Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Eye Fundus Image Analysis for Automatic Detection of Diabetic Retinopathy

Diabetes is a rapidly increasing worldwide problem which is characterised by defective metabolism of glucose that causes long-term dysfunction and failure of various organs. The most common complication of diabetes is diabetic retinopathy (DR), which is one of the primary causes of blindness and visual impairment in adults. The rapid increase of diabetes pushes the limits of the current DR screening capabilities for which the digital imaging of the eye fundus (retinal imaging), and automatic or semi-automatic image analysis algorithms provide a potential solution. In this work, the use of colour in the detection of diabetic retinopathy is statistically studied using a supervised algorithm based on one-class classification and Gaussian mixture model estimation. The presented algorithm distinguishes a certain diabetic lesion type from all other possible objects in eye fundus images by only estimating the probability density function of that certain lesion type. For the training and ground truth estimation, the algorithm combines manual annotations of several experts for which the best practices were experimentally selected. By assessing the algorithm’s performance while conducting experiments with the colour space selection, both illuminance and colour correction, and background class information, the use of colour in the detection of diabetic retinopathy was quantitatively evaluated. Another contribution of this work is the benchmarking framework for eye fundus image analysis algorithms needed for the development of the automatic DR detection algorithms. The benchmarking framework provides guidelines on how to construct a benchmarking database that comprises true patient images, ground truth, and an evaluation protocol. The evaluation is based on the standard receiver operating characteristics analysis and it follows the medical practice in the decision making providing protocols for image- and pixel-based evaluations. During the work, two public medical image databases with ground truth were published: DIARETDB0 and DIARETDB1. The framework, DR databases and the final algorithm, are made public in the web to set the baseline results for automatic detection of diabetic retinopathy. Although deviating from the general context of the thesis, a simple and effective optic disc localisation method is presented. The optic disc localisation is discussed, since normal eye fundus structures are fundamental in the characterisation of DR.

Non-Markovian dynamics and quantum information probes

This Thesis discusses the phenomenology of the dynamics of open quantum systems marked by non-Markovian memory effects. Non-Markovian open quantum systems are the focal point of a flurry of recent research aiming to answer, e.g., the following questions: What is the characteristic trait of non-Markovian dynamical processes that discriminates it from forgetful Markovian dynamics? What is the microscopic origin of memory in quantum dynamics, and how can it be controlled? Does the existence of memory effects open new avenues and enable accomplishments that cannot be achieved with Markovian processes? These questions are addressed in the publications forming the core of this Thesis with case studies of both prototypical and more exotic models of open quantum systems. In the first part of the Thesis several ways of characterizing and quantifying non-Markovian phenomena are introduced. Their differences are then explored using a driven, dissipative qubit model. The second part of the Thesis focuses on the dynamics of a purely dephasing qubit model, which is used to unveil the origin of non-Markovianity for a wide class of dynamical models. The emergence of memory is shown to be strongly intertwined with the structure of the spectral density function, as further demonstrated in a physical realization of the dephasing model using ultracold quantum gases. Finally, as an application of memory effects, it is shown that non- Markovian dynamical processes facilitate a novel phenomenon of timeinvariant discord, where the total quantum correlations of a system are frozen to their initial value. Non-Markovianity can also be exploited in the detection of phase transitions using quantum information probes, as shown using the physically interesting models of the Ising chain in a transverse field and a Coulomb chain undergoing a structural phase transition.

