Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Monitoring Indigenous Tropical Montane Forests in the Taita Hills Using Airborne Digital Camera Imagery

The loss and degradation of forest cover is currently a globally recognised problem. The fragmentation of forests is further affecting the biodiversity and well-being of the ecosystems also in Kenya. This study focuses on two indigenous tropical montane forests in the Taita Hills in southeastern Kenya. The study is a part of the TAITA-project within the Department of Geography in the University of Helsinki. The study forests, Ngangao and Chawia, are studied by remote sensing and GIS methods. The main data includes black and white aerial photography from 1955 and true colour digital camera data from 2004. This data is used to produce aerial mosaics from the study areas. The land cover of these study areas is studied by visual interpretation, pixel-based supervised classification and object-oriented supervised classification. The change of the forest cover is studied with GIS methods using the visual interpretations from 1955 and 2004. Furthermore, the present state of the study forests is assessed with leaf area index and canopy closure parameters retrieved from hemispherical photographs as well as with additional, previously collected forest health monitoring data. The canopy parameters are also compared with textural parameters from digital aerial mosaics. This study concludes that the classification of forest areas by using true colour data is not an easy task although the digital aerial mosaics are proved to be very accurate. The best classifications are still achieved with visual interpretation methods as the accuracies of the pixel-based and object-oriented supervised classification methods are not satisfying. According to the change detection of the land cover in the study areas, the area of indigenous woodland in both forests has decreased in 1955 2004. However in Ngangao, the overall woodland area has grown mainly because of plantations of exotic species. In general, the land cover of both study areas is more fragmented in 2004 than in 1955. Although the forest area has decreased, forests seem to have a more optimistic future than before. This is due to the increasing appreciation of the forest areas.

Parameters Affecting the Extraction of Polycyclic Aromatic Hydrocarbons with Pressurised Hot Water

Pressurised hot water extraction (PHWE) exploits the unique temperature-dependent solvent properties of water minimising the use of harmful organic solvents. Water is environmentally friendly, cheap and easily available extraction medium. The effects of temperature, pressure and extraction time in PHWE have often been studied, but here the emphasis was on other parameters important for the extraction, most notably the dimensions of the extraction vessel and the stability and solubility of the analytes to be extracted. Non-linear data analysis and self-organising maps were employed in the data analysis to obtain correlations between the parameters studied, recoveries and relative errors. First, pressurised hot water extraction (PHWE) was combined on-line with liquid chromatography-gas chromatography (LC-GC), and the system was applied to the extraction and analysis of polycyclic aromatic hydrocarbons (PAHs) in sediment. The method is of superior sensitivity compared with the traditional methods, and only a small 10 mg sample was required for analysis. The commercial extraction vessels were replaced by laboratory-made stainless steel vessels because of some problems that arose. The performance of the laboratory-made vessels was comparable to that of the commercial ones. In an investigation of the effect of thermal desorption in PHWE, it was found that at lower temperatures (200ºC and 250ºC) the effect of thermal desorption is smaller than the effect of the solvating property of hot water. At 300ºC, however, thermal desorption is the main mechanism. The effect of the geometry of the extraction vessel on recoveries was studied with five specially constructed extraction vessels. In addition to the extraction vessel geometry, the sediment packing style and the direction of water flow through the vessel were investigated. The geometry of the vessel was found to have only minor effect on the recoveries, and the same was true of the sediment packing style and the direction of water flow through the vessel. These are good results because these parameters do not have to be carefully optimised before the start of extractions. Liquid-liquid extraction (LLE) and solid-phase extraction (SPE) were compared as trapping techniques for PHWE. LLE was more robust than SPE and it provided better recoveries and repeatabilities than did SPE. Problems related to blocking of the Tenax trap and unrepeatable trapping of the analytes were encountered in SPE. Thus, although LLE is more labour intensive, it can be recommended over SPE. The stabilities of the PAHs in aqueous solutions were measured using a batch-type reaction vessel. Degradation was observed at 300ºC even with the shortest heating time. Ketones and quinones and other oxidation products were observed. Although the conditions of the stability studies differed considerably from the extraction conditions in PHWE, the results indicate that the risk of analyte degradation must be taken into account in PHWE. The aqueous solubilities of acenaphthene, anthracene and pyrene were measured, first below and then above the melting point of the analytes. Measurements below the melting point were made to check that the equipment was working, and the results were compared with those obtained earlier. Good agreement was found between the measured and literature values. A new saturation cell was constructed for the solubility measurements above the melting point of the analytes because the flow-through saturation cell could not be used above the melting point. An exponential relationship was found between the solubilities measured for pyrene and anthracene and temperature.

