categories, including several subcategories, emerge to describe the personal epistemology of students. Furthermore, three personal epistemology profiles can be identified from the data. The comparison between students reveals interesting differences and similarities among student groups, and developmental trends of personal epistemology.

Search For Susceptibility Genes In Schizophrenia

Schizophrenia is a severe mental disorder affecting 0.4-1% of the population worldwide. It is characterized by impairments in the perception of reality and by significant social or occupational dysfunction. The disorder is one of the major contributors to the global burden of diseases. Studies of twins, families, and adopted children point to strong genetic components for schizophrenia, but environmental factors also play a role in the pathogenesis of disease. Molecular genetic studies have identified several potential positional candidate genes. The strongest evidence for putative schizophrenia susceptibility loci relates to the genes encoding dysbindin (DTNBP1) and neuregulin (NRG1), but studies lack impressive consistency in the precise genetic regions and alleles implicated. We have studied the role of three potential candidate genes by genotyping 28 single nucleotide polymorphisms in the DNTBP1, NRG1, and AKT1 genes in a large schizophrenia family sample consisting of 441 families with 865 affected individuals from Finland. Our results do not support a major role for these genes in the pathogenesis of schizophrenia in Finland. We have previously identified a region on chromosome 5q21-34 as a susceptibility locus for schizophrenia in a Finnish family sample. Recently, two studies reported association between the γ-aminobutyric acid type A receptor cluster of genes in this region and one study showed suggestive evidence for association with another regional gene encoding clathrin interactor 1 (CLINT1, also called Epsin 4 and ENTH). To further address the significance of these genes under the linkage peak in the Finnish families, we genotyped SNPs of these genes, and observed statistically significant association of variants between GABRG2 and schizophrenia. Furthermore, these variants also seem to affect the functioning of the working memory. Fetal events and obstetric complications are associated with schizophrenia. Rh incompatibility has been implicated as a risk factor for schizophrenia in several epidemiological studies. We conducted a family-based candidate-gene study that assessed the role of maternal-fetal genotype incompatibility at the RhD locus in schizophrenia. There was significant evidence for an RhD maternal-fetal genotype incompatibility, and the risk ratio was estimated at 2.3. This is the first candidate-gene study to explicitly test for and provide evidence of a maternal-fetal genotype incompatibility mechanism in schizophrenia. In conclusion, in this thesis we found evidence that one GABA receptor subunit, GABRG2, is significantly associated with schizophrenia. Furthermore, it also seems to affect to the functioning of the working memory. In addition, an RhD maternal-fetal genotype incompatibility increases the risk of schizophrenia by two-fold.

The Miocene of Western Asia; Fossil mammals at the crossroads of faunal provinces and climate regimes