Aircraft tracking and classification with vhf passive bistatic radar

Since the times preceding the Second World War the subject of aircraft tracking has been a core interest to both military and non-military aviation. During subsequent years both technology and configuration of the radars allowed the users to deploy it in numerous fields, such as over-the-horizon radar, ballistic missile early warning systems or forward scatter fences. The latter one was arranged in a bistatic configuration. The bistatic radar has continuously re-emerged over the last eighty years for its intriguing capabilities and challenging configuration and formulation. The bistatic radar arrangement is used as the basis of all the analyzes presented in this work. The aircraft tracking method of VHF Doppler-only information, developed in the first part of this study, is solely based on Doppler frequency readings in relation to time instances of their appearance. The corresponding inverse problem is solved by utilising a multistatic radar scenario with two receivers and one transmitter and using their frequency readings as a base for aircraft trajectory estimation. The quality of the resulting trajectory is then compared with ground-truth information based on ADS-B data. The second part of the study deals with the developement of a method for instantaneous Doppler curve extraction from within a VHF time-frequency representation of the transmitted signal, with a three receivers and one transmitter configuration, based on a priori knowledge of the probability density function of the first order derivative of the Doppler shift, and on a system of blocks for identifying, classifying and predicting the Doppler signal. The extraction capabilities of this set-up are tested with a recorded TV signal and simulated synthetic spectrograms. Further analyzes are devoted to more comprehensive testing of the capabilities of the extraction method. Besides testing the method, the classification of aircraft is performed on the extracted Bistatic Radar Cross Section profiles and the correlation between them for different types of aircraft. In order to properly estimate the profiles, the ADS-B aircraft location information is adjusted based on extracted Doppler frequency and then used for Bistatic Radar Cross Section estimation. The classification is based on seven types of aircraft grouped by their size into three classes.

Vascular Function in Chronic Kidney Disease and in Renovascular Disease

Cardiovascular mortality is 15 to 30 times higher in patients with chronic kidney disease than in the age-adjusted general population. Even minor renal dysfunction predicts cardiovascular events and death in the general population. In patients with atherosclerotic renovascular disease the annual cardiovascular event and death rate is even higher. The abnormalities in coronary and peripheral artery function in the different stages of chronic kidney disease and in renovascular disease are still poorly understood, nor have the cardiac effects of renal artery revascularization been well characterized, although considered to be beneficial. This study was conducted to characterize myocardial perfusion and peripheral endothelial function in patients with chronic kidney disease and in patients with atherosclerotic renovascular disease. Myocardial perfusion was measured with positron emission tomography (PET) and peripheral endothelial function with brachial artery flow-mediated dilatation. It has been suggested that the poor renal outcomes after the renal artery revascularization could be due to damage in the stenotic kidney parenchyma; especially the reduction in the microvascular density, changes mainly evident at the cortical level which controls almost 80% of the total renal blood flow. This study was also performed to measure the effect of renal artery stenosis revascularization on renal perfusion in patients with renovascular disease. In order to do that a PET-based method for quantification of renal perfusion was developed. The coronary flow reserve of patients with chronic kidney disease was similar to the coronary flow reserve of healthy controls. In renovascular disease the coronary flow reserve was, however, markedly reduced. Flow-mediated dilatation of brachial artery was decreased in patients with chronic kidney disease compared to healthy controls, and even more so in patients with renovascular disease. After renal artery stenosis revascularization, coronary vascular function and renal perfusion did not improve in patients with atherosclerotic renovascular disease, but in patients with bilateral renal artery stenosis, flow-mediated dilatation improved. Chronic kidney disease does not significantly affect coronary vascular function. On the contrary, coronary vascular function was severely deteriorated in patients with atherosclerotic renovascular disease, possibly because of diffuse coronary artery disease and/or diffuse microvascular disease. The peripheral endothelial function was disturbed in patients with chronic kidney disease and even more so in patient with atherosclerotic renovascular disease. Renal artery stenosis dilatation does not seem to offer any benefits over medical treatment in patients with renovascular disease, since revascularization does not improve coronary vascular function or renal perfusion.

