Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

Rigorous scaling law for the heat current in disordered harmonic chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T_1 and T_n. Let EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.

Nonequilibrium stationary states of harmonic chains with bulk noises

We consider a chain composed of $N$ coupled harmonic oscillators in contact with heat baths at temperature $T_\ell$ and $T_r$ at sites 1 and $N$ respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier's law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.

Theory and Analysis of Classic Heavy Metal Harmony

This thesis explores melodic and harmonic features of heavy metal, and while doing so, explores various methods of music analysis; their applicability and limitations regarding the study of heavy metal music. The study is built on three general hypotheses according to which 1) acoustic characteristics play a significant role for chord constructing in heavy metal, 2) heavy metal has strong ties and similarities with other Western musical styles, and 3) theories and analytical methods of Western art music may be applied to heavy metal. It seems evident that in heavy metal some chord structures appear far more frequently than others. It is suggested here that the fundamental reason for this is the use of guitar distortion effect. Subsequently, theories as to how and under what principles heavy metal is constructed need to be put under discussion; analytical models regarding the classification of consonance and dissonance and chord categorization are here revised to meet the common practices of this music. It is evident that heavy metal is not an isolated style of music; it is seen here as a cultural fusion of various musical styles. Moreover, it is suggested that the theoretical background to the construction of Western music and its analysis can offer invaluable insights to heavy metal. However, the analytical methods need to be reformed to some extent to meet the characteristics of the music. This reformation includes an accommodation of linear and functional theories that has been found rather rarely in music theory and musicology.

Olla elävän sanat : Roolirunon laji Maila Pylkkösen teoksessa Arvo. Vanhaäiti puhuu runonsa

Maila Pylkkönen (1931 1986) was one of the most important modernist poets in Finland and a central figure in developing the dramatic monologue in Finnish literature. The study examines Pylkkönen s poetic work Arvo. Vanhaäiti puhuu runonsa (Value. An old woman speaks her poem, 1959) as an example of the dramatic monologue, approaching it from three perspectives: its generic features and background, and the poetic framework to which it connects in the context of Pylkkönen s poetry. In addition to methods of literary scholarship, the poetic analysis benefits from a linguistic approach. The study shows that the dramatic monologue genre drives Pylkkönen s first work, Klassilliset tunteet (Classical feelings, 1957), in a context of finding poetic identity, characterised by the expression to be the words of a living creature . The study demonstrates that important generic features of the dramatic monologue, namely, a poem representing a speech-event and a hierarchical structure, are also Arvo s most significant generic features. Arvo s poems as speech-events are examined for their internal progressive, pragmatic unity constructed through single line units; for their function as narratives dealing with the life story of an old woman, Arvo s speaker; and from the perspective of the communication between the old woman and the poems other characters. Arvo s speech-events can also be seen as semantic shifts from one poem to another: the poems construct semantic stages representing different phases of the old woman s life. The study demonstrates that analysis of Arvo s hierarchical structure, that is, the relationship between the speaker and the rhetorical levels, reveals the work s structural and ideological wholeness by focusing on the old woman s emotions: longing, loneliness and alienation from the world. In other words, the contradictions between the explicit level of the speaker and an implied rhetorical level open up the tragedy of an old woman s daily life. Study of Arvo s hierarchical structure also highlights the special position of the reader in the framework of a dramatic monologue. The elements of a dramatic present in which the old woman s emotions are conveyed, an italicized opening poem, and the work s title Value invite the reader to consider Arvo as a structural and ideological whole. The function of Arvo s hierarchical structure is to ask the reader to recognise the hopelessness of the old woman s situation, understand it, and even identify with it.

