Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

Primordial Perturbations from a Self-interacting Curvaton

Inflation is a period of accelerated expansion in the very early universe, which has the appealing aspect that it can create primordial perturbations via quantum fluctuations. These primordial perturbations have been observed in the cosmic microwave background, and these perturbations also function as the seeds of all large-scale structure in the universe. Curvaton models are simple modifications of the standard inflationary paradigm, where inflation is driven by the energy density of the inflaton, but another field, the curvaton, is responsible for producing the primordial perturbations. The curvaton decays after inflation as ended, where the isocurvature perturbations of the curvaton are converted into adiabatic perturbations. Since the curvaton must decay, it must have some interactions. Additionally realistic curvaton models typically have some self-interactions. In this work we consider self-interacting curvaton models, where the self-interaction is a monomial in the potential, suppressed by the Planck scale, and thus the self-interaction is very weak. Nevertheless, since the self-interaction makes the equations of motion non-linear, it can modify the behaviour of the model very drastically. The most intriguing aspect of this behaviour is that the final properties of the perturbations become highly dependent on the initial values. Departures of Gaussian distribution are important observables of the primordial perturbations. Due to the non-linearity of the self-interacting curvaton model and its sensitivity to initial conditions, it can produce significant non-Gaussianity of the primordial perturbations. In this work we investigate the non-Gaussianity produced by the self-interacting curvaton, and demonstrate that the non-Gaussianity parameters do not obey the analytically derived approximate relations often cited in the literature. Furthermore we also consider a self-interacting curvaton with a mass in the TeV-scale. Motivated by realistic particle physics models such as the Minimally Supersymmetric Standard Model, we demonstrate that a curvaton model within the mass range can be responsible for the observed perturbations if it can decay late enough.

Modelling vacuum arcs : from plasma initiation to surface interactions

A better understanding of vacuum arcs is desirable in many of today's 'big science' projects including linear colliders, fusion devices, and satellite systems. For the Compact Linear Collider (CLIC) design, radio-frequency (RF) breakdowns occurring in accelerating cavities influence efficiency optimisation and cost reduction issues. Studying vacuum arcs both theoretically as well as experimentally under well-defined and reproducible direct-current (DC) conditions is the first step towards exploring RF breakdowns. In this thesis, we have studied Cu DC vacuum arcs with a combination of experiments, a particle-in-cell (PIC) model of the arc plasma, and molecular dynamics (MD) simulations of the subsequent surface damaging mechanism. We have also developed the 2D Arc-PIC code and the physics model incorporated in it, especially for the purpose of modelling the plasma initiation in vacuum arcs. Assuming the presence of a field emitter at the cathode initially, we have identified the conditions for plasma formation and have studied the transitions from field emission stage to a fully developed arc. The 'footing' of the plasma is the cathode spot that supplies the arc continuously with particles; the high-density core of the plasma is located above this cathode spot. Our results have shown that once an arc plasma is initiated, and as long as energy is available, the arc is self-maintaining due to the plasma sheath that ensures enhanced field emission and sputtering. The plasma model can already give an estimate on how the time-to-breakdown changes with the neutral evaporation rate, which is yet to be determined by atomistic simulations. Due to the non-linearity of the problem, we have also performed a code-to-code comparison. The reproducibility of plasma behaviour and time-to-breakdown with independent codes increased confidence in the results presented here. Our MD simulations identified high-flux, high-energy ion bombardment as a possible mechanism forming the early-stage surface damage in vacuum arcs. In this mechanism, sputtering occurs mostly in clusters, as a consequence of overlapping heat spikes. Different-sized experimental and simulated craters were found to be self-similar with a crater depth-to-width ratio of about 0.23 (sim) - 0.26 (exp). Experiments, which we carried out to investigate the energy dependence of DC breakdown properties, point at an intrinsic connection between DC and RF scaling laws and suggest the possibility of accumulative effects influencing the field enhancement factor.

