Diffusion Tensor Imaging as a Diagnostic and Research Tool: A Study on Preterm Infants

Diffusion tensor imaging (DTI) is an advanced magnetic resonance imaging (MRI) technique. DTI is based on free thermal motion (diffusion) of water molecules. The properties of diffusion can be represented using parameters such as fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity, which are calculated from DTI data. These parameters can be used to study the microstructure in fibrous structure such as brain white matter. The aim of this study was to investigate the reproducibility of region-of-interest (ROI) analysis and determine associations between white matter integrity and antenatal and early postnatal growth at term age using DTI. Antenatal growth was studied using both the ROI and tract-based spatial statistics (TBSS) method and postnatal growth using only the TBSS method. The infants included to this study were born below 32 gestational weeks or birth weight less than 1,501 g and imaged with a 1.5 T MRI system at term age. Total number of 132 infants met the inclusion criteria between June 2004 and December 2006. Due to exclusion criteria, a total of 76 preterm infants (ROI) and 36 preterm infants (TBSS) were accepted to this study. The ROI analysis was quite reproducible at term age. Reproducibility varied between white matter structures and diffusion parameters. Normal antenatal growth was positively associated with white matter maturation at term age. The ROI analysis showed associations only in the corpus callosum. Whereas, TBSS revealed associations in several brain white matter areas. Infants with normal antenatal growth showed more mature white matter compared to small for gestational age infants. The gestational age at birth had no significant association with white matter maturation at term age. It was observed that good early postnatal growth associated negatively with white matter maturation at term age. Growth-restricted infants seemed to have delayed brain maturation that was not fully compensated at term, despite catchup growth.

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.

Initialization of Continuous Nonlinear Models Using Extended Kalman Filter

The two main objectives of Bayesian inference are to estimate parameters and states. In this thesis, we are interested in how this can be done in the framework of state-space models when there is a complete or partial lack of knowledge of the initial state of a continuous nonlinear dynamical system. In literature, similar problems have been referred to as diffuse initialization problems. This is achieved first by extending the previously developed diffuse initialization Kalman filtering techniques for discrete systems to continuous systems. The second objective is to estimate parameters using MCMC methods with a likelihood function obtained from the diffuse filtering. These methods are tried on the data collected from the 1995 Ebola outbreak in Kikwit, DRC in order to estimate the parameters of the system.

The northern provinces of Sweden and Norway with part I, of Russia / published under the superintendence of the Society for the Diffusion of Useful Knowledge.

[N. 1:4400000].

Bayesian analysis of SEIR epidemic models

This thesis concerns the analysis of epidemic models. We adopt the Bayesian paradigm and develop suitable Markov Chain Monte Carlo (MCMC) algorithms. This is done by considering an Ebola outbreak in the Democratic Republic of Congo, former Zaïre, 1995 as a case of SEIR epidemic models. We model the Ebola epidemic deterministically using ODEs and stochastically through SDEs to take into account a possible bias in each compartment. Since the model has unknown parameters, we use different methods to estimate them such as least squares, maximum likelihood and MCMC. The motivation behind choosing MCMC over other existing methods in this thesis is that it has the ability to tackle complicated nonlinear problems with large number of parameters. First, in a deterministic Ebola model, we compute the likelihood function by sum of square of residuals method and estimate parameters using the LSQ and MCMC methods. We sample parameters and then use them to calculate the basic reproduction number and to study the disease-free equilibrium. From the sampled chain from the posterior, we test the convergence diagnostic and confirm the viability of the model. The results show that the Ebola model fits the observed onset data with high precision, and all the unknown model parameters are well identified. Second, we convert the ODE model into a SDE Ebola model. We compute the likelihood function using extended Kalman filter (EKF) and estimate parameters again. The motivation of using the SDE formulation here is to consider the impact of modelling errors. Moreover, the EKF approach allows us to formulate a filtered likelihood for the parameters of such a stochastic model. We use the MCMC procedure to attain the posterior distributions of the parameters of the SDE Ebola model drift and diffusion parts. In this thesis, we analyse two cases: (1) the model error covariance matrix of the dynamic noise is close to zero , i.e. only small stochasticity added into the model. The results are then similar to the ones got from deterministic Ebola model, even if methods of computing the likelihood function are different (2) the model error covariance matrix is different from zero, i.e. a considerable stochasticity is introduced into the Ebola model. This accounts for the situation where we would know that the model is not exact. As a results, we obtain parameter posteriors with larger variances. Consequently, the model predictions then show larger uncertainties, in accordance with the assumption of an incomplete model.