Spin and relativistic motion of bound states

The wave functions of moving bound states may be expected to contract in the direction of motion, in analogy to a rigid rod in classical special relativity, when the constituents are at equal (ordinary) time. Indeed, the Lorentz contraction of wave functions is often appealed to in qualitative discussions. However, only few field theory studies exist of equal-time wave functions in motion. In this thesis I use the Bethe-Salpeter formalism to study the wave function of a weakly bound state such as a hydrogen atom or positronium in a general frame. The wave function of the e^-e^+ component of positronium indeed turns out to Lorentz contract both in 1+1 and in 3+1 dimensional quantum electrodynamics, whereas the next-to-leading e^-e^+\gamma Fock component of the 3+1 dimensional theory deviates from classical contraction. The second topic of this thesis concerns single spin asymmetries measured in scattering on polarized bound states. Such spin asymmetries have so far mainly been analyzed using the twist expansion of perturbative QCD. I note that QCD vacuum effects may give rise to a helicity flip in the soft rescattering of the struck quark, and that this would cause a nonvanishing spin asymmetry in \ell p^\uparrow -> \ell' + \pi + X in the Bjorken limit. An analogous asymmetry may arise in p p^\uparrow -> \pi + X from Pomeron-Odderon interference, if the Odderon has a helicity-flip coupling. Finally, I study the possibility that the large single spin asymmetry observed in p p^\uparrow -> \pi(x_F,k_\perp) + X when the pion carries a high momentum fraction x_F of the polarized proton momentum arises from coherent effects involving the entire polarized bound state.

Multiwavelength studies of regolith effects in planetary remote sensing

A large proportion of our knowledge about the surfaces of atmosphereless solar-system bodies is obtained through remote-sensing measurements. The measurements can be carried out either as ground-based telescopic observations or space-based observations from orbiting spacecraft. In both cases, the measurement geometry normally varies during the observations due to the orbital motion of the target body, the spacecraft, etc.. As a result, the data are acquired over a variety of viewing and illumination angles. Surfaces of planetary bodies are usually covered with a layer of loose, broken-up rock material called the regolith whose physical properties affect the directional dependence of remote-sensed measurements. It is of utmost importance for correct interpretation of the remote-sensed data to understand the processes behind this alteration. In the thesis, the multi-angular effects that the physical properties of the regolith have on remote-sensing measurements are studied in two regimes of electromagnetic radiation, visible to near infrared and soft X-rays. These effects are here termed generally the regolith effects in remote sensing. Although the physical mechanisms that are important in these regions are largely different, notable similarities arise in the methodology that is used in the study of the regolith effects, including the characterization of the regolith both in experimental studies and in numerical simulations. Several novel experimental setups have been constructed for the thesis. Alongside the experimental work, theoretical modelling has been carried out, and results from both approaches are presented. Modelling of the directional behaviour of light scattered from a regolith is utilized to obtain shape and spin-state information of several asteroids from telescopic observations and to assess the surface roughness and single-scattering properties of lunar maria from spacecraft observations. One of the main conclusions is that the azimuthal direction is an important factor in detailed studies of planetary surfaces. In addition, even a single parameter, such as porosity, can alter the light scattering properties of a regolith significantly. Surface roughness of the regolith is found to alter the elemental fluorescence line ratios of a surface obtained through planetary soft X-ray spectrometry. The results presented in the thesis are among the first to report this phenomenon. Regolith effects need to be taken into account in the analysis of remote-sensed data, providing opportunities for retrieving physical parameters of the surface through inverse methods.

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.