The non-literary Latin letters. A study of their syntax and pragmatics

This dissertation studies the language of Latin letters that were written in Egypt and Vindolanda (in northern Britain) during the period 1st century BC 3rd century AD on papyri, ostraca, and wooden tablets. The majority of the texts is, in one way or another, connected with the Roman army. The focus of the study is on syntax and pragmatics. Besides traditional philological methods, modern syntactic theory is used as well, especially in the pragmatic analysis. The study begins with a critical survey of certain concepts that are current in the research on the Latin language, most importantly the concept of vulgar Latin , which, it is argued, seems to be used as an abstract noun for variation and change in Latin . Further, it is necessary to treat even the non-literary material primarily as written texts and not as straightforward reflections of spoken language. An examination of letter phraseology shows that there is considerable variation between the two major geographical areas of provenance. Latin letter writing in Egypt was influenced by Greek. The study highlights the importance of seeing the letters as a text type, with recurring phraseological elements appearing in the body text as well. It is argued that recognising these elements is essential for the correct analysis of the syntax. Three areas of syntax are discussed in detail: sentence connection (mainly parataxis), syntactically incoherent structures and word order (the order of the object and the verb). For certain types of sentence connection we may plausibly posit an origin in spoken Latin, but for many other linguistic phenomena attested in this material the issue of spoken Latin is anything but simple. Concerning the study of historical syntax, the letters offer information about the changing status of the accusative case. Incoherent structures may reflect contaminations in spoken language but usually the reason for them is the inability of the writer to put his thoughts into writing, especially when there is something more complicated to be expressed. Many incoherent expressions reflect the need to start the predication with a thematic constituent. Latin word order is seen as resulting from an interaction of syntactic and pragmatic factors. The preference for an order where the topic is placed sentence-initially can be seen in word order more generally as well. Furthermore, there appears a difference between Egypt and Vindolanda. The letters from Vindolanda show the order O(bject) V(erb) clearly more often than the letters from Egypt. Interestingly, this difference correlates with another, namely the use of the anaphoric pronoun is. This is an interesting observation in view of the fact that both of these are traditional Latin features, as opposed to those that foreshadow the Romance development (VO order and use of the anaphoric ille). However, it is difficult to say whether this is an indication of social or regional variation.

"Do Not Celebrate Your Feast without Your Neighbours" : A Study of References to Feasts and Festivals in Non-Literary Documents from Ramesside Period Deir el-Medina

This dissertation is a study of the forms and functions of feasts and feasting in the ancient Egyptian village of Deir el-Medina in Thebes (modern Luxor). This particular village, during the New Kingdom (c. 1550 1069 BC), was inhabited by the men (and their families) who constructed the Royal Tombs in the Valley of the Kings and the Valley of the Queens. The royal artisans were probably more literate than the average Egyptians and the numerous Ramesside Period (c. 1295 1069 BC) non-literary texts found in the excavations of the village and its surroundings form the source material for this study. In this study, the methods used are mainly Egyptological and the references to feasts and feasting are considered in view of what is known of New Kingdom Egypt, Thebes, and Deir el-Medina. Nevertheless, it is the use of the methodological concept local vernacular religion that has resulted in the division of the research findings into two sections, i.e., references to feasts celebrated both in and outside the community and other references to feasts and feasting in the village. When considering the function of the feasts celebrated at Deir el-Medina, a functional approach to feasts introduced by anthropologists and archaeologists is utilized. The Deir el-Medina feasts which were associated with the official religion form a festival calendar of feasts celebrated annually on the same civil calendar day. The reconstructed festival calendar of Deir el-Medina reflects the feasts celebrated around Thebes or, at least, in Western Thebes. The function of the nationally and regionally observed feasts (which, at least at Deir el-Medina, resulted in a work-free day) may have been to keep people content so that they would continue to work which was to the advantage of the king and the elite surrounding him. Local feasts appear to have been observed more irregularly at Deir el-Medina or perhaps according to the lunar calendar. Feasts celebrated by the community as a whole served to maintain the unity of the group. In addition to feasts celebrated by the entire community, the inhabitants of Deir el-Medina could mark their own personal feasts and organize small gatherings during public feasts. Through such feasts, an individual man might form alliances and advance his chances of a favourable marriage or of acquiring a position on the work crew.