Prospects of Bitcoin diffusion

Currency is something people deal with every day in their lives. The contemporary society is very much revolving around currencies. Even though technological development has been rapid, the principle of currency has stayed relatively unchanged for a long time. Bitcoin is a digital currency that introduced an alternative to other digital currencies, and to the traditional physical currencies. Bitcoin is peer-to-peer, open source, and it erases the need of a third party in transactions. Bitcoin has since inception gained certain fame, but it has not established itself as a common currency in the world. The purpose of this study was to analyse what kind of potential does Bitcoin have to become a widely accepted currency in day-to-day transactions. The main research question was divided into three sub questions: • What kind of a process is the diffusion of new innovations? • What kinds of factors speak for the wider adoption of Bitcoin? • What kinds of factors speak against the wider adoption of Bitcoin? The purpose of the study was approached by having diffusion of innovations as the theoretical framework. The four elements in diffusion of innovations are, innovation, communication, time, and social system. The theoretical framework is applied to Bitcoin, and the research questions answered by analysing Bitcoin’s potential diffusion prospects. The body of research data consisted of media texts and statistics. In this study, content analysis was the research method. The main findings of the study are that Bitcoin has clear strengths, but it faces a large amount of uncertainty. Bitcoin’s strong areas are the transactions. They are fast, easy, and cheap. From the innovation diffusion perspective Bitcoin is still relatively unknown, and the general public’s attitudes towards it are sceptical. The research findings purport that Bitcoin has potential demand especially when the financial system of a region is dysfunctional, or when there is a financial crisis. Bitcoin is not very trusted, and the majority of people do not see a reason to start using Bitcoin in the future. A large number of people associate it with illegal activities. In general people are largely unaware of what Bitcoin is or what are the strengths and weaknesses. Bitcoin is an innovative alternative currency. However, unless people see a major need for Bitcoin due to a financial crisis, or dysfunctionality in the financial system, Bitcoin will not become much more widespread as it is today. Bitcoin’s underlying technology can be harnessed to multiple uses. Developments in that field in the future are something that future researchers could look into.

Two-dimensional drift-diffusion simulation of organic solar cells

The aim of this master's thesis is to develop a two-dimensional drift-di usion model, which describes charge transport in organic solar cells. The main bene t of a two-dimensional model compared to a one-dimensional one is the inclusion of the nanoscale morphology of the active layer of a bulk heterojunction solar cell. The developed model was used to study recombination dynamics at the donor-acceptor interface. In some cases, it was possible to determine e ective parameters, which reproduce the results of the two-dimensional model in the one-dimensional case. A summary of the theory of charge transport in semiconductors was presented and discussed in the context of organic materials. Additionally, the normalization and discretization procedures required to nd a numerical solution to the charge transport problem were outlined. The charge transport problem was solved by implementing an iterative scheme called successive over-relaxation. The obtained solution is given as position-dependent electric potential, free charge carrier concentrations and current densities in the active layer. An interfacial layer, separating the pure phases, was introduced in order to describe charge dynamics occurring at the interface between the donor and acceptor. For simplicity, an e ective generation of free charge carriers in the interfacial layer was implemented. The pure phases simply act as transport layers for the photogenerated charges. Langevin recombination was assumed in the two-dimensional model and an analysis of the apparent recombination rate in the one-dimensional case is presented. The recombination rate in a two-dimensional model is seen to e ectively look like reduced Langevin recombination at open circuit. Replicating the J-U curves obtained in the two-dimensional model is, however, not possible by introducing a constant reduction factor in the Langevin recombination rate. The impact of an acceptor domain in the pure donor phase was investigated. Two cases were considered, one where the acceptor domain is isolated and another where it is connected to the bulk of the acceptor. A comparison to the case where no isolated domains exist was done in order to quantify the observed reduction in the photocurrent. The results show that all charges generated at the isolated domain are lost to recombination, but the domain does not have a major impact on charge transport. Trap-assisted recombination at interfacial trap states was investigated, as well as the surface dipole caused by the trapped charges. A theoretical expression for the ideality factor n_id as a function of generation was derived and shown to agree with simulation data. When the theoretical expression was fitted to simulation data, no interface dipole was observed.