Genetic variation in the LDL receptor-related protein 5 (LRP5) gene : Association with bone health and metabolic parameters

Bone mass accrual and maintenance are regulated by a complex interplay between genetic and environmental factors. Recent studies have revealed an important role for the low-density lipoprotein receptor-related protein 5 (LRP5) in this process. The aim of this thesis study was to identify novel variants in the LRP5 gene and to further elucidate the association of LRP5 and its variants with various bone health related clinical characteristics. The results of our studies show that loss-of-function mutations in LRP5 cause severe osteoporosis not only in homozygous subjects but also in the carriers of these mutations, who have significantly reduced bone mineral density (BMD) and increased susceptibility to fractures. In addition, we demonstrated for the first time that a common polymorphic LRP5 variant (p.A1330V) was associated with reduced peak bone mass, an important determinant of BMD and osteoporosis in later life. The results from these two studies are concordant with results seen in other studies on LRP5 mutations and in association studies linking genetic variation in LRP5 with BMD and osteoporosis. Several rare LRP5 variants were identified in children with recurrent fractures. Sequencing and multiplex ligation-dependent probe amplification (MLPA) analyses revealed no disease-causing mutations or whole-exon deletions. Our findings from clinical assessments and family-based genotype-phenotype studies suggested that the rare LRP5 variants identified are not the definite cause of fractures in these children. Clinical assessments of our study subjects with LPR5 mutations revealed an unexpectedly high prevalence of impaired glucose tolerance and dyslipidaemia. Moreover, in subsequent studies we discovered that common polymorphic LRP5 variants are associated with unfavorable metabolic characteristics. Changes in lipid profile were already apparent in pre-pubertal children. These results, together with the findings from other studies, suggest an important role for LRP5 also in glucose and lipid metabolism. Our results underscore the important role of LRP5 not only in bone mass accrual and maintenance of skeletal health but also in glucose and lipid metabolism. The role of LRP5 in bone metabolism has long been studied, but further studies with larger study cohorts are still needed to evaluate the specific role of LRP5 variants as metabolic risk factors.

The connection between on-farm assessed welfare (A-index) and production parameters of the sows

Tämän tutkimuksen tavoitteena oli selvittää tilalla määritetyn hyvinvoinnin yhteyttä emakoiden tuotantotuloksiin. Hyvinvointia arvioitiin suomalaisen hyvinvointi-indeksin, A-indeksi, avulla. Tuotantotuloksina käytettiin kahta erilaista tuotosaineistoa, jotka molemmat pohjautuivat kansalliseen tuotosseuranta aineistoon. Hyvinvointimääritykset tehtiin 30 porsastuotantosikalassa maaliskuun 2007 aikana. A-indeksi koostuu kuudesta kategoriasta ’liikkumismahdollisuudet’, ’alustan ominaisuudet’, ’sosiaaliset kontaktit’, ’valo, ilma ja melu’, ’ruokinta ja veden saanti’ sekä ’eläinten terveys ja hoidon taso’. Jokaisessa kategoriassa on 3-10 pääosin ympäristöperäistä muuttujaa, jotka vaihtelevat osastoittain. Maksimipistemäärä osastolle on 100. Hyvinvointimittaukset tehtiin porsitus-, tiineytys- ja joutilasosastoilla. Erillisten tiineytysosastojen pienen lukumäärän takia (n=7) tilakohtaiset tiineytys- ja joutilasosastopisteet yhdistettiin ja keskiarvoja käytettiin analyyseissä. Yhteyksiä tuotokseen tutkittiin kahden eri aineiston avulla 1) Tilaraportti aineisto (n=29) muodostuu muokkaamattomista tila- ja tuotostuloksista tilavierailua edeltävän vuoden ajalta, 2) POTSIaineisto (n=30) muodostuu POTSI-ohjelmalla (MTT) muokatusta tuotantoaineistosta, joka sisältää managementtiryhmän (tila, vuosi, vuodenaika) vaikutuksen ensikoiden ja emakoiden pahnuekohtaiseen tuotokseen. Yhteyksiä analysointiin korrelaatio- ja regressioanalyysien avulla. Vaikka osallistuminen tutkimukseen oli vapaaehtoista, molempien tuotantoaineistojen perusteella tutkimustilat edustavat keskituottoista suomalaista sikatilaa. A-indeksin kokonaispisteet vaihtelivat välillä 37,5–64,0 porsitusosastolla ja 39,5–83,5 joutilasosastolla. Tilaraporttiaineistoa käytettäessä paremmat pisteet porsitusosaston ’eläinten terveys ja hoidon taso’ -kategoriasta lyhensivät eläinten lisääntymissykliä, lisäsivät syntyvien pahnueiden ja porsaiden määrää sekä alensivat kuolleena syntyneiden lukumäärää. Regressiomallin mukaan ’eläinten terveys ja hoidon taso’ -kategoria selitti syntyvien porsaiden lukumäärän, porsimisvälin pituuden sekä keskiporsimiskerran vaihtelua. Paremmat pisteet joutilasosaston ’liikkumismahdollisuudet’ kategoriasta alensivat syntyneiden pahnueiden sekä syntyneiden että vieroitettujen porsaiden lukumäärää. Regressiomallin mukaan ensikkopahnueiden osuus ja ”liikkumismahdollisuudet” kategorian pisteet selittivät vieroitettujen porsaiden lukumäärän vaihtelua. POTSI-aineiston yhteydessä kuolleena syntyneiden porsaiden lukumäärän aleneminen oli ensikoilla yhteydessä parempiin porsitusosaston ’sosiaalisiin kontakteihin’ ja emakoilla puolestaan joutilasosaston parempiin ’eläinten terveys ja hoidon taso’ pisteisiin. Kahden eri tuotantoaineiston avulla saadut tulokset erosivat toisistaan. Seuraavissa tutkimuksissa onkin suositeltavampaa käyttää Tilaraporttiaineistoja, joissa tuotokset ilmoitetaan vuosikohtaisina. Tämän tutkimuksen perusteella hyvinvoinnilla ja tuotoksella on yhteyksiä, joilla on myös merkittävää taloudellista vaikutusta. Erityisesti hyvä eläinten hoito ja eläinten terveys lisäävät tuotettujen porsaiden määrää ja lyhentävät lisääntymiskiertoa. Erityishuomiota tulee kiinnittää vapaana olevien joutilaiden emakoiden sosiaaliseen stressiin ja rehunsaannin varmistamiseen kaikille yksilöille.

