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.

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.

Bayesian statistical analysis of bacterial diversity

Bacteria play an important role in many ecological systems. The molecular characterization of bacteria using either cultivation-dependent or cultivation-independent methods reveals the large scale of bacterial diversity in natural communities, and the vastness of subpopulations within a species or genus. Understanding how bacterial diversity varies across different environments and also within populations should provide insights into many important questions of bacterial evolution and population dynamics. This thesis presents novel statistical methods for analyzing bacterial diversity using widely employed molecular fingerprinting techniques. The first objective of this thesis was to develop Bayesian clustering models to identify bacterial population structures. Bacterial isolates were identified using multilous sequence typing (MLST), and Bayesian clustering models were used to explore the evolutionary relationships among isolates. Our method involves the inference of genetic population structures via an unsupervised clustering framework where the dependence between loci is represented using graphical models. The population dynamics that generate such a population stratification were investigated using a stochastic model, in which homologous recombination between subpopulations can be quantified within a gene flow network. The second part of the thesis focuses on cluster analysis of community compositional data produced by two different cultivation-independent analyses: terminal restriction fragment length polymorphism (T-RFLP) analysis, and fatty acid methyl ester (FAME) analysis. The cluster analysis aims to group bacterial communities that are similar in composition, which is an important step for understanding the overall influences of environmental and ecological perturbations on bacterial diversity. A common feature of T-RFLP and FAME data is zero-inflation, which indicates that the observation of a zero value is much more frequent than would be expected, for example, from a Poisson distribution in the discrete case, or a Gaussian distribution in the continuous case. We provided two strategies for modeling zero-inflation in the clustering framework, which were validated by both synthetic and empirical complex data sets. We show in the thesis that our model that takes into account dependencies between loci in MLST data can produce better clustering results than those methods which assume independent loci. Furthermore, computer algorithms that are efficient in analyzing large scale data were adopted for meeting the increasing computational need. Our method that detects homologous recombination in subpopulations may provide a theoretical criterion for defining bacterial species. The clustering of bacterial community data include T-RFLP and FAME provides an initial effort for discovering the evolutionary dynamics that structure and maintain bacterial diversity in the natural environment.

Stochastic Filtering

The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the Kushner-Stratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by Fujisaki-Kallianpur-Kunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the so-called Kalman-Bucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter.

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.

Service-based Requirements for Future Mobile Networks

The mobile phone has, as a device, taken the world by storm in the past decade; from only 136 million phones globally in 1996, it is now estimated that by the end of 2008 roughly half of the worlds population will own a mobile phone. Over the years, the capabilities of the phones as well as the networks have increased tremendously, reaching the point where the devices are better called miniature computers rather than simply mobile phones. The mobile industry is currently undertaking several initiatives of developing new generations of mobile network technologies; technologies that to a large extent focus at offering ever-increasing data rates. This thesis seeks to answer the question of whether the future mobile networks in development and the future mobile services are in sync; taking a forward-looking timeframe of five to eight years into the future, will there be services that will need the high-performance new networks being planned? The question is seen to be especially pertinent in light of slower-than-expected takeoff of 3G data services. Current and future mobile services are analyzed from two viewpoints; first, looking at the gradual, evolutionary development of the services and second, through seeking to identify potential revolutionary new mobile services. With information on both current and future mobile networks as well as services, a network capability - service requirements mapping is performed to identify which services will work in which networks. Based on the analysis, it is far from certain whether the new mobile networks, especially those planned for deployment after HSPA, will be needed as soon as they are being currently roadmapped. The true service-based demand for the "beyond HSPA" technologies may be many years into the future - or, indeed, may never materialize thanks to the increasing deployment of local area wireless broadband technologies.

