Tuning and stability of a singly resonant continuous-wave optical parametric oscillator close to degeneracy

Wavelength tuning and stability characteristics of a singly resonant continuous-wave optical parametric oscillator (cw OPO) in the proximity of signal-idler degeneracy have been studied. The OPO is made singly resonant by using a Bragg grating as a spectral filter in the OPO cavity. The signal-idler frequency difference can be tuned from 0.5 to 7 THz, which makes the OPO suitable for cw THz generation by optical heterodyning. The operation of the OPO within this singly-resonant regime is characterized by a strong self-stabilization effect. A gradual transition to an unstable, doubly-resonant regime is observed for a signal-idler detuning smaller than ~ 0.5 THz.

Soveltuvuuskokeella täydennetty opiskelijavalinta : Seurantatutkimus eräiden sosiaali- ja terveysalan teknisluonteisten koulutusohjelmien (apuvälinetekniikka, hammastekniikka ja optometria) opiskelijavalinnan toteuttamisesta

Aptitude-based student selection: A study concerning the admission processes of some technically oriented healthcare degree programmes in Finland (Orthotics and Prosthetics, Dental Technology and Optometry). The data studied consisted of conveniencesamples of preadmission information and the results of the admission processes of three technically oriented healthcare degree programmes (Orthotics and Prosthetics, Dental Technology and Optometry) in Finland during the years 1977-1986 and 2003. The number of the subjects tested and interviewed in the first samples was 191, 615 and 606, and in the second 67, 64 and 89, respectively. The questions of the six studies were: I. How were different kinds of preadmission data related to each other? II. Which were the major determinants of the admission decisions? III. Did the graduated students and those who dropped out differ from each other? IV. Was it possible to predict how well students would perform in the programmes? V. How was the student selection executed in the year 2003? VI. Should clinical vs. statistical prediction or both be used? (Some remarks are presented on Meehl's argument: "Always, we might as well face it, the shadow of the statistician hovers in the background; always the actuary will have the final word.") The main results of the study were as follows: Ability tests, dexterity tests and judgements of personality traits (communication skills, initiative, stress tolerance and motivation) provided unique, non-redundant information about the applicants. Available demographic variables did not bias the judgements of personality traits. In all three programme settings, four-factor solutions (personality, reasoning, gender-technical and age-vocational with factor scores) could be extracted by the Maximum Likelihood method with graphical Varimax rotation. The personality factor dominated the final aptitude judgements and very strongly affected the selection decisions. There were no clear differences between graduated students and those who had dropped out in regard to the four factors. In addition, the factor scores did not predict how well the students performed in the programmes. Meehl's argument on the uncertainty of clinical prediction was supported by the results, which on the other hand did not provide any relevant data for rules on statistical prediction. No clear arguments for or against the aptitude-based student selection was presented. However, the structure of the aptitude measures and their impact on the admission process are now better known. The concept of "personal aptitude" is not necessarily included in the values and preferences of those in charge of organizing the schooling. Thus, obviously the most well-founded and cost-effective way to execute student selection is to rely on e.g. the grade point averages of the matriculation examination and/or written entrance exams. This procedure, according to the present study, would result in a student group which has a quite different makeup (60%) from the group selected on the basis of aptitude tests. For the recruiting organizations, instead, "personal aptitude" may be a matter of great importance. The employers, of course, decide on personnel selection. The psychologists, if consulted, are responsible for the proper use of psychological measures.

The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

Neutrinos and Thermal Leptogenesis

One of the unanswered questions of modern cosmology is the issue of baryogenesis. Why does the universe contain a huge amount of baryons but no antibaryons? What kind of a mechanism can produce this kind of an asymmetry? One theory to explain this problem is leptogenesis. In the theory right-handed neutrinos with heavy Majorana masses are added to the standard model. This addition introduces explicit lepton number violation to the theory. Instead of producing the baryon asymmetry directly, these heavy neutrinos decay in the early universe. If these decays are CP-violating, then they produce lepton number. This lepton number is then partially converted to baryon number by the electroweak sphaleron process. In this work we start by reviewing the current observational data on the amount of baryons in the universe. We also introduce Sakharov's conditions, which are the necessary criteria for any theory of baryogenesis. We review the current data on neutrino oscillation, and explain why this requires the existence of neutrino mass. We introduce the different kinds of mass terms which can be added for neutrinos, and explain how the see-saw mechanism naturally explains the observed mass scales for neutrinos motivating the addition of the Majorana mass term. After introducing leptogenesis qualitatively, we derive the Boltzmann equations governing leptogenesis, and give analytical approximations for them. Finally we review the numerical solutions for these equations, demonstrating the capability of leptogenesis to explain the observed baryon asymmetry. In the appendix simple Feynman rules are given for theories with interactions between both Dirac- and Majorana-fermions and these are applied at the tree level to calculate the parameters relevant for the theory.