Non-finite constructions in Old English : with special reference to syntactic borrowing from Latin

My dissertation is a corpus-based study of non-finite constructions in Old English (OE). It revisits the question of Latin influence on the OE syntax, offering a new evaluation of syntactic interference between Latin and OE, and, more generally, of the contact situation in the OE period, drawing on methods used in studying grammaticalization and language contact. I address three non-finite constructions: absolute participial construction, accusative-and-infinitive construction, and nominative-and-infinitive construction, exemplified respectively in present-day English as - She looked like a pixie sometimes, her eyes darting here and there, forever watchful (BNC CCM 98); - My first acquaintance with her was when I heard her sing (BNC CFY 2215); - Charles the Bald was said to resemble his grandfather physically (BNC HPT 175). This study compares data from translated texts against the background of original OE writings, establishing dependencies and differences between the two. Although the contrastive analysis of source and target texts is one of the major methods employed in the study, translation and translation strategies as such are only my secondary foci. The emphasis is rather on what source/target comparison can tell us about the OE non-finite syntax and the typological differences between Latin and OE in this domain, and on whether contact-induced change can originate in translation. In terms of theoretical framework, I have adopted functional-typological approach, which rests on the principles of iconicity and event integration, and to the best of my knowledge, has not been applied systematically to OE non-finite constructions. Therefore one more aim of the dissertation is to test this framework and to see how OE fits into the cross-linguistic picture of non-finites. My research corpus consists of two samples: 1) written OE closely dependent on the Latin originals, based on editions of two gloss texts, five translations, and Latin originals of these texts, representing four text types: hymns, religious regulations, homily/life narrative, and biblical narrative (180,622 words); and 2) written OE as far independent from Latin as possible, based on a selection from the York-Toronto-Helsinki Parsed Corpus of Old English Prose (YCOE) and representing five text types: laws, charters, correspondence, chronicle narrative, and homily/life narrative (274,757 words).

Non-reductive Physicalism, Irreducibility of the Mental and the Problem of Mental Causation : A study of Donald Davidson's and Georg Henrik von Wright's positions in the philosophy of mind

In this study I consider what kind of perspective on the mind body problem is taken and can be taken by a philosophical position called non-reductive physicalism. Many positions fall under this label. The form of non-reductive physicalism which I discuss is in essential respects the position taken by Donald Davidson (1917-2003) and Georg Henrik von Wright (1916-2003). I defend their positions and discuss the unrecognized similarities between their views. Non-reductive physicalism combines two theses: (a) Everything that exists is physical; (b) Mental phenomena cannot be reduced to the states of the brain. This means that according to non-reductive physicalism the mental aspect of humans (be it a soul, mind, or spirit) is an irreducible part of the human condition. Also Davidson and von Wright claim that, in some important sense, the mental aspect of a human being does not reduce to the physical aspect, that there is a gap between these aspects that cannot be closed. I claim that their arguments for this conclusion are convincing. I also argue that whereas von Wright and Davidson give interesting arguments for the irreducibility of the mental, their physicalism is unwarranted. These philosophers do not give good reasons for believing that reality is thoroughly physical. Notwithstanding the materialistic consensus in the contemporary philosophy of mind the ontology of mind is still an uncharted territory where real breakthroughs are not to be expected until a radically new ontological position is developed. The third main claim of this work is that the problem of mental causation cannot be solved from the Davidsonian - von Wrightian perspective. The problem of mental causation is the problem of how mental phenomena like beliefs can cause physical movements of the body. As I see it, the essential point of non-reductive physicalism - the irreducibility of the mental - and the problem of mental causation are closely related. If mental phenomena do not reduce to causally effective states of the brain, then what justifies the belief that mental phenomena have causal powers? If mental causes do not reduce to physical causes, then how to tell when - or whether - the mental causes in terms of which human actions are explained are actually effective? I argue that this - how to decide when mental causes really are effective - is the real problem of mental causation. The motivation to explore and defend a non-reductive position stems from the belief that reductive physicalism leads to serious ethical problems. My claim is that Davidson's and von Wright's ultimate reason to defend a non-reductive view comes back to their belief that a reductive understanding of human nature would be a narrow and possibly harmful perspective. The final conclusion of my thesis is that von Wright's and Davidson's positions provide a starting point from which the current scientistic philosophy of mind can be critically further explored in the future.