Being at the crossroads of the Old World continents, Western Asia has a unique position through which the dispersal and migration of mammals and the interaction of faunal bioprovinces occurred. Despite its critical position, the record of Miocene mammals in Western Asia is sporadic and there are large spatial and temporal gaps between the known fossil localities. Although the development of the mammalian faunas in the Miocene of the Old World is well known and there is ample evidence for environmental shifts in this epoch, efforts toward quantification of habitat changes and development of chronofaunas based on faunal compositions were mostly neglected. Advancement of chronological, paleoclimatological, and paleogeographical reconstruction tools and techniques and increased numbers of new discoveries in recent decades have brought the need for updating and modification of our level of understanding. We under took fieldwork and systematic study of mammalian trace and body fossils from the northwestern parts of Iran along with analysis of large mammal data from the NOW database. The data analysis was used to study the provinciality, relative abundance, and distribution history of the closed- and open-adapted taxa and chronofaunas in the Miocene of the Old World and Western Asia. The provinciality analysis was carried out, using locality clustering, and the relative abundance of the closed- and open-adapted taxa was surveyed at the family level. The distribution history of the chronofaunas was studied, using faunal resemblance indices and new mapping techniques, together with humidity analysis based on mean ordinated hypsodonty. Paleoichnological studies revealed the abundance of mammalian footprints in several parts of the basins studied, which are normally not fossiliferous in terms of body fossils. The systematic study and biochronology of the newly discovered mammalian fossils in northwestern Iran indicates their close affinities with middle Turolian faunas. Large cranial remains of hipparionine horses, previously unknown in Iran and Western Asia, are among the material studied. The initiation of a new field project in the famous Maragheh locality also brings new opportunities to address questions regarding the chronology and paleoenvironment of this classical site. Provinciality analysis modified our previous level of understandings, indicating the interaction of four provinces in Western Asia. The development of these provinces was apparently due to the presence of high mountain ranges in the area, which affected the dispersal of mammals and also climatic patterns. Higher temperatures and possibly higher co2 levels in the Middle Miocene Climatic Optimum apparently favored the development of the closed forested environments that supported the dominance of the closed-adapted taxa. The increased seasonality and the progressive cooling and drying of the midlatitudes toward the Late Miocene maintained the dominance of open-adapted faunas. It appears that the late Middle Miocene was the time of transition from a more forested to a less forested world. The distribution history of the closed- and open-adapted chronofaunas shows the presence of cosmopolitan and endemic faunas in Western Asia. The closed-adapted faunas, such as the Arabian chronofauna of the late Early‒early Middle Miocene, demonstrated a rapid buildup and gradual decline. The open-adapted chronofaunas, such as the Late Miocene Maraghean fauna, climaxed gradually by filling the opening environments and moving in response to changes in humidity patterns. They abruptly declined due to demise of their favored environments. The Siwalikan chronofauna of the early Late Miocene remained endemic and restricted through all its history. This study highlights the importance of field investigations and indicates that new surveys in the vast areas of Western Asia, which are poorly sampled in terms of fossil mammal localities, can still be promising. Clustering of the localities supports the consistency of formerly known patterns and augments them. Although the quantitative approach to relative abundance history of the closed- and open-adapted mammals harks back to more than half a century ago, it is a novel technique providing robust results. Tracking the history of the chronofaunas in space and time by means of new computational and illustration methods is also a new practice that can be expanded to new areas and time spans.

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 Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Specifying Reuse Interfaces for Task-Oriented Framework Specialization

Reuse of existing carefully designed and tested software improves the quality of new software systems and reduces their development costs. Object-oriented frameworks provide an established means for software reuse on the levels of both architectural design and concrete implementation. Unfortunately, due to frame-works complexity that typically results from their flexibility and overall abstract nature, there are severe problems in using frameworks. Patterns are generally accepted as a convenient way of documenting frameworks and their reuse interfaces. In this thesis it is argued, however, that mere static documentation is not enough to solve the problems related to framework usage. Instead, proper interactive assistance tools are needed in order to enable system-atic framework-based software production. This thesis shows how patterns that document a framework s reuse interface can be represented as dependency graphs, and how dynamic lists of programming tasks can be generated from those graphs to assist the process of using a framework to build an application. This approach to framework specialization combines the ideas of framework cookbooks and task-oriented user interfaces. Tasks provide assistance in (1) cre-ating new code that complies with the framework reuse interface specification, (2) assuring the consistency between existing code and the specification, and (3) adjusting existing code to meet the terms of the specification. Besides illustrating how task-orientation can be applied in the context of using frameworks, this thesis describes a systematic methodology for modeling any framework reuse interface in terms of software patterns based on dependency graphs. The methodology shows how framework-specific reuse interface specifi-cations can be derived from a library of existing reusable pattern hierarchies. Since the methodology focuses on reusing patterns, it also alleviates the recog-nized problem of framework reuse interface specification becoming complicated and unmanageable for frameworks of realistic size. The ideas and methods proposed in this thesis have been tested through imple-menting a framework specialization tool called JavaFrames. JavaFrames uses role-based patterns that specify a reuse interface of a framework to guide frame-work specialization in a task-oriented manner. This thesis reports the results of cases studies in which JavaFrames and the hierarchical framework reuse inter-face modeling methodology were applied to the Struts web application frame-work and the JHotDraw drawing editor framework.

