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.

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.

Analysts' Accuracy of Estimation and the Relative Trading Volume

This study contributes to the neglect effect literature by looking at the relative trading volume in terms of value. The results for the Swedish market show a significant positive relationship between the accuracy of estimation and the relative trading volume. Market capitalisation and analyst coverage have in prior studies been used as proxies for neglect. These measures however, do not take into account the effort analysts put in when estimating corporate pre-tax profits. I also find evidence that the industry of the firm influence the accuracy of estimation. In addition, supporting earlier findings, loss making firms are associated with larger forecasting errors. Further, I find that the average forecast error increased in the year 2000 – in Sweden.

Relative Contribution of Cell Proliferation and Microvascularity to Metastasis in Malignant Uveal Melanoma

Uveal melanoma (UM) is the second most common primary intraocular cancer worldwide. It is a relatively rare cancer, but still the second most common type of primary malignant melanoma in humans. UM is a slowly growing tumor, and gives rise to distant metastasis mainly to the liver via the bloodstream. About 40% of patients with UM die of metastatic disease within 10 years of diagnosis, irrespective of the type of treatment. During the last decade, two main lines of research have aimed to achieve enhanced understanding of the metastasis process and accurate prognosis of patients with UM. One emphasizes the characteristics of tumor cells, particularly their nucleoli, and markers of proliferation, and the other the characteristics of tumor blood vessels. Of several morphometric measurements, the mean diameter of the ten largest nucleoli (MLN) has become the most widely applied. A large MLN has consistently been associated with high likelihood of dying from UM. Blood vessels are of paramount importance in metastasis of UM. Different extravascular matrix patterns can be seen in UM, like loops and networks. This presence is associated with death from metastatic melanoma. However, the density of microvessels is also of prognostic importance. This study was undertaken to help understanding some histopathological factors which might contribute to developing metastasis in UM patients. Factors which could be related to tumor progression to metastasis disease, namely nucleolar size, MLN, microvascular density (MVD), cell proliferation, and The Insulin-like Growth Factor 1 Receptor(IGF-1R), were investigated. The primary aim of this thesis was to study the relationship between prognostic factors such as tumor cell nucleolar size, proliferation, extravascular matrix patterns, and dissemination of UM, and to assess to what extent there is a relationship to metastasis. The secondary goal was to develop a multivariate model which includes MLN and cell proliferation in addition to MVD, and which would fit better with population-based, melanoma-related survival data than previous models. I studied 167 patients with UM, who developed metastasis even after a very long time following removal of the eye, metastatic disease was the main cause of death, as documented in the Finnish Cancer Registry and on death certificates. Using an independent population-based data set, it was confirmed that MLN and extravascular matrix loops and networks were unrelated, independent predictors of survival in UM. Also, it has been found that multivariate models including MVD in addition to MLN fitted significantly better with survival data than models which excluded MVD. This supports the idea that both the characteristics of the blood vessels and the cells are important, and the future direction would be to look for the gene expression profile, whether it is associated more with MVD or MLN. The former relates to the host response to the tumor and may not be as tightly associated with the gene expression profile, yet most likely involved in the process of hematogenous metastasis. Because fresh tumor material is needed for reliable genetic analysis, such analysis could not be performed Although noninvasive detection of certain extravascular matrix patterns is now technically possible,in managing patients with UM, this study and tumor genetics suggest that such noninvasive methods will not fully capture the process of clinical metastasis. Progress in resection and biopsy techniques is likely in the near future to result in fresh material for the ophthalmic pathologist to correlate angiographic data, histopathological characteristics such as MLN, and genetic data. This study supported the theory that tumors containing epithelioid cells grow faster and have poorer prognosis when studied by cell proliferation in UM based on Ki-67 immunoreactivity. Cell proliferation index fitted best with the survival data when combined with MVD, MLN, and presence of epithelioid cells. Analogous with the finding that high MVD in primary UM is associated with shorter time to metastasis than low MVD, high MVD in hepatic metastasis tends to be associated with shorter survival after diagnosis of metastasis. Because the liver is the main organ for metastasis from UM, growth factors largely produced in the liver hepatocyte growth factor, epidermal growth factor and insulin-like growth factor-1 (IGF-1) together with their receptors may have a role in the homing and survival of metastatic cells. Therefore the association between immunoreactivity for IGF-1R in primary UM and metastatic death was studied. It was found that immunoreactivity for IGF-IR did not independently predict metastasis from primary UM in my series.

Computational Methods for Studies of Quantum Dots and Boson Condensates

This thesis presents ab initio studies of two kinds of physical systems, quantum dots and bosons, using two program packages of which the bosonic one has mainly been developed by the author. The implemented models, \emph{i.e.}, configuration interaction (CI) and coupled cluster (CC) take the correlated motion of the particles into account, and provide a hierarchy of computational schemes, on top of which the exact solution, within the limit of the single-particle basis set, is obtained. The theory underlying the models is presented in some detail, in order to provide insight into the approximations made and the circumstances under which they hold. Some of the computational methods are also highlighted. In the final sections the results are summarized. The CI and CC calculations on multiexciton complexes in self-assembled semiconductor quantum dots are presented and compared, along with radiative and non-radiative transition rates. Full CI calculations on quantum rings and double quantum rings are also presented. In the latter case, experimental and theoretical results from the literature are re-examined and an alternative explanation for the reported photoluminescence spectra is found. The boson program is first applied on a fictitious model system consisting of bosonic electrons in a central Coulomb field for which CI at the singles and doubles level is found to account for almost all of the correlation energy. Finally, the boson program is employed to study Bose-Einstein condensates confined in different anisotropic trap potentials. The effects of the anisotropy on the relative correlation energy is examined, as well as the effect of varying the interaction potential.}