Locality and order-invariant logics

Malli on logiikassa käytetty abstraktio monille matemaattisille objekteille. Esimerkiksi verkot, ryhmät ja metriset avaruudet ovat malleja. Äärellisten mallien teoria on logiikan osa-alue, jossa tarkastellaan logiikkojen, formaalien kielten, ilmaisuvoimaa malleissa, joiden alkioiden lukumäärä on äärellinen. Rajoittuminen äärellisiin malleihin mahdollistaa tulosten soveltamisen teoreettisessa tietojenkäsittelytieteessä, jonka näkökulmasta logiikan kaavoja voidaan ajatella ohjelmina ja äärellisiä malleja niiden syötteinä. Lokaalisuus tarkoittaa logiikan kyvyttömyyttä erottaa toisistaan malleja, joiden paikalliset piirteet vastaavat toisiaan. Väitöskirjassa tarkastellaan useita lokaalisuuden muotoja ja niiden säilymistä logiikkoja yhdistellessä. Kehitettyjä työkaluja apuna käyttäen osoitetaan, että Gaifman- ja Hanf-lokaalisuudeksi kutsuttujen varianttien välissä on lokaalisuuskäsitteiden hierarkia, jonka eri tasot voidaan erottaa toisistaan kasvavaa dimensiota olevissa hiloissa. Toisaalta osoitetaan, että lokaalisuuskäsitteet eivät eroa toisistaan, kun rajoitutaan tarkastelemaan äärellisiä puita. Järjestysinvariantit logiikat ovat kieliä, joissa on käytössä sisäänrakennettu järjestysrelaatio, mutta sitä on käytettävä siten, etteivät kaavojen ilmaisemat asiat riipu valitusta järjestyksestä. Määritelmää voi motivoida tietojenkäsittelyn näkökulmasta: vaikka ohjelman syötteen tietojen järjestyksellä ei olisi odotetun tuloksen kannalta merkitystä, on syöte tietokoneen muistissa aina jossakin järjestyksessä, jota ohjelma voi laskennassaan hyödyntää. Väitöskirjassa tutkitaan minkälaisia lokaalisuuden muotoja järjestysinvariantit ensimmäisen kertaluvun predikaattilogiikan laajennukset yksipaikkaisilla kvanttoreilla voivat toteuttaa. Tuloksia sovelletaan tarkastelemalla, milloin sisäänrakennettu järjestys lisää logiikan ilmaisuvoimaa äärellisissä puissa.

Mathematical models on the impact of noise and dyadic molecular structures on the properties of a cardiac myocyte

In cardiac myocytes (heart muscle cells), coupling of electric signal known as the action potential to contraction of the heart depends crucially on calcium-induced calcium release (CICR) in a microdomain known as the dyad. During CICR, the peak number of free calcium ions (Ca) present in the dyad is small, typically estimated to be within range 1-100. Since the free Ca ions mediate CICR, noise in Ca signaling due to the small number of free calcium ions influences Excitation-Contraction (EC) coupling gain. Noise in Ca signaling is only one noise type influencing cardiac myocytes, e.g., ion channels playing a central role in action potential propagation are stochastic machines, each of which gates more or less randomly, which produces gating noise present in membrane currents. How various noise sources influence macroscopic properties of a myocyte, how noise is attenuated and taken advantage of are largely open questions. In this thesis, the impact of noise on CICR, EC coupling and, more generally, macroscopic properties of a cardiac myocyte is investigated at multiple levels of detail using mathematical models. Complementarily to the investigation of the impact of noise on CICR, computationally-efficient yet spatially-detailed models of CICR are developed. The results of this thesis show that (1) gating noise due to the high-activity mode of L-type calcium channels playing a major role in CICR may induce early after-depolarizations associated with polymorphic tachycardia, which is a frequent precursor to sudden cardiac death in heart failure patients; (2) an increased level of voltage noise typically increases action potential duration and it skews distribution of action potential durations toward long durations in cardiac myocytes; and that (3) while a small number of Ca ions mediate CICR, Excitation-Contraction coupling is robust against this noise source, partly due to the shape of ryanodine receptor protein structures present in the cardiac dyad.

Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.

Using Mathematical Morphology for Geometric Music Retrieval

The usual task in music information retrieval (MIR) is to find occurrences of a monophonic query pattern within a music database, which can contain both monophonic and polyphonic content. The so-called query-by-humming systems are a famous instance of content-based MIR. In such a system, the user's hummed query is converted into symbolic form to perform search operations in a similarly encoded database. The symbolic representation (e.g., textual, MIDI or vector data) is typically a quantized and simplified version of the sampled audio data, yielding to faster search algorithms and space requirements that can be met in real-life situations. In this thesis, we investigate geometric approaches to MIR. We first study some musicological properties often needed in MIR algorithms, and then give a literature review on traditional (e.g., string-matching-based) MIR algorithms and novel techniques based on geometry. We also introduce some concepts from digital image processing, namely the mathematical morphology, which we will use to develop and implement four algorithms for geometric music retrieval. The symbolic representation in the case of our algorithms is a binary 2-D image. We use various morphological pre- and post-processing operations on the query and the database images to perform template matching / pattern recognition for the images. The algorithms are basically extensions to classic image correlation and hit-or-miss transformation techniques used widely in template matching applications. They aim to be a future extension to the retrieval engine of C-BRAHMS, which is a research project of the Department of Computer Science at University of Helsinki.

