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.

Patriarkkana ikuisuuden performanssissa : Maskuliinisuuden ja miehen ruumiillisuuden rakentuminen mormonien Duties and Blessings of the Priesthood -opetuskäsikirjassa

The material I analyze for my master's thesis is a teaching manual used by the Mormons (the Church of Jesus Christ of Latter-day Saints), called "Duties and Blessings of the Priesthood". This work includes numerous lesson plans, each one with a separate topic. The manual is intended especially for teaches, but can also be used for individual study. The main target of my research is to find out how men and their bodies are constructed in the manual. Prescriptive texts together with narrative stories and illustrations create a multifaceted picture of Mormon notions of masculinity and corporeality. I approach my research material from a constructivist perspective. I build my interpretative reading upon Critical Discourse Analysis. I am especially interested in how the manual interprets and understands connections between gender, embodiment and religion. I understand gender in Judith Butler's terms, as a performance of styled and repeated gestures. Some of the discussions I raise in my work draw upon the disciplines of Critical Men's Studies and Sociology of Religion. In Mormonism, gender is thought to be an elementary part of human ontology. It is an eternal trait inherited from God the Father (and God the Mother). The place of men in Mormon cosmology is determined by their double role as patriarchs, fathers and priests. The main objective of mortal life is to gain salvation together with one's family. The personal goal of a Mormon man is to one day become a god. Patriarchs are responsible for the spiritual and material well-being of their family. The head of a household should be gentle and loving, but still an unconditional authority. In the manual, a Mormon man is depicted as a successor of mythical and exemplary men of sacred history. The perfect and sinless body of Jesus Christ serves as an ideal for the male body. Mormon masculinity is also defined by priesthood - the holy power of God - which is given to practically all male Mormons. Through the priesthood, a Mormon man serves as the governor of God on Earth. The Mormon priest has the authority to bind the immanent and the transcendent worlds together with gestures, poses and motions performed with his body. In Mormonism, the body also symbolizes a temple or a space where the sacred meets the profane. Because the priesthood borne by a man is holy, he has to treat his body accordingly. The body is valuable in itself, without it one cannot be saved. Men are forbidden of polluting their bodies by using stimulants or by having sexual relations out of wedlock. A priesthood holder must uphold healthy habits, dress neatly, and conduct himself in a temperate manner. He must also be outgoing and attentive. The manual suggests that a man's goodness or wickedness can be perceived from his external appearance. The Church of Jesus Christ of Latter-day Saints is a hierarchical and man-led organisation. The ideals of gender and corporeality are set by a homogenous priesthood leadership that consists mainly of white heterosexual American men. The larger Mormon community can control individual men by sanctioning. Growing as a Mormon man happens under the guidance of one's reference group.

Two views on interstellar dust: near-infrared scattering and polarized thermal dust emission

Interstellar clouds are not featureless, but show quite complex internal structures of filaments and clumps when observed with high enough resolution. These structures have been generated by 1) turbulent motions driven mainly by supernovae, 2) magnetic fields working on the ions and, through neutral-ion collisions, on neutral gas as well, and 3) self-gravity pulling a dense clump together to form a new star. The study of the cloud structure gives us information on the relative importance of each of these mechanisms, and helps us to gain a better understanding of the details of the star formation process. Interstellar dust is often used as a tracer for the interstellar gas which forms the bulk of the interstellar matter. Some of the methods that are used to derive the column density are summarized in this thesis. A new method, which uses the scattered light to map the column density in large fields with high spatial resolution, is introduced. This thesis also takes a look at the grain alignment with respect to the magnetic fields. The aligned grains give rise to the polarization of starlight and dust emission, thus revealing the magnetic field. The alignment mechanisms have been debated for the last half century. The strongest candidate at present is the radiative torques mechanism. In the first four papers included in this thesis, the scattered light method of column density estimation is formulated, tested in simulations, and finally used to obtain a column density map from observations. They demonstrate that the scattered light method is a very useful and reliable tool in column density estimation, and is able to provide higher resolution than the near-infrared color excess method. These two methods are complementary. The derived column density maps are also used to gain information on the dust emissivity within the observed cloud. The two final papers present simulations of polarized thermal dust emission assuming that the alignment happens by the radiative torques mechanism. We show that the radiative torques can explain the observed decline of the polarization degree towards dense cores. Furthermore, the results indicate that the dense cores themselves might not contribute significantly to the polarized signal, and hence one needs to be careful when interpreting the observations and deriving the magnetic field.