Cortical processing of speech and non-speech sounds in adults and newborns

Comprehension of a complex acoustic signal - speech - is vital for human communication, with numerous brain processes required to convert the acoustics into an intelligible message. In four studies in the present thesis, cortical correlates for different stages of speech processing in a mature linguistic system of adults were investigated. In two further studies, developmental aspects of cortical specialisation and its plasticity in adults were examined. In the present studies, electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings of the mismatch negativity (MMN) response elicited by changes in repetitive unattended auditory events and the phonological mismatch negativity (PMN) response elicited by unexpected speech sounds in attended speech inputs served as the main indicators of cortical processes. Changes in speech sounds elicited the MMNm, the magnetic equivalent of the electric MMN, that differed in generator loci and strength from those elicited by comparable changes in non-speech sounds, suggesting intra- and interhemispheric specialisation in the processing of speech and non-speech sounds at an early automatic processing level. This neuronal specialisation for the mother tongue was also reflected in the more efficient formation of stimulus representations in auditory sensory memory for typical native-language speech sounds compared with those formed for unfamiliar, non-prototype speech sounds and simple tones. Further, adding a speech or non-speech sound context to syllable changes was found to modulate the MMNm strength differently in the left and right hemispheres. Following the acoustic-phonetic processing of speech input, phonological effort related to the selection of possible lexical (word) candidates was linked with distinct left-hemisphere neuronal populations. In summary, the results suggest functional specialisation in the neuronal substrates underlying different levels of speech processing. Subsequently, plasticity of the brain's mature linguistic system was investigated in adults, in whom representations for an aurally-mediated communication system, Morse code, were found to develop within the same hemisphere where representations for the native-language speech sounds were already located. Finally, recording and localization of the MMNm response to changes in speech sounds was successfully accomplished in newborn infants, encouraging future MEG investigations on, for example, the state of neuronal specialisation at birth.

Cortical processing of speech and non-speech sounds in autism and Asperger syndrome

Autism and Asperger syndrome (AS) are neurodevelopmental disorders characterised by deficient social and communication skills, as well as restricted, repetitive patterns of behaviour. The language development in individuals with autism is significantly delayed and deficient, whereas in individuals with AS, the structural aspects of language develop quite normally. Both groups, however, have semantic-pragmatic language deficits. The present thesis investigated auditory processing in individuals with autism and AS. In particular, the discrimination of and orienting to speech and non-speech sounds was studied, as well as the abstraction of invariant sound features from speech-sound input. Altogether five studies were conducted with auditory event-related brain potentials (ERP); two studies also included a behavioural sound-identification task. In three studies, the subjects were children with autism, in one study children with AS, and in one study adults with AS. In children with autism, even the early stages of sound encoding were deficient. In addition, these children had altered sound-discrimination processes characterised by enhanced spectral but deficient temporal discrimination. The enhanced pitch discrimination may partly explain the auditory hypersensitivity common in autism, and it may compromise the filtering of relevant auditory information from irrelevant information. Indeed, it was found that when sound discrimination required abstracting invariant features from varying input, children with autism maintained their superiority in pitch processing, but lost it in vowel processing. Finally, involuntary orienting to sound changes was deficient in children with autism in particular with respect to speech sounds. This finding is in agreement with previous studies on autism suggesting deficits in orienting to socially relevant stimuli. In contrast to children with autism, the early stages of sound encoding were fairly unimpaired in children with AS. However, sound discrimination and orienting were rather similarly altered in these children as in those with autism, suggesting correspondences in the auditory phenotype in these two disorders which belong to the same continuum. Unlike children with AS, adults with AS showed enhanced processing of duration changes, suggesting developmental changes in auditory processing in this disorder.

Temporomandibular disorders and related psychosocial factors in non-patients : A survey and a clinical follow-up study based on the RDC/TMD

Temporomandibular disorders (TMD) and psychosocial factors reportedly associate. The underlying factors remain partially obscure, however, and further studies are required to clarify the relationships. The aims of this study were thus to assess in a non-patient working population the prevalence of TMD and related symptoms, and to clinically diagnose and follow the natural courses of TMD over a one-year period. In addition, possible comorbidity of temporomandibular and/or neck muscle pain and perceived stress and their impact on work performance were investigated, as well as how various psychosocial aspects relate to TMD. A questionnaire was mailed to all 30- to 55-year-old employees of the Finnish Broadcasting Company Ltd. whose employment in the Helsinki area had lasted at least five years (n = 1784). Of the 1339 subjects, who returned the questionnaire, 241 were examined according to the RDC/TMD and standard neck muscle palpation methods. Clinical signs of temporomandibular and/or neck muscle pain were found in 118 subjects. One-year follow-up TMD examinations were conducted on 211 subjects. The prevalence of frequent painless TMJ-related symptoms was 10%, orofacial pain 7%, neck pain 38%, and headache 15%. TMD diagnoses were: myofascial pain (13%), disc displacements (16%), and arthralgia, osteoarthritis, osteoarthrosis (4%). Chronic myofascial pain was present in 7% and chronic disc displacement with reduction in 11% of the subjects. Symptoms were significantly associated with almost all the studied psychosocial symptoms. Reduced work performance was significantly positively associated with continuous pain, severity of pain, and health stress perception, and according to logistic regression, somatization with the probability of having chronic myofascial pain. It could be concluded based on the results of this study among a non-patient working population that TMD and related symptoms are common and associated with psychosocial factors. Moreover, myofascial pain and disc displacement with reduction are the most common diagnoses of TMD. In addition, self-reported health related stress, and continuous pain in temporomandibular and/or neck muscles are associated with reduced work performance, and somatization is significantly associated with chronic myofascial pain.