The influence of school smoking policy and school prevention programs on the smoking behaviour of high school students in Prince Edward Island, Canada

The aim of the study was to examine the influence of school smoking policy and school smoking prevention programs on the smoking behaviour of students in high schools in Prince Edward Island using the School Health Action Planning Evaluation System (SHAPES). A total sample included 13,131 observations of students in grades 10-12 in ten high schools in Prince Edward Island over three waves of data collection (1999, 2000, and 2001). Changes in prevalence of smoking and factors influencing smoking behaviour were analyzed using descriptive statistics and Chi-Square tests. Multi-level logistic regression analyses were used to examine how both school and student characteristics were associated with smoking behaviour (I, II, III, IV). Since students were located within schools, a basic 2-level nested structure was used in which individual students (level 1) were nested within schools (level 2). For grade 12 students, the combination of both school policies and programs was not associated with the risk of smoking and the presence of the new policy was not associated with decreased risk of smoking, unless there were clear rules in place (I). For the grade 10 study, (II) schools with both policies and programs were not associated with decreased risk of smoking. However, the smoking behaviour of older students (grade 12) at a school was associated with younger students’ (grade 10) smoking behaviour. Students first enrolled in a high school in grade 9, rather than grade 10, were at increased risk of occasional smoking. For students who transitioned from grade 10 to 12 (III), close friends smoking had a substantial influence on smoking behaviour for both males and females (III). Having one or more close friends who smoke (Odds Ratio (OR) = 37.46; 95% CI = 19.39 to 72.36), one or more smokers in the home (OR = 2.35; 95% CI = 1.67 to 3.30) and seeing teachers and staff smoking on or near school property (OR=1.78; 95% CI = 1.13 to 2.80), were strongly associated with increased risk of smoking for grade 12 students. Smoking behaviour increased for both junior (Group 1) and senior (Group 2) students (IV). Group 1 students indicated a greater decrease in smoking behaviour and factors influencing smoking behaviour compared to those of Group 2. Students overestimating the percentage of youth their age who smoke was strongly associated with increased likelihood of smoking. Smoking rates showed a decreasing trend (1999, 2000, and 2001). However, policies and programs alone were not successful in influencing smoking behaviour of youth. Rather, factors within the students and schools contextual environment influenced smoking behaviour. Comprehensive approaches are required for school-based tobacco prevention interventions. Keywords: schools, policy, programs, smoking prevention, adolescents Subject Terms: school-based programming, public health, health promotion

Relationship Drivers in Provider - Consumer Relationships. Empirical Studies of Customer Loyalty Programs (första upplagan slutsåld / first edition sold out, 'print on demand' 60 €)

The study addressed a phenomenon that has become common marketing practice, customer loyalty programs. Although a common type of consumer relationship, there is limited knowledge of its nature. The purpose of the study was to create structured understanding of the nature of customer relationships from both the provider’s and the consumer’s viewpoints by studying relationship drivers and proposing the concept of relational motivation as a provider of a common framework for the analysis of these views. The theoretical exploration focused on reasons for engaging in customer relationships for both the consumer and the provider. The themes of buying behaviour, industrial and network marketing and relationship marketing, as well as the concepts of a customer relationship, customer loyalty, relationship conditions, relational benefits, bonds and commitment were explored and combined in a new way. Concepts from the study of business-to-business relationships were brought over and their power in explaining the nature of consumer relationships examined. The study provided a comprehensive picture of loyalty programs, which is an important contribution to the academic as well as the managerial discussions. The consumer study provided deep insights into the nature of customer relationships. The study provides a new frame of reference to support the existing concepts of loyalty and commitment with the introduction of the relationship driver and relational motivation concepts. The result is a novel view of the nature of customer relationships that creates new understanding of the forces leading to loyal behaviour and commitment. The study concludes with managerial implications.

Mathematical modelling of groundwater pollution in a small heterogeneous aquifer at Kärkölä, southern Finland

Yhteenveto: Kärkölän likaantuneen pohjavesialueen matemaattinen mallinnus

Search for innovative forest policies and programs.

XVIII IUFRO World Congress, Ljubljana 1986.

Quantification problems in the design of forest policy programs.

XVIII IUFRO World Congress, Ljubljana 1986.

Economic evaluation of forest policy programs.

XVIII IUFRO World Congress, Ljubljana 1986.