Analysis of Heterogeneous IP Traffic in Wireless Environment

Wireless access is expected to play a crucial role in the future of the Internet. The demands of the wireless environment are not always compatible with the assumptions that were made on the era of the wired links. At the same time, new services that take advantage of the advances in many areas of technology are invented. These services include delivery of mass media like television and radio, Internet phone calls, and video conferencing. The network must be able to deliver these services with acceptable performance and quality to the end user. This thesis presents an experimental study to measure the performance of bulk data TCP transfers, streaming audio flows, and HTTP transfers which compete the limited bandwidth of the GPRS/UMTS-like wireless link. The wireless link characteristics are modeled with a wireless network emulator. We analyze how different competing workload types behave with regular TPC and how the active queue management, the Differentiated services (DiffServ), and a combination of TCP enhancements affect the performance and the quality of service. We test on four link types including an error-free link and the links with different Automatic Repeat reQuest (ARQ) persistency. The analysis consists of comparing the resulting performance in different configurations based on defined metrics. We observed that DiffServ and Random Early Detection (RED) with Explicit Congestion Notification (ECN) are useful, and in some conditions necessary, for quality of service and fairness because a long queuing delay and congestion related packet losses cause problems without DiffServ and RED. However, we observed situations, where there is still room for significant improvements if the link-level is aware of the quality of service. Only very error-prone link diminishes the benefits to nil. The combination of TCP enhancements improves performance. These include initial window of four, Control Block Interdependence (CBI) and Forward RTO recovery (F-RTO). The initial window of four helps a later starting TCP flow to start faster but generates congestion under some conditions. CBI prevents slow-start overshoot and balances slow start in the presence of error drops, and F-RTO reduces unnecessary retransmissions successfully.

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.

Describing and validating functional requirements as use cases

Requirements engineering is an important phase in software development where customer's needs and expectations are transformed into a software requirements specification. The requirements specification can be considered as an agreement between the customer and the developer where both parties agree on the expected system features and behaviour. However, requirements engineers must deal with a variety of issues that complicate the requirements process. The communication gap between the customer and the developers is among typical reasons for unsatisfactory requirements. In this thesis we study how the use case technique could be used in requirements engineering in bridging the communication gap between the customer and development team. We also discuss how a use case description can be use cases can be used as a basis for acceptance test cases.

Optimaalinen rangaistus talousrikoksesta : Tutkimus velallisen rikoksista

Optimal Punishment of Economic Crime: A Study on Bankruptcy Crime This thesis researches whether the punishment practise of bankruptcy crimes is optimal in light of Gary S. Becker’s theory of optimal punishment. According to Becker, a punishment is optimal if it eliminates the expected utility of the crime for the offender and - on the other hand - minimizes the cost of the crime to society. The decision process of the offender is observed through their expected utility of the crime. The expected utility is calculated based on the offender's probability of getting caught, the cost of getting caught and the profit from the crime. All objects including the punishment are measured in cash. The cost of crimes to the society is observed defining the disutility caused by the crime to the society. The disutility is calculated based on the cost of crime prevention, crime damages, punishment execution and the probability of getting caught. If the goal is to minimize the crime profits, the punishments of bankruptcy crimes are not optimal. If the debtors would decide whether or not to commit the crime solely based on economical consideration, the crime rate would be multiple times higher than the current rate is. The prospective offender relies heavily on non-economic aspects in their decision. Most probably social pressure and personal commitment to oblige the laws are major factors in the prospective criminal’s decision-making. The function developed by Becker measuring the cost to society was not useful in the measurement of the optimality of a punishment. The premise of the function that the costs of the society correlate to the costs for the offender from the punishment proves to be unrealistic in observation of the bankruptcy crimes. However, it was observed that majority of the cost of crime for the society are caused by the crime damages. This finding supports the preventive criminal politics.