Preadolescents and Their Mothers as Oral Health-Promoting Actors : Non-biologic Determinants of Oral Health among Turkish and Finnish Preadolescents

Is oral health becoming a part of the global health culture? Oral health seems to turn out to be part of the global health culture, according to the findings of a thesis-research, Institute of Dentistry, University of Helsinki. The thesis is entitled as “Preadolescents and Their Mothers as Oral Health-Promoting Actors: Non-biologic Determinants of Oral Health among Turkish and Finnish Preadolescents.” The research was supervised by Prof.Murtomaa and led by Dr.A.Basak Cinar. It was conducted as a cross-sectional study of 611 Turkish and 223 Finnish school preadolescents in Istanbul and Helsinki, from the fourth, fifth, and sixth grades, aged 10 to 12, based on self-administered and pre-tested health behavior questionnaires for them and their mothers as well as the youth’s oral health records. Clinically assessed dental status (DMFT) and self-reported oral health of Turkish preadolescents was significantly poorer than the Finns`. A similar association occurred for well-being measures (height and weight, self-esteem), but not for school performance. Turkish preadolescents were more dentally anxious and reported lower mean values of toothbrushing self-efficacy and dietary self-efficacy than did Finns. The Turks less frequently reported recommended oral health behaviors (twice daily or more toothbrushing, sweet consumption on 2 days or less/week, decreased between-meal sweet consumption) than did the Finns. Turkish mothers reported less frequently dental health as being above average and recommended oral health behaviors as well as regular dental visits. Their mean values for dental anxiety was higher and self-efficacy on implementation of twice-daily toothbrushing were lower than those of the Finnish. Despite these differences between the Turks and Finns, the associations found in common for all preadolescents, regardless of cultural differences and different oral health care systems, assessed for the first time in a holistic framework, were as follows: There seems to be interrelation between oral health and general-well being (body height-weight measures, school performance, and self-esteem) among preadolescents: • The body height was an explanatory factor for dental health, underlining the possible common life-course factors for dental health and general well-being. • Better school performance, high levels of self-esteem and self-efficacy were interrelated and they contributed to good oral health. • Good school performance was a common predictor for twice-daily toothbrushing. Self-efficacy and maternal modelling have significant role for maintenance and improvement of both oral- and general health- related behaviors. In addition, there is need for integration of self-efficacy based approaches to promote better oral health. • All preadolescents with high levels of self-efficacy were more likely to report more frequent twice-daily toothbrushing and less frequent sweet consumption. • All preadolescents were likely to imitate toothbrushing and sweet consumption behaviors of their mothers. • High levels of self-efficacy contributed to low dental anxiety in various patterns in both groups. As a conclusion: • Many health-detrimental behaviors arise from the school age years and are unlikely to change later. Schools have powerful influences on children’s development and well-being. Therefore, oral health promotion in schools should be integrated into general health promotion, school curricula, and other activities. • Health promotion messages should be reinforced in schools, enabling children and their families to develop lifelong sustainable positive health-related skills (self-esteem, self-efficacy) and behaviors. • Placing more emphasis on behavioral sciences, preventive approaches, and community-based education during undergraduate studies should encourage social responsibility and health-promoting roles among dentists. Attempts to increase general well-being and to reduce oral health inequalities among preadolescents will remain unsuccessful if the individual factors, as well as maternal and societal influences, are not considered by psycho-social holistic approaches.