Passion vallassa : Hermostunut aika Minna Canthin teoksissa

Under the power of passion. The age of nervousness in Minna Canth s works This research contemplates the psychology of Minna Canth s characters through the historical image of man in late 19th century Europe. The central operative term of the study is passion , understood as a twofold philosophical concept that includes both desire and suffering. The method of this study is historical and contextual. The study interprets the passions and the psychology of Canth s characters as they were understood in their own time. The indicator of the relevant contexts is the realist and naturalist genre of Canth s works. New research on the genre of the time is also the basis of a new kind of psychological approach to Canth s works. The most important context of passion in Canth s works is the positivistic and pathological image of man at the end of the 19th century. Then, passion was widely discussed, and was perceived as a physiological phenomenon that influenced humans neurologically and caused different kinds of physiological symptoms and nervous disorders. But at the same time, passion was understood as a manifestation of human instincts and drives. The naturalistic literature of the day aimed at creating deterministic studies of human morality and psychology following Émile Zola s application of experimental science methods in his writing. The pathological image of man is most explicitly manifested in Canth s formerly unknown short story Lääkäri (Doctor, 1891), in which a doctor who is interested in psychology visits a jail to meet a peculiar criminal, a girl who feels no remorse for her multiple crimes. In other works of Canth the medically motivated viewpoint is more hidden in the deterministic narrative and depiction of the characters. The present study approaches the passion in Minna Canth s works through five thematic chapters, in witch characters are interpreted suffering from blind love, ennui, crippling romantic idealism, melancholy, guilt and nostalgia, and their stories can be prescribed as medical histories which depict the born of the passion and its development towards ruin. All protagonists are also manifestations of their own time. Canth criticises the modern life and its demands as well as social defects through the tragic stories of individuals. The study demonstrates that Canth did not, like previous research has suggested, wait until the 1890s before writing works of a psychological nature but had already written according to the psychological paradigm of her time in Työmiehen vaimo (1885). The social and psychological interests intertwine in Canth s works and are not exclusionary as has formerly been interpreted. Canth is also critical of the medical power implicit in the naturalist experimental method and this shows itself especially in her depiction of working class women.

Pitch discrimination in optimal and suboptimal acoustic environments: electroencephalographic, magnetoencephalographic, and behavioral evidence

Pitch discrimination is a fundamental property of the human auditory system. Our understanding of pitch-discrimination mechanisms is important from both theoretical and clinical perspectives. The discrimination of spectrally complex sounds is crucial in the processing of music and speech. Current methods of cognitive neuroscience can track the brain processes underlying sound processing either with precise temporal (EEG and MEG) or spatial resolution (PET and fMRI). A combination of different techniques is therefore required in contemporary auditory research. One of the problems in comparing the EEG/MEG and fMRI methods, however, is the fMRI acoustic noise. In the present thesis, EEG and MEG in combination with behavioral techniques were used, first, to define the ERP correlates of automatic pitch discrimination across a wide frequency range in adults and neonates and, second, they were used to determine the effect of recorded acoustic fMRI noise on those adult ERP and ERF correlates during passive and active pitch discrimination. Pure tones and complex 3-harmonic sounds served as stimuli in the oddball and matching-to-sample paradigms. The results suggest that pitch discrimination in adults, as reflected by MMN latency, is most accurate in the 1000-2000 Hz frequency range, and that pitch discrimination is facilitated further by adding harmonics to the fundamental frequency. Newborn infants are able to discriminate a 20% frequency change in the 250-4000 Hz frequency range, whereas the discrimination of a 5% frequency change was unconfirmed. Furthermore, the effect of the fMRI gradient noise on the automatic processing of pitch change was more prominent for tones with frequencies exceeding 500 Hz, overlapping with the spectral maximum of the noise. When the fundamental frequency of the tones was lower than the spectral maximum of the noise, fMRI noise had no effect on MMN and P3a, whereas the noise delayed and suppressed N1 and exogenous N2. Noise also suppressed the N1 amplitude in a matching-to-sample working memory task. However, the task-related difference observed in the N1 component, suggesting a functional dissociation between the processing of spatial and non-spatial auditory information, was partially preserved in the noise condition. Noise hampered feature coding mechanisms more than it hampered the mechanisms of change detection, involuntary attention, and the segregation of the spatial and non-spatial domains of working-memory. The data presented in the thesis can be used to develop clinical ERP-based frequency-discrimination protocols and combined EEG and fMRI experimental paradigms.