Affektiivisuuden laskennallinen määritteleminen

One of the most tangled fields of research is the field of defining and modeling affective concepts, i. e. concepts regarding emotions and feelings. The subject can be approached from many disciplines. The main problem is lack of generally approved definitions. However, e.g. linguists have recently started to check the consistency of their theories with the help of computer simulations. Definitions of affective concepts are needed for performing similar simulations in behavioral sciences. In this thesis, preliminary computational definitions of affects for a simple utility-maximizing agent are given. The definitions have been produced by synthetizing ideas from theories from several fields of research. The class of affects is defined as a superclass of emotions and feelings. Affect is defined as a process, in which a change in an agent's expected utility causes a bodily change. If the process is currently under the attention of the agent (i.e. the agent is conscious of it), the process is a feeling. If it is not, but can in principle be taken into attention (i.e. it is preconscious), the process is an emotion. Thus, affects do not presuppose consciousness, but emotions and affects do. Affects directed at unexpected materialized (i.e. past) events are delight and fright. Delight is the consequence of an unexpected positive event and fright is the consequence of an unexpected negative event. Affects directed at expected materialized (i.e. past) events are happiness (expected positive event materialized), disappointment (expected positive event did not materialize), sadness (expected negative event materialized) and relief (expected negative event did not materialize). Affects directed at expected unrealized (i.e. future) events are fear and hope. Some other affects can be defined as directed towards originators of the events. The affect classification has also been implemented as a computer program, the purpose of which is to ensure the coherence of the definitions and also to illustrate the capabilities of the model. The exact content of bodily changes associated with specific affects is not considered relevant from the point of view of the logical structure of affective phenomena. The utility function need also not be defined, since the target of examination is only its dynamics.

Tutkimusetiikka ja tutkimusympäristön normit

According to some scientists it is not useful to integrate ethics into research practices. Their claim is that only unethical persons have ethical problems and because of this we must accept ethical misbehaviour as a phenomenon typical of human society. In the present study the argument that the moral personality of scientists explains ethical problems in science is questioned; in addition, the focus is shifted from individuals to the level of the research environment. The question asked is whether the research environment somehow contributes to research ethics violations. To answer this question the focus was turned towards the research environment norms. The aim of the study was to investigate whether or not these norms are consistent with the norms of research ethics, so that it would be possible to evaluate if the research environment supports scientists in their task of meeting the ethical standards of scientific research. In the study the research environment was examined in three parts. The first deals with society especially Finnish society as a research environment. The second deals with the autonomous science institution as a research environment, while the third deals with scientific society (working according to scientific criteria) as a research environment. The conceptual analysis method was used. This means that various normative arguments were analysed, the primary assumptions behind them were recognized, and the acceptability of normative claims was evaluated according to their consistency. The results of the study do not support the claim that ethical violations in science could be satisfactorily explained by referring only to the personal qualities of scientists. The research environment can limit the freedom to follow the ethical principles of science, it can prevent scientists from handling ethical problems openly and from integrating ethical norms effectively into research practices. The norms of research environment are often implicit but nevertheless influence scientific practices. Further, the results indicate that handling ethical questions should be a part of scientific training.

On cluster approximations of cellular automata

In this thesis I examine one commonly used class of methods for the analytic approximation of cellular automata, the so-called local cluster approximations. This class subsumes the well known mean-field and pair approximations, as well as higher order generalizations of these. While a straightforward method known as Bayesian extension exists for constructing cluster approximations of arbitrary order on one-dimensional lattices (and certain other cases), for higher-dimensional systems the construction of approximations beyond the pair level becomes more complicated due to the presence of loops. In this thesis I describe the one-dimensional construction as well as a number of approximations suggested for higher-dimensional lattices, comparing them against a number of consistency criteria that such approximations could be expected to satisfy. I also outline a general variational principle for constructing consistent cluster approximations of arbitrary order with minimal bias, and show that the one-dimensional construction indeed satisfies this principle. Finally, I apply this variational principle to derive a novel consistent expression for symmetric three cell cluster frequencies as estimated from pair frequencies, and use this expression to construct a quantitatively improved pair approximation of the well-known lattice contact process on a hexagonal lattice.