Evaluation of the Efficiency of Line-Start Permanent-Magnet Machines as a Function of the Operating Temperature

The standard squirrel-cage induction machine has nearly reached its maximum efficiency. In order to further increase the energy efficiency of electrical machines, the use of permanent magnets in combination with the robust design and the line start capability of the induction machine is extensively investigated. Many experimental designs have been suggested in literature, but recently, these line-start permanent-magnet machines (LSPMMs) have become off-the-shelf products available in a power range up to 7.5 kW. The permanent magnet flux density is a function of the operating temperature. Consequently, the temperature will affect almost every electrical quantity of the machine, including current, torque, and efficiency. In this paper, the efficiency of an off-the-shelf 4-kW three-phase LSPMM is evaluated as a function of the temperature by both finite-element modeling and by practical measurements. In order to obtain stator, rotor, and permanent magnet temperatures, lumped thermal modeling is used.

Thyroid function in the elderly and sex hormones in elderly men: reference intervals and associations with health

Aims: The aims were to create clinically feasible reference intervals for thyroidstimulating hormone (TSH) and free thyroxine (FT4) and to analyze associations between thyroid function and self-rated health, neuropsychiatric symptoms, depression and dementia in the elderly. The second aim was also to establish reference intervals for sex hormones and to analyze associations between sex hormone levels and self-rated health, symptoms, depression and dementia in elderly men. Subjects and methods: The study population comprised 1252 subjects aged 65 years or over, living in the municipality of Lieto, south-western Finland. Self-rated health, life satisfaction, symptoms, depression, and dementia were assessed with specific questions, clinical examination and tools such as the Zung Self-report Depression Scale and the Mini-Mental State Examination. Independent variables were dichotomized, and associations of these variables with TSH, FT4 or sex hormone levels were assessed. Levels of TSH and FT4 in thyroid disease–free women and women treated with thyroxine were also compared. Results: Elevated concentrations of thyroid peroxidase antibodies (TPOAb) or thyroglobulin antibodies (TgAb) were found to have a marked effect on the upper reference limit for TSH among women, who were thyroid antibody positive more higher than suggested in several recent guidelines. After age adjustment, there were no associations between TSH levels and self-rated health, life satisfaction, or most neuropsychiatric symptoms in the thyroid disease-free population. Although women with thyroxine treatment for primary hypothyroidism had far higher TSH levels than thyroid disease-free women, there were no differences between thyroid-disease free women and women with stable thyroxine treatment regarding self-rated health, life satisfaction or symptoms. Age had a significant positive association with luteinizing hormone (LH), follicle 2 practice, one range in men aged 65 years or over can be used for T, E2 and FSH measured with the AutoDelfia method, but two separate reference intervals should be used for fT, LH and SHBG. After adjustment for age, higher levels of T and fT were associated with better self-rated health (SRH) in the reference population. After adjustment for age and body mass index (BMI), there were no associations between sex hormone concentrations and self-rated health, life satisfaction or most symptoms in concentration. Conclusion: Age-specific reference intervals were derived for thyroid function and sex hormones based on comprehensive data from a community-dwelling population with a high participation rate. The results do not support the need to decrease the upper reference limit for TSH or to lower the optimal TSH target in levothyroxine treatment in older adults, as recommended in recent guidelines. Older age or being overweight symptoms among elderly men. The associations of single symptoms with T levels were inconsistent among elderly men, although the association of low T level with diagnosed depression might be clinically significant.

The Regulation of Skeletal and Cardiac Muscle Blood Flow in Humans. Studies by positron emission tomography with special reference to exercise, adenosine and nitric oxide