Aivojen jännitevasteiden rekisteröinti useaan äänen piirteeseen yhdellä mittauskerralla terveillä musiikkileikkikoulua käyvillä kaksivuotiailla

The early detection of hearing deficits is important to a child's development. However, examining small children with behavioural methods is often difficult. Research with ERPs (event-related potentials), recorded with EEG (electroencephalography), does not require attention or action from the child. Especially in children's ERP research, it is essential that the duration of a recording session is not too long. A new, faster optimum paradigm has been developed to record MMN (mismatch negativity), where ERPs to several sound features can be recorded in one recording session. This substantially shortens the time required for the experiment. So far, the new paradigm has been used in adult and school-aged children research. This study examines if MMN, LDN (late discriminative negativity) and P3a components can be recorded in two-year-olds with the new paradigm. The standard stimulus (p=0.50) was an 80 dB harmonic tone consisting of three harmonic frequencies (500 Hz, 1000 Hz and 1500 Hz) with a duration of 200 ms. The loudness deviants (p=0.067) were at a level of +6 dB or -6 dB compared to the standards. The frequency deviants (p=0.112) had a fundamental frequency of 550 or 454.4 Hz (small deviation), 625 or 400 Hz (medium deviation) or 750 or 333.3 Hz (large deviation). The duration deviants (p=0.112) had a duration of 175 ms (small deviation), 150 ms (medium deviation) or 100 ms (large deviation). The direction deviants (p=0.067) were presented from the left or right loudspeaker only. The gap deviant (p=0.067) included a 5-ms silent gap in the middle of the sound. Altogether 17 children participated in the experiment, of whom the data of 12 children was used in the analysis. ERP components were observed for all deviant types. The MMN was significant for duration and gap deviants. The LDN was significant for the large duration deviant and all other deviant types. No significant P3a was observed. These results indicate that the optimum paradigm can be used with two-year-olds. With this paradigm, data on several sound features can be recorded in a shorter time than with the previous paradigms used in ERP research.

Kotitaloustaidon ulottuvuuksia : Analyysi kotitaloustaidosta eksistentialistis-hermeneuttisen fenomenologian valossa

DOMESTIC SKILLS AS THE ART OF EVERYDAY LIFE. An inquiry about domestic skills as a way of being-in-the-world in the light of existentialist-hermeneutics phenomenology. This study focuses on analyzing domestic skills in a phenomenological manner. The description phenomenological emerges from the interpretation process, which originates from the ontological question of domestic skills. The ontological question of how domestic skills are directs one s phenomenological gaze to the experiencing of domestic skills, rather than merely viewing their action or technical aspects. Along with the ontological question, the axiological question of what the meaning of domestic skills is drives the analysis. This study is both theoretical and philosophical. Phenomenology is the guiding philosophy, theory and methodology of the inquiry. Existentialist-hermeneutics is the emphasis which most appropriately describes the phenomenological attitude adopted within the analysis. Martin Heidegger s philosophy of being and Maurice Merleau-Ponty s philosophy of the lived body essentially form the theoretical base for the inquiry. The analysis reveals domestic skills within a core of Care and the Other. Care and the Other are anchored both in Heidegger s analysis of Dasein and in Merleau-Ponty s analysis of the reversible being-in-the-world. The social nature of being and the action-oriented intentionality of the lived body are embodied in Care and the Other. This ontological base of domestic skills enables us to see the extensions that inhabit in it. These extensions are redoing, emotional experiencing, adapting and emancipating. The analysis connects ability and action, which is why domestic skills and household activity must be seen as a united whole. This united whole is not the matter of the two components of the phenomenon, but is rather the matter of domestic skills as a way of being-in-the-world. Domestic skills are a channel for the phenomenon Home Economics to manifest in our lives. This is the gaze that presents domestic skills as to be like the poetry of everyday life. The main result of the study is the elucidation of the ontology of domestic skills and the naming of its extensions. This growth of philosophical understanding makes it possible to strengthen the science of home economics.