Viilin varahapatteen kehittäminen

Kirjallisuuskatsauksessa käsiteltiin viiliä hapanmaitotuotteena, viilin arviointimenetelmiä sekä viilihapatteissa käytettyjen hapatekantojen vaikutuksia maidossa ja niiden vuorovaikutuksia toisiinsa. Lisäksi pohdittiin viilihapatteiden bakteriofaageja, niiden ehkäisyä sekä solunsisäisiä että -ulkoisia faagiresistenssimekanismeja. Kokeellisessa osassa tutkittiin, onko nykyisten tuotantohapatteiden koostaminen yksittäiskannoista mahdollista, sekä koostettiin uusista Lactococcus lactis ssp. cremoris -kannoista varahapate. Hapatteiden käyttökelpoisuutta tutkittiin rakennemittauksin ja aistinvaraisin menetelmin. Varahapatteen faagikestävyyttä testattiin valmistamalla viiliä ja infektoimalla viilit faaginäytteillä. Hapatekannat viljeltiin fermentorissa, konsentroitiin sentrifugoimalla ja pakastettiin –75 °C:ssa. Hapatteet koostettiin noin 1 päivä ennen viilin valmistusta. Viilit arvioitiin aistinvaraisesti 3–6 hengen ryhmässä ja viileille tehtiin rakennemittaukset (kiinteys, sakeus ja koossapysyvyys) sekä kemialliset analyysit. Aistinvaraisen arvioinnin tulokset käsiteltiin tilastollisesti ja tulosten perusteella tehtiin uudet kantakombinaatiot ja viilit. Tuotantohapatekannoilla valmistetut viilit arvioitiin kolmitestillä (n = 10–11) ja uusilla kannoilla valmistetut viilit arvioitiin profiilitestillä (n = 8). Lisäksi viileille tehtiin rakennemittaukset ja kemialliset analyysit. Varahapatekoosteilla valmistettujen viilien pH laski 4,5:een faagin läsnäollessa 0–10 tunnin viiveellä verrattuna faagivapaisiin viileihin, kun taas tuotantohapatteet eivät hapantuneet faagin läsnäollessa. Aromintuottajat eivät kasvaneet viileissä kunnolla, kun hapate koostettiin yksittäiskannoista. Kolmitestissä ei erotettu nykyisillä tuotantohapatteilla valmistettua viiliä yksittäin koostetusta hapatteesta, eli hapatteita on mahdollista koostaa yksittäiskannoista. Varahapatteilla koostetut viilit poikkesivat profiilitestissä tuotantohapatteella koostetusta viilistä ulkonäkö- ja rakenneominaisuuksiltaan. Makuominaisuuksien suhteen ei viilien välille saatu eroa.