Kirkko, Kekkonen ja kommunismi poliittisina kriisivuosina 1958-1962

This study explores the relationship of the Evangelical Lutheran Church of Finland to communism and political power during the period of crises in Finnish foreign relations with the Soviet Union from 1958 to 1962. During this period the USSR repeatedly interfered in Finland´s domestic affairs and limited her foreign political freedom of action. The research subjects for this dissertation are the bishops of the Church of Finland and the newspaper Kotimaa, which can be regarded as the unofficial organ of the church at the time. A typical characteristic of the Church of Finland from the beginning of the twentieth century was patriotism. During the interwar years the church was strongly anti-communist and against the Soviet Union. This tendency was also evident during the Second World War. After the war the Finnish Church feared that the rise of the extreme left would jeopardize its position. The church, however, succeeded in maintaining its status as a state church throughout the critical years immediately following the war. This study indicates that, although the manner of expression altered, the political attitude of the church did not substantially change during the postwar period. In the late 1950s and early 1960s the church was still patriotic and fear of the extreme left was also evident among the leaders of the church. The victory of the Finnish People's Democratic League in the general election of 1958 was an unwelcome surprise to the church. This generated fear in the church that, with Soviet support, the Finnish communists might return to governmental power and the nation could become a people's democracy. Accordingly, the church tried to encourage other parties to set aside their disagreements and act together against the extreme left throughout the period under study. The main characteristics of the church´s political agenda during this period of crisis were to support the Finnish foreign policy led by the president of the republic, Urho Kekkonen, and to resist Finnish communism. The attitude of Finnish bishops and the newspaper Kotimaa to the Cold War in general was generally in agreement with the majority of western Christians. They feared communism, were afraid of the USSR, but supported peaceful co-existence because they did not want an open conflict with the Soviets. Because of uncertainties in Finland's international position the Finnish Church regarded it as necessary to support the Finnish policy of friendship towards the USSR. The Finnish Church considerer it unwise to openly criticize the Soviet Union, tried resist the spread of communism in Finnish domestic policy. This period of foreign policy crises was principally seen by the church as a time when there was a need to strengthen Finland's unstable national position.

Q-evankeliumi ja psykohistoria : Uuden testamentin eksegetiikan väitöskirja

In the course of my research for my thesis The Q Gospel and Psychohistory, I moved on from the accounts of the Cynics ideals to psychohistorical explanations. Studying the texts dealing with the Cynics and the Q Gospel, I was amazed by the fact that these texts actually portrayed people living in greater poverty than they had to. I paid particular attention to the fact that the Q Gospel was born in traumatising, warlike circumstances. Psychiatric traumatology helped me understand the Q Gospel and other ancient documents using historical approaches in a way that would comply with modern behavioural science. Even though I found some answers to the questions I had posed in my research, the main result of my research work is the justification of the question: Is it important to ask whether there is a connection between the ethos expressed by means of the religious language of the Q Gospel and the predominantly war-related life experiences typical to Palestine at the time. As has been convincingly revealed by a number of studies, traumatic events contribute to the development of psychotic experiences. I approached the problematic nature, significance and complexity of the ideal of poverty and this warlike environment by clarifying the history of psychohistorical literary research and the interpretative contexts associated with Sigmund Freud, Jacques Lacan and Melanie Klein. It is justifiable to question abnormal mentality, but there is no reliable return from the abnormal mentality described in any particular text to the only affecting factor. The popular research tendency based on the Oedipus complex is just as controversial as the Oedipus complex itself. The sociological frameworks concerning moral panics and political paranoia of an outer and inner danger fit quite well with the construction of the Q Gospel. Jerrold M. Post, M.D., Professor of Psychiatry, Political Psychology and Interna-tional Affairs at George Washington University, and founder and director of the Center for the Analysis of Personality and Political Behavior for the Central Intelligence Agency, has focused on the role played by charisma in the attracting of followers and detailed the psychological styles of a "charismatic" leader. He wrote the books Political Paranoia and Leaders and Their Followers in a Dangerous World: the Psychology of Political Behavior among others. His psychoanalytic vocabulary was useful for my understanding of the minds and motivations involved in the Q Gospel s formation. The Q sect began to live in a predestined future, with the reality and safety of this world having collapsed in both their experience and their fantasies. The deep and clear-cut divisions into good and evil that are expressed in the Q Gospel reveal the powerful nature of destructive impulses, envy and overwhelming anxiety. Responsible people who influenced the Q Gospel's origination tried to mount an ascetic defense against anxiety, denying their own needs, focusing their efforts on another objective (God s Kingdom) and a regressive, submissive earlier phase of development (a child s carelessness). This spiritual process was primarily an ecclesiastic or group-dynamical tactic to give support to the power of group leaders.