Virtually every cell and organ in the human body is dependent on a proper oxygen supply. This is taken care of by the cardiovascular system that supplies tissues with oxygen precisely according to their metabolic needs. Physical exercise is one of the most demanding challenges the human circulatory system can face. During exercise skeletal muscle blood flow can easily increase some 20-fold and its proper distribution to and within muscles is of importance for optimal oxygen delivery. The local regulation of skeletal muscle blood flow during exercise remains little understood, but adenosine and nitric oxide may take part in this process. In addition to acute exercise, long-term vigorous physical conditioning also induces changes in the cardiovasculature, which leads to improved maximal physical performance. The changes are largely central, such as structural and functional changes in the heart. The function and reserve of the heart’s own vasculature can be studied by adenosine infusion, which according to animal studies evokes vasodilation via it’s a_2A receptors. This has, however, never been addressed in humans in vivo and also studies in endurance athletes have shown inconsistent results regarding the effects of sport training on myocardial blood flow. This study was performed on healthy young adults and endurance athletes and local skeletal and cardiac muscle blod flow was measured by positron emission tomography. In the heart, myocardial blood flow reserve and adenosine A_2A receptor density, and in skeletal muscle, oxygen extraction and consumption was also measured. The role of adenosine in the control of skeletal muscle blood flow during exercise, and its vasodilator effects, were addressed by infusing competitive inhibitors and adenosine into the femoral artery. The formation of skeletal muscle nitric oxide was also inhibited by a drug, with and without prostanoid blockade. As a result and conclusion, it can be said that skeletal muscle blood flow heterogeneity decreases with increasing exercise intensity most likely due to increased vascular unit recruitment, but exercise hyperemia is a very complex phenomenon that cannot be mimicked by pharmacological infusions, and no single regulator factor (e.g. adenosine or nitric oxide) accounts for a significant part of exercise-induced muscle hyperemia. However, in the present study it was observed for the first time in humans that nitric oxide is not only important regulator of the basal level of muscle blood flow, but also oxygen consumption, and together with prostanoids affects muscle blood flow and oxygen consumption during exercise. Finally, even vigorous endurance training does not seem to lead to supranormal myocardial blood flow reserve, and also other receptors than A_2A mediate the vasodilator effects of adenosine. In respect to cardiac work, atheletes heart seems to be luxuriously perfused at rest, which may result from reduced oxygen extraction or impaired efficiency due to pronouncedly enhanced myocardial mass developed to excel in strenuous exercise.

Privileged Words and Sturmian Words

This dissertation has two almost unrelated themes: privileged words and Sturmian words. Privileged words are a new class of words introduced recently. A word is privileged if it is a complete first return to a shorter privileged word, the shortest privileged words being letters and the empty word. Here we give and prove almost all results on privileged words known to date. On the other hand, the study of Sturmian words is a well-established topic in combinatorics on words. In this dissertation, we focus on questions concerning repetitions in Sturmian words, reproving old results and giving new ones, and on establishing completely new research directions. The study of privileged words presented in this dissertation aims to derive their basic properties and to answer basic questions regarding them. We explore a connection between privileged words and palindromes and seek out answers to questions on context-freeness, computability, and enumeration. It turns out that the language of privileged words is not context-free, but privileged words are recognizable by a linear-time algorithm. A lower bound on the number of binary privileged words of given length is proven. The main interest, however, lies in the privileged complexity functions of the Thue-Morse word and Sturmian words. We derive recurrences for computing the privileged complexity function of the Thue-Morse word, and we prove that Sturmian words are characterized by their privileged complexity function. As a slightly separate topic, we give an overview of a certain method of automated theorem-proving and show how it can be applied to study privileged factors of automatic words. The second part of this dissertation is devoted to Sturmian words. We extensively exploit the interpretation of Sturmian words as irrational rotation words. The essential tools are continued fractions and elementary, but powerful, results of Diophantine approximation theory. With these tools at our disposal, we reprove old results on powers occurring in Sturmian words with emphasis on the fractional index of a Sturmian word. Further, we consider abelian powers and abelian repetitions and characterize the maximum exponents of abelian powers with given period occurring in a Sturmian word in terms of the continued fraction expansion of its slope. We define the notion of abelian critical exponent for Sturmian words and explore its connection to the Lagrange spectrum of irrational numbers. The results obtained are often specialized for the Fibonacci word; for instance, we show that the minimum abelian period of a factor of the Fibonacci word is a Fibonacci number. In addition, we propose a completely new research topic: the square root map. We prove that the square root map preserves the language of any Sturmian word. Moreover, we construct a family of non-Sturmian optimal squareful words whose language the square root map also preserves.This construction yields examples of aperiodic infinite words whose square roots are periodic.