Maan magneettikentän dipolimallin toimivuus inklinaatiojakauman perusteella

The magnetic field of the Earth is 99 % of the internal origin and generated in the outer liquid core by the dynamo principle. In the 19th century, Carl Friedrich Gauss proved that the field can be described by a sum of spherical harmonic terms. Presently, this theory is the basis of e.g. IGRF models (International Geomagnetic Reference Field), which are the most accurate description available for the geomagnetic field. In average, dipole forms 3/4 and non-dipolar terms 1/4 of the instantaneous field, but the temporal mean of the field is assumed to be a pure geocentric axial dipolar field. The validity of this GAD (Geocentric Axial Dipole) hypothesis has been estimated by using several methods. In this work, the testing rests on the frequency dependence of inclination with respect to latitude. Each combination of dipole (GAD), quadrupole (G2) and octupole (G3) produces a distinct inclination distribution. These theoretical distributions have been compared with those calculated from empirical observations from different continents, and last, from the entire globe. Only data from Precambrian rocks (over 542 million years old) has been used in this work. The basic assumption is that during the long-term course of drifting continents, the globe is sampled adequately. There were 2823 observations altogether in the paleomagnetic database of the University of Helsinki. The effect of the quality of observations, as well as the age and rocktype, has been tested. For comparison between theoretical and empirical distributions, chi-square testing has been applied. In addition, spatiotemporal binning has effectively been used to remove the errors caused by multiple observations. The modelling from igneous rock data tells that the average magnetic field of the Earth is best described by a combination of a geocentric dipole and a very weak octupole (less than 10 % of GAD). Filtering and binning gave distributions a more GAD-like appearance, but deviation from GAD increased as a function of the age of rocks. The distribution calculated from so called keypoles, the most reliable determinations, behaves almost like GAD, having a zero quadrupole and an octupole 1 % of GAD. In no earlier study, past-400-Ma rocks have given a result so close to GAD, but low inclinations have been prominent especially in the sedimentary data. Despite these results, a greater deal of high-quality data and a proof of the long-term randomness of the Earth's continental motions are needed to make sure the dipole model holds true.

Field intercomparison of four methane gas analysers suitable for eddy covariance flux measurements

Eddy covariance (EC)-flux measurement technique is based on measurement of turbulent motions of air with accurate and fast measurement devices. For instance, in order to measure methane flux a fast methane gas analyser is needed which measures methane concentration at least ten times in a second in addition to a sonic anemometer, which measures the three wind components with the same sampling interval. Previously measurement of methane flux was almost impossible to carry out with EC-technique due to lack of fast enough gas analysers. However during the last decade new instruments have been developed and thus methane EC-flux measurements have become more common. Performance of four methane gas analysers suitable for eddy covariance measurements are assessed in this thesis. The assessment and comparison was performed by analysing EC-data obtained during summer 2010 (1.4.-26.10.) at Siikaneva fen. The four participating methane gas analysers are TGA-100A (Campbell Scientific Inc., USA), RMT-200 (Los Gatos Research, USA), G1301-f (Picarro Inc., USA) and Prototype-7700 (LI-COR Biosciences, USA). RMT-200 functioned most reliably throughout the measurement campaign and the corresponding methane flux data had the smallest random error. In addition, methane fluxes calculated from data obtained from G1301-f and RMT-200 agree remarkably well throughout the measurement campaign. The calculated cospectra and power spectra agree well with corresponding temperature spectra. Prototype-7700 functioned only slightly over one month in the beginning of the measurement campaign and thus its accuracy and long-term performance is difficult to assess.

3D MHD simulations of subsurface convection in OB stars

During their main sequence evolution, massive stars can develop convective regions very close to their surface. These regions are caused by an opacity peak associated with iron ionization. Cantiello et al. (2009) found a possible connection between the presence of sub-photospheric convective motions and small scale stochastic velocities in the photosphere of early-type stars. This supports a physical mechanism where microturbulence is caused by waves that are triggered by subsurface convection zones. They further suggest that clumping in the inner parts of the winds of OB stars could be related to subsurface convection, and that the convective layers may also be responsible for stochastic excitation of non-radial pulsations. Furthermore, magnetic fields produced in the iron convection zone could appear at the surface of such massive stars. Therefore subsurface convection could be responsible for the occurrence of observable phenomena such as line profile variability and discrete absorption components. These phenomena have been observed for decades, but still evade a clear theoretical explanation. Here we present preliminary results from 3D MHD simulations of such subsurface convection.