Molecular and clinical characteristics of tricarboxylic acid cycle-associated tumors

Hereditary leiomyomatosis and renal cell cancer (HLRCC) is a rare, dominantly inherited tumor predisposition syndrome characterized by benign cutaneous and uterine (ULM) leiomyomas, and sometimes renal cell cancer (RCC). A few cases of uterine leiomyosarcoma (ULMS) have also been reported. Mutations in a nuclear gene encoding fumarate hydratase (FH), an enzyme of the mitochondrial tricarboxylic acid cycle (TCA cycle), underlie HLRCC. As a recessive condition, germline mutations in FH predispose to a neurological defect, FH deficiency (FHD). Hereditary paragangliomatosis (HPGL) is a dominant disorder associated with paragangliomas and pheochromocytomas. Inherited mutations in three genes encoding subunits of succinate dehydrogenase (SDH), also a TCA cycle enzyme, predispose to HPGL. Both FH and SDH seem to act as tumor suppressors. One of the consequences of the TCA cycle defect is abnormal activation of HIF1 pathway ( pseudohypoxia ) in the HLRCC and HPGL tumors. HIF1 drives transcription of genes encoding e.g. angiogenetic factors which can facilitate tumor growth. Recently hypoxia/HIF1 has been suggested to be one of the causes of genetic instability as well. One of the aims of this study was to broaden the clinical definers of HLRCC. To determine the cancer risk and to identify possible novel tumor types associated with FH mutations eight Finnish HLRCC/FHD families were extensively evaluated. The extension of the pedigrees and the Finnish Cancer Registry based tumor search yielded genealogical and cancer data of altogether 868 individuals. The standardized incidence ratio-based comparison of HLRCC/FHD family members with general Finnish population revealed 6.5-fold risk for RCC. Moreover, risk for ULMS was highly increased. However, according to the recent and more stringent diagnosis criteria of ULMS many of the HLRCC uterine tumors previously considered malignant are at present diagnosed as atypical or proliferative ULMs (with a low risk of recurrence). Thus, the formation of ULMS (as presently defined) in HLRCC appears to be uncommon. Though increased incidence was not observed, interestingly the genetic analyses suggested possible association of breast and bladder cancer with loss of FH. Moreover, cancer cases were exceptionally detected in an FHD family. Another clinical finding was the conventional (clear cell) type RCC of a young Spanish HLRCC patient. Conventional RCC is distinct from the types previously observed in this syndrome but according to these results, FH mutation may underlie some of young conventional cancer cases. Secondly, the molecular pathway from defective TCA cycle to tumor formation was intended to clarify. Since HLRCC and HPGL tumors display abnormally activated HIF1, the hypothesis on the link between HIF1/hypoxia and genetic instability was of interest to study in HLRCC and HPGL tumor material. HIF1α (a subunit of HIF1) stabilization was confirmed in the majority of the specimens. However, no repression of MSH2, a protein of DNA mismatch repair system, or microsatellite instability (MSI), an indicator of genetic instability, was observed. Accordingly, increased instability seems not to play a role in the tumorigenesis of pseudohypoxic TCA cycle-deficient tumors. Additionally, to study the putative alternative functions of FH, a recently identified alternative FH transcript (FHv) was characterized. FHv was found to contain instead of exon 1, an alternative exon 1b. Differential subcellular distribution, lack of FH enzyme activity, low mRNA expression compared to FH, and induction by cellular stress suggest FHv to have a role distinct from FH, for example in apoptosis or survival. However, the physiological significance of FHv requires further elucidation.