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.

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.

Kategoriat oppaina Jumalan olemuksen ilmaisuun Lutherin teologiassa

Tutkielmassa selvitetään, miten Luther käyttää kategoriaoppia oppaana Jumalan olemuksen ilmaisuun. Päälähteenä on Genesis-kommentaari (1535-1545) mutta muitakin Lutherin tekstejä käytetään soveltuvin osin käsitteiden ja ajatusrakenteiden selventäjinä. Tutkielma jakautuu johdannon jälkeen taustalukuun ja kolmeen analyysilukuun ja loppukatsaukseen, jossa esitetään tutkimuksen tulokset. Taustaluvussa luodaan katsaus filosofisen kategoriaopin sisältöön ja historiaan uskonpuhdistukseen saakka. Aristoteleen luoma olemista määrittävä kategoriaoppi substansseista ja niiden satunnaisista ominaispiirteistä, aksidensseista, tulkitaan aina uudelleen jokaisessa filosofianhistoriallisessa kontekstissa. Länsimaisen teologian ja Lutherin ajattelun kannalta merkittävimmät kategoriaopin tulkisijat ovat Augustinus ja Tuomas Akvinolainen. Luvussa kolme selvitetään Lutherin suhdetta filosofiaan yleensä ja hänen kategoriaopin käyttöään. Luther yhtyy Augustinukseen siinä, että Jumalaa olemuksessaan ei voida tavoittaa kategorioiden avulla, mutta niitä voidaan käyttää oppaana sen ilmaisussa. Lutherin kritisoi skolastista kategoriaoppia, jossa kaikki muut kategoriat predikoidaan ensimmäisistä substansseista, ja käyttää itse Quintilianuksen tapaa, jossa mikä tahansa asia voidaan ottaa tarkasteluun kaikissa siihen soveltuvissa kategorioissa sen ymmärtämiseksi paremmin kokonaisuutena. Neljännessä luvussa analysoidaan substanssi-käsitettä ja substanssin kategoriaa ja viidennessä relaatiota ja relaation kategoriaa Lutherin jumalakäsityksessä ottaen huomioon myös skolastinen tausta. Substanssin Luther ymmärtää sekä raamatullisesti, että filosofisesti. Kategoriaopissa on kysymys filosofisesta substanssi-käsitteestä kokonaisyhteyden ollessa kuitenkin teologinen. Jumala substanssin kategoriassa on tavoittamaton ja absoluuttinen filosofian Jumala, johon ei liity Jumalan ristinteologista ja vastakohtiinsa kätkeytyvää ilmoitusta itsestään.Tällä tavalla ymmärretty Jumala ei ole tekemisissä ihmisten kanssa ja hänen tuntemisensa tavoitteleminen tällaisena on ihmisen omista lähtökohdista tapahtuvaa kunnian teologiaa. Relaation käsitteessä Luther liittyy Aristoteleen määritelmään: Relatiivit ovat subjektissaan ja suhteessa toisiinsa. Relationaalisuus kuuluu Lutherin teologiaan, sekä luotuisuuden että uskon relaationa. Jumalan ja ihmisen suhteessa on kaksi reaalista relaatiota, Jumalan relaatio ihmiseen ja ihmisen relaatio Jumalaan. Edellistä Luther kutsuu ilmoitukseksi ja jälkimmäistä uskoksi tai jumalanpalvelukseksi. Luther hyödyntää myös relatiivien käänteisyyttä ja yhtä aikaa olemassa olemista teologiassaan: Ihmisen käänteisjäsenenä voi olla vain hänelle ilmoitettu Jumala, joka antaa osallisuuden omasta ikuisesta elämästään ja itsestään tässä relaatiossa. Näin relaatiolla on myös ontologinen sisältö. Se tulee näkyviin myös jumalanpalveluksen nimityksessä ”Herran nimen avuksi huutamisena”, sillä Jumalan on nimessään olemuksellisesti läsnä. Tutkielman johdannossa esitetty hypoteesi filosofisen terminologian käytöstä teologisesti osoittautuu oikeaksi: Luther pysyy alkuperäisissä Aristoteleen kategorioiden määritelmissä ja merkityksissä ja käyttää niitä teologiansa ilmaisuvälineenä viittaussuhteenaan teologinen totuus. Kategoriaoppiaan esittäessään Lutherin varsinainen vastustaja ei ole Aristoteles vaan skolastinen teologia, jossa aristoteelinen filosofia on saanut ylivallan ja sivuuttanut Jumalan oman ilmoituksen itsestään. Summa summarum: Luther asettaa Jumalan relaation kategoriaan ilmaistakseen Jumalan olemuksen ristinteologisen itseilmoituksen ihmisille. Avainsanat: aristotelismi - Jumala - kategoriat – Luther-tutkimus - relaatio – skolastiikka –ontologia