Christian-Muslim Dialogue : Perspectives of Four Lebanese Thinkers

This study describes and analyses two Lebanese Muslims and two Lebanese Christians ideas about Christian-Muslim dialogue, its nature, aims, and methods and its different dimensions, which include doctrinal, ethical, and social dimensions. On the basis of the analysis, the four thinkers contributions for promoting constructive dialogue are evaluated. The persons studied are two religious authorities, the Shiite Great Ayatollah Muhammad Husayn Fadlallah (b. 1935) and the Eastern Orthodox Metropolitan of Mount Lebanon, Georges Khodr (b. 1923), and two academic scholars, Doctor Mahmoud Ayoub (b. 1935) and Doctor, Father Mouchir Aoun (b. 1964), from the Shiite and Greek Catholic communities, respectively. The method of the study is systematic analysis. The sources consist of the four thinkers writings on Christian-Muslim relations, the most of which have been published in Lebanon in the 1990s and 2000s in the Arabic language. In their general guidelines for Christian-Muslim dialogue, the four authors do not offer any novel or unusual insights. However, their dialogue visions are multi-faceted, motivating interreligious encounter both on religious and practical grounds and clarifying the theological grounds and socio-political conditions of this endeavour. The major challenge appears to be the tension between loyalty to one s own convictions and taking into account the particular self-understanding of the other. While this tension may be ultimately unsolvable, it is obvious that linking dialogue tightly to missionary motivations or certain theological agenda imposed on the others is not conducive for better mutual understanding. As for how diverse theologies of religions affect interreligious dialogue, narrow exclusivism hardly promotes mutual knowledge and appreciation, but also inclusive and pluralistic positions have their particular dilemmas. In the end, dialogue is possible from diverse positions on theology of religions. All the authors discuss the theological themes of divine revelation, concept of God, and human condition and ultimate destiny. The two religions particular views on these issues cannot be reconciled, but the authors offer diverse means to facilitate mutual understanding on them, such as increasing mutual knowledge, questioning certain traditional condemnations, showing theological parallels between the two religions, and transcending doctrinal disagreements by stressing common religious experience or ethical concerns. Among the theological themes, especially the concept of God seems to offer possibilities for better understanding than has traditionally been the case. Significantly, all the four authors maintain that Christians and Muslims share the faith in the one God, irrespective of their disagreements about the nature of his oneness. Basic ethical principles are not discussed as widely by the four authors as might be expected, which may reflect the shared cultural background and common ethical values of the Lebanese Muslims and Christians. On this level, Christians alienation from the Islamic law appears as the most significant challenge to mutual understanding, while neighbourly love and the golden rule of ethics offer a fruitful basis for further dialogue. As for the issue of political power-sharing in Lebanon, it is clear that the proposal of an Islamic state is problematic in a country with a sizable Christian minority and a heterogeneous Muslim population. Some form of democracy seems more viable for a multireligious country, but the question remains how to retain religion as a vital force in society, which is felt to be important by all the four Lebanese authors.