Electrocardiographic parameters of ventricular repolarization : modifiers and the prognostic value

Electric activity of the heart consists of repeated cardiomyocyte depolarizations and repolarizations. Abnormalities in repolarization predispose to ventricular arrhythmias. In body surface electrocardiogram, ventricular repolarization generates the T wave. Several electrocardiographic measures have been developed both for clinical and research purposes to detect repolarization abnormalities. The study aim was to investigate modifiers of ventricular repolarization with the focus on the relationship of the left ventricular mass, antihypertensive drugs, and common gene variants, to electrocardiographic repolarization parameters. The prognostic value of repolarization parameters was also assessed. The study subjects originated from a population of more than 200 middle-aged hypertensive men attending the GENRES hypertension study, and from an epidemiological survey, the Health 2000 Study, including more than 6000 participants. Ventricular repolarization was analysed from digital standard 12-lead resting electrocardiograms with two QT-interval based repolarization parameters (QT interval, T-wave peak to T-wave end interval) and with a set of four T-wave morphology parameters. The results showed that in hypertensive men, a linear change in repolarization parameters is present even in the normal range of left ventricular mass, and that even mild left ventricular hypertrophy is associated with potentially adverse electrocardiographic repolarization changes. In addition, treatments with losartan, bisoprolol, amlodipine, and hydrochlorothiazide have divergent short-term effects on repolarization parameters in hypertensive men. Analyses of the general population sample showed that single nucleotide polymorphisms in KCNH2, KCNE1, and NOS1AP genes are associated with changes in QT-interval based repolarization parameters but not consistently with T-wave morphology parameters. T-wave morphology parameters, but not QT interval or T-wave peak to T-wave end interval, provided independent prognostic information on mortality. The prognostic value was specifically related to cardiovascular mortality. The results indicate that, in hypertension, altered ventricular repolarization is already present in mild left ventricular mass increase, and that commonly used antihypertensive drugs may relatively rapidly and treatment-specifically modify electrocardiographic repolarization parameters. Common variants in cardiac ion channel genes and NOS1AP gene may also modify repolarization-related arrhythmia vulnerability. In the general population, T-wave morphology parameters may be useful in the risk assessment of cardiovascular mortality.