Dynamics of free-running, pump-modulated and coupled semiconductor and solid-state lasers

The output of a laser is a high frequency propagating electromagnetic field with superior coherence and brightness compared to that emitted by thermal sources. A multitude of different types of lasers exist, which also translates into large differences in the properties of their output. Moreover, the characteristics of the electromagnetic field emitted by a laser can be influenced from the outside, e.g., by injecting an external optical field or by optical feedback. In the case of free-running solitary class-B lasers, such as semiconductor and Nd:YVO4 solid-state lasers, the phase space is two-dimensional, the dynamical variables being the population inversion and the amplitude of the electromagnetic field. The two-dimensional structure of the phase space means that no complex dynamics can be found. If a class-B laser is perturbed from its steady state, then the steady state is restored after a short transient. However, as discussed in part (i) of this Thesis, the static properties of class-B lasers, as well as their artificially or noise induced dynamics around the steady state, can be experimentally studied in order to gain insight on laser behaviour, and to determine model parameters that are not known ab initio. In this Thesis particular attention is given to the linewidth enhancement factor, which describes the coupling between the gain and the refractive index in the active material. A highly desirable attribute of an oscillator is stability, both in frequency and amplitude. Nowadays, however, instabilities in coupled lasers have become an active area of research motivated not only by the interesting complex nonlinear dynamics but also by potential applications. In part (ii) of this Thesis the complex dynamics of unidirectionally coupled, i.e., optically injected, class-B lasers is investigated. An injected optical field increases the dimensionality of the phase space to three by turning the phase of the electromagnetic field into an important variable. This has a radical effect on laser behaviour, since very complex dynamics, including chaos, can be found in a nonlinear system with three degrees of freedom. The output of the injected laser can be controlled in experiments by varying the injection rate and the frequency of the injected light. In this Thesis the dynamics of unidirectionally coupled semiconductor and Nd:YVO4 solid-state lasers is studied numerically and experimentally.

Heavy-light mesons on a lattice

Several excited states of Ds and Bs mesons have been discovered in the last six years: BaBar, Cleo and Belle discovered the very narrow states D(s0)*(2317)+- and D(s1)(2460)+- in 2003, and CDF and DO Collaborations reported the observation of two narrow Bs resonances, B(s1)(5830)0 and B*(s2)(5840)0 in 2007. To keep up with experiment, meson excited states should be studied from the theoretical aspect as well. The theory that describes the interaction between quarks and gluons is quantum chromodynamics (QCD). In this thesis the properties of the meson states are studied using the discretized version of the theory - lattice QCD. This allows us to perform QCD calculations from first principles, and "measure" not just energies but also the radial distributions of the states on the lattice. This gives valuable theoretical information on the excited states, as we can extract the energy spectrum of a static-light meson up to D wave states (states with orbital angular momentum L=2). We are thus able to predict where some of the excited meson states should lie. We also pay special attention to the order of the states, to detect possible inverted spin multiplets in the meson spectrum, as predicted by H. Schnitzer in 1978. This inversion is connected to the confining potential of the strong interaction. The lattice simulations can also help us understand the strong interaction better, as the lattice data can be treated as "experimental" data and used in testing potential models. In this thesis an attempt is made to explain the energies and radial distributions in terms of a potential model based on a one-body Dirac equation. The aim is to get more information about the nature of the confining potential, as well as to test how well the one-gluon exchange potential explains the short range part of the interaction.