4QMMT - The Problem of the Epilogue

The main focus of this study is the epilogue of 4QMMT (4QMiqsat Ma aseh ha-Torah), a text of obscure genre containing a halakhic section found in cave 4 at Qumran. In the official edition published in the series Discoveries of the Judaean Desert (DJD X), the extant document was divided by its editors, Elisha Qimron and John Strugnell, into three literary divisions: Section A) the calendar section representing a 364-day solar calendar, Section B) the halakhot, and Section C) an epilogue. The work begins with text critical inspection of the manuscripts containing text from the epilogue (mss 4Q397, 4Q398, and 4Q399). However, since the relationship of the epilogue to the other sections of the whole document 4QMMT is under investigation, the calendrical fragments (4Q327 and 4Q394 3-7, lines 1-3) and the halakhic section also receive some attention, albeit more limited and purpose oriented. In Ch. 2, after a transcription of the fragments of the epilogue, a synopsis is presented in order to evaluate the composite text of the DJD X edition in light of the evidence provided by the individual manuscripts. As a result, several critical comments are offered, and finally, an alternative arrangement of the fragments of the epilogue with an English translation. In the following chapter (Ch. 3), the diversity of the two main literary divisions, the halakhic section and the epilogue, is discussed, and it is demonstrated that the author(s) of 4QMMT adopted and adjusted the covenantal pattern known from biblical law collections, more specifically Deuteronomy. The question of the genre of 4QMMT is investigated in Ch. 4. The final chapter (Ch. 5) contains an analysis of the use of Scripture in the epilogue. In a close reading, both the explicit citations and the more subtle allusions are investigated in an attempt to trace the theology of the epilogue. The main emphases of the epilogue are covenantal faithfulness, repentance and return. The contents of the document reflect a grave concern for the purity of the cult in Jerusalem, and in the epilogue Deuteronomic language and expressions are used to convince the readers of the necessity of a reformation. The large number of late copies found in cave 4 at Qumran witness the significance of 4QMMT and the continuous importance of the Jerusalem Temple for the Qumran community.

Ihanne ja todellisuus : Jäsenyyteen sitoutuminen Suomen evankelis-luterilaisessa kirkossa 1960-luvulta 2000-luvulle

The subject of the study is the ideal and reality of commitment to membership in the Evangelical Lutheran Church of Finland from the 1960s to the 2000s. The research task is to ascertain what manner of commitment the Evangelical Lutheran Church of Finland expects from its members (the ideal) and how in reality membership of the Church is realized (empiria). The research object is also to study the extent to which the ideal of commitment evinced by the Church and the actual relation of commitment to the Church changed during the research period. Additionally, those factors were analysed which influence the relation between the ideal and reality of commitment. In the analysis of the ideal of commitment the research data are official documents of the Evangelical Lutheran Church of Finland. They include confessions of the Church, Catechisms, Christian doctrine, joint strategies and plans of the Church, likewise the Church Act and Church Order. The reality of commitment is explored on the basis of Church membership, participation in parish activity and the private practice of religion, likewise attitude to Christian faith. The empirical data of the study comprise Church statistics, material from Statistics Finland and relevant surveys implemented during the research period. The ideal of commitment alongside membership includes knowing the basic tenets of Christian faith and family life based on prayer and participation in liturgical cycles. A member of the Church is expected to take care of his/her faith by living in participation of the Word and sacrament, bearing responsibility for the parish and faithfully discharging his/her worldly obligations. There have been no major changes in the ideal of commitment during the research period. On the contrary, the reality of commitment has changed. Although the majority of Finns are still members of the Church, there has been a constant decline in their share of the population. The same can be stated with respect to parish life. This has its own strengths, among them Church rites, parish activity around feast days and also work with children and confirmation training. However, the general trend is towards a decline in participation. There has also been a decrease in commitment to belief in God as taught by the Church. On the other hand, private religious observance has not changed at all. From the perspective of commitment the Evangelical Lutheran Church of Finland exists in a state of tension between the theological ideal and sociological empiria. Matters exerting a particular influence over the relation between ideal and reality are communality and varying conceptions of the Church, likewise contextuality and the related private Christianity. Societal change poses a challenge to traditional Church communality. A decline in communality has in turn led to a decline in belonging to the Church. Weakening awareness of membership has undermined the handing down of the tradition among younger generations. Modernization has influence the identity of the Church and brought the Church to an internal divergence. This way it has been able to retain its structure as a folk church but at the same time it has lost its opportunities for the formation of a clear identity. The Church has adjusted to societal change by outward-directed activities (performance) alongside the purely religious message (function). The tension between an unchanged message and a changed operating environment has increased. The challenge of contextuality has led the Church to review parish life, the nature of teaching and activity and the language used by the Church, likewise the cultural modus. Increasingly privatized Christianity challenges above all the theology and teaching of the Church, but also the life of worship and relation to cultural life.