The Path to a Porous Semiconductor Multilayer

Thin films are the basis of much of recent technological advance, ranging from coatings with mechanical or optical benefits to platforms for nanoscale electronics. In the latter, semiconductors have been the norm ever since silicon became the main construction material for a multitude of electronical components. The array of characteristics of silicon-based systems can be widened by manipulating the structure of the thin films at the nanoscale - for instance, by making them porous. The different characteristics of different films can then to some extent be combined by simple superposition. Thin films can be manufactured using many different methods. One emerging field is cluster beam deposition, where aggregates of hundreds or thousands of atoms are deposited one by one to form a layer, the characteristics of which depend on the parameters of deposition. One critical parameter is deposition energy, which dictates how porous, if at all, the layer becomes. Other parameters, such as sputtering rate and aggregation conditions, have an effect on the size and consistency of the individual clusters. Understanding nanoscale processes, which cannot be observed experimentally, is fundamental to optimizing experimental techniques and inventing new possibilities for advances at this scale. Atomistic computer simulations offer a window to the world of nanometers and nanoseconds in a way unparalleled by the most accurate of microscopes. Transmission electron microscope image simulations can then bridge this gap by providing a tangible link between the simulated and the experimental. In this thesis, the entire process of cluster beam deposition is explored using molecular dynamics and image simulations. The process begins with the formation of the clusters, which is investigated for Si/Ge in an Ar atmosphere. The structure of the clusters is optimized to bring it as close to the experimental ideal as possible. Then, clusters are deposited, one by one, onto a substrate, until a sufficiently thick layer has been produced. Finally, the concept is expanded by further deposition with different parameters, resulting in multiple superimposed layers of different porosities. This work demonstrates how the aggregation of clusters is not entirely understood within the scope of the approximations used in the simulations; yet, it is also shown how the continued deposition of clusters with a varying deposition energy can lead to a novel kind of nanostructured thin film: a multielemental porous multilayer. According to theory, these new structures have characteristics that can be tailored for a variety of applications, with precision heretofore unseen in conventional multilayer manufacture.

Spatial ecology of food webs : herbivore-parasitoid communities on the pedunculate oak

Herbivorous insects, their host plants and natural enemies form the largest and most species-rich communities on earth. But what forces structure such communities? Do they represent random collections of species, or are they assembled by given rules? To address these questions, food webs offer excellent tools. As a result of their versatile information content, such webs have become the focus of intensive research over the last few decades. In this thesis, I study herbivore-parasitoid food webs from a new perspective: I construct multiple, quantitative food webs in a spatially explicit setting, at two different scales. Focusing on food webs consisting of specialist herbivores and their natural enemies on the pedunculate oak, Quercus robur, I examine consistency in food web structure across space and time, and how landscape context affects this structure. As an important methodological development, I use DNA barcoding to resolve potential cryptic species in the food webs, and to examine their effect on food web structure. I find that DNA barcoding changes our perception of species identity for as many as a third of the individuals, by reducing misidentifications and by resolving several cryptic species. In terms of the variation detected in food web structure, I find surprising consistency in both space and time. From a spatial perspective, landscape context leaves no detectable imprint on food web structure, while species richness declines significantly with decreasing connectivity. From a temporal perspective, food web structure remains predictable from year to year, despite considerable species turnover in local communities. The rate of such turnover varies between guilds and species within guilds. The factors best explaining these observations are abundant and common species, which have a quantitatively dominant imprint on overall structure, and suffer the lowest turnover. By contrast, rare species with little impact on food web structure exhibit the highest turnover rates. These patterns reveal important limitations of modern metrics of quantitative food web structure. While they accurately describe the overall topology of the web and its most significant interactions, they are disproportionately affected by species with given traits, and insensitive to the specific identity of species. As rare species have been shown to be important for food web stability, metrics depicting quantitative food web structure should then not be used as the sole descriptors of communities in a changing world. To detect and resolve the versatile imprint of global environmental change, one should rather use these metrics as one tool among several.

Prevalence and Forms of Bullying among Business Professionals: A Comparison of Two Different Strategies for Measuring Bullying

The aim of this study was to analyse the prevalence and forms of workplace bullying among business professionals holding predominantly managerial or expert positions. A cross-sectional survey study was conducted among Finnish professionals with a university degree in business studies. In the study two different strategies for measuring bullying were used and compared. When provided a definition of bullying, 8.8% of the respondents reported that they had at least occasionally been bullied during the past 12 months. However, when using a slightly modified version of the Negative Acts Questionnaire (Einarsen & Hoel 2001), containing a list of 32 predefined negative and potentially harassing acts, as many as 24.1% of the respondents reported that they had been subjected to at least one of the negative acts on a weekly basis. The respondents had experienced predominantly work-related negative acts, e.g. that their opinions and views were ignored, that they were given unreasonable deadlines or that information was withheld. Although the prevalence rates reported with the two strategies varied considerably, there was still consistency between the two strategies in the sense that those who had classified themselves as bullied also reported higher exposure rates to almost all of the negative acts included.