Key Factors Influencing Economic Relationships and Communication in Finnish Food Chains

The aim of this report is to discuss the role of the relationship type and communication in two Finnish food chains, namely the pig meat-to-sausage (pig meat chain) and the cereal-to-rye bread (rye chain) chains. Furthermore, the objective is to examine those factors influencing the choice of a relationship type and the sustainability of a business relationship. Altogether 1808 questionnaires were sent to producers, processors and retailers operating in these two chains of which 224 usable questionnaires were returned (the response rate being 12.4%). The great majority of the respondents (98.7%) were small businesses employing less than 50 people. Almost 70 per cent of the respondents were farmers. In both chains, formal contracts were stated to be the most important relationship type used with business partners. Although for many businesses written contracts are a common business practice, the essential role of the contracts was the security they provide regarding the demand/supply and quality issues. Relative to the choice of the relationship types, the main difference between the two chains emerged especially with the prevalence of spot markets and financial participation arrangements. The usage of spot markets was significantly more common in the rye chain when compared to the pig meat chain, while, on the other hand, financial participation arrangements were much more common among the businesses in the pig meat chain than in the rye chain. Furthermore, the analysis showed that most of the businesses in the pig meat chain claimed not to be free to choose the relationship type they use. Especially membership in a co-operative and practices of a business partner were mentioned as the reasons limiting this freedom of choice. The main business relations in both chains were described as having a long-term orientation and being based on formal written contracts. Typical for the main business relationships was also that they are not based on the existence of the key persons only; the relationship would remain even if the key people left the business. The quality of these relationships was satisfactory in both chains and across all the stakeholder groups, though the downstream processors and the retailers had a slightly more positive view on their main business partners than the farmers and the upstream processors. The businesses operating in the pig meat chain seemed also to be more dependent on their main business relations when compared to the businesses in the rye chain. Although the communication means were rather similar in both chains (the phone being the most important), there was some variation between the chains concerning the communication frequency necessary to maintain the relationship with the main business partner. In short, the businesses in the pig meat chain seemed to appreciate more frequent communication with their main business partners when compared to the businesses in the rye chain. Personal meetings with the main business partners were quite rare in both chains. All the respondent groups were, however, fairly satisfied with the communication frequency and information quality between them and the main business partner. The business cultures could be argued to be rather hegemonic among the businesses both in the pig meat and rye chains. Avoidance of uncertainty, appreciation of long-term orientation and independence were considered important factors in the business cultures. Furthermore, trust, commitment and satisfaction in business partners were thought to be essential elements of business operations in all the respondent groups. In order to investigate which factors have an effect on the choice of a relationship type, several hypotheses were tested by using binary and multinomial logit analyses. According to these analyses it could be argued that avoidance of uncertainty and risk has a certain effect on the relationship type chosen, i.e. the willingness to avoid uncertainty increases the probability to choose stable relationships, like repeated market transactions and formal written contracts, but not necessary those, which require high financial commitment (like financial participation arrangements). The probability of engaging in financial participation arrangements seemed to increase with long-term orientation. The hypotheses concerning the sustainability of the economic relations were tested by using structural equation model (SEM). In the model, five variables were found to have a positive and statistically significant impact on the sustainable economic relationship construct. Ordered relative to their importance, those factors are: (i) communication quality, (ii) personal bonds, (iii) equal power distribution, (iv) local embeddedness and (v) competition.

Gauge Field Theories, Quantum Space-Time and Some Applications

In this thesis, the possibility of extending the Quantization Condition of Dirac for Magnetic Monopoles to noncommutative space-time is investigated. The three publications that this thesis is based on are all in direct link to this investigation. Noncommutative solitons have been found within certain noncommutative field theories, but it is not known whether they possesses only topological charge or also magnetic charge. This is a consequence of that the noncommutative topological charge need not coincide with the noncommutative magnetic charge, although they are equivalent in the commutative context. The aim of this work is to begin to fill this gap of knowledge. The method of investigation is perturbative and leaves open the question of whether a nonperturbative source for the magnetic monopole can be constructed, although some aspects of such a generalization are indicated. The main result is that while the noncommutative Aharonov-Bohm effect can be formulated in a gauge invariant way, the quantization condition of Dirac is not satisfied in the case of a perturbative source for the point-like magnetic monopole.