Mathematical models on the impact of noise and dyadic molecular structures on the properties of a cardiac myocyte

In cardiac myocytes (heart muscle cells), coupling of electric signal known as the action potential to contraction of the heart depends crucially on calcium-induced calcium release (CICR) in a microdomain known as the dyad. During CICR, the peak number of free calcium ions (Ca) present in the dyad is small, typically estimated to be within range 1-100. Since the free Ca ions mediate CICR, noise in Ca signaling due to the small number of free calcium ions influences Excitation-Contraction (EC) coupling gain. Noise in Ca signaling is only one noise type influencing cardiac myocytes, e.g., ion channels playing a central role in action potential propagation are stochastic machines, each of which gates more or less randomly, which produces gating noise present in membrane currents. How various noise sources influence macroscopic properties of a myocyte, how noise is attenuated and taken advantage of are largely open questions. In this thesis, the impact of noise on CICR, EC coupling and, more generally, macroscopic properties of a cardiac myocyte is investigated at multiple levels of detail using mathematical models. Complementarily to the investigation of the impact of noise on CICR, computationally-efficient yet spatially-detailed models of CICR are developed. The results of this thesis show that (1) gating noise due to the high-activity mode of L-type calcium channels playing a major role in CICR may induce early after-depolarizations associated with polymorphic tachycardia, which is a frequent precursor to sudden cardiac death in heart failure patients; (2) an increased level of voltage noise typically increases action potential duration and it skews distribution of action potential durations toward long durations in cardiac myocytes; and that (3) while a small number of Ca ions mediate CICR, Excitation-Contraction coupling is robust against this noise source, partly due to the shape of ryanodine receptor protein structures present in the cardiac dyad.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Gene flow from transgenic plant populations: models and applications for risk assessment

The future use of genetically modified (GM) plants in food, feed and biomass production requires a careful consideration of possible risks related to the unintended spread of trangenes into new habitats. This may occur via introgression of the transgene to conventional genotypes, due to cross-pollination, and via the invasion of GM plants to new habitats. Assessment of possible environmental impacts of GM plants requires estimation of the level of gene flow from a GM population. Furthermore, management measures for reducing gene flow from GM populations are needed in order to prevent possible unwanted effects of transgenes on ecosystems. This work develops modeling tools for estimating gene flow from GM plant populations in boreal environments and for investigating the mechanisms of the gene flow process. To describe spatial dimensions of the gene flow, dispersal models are developed for the local and regional scale spread of pollen grains and seeds, with special emphasis on wind dispersal. This study provides tools for describing cross-pollination between GM and conventional populations and for estimating the levels of transgenic contamination of the conventional crops. For perennial populations, a modeling framework describing the dynamics of plants and genotypes is developed, in order to estimate the gene flow process over a sequence of years. The dispersal of airborne pollen and seeds cannot be easily controlled, and small amounts of these particles are likely to disperse over long distances. Wind dispersal processes are highly stochastic due to variation in atmospheric conditions, so that there may be considerable variation between individual dispersal patterns. This, in turn, is reflected to the large amount of variation in annual levels of cross-pollination between GM and conventional populations. Even though land-use practices have effects on the average levels of cross-pollination between GM and conventional fields, the level of transgenic contamination of a conventional crop remains highly stochastic. The demographic effects of a transgene have impacts on the establishment of trangenic plants amongst conventional genotypes of the same species. If the transgene gives a plant a considerable fitness advantage in comparison to conventional genotypes, the spread of transgenes to conventional population can be strongly increased. In such cases, dominance of the transgene considerably increases gene flow from GM to conventional populations, due to the enhanced fitness of heterozygous hybrids. The fitness of GM plants in conventional populations can be reduced by linking the selectively favoured primary transgene to a disfavoured mitigation transgene. Recombination between these transgenes is a major risk related to this technique, especially because it tends to take place amongst the conventional genotypes and thus promotes the establishment of invasive transgenic plants in conventional populations.

Cancer incidence, mortality, and pregnancy outcome among women treated for cervical intraepithelial neoplasia

Cervical cancer develops through precursor lesions, i.e. cervical intraepithelialneoplasms (CIN). These can be detected and treated before progression to invasive cancer. The major risk factor for developing cervical cancer or CIN is persistent or recurrent infection with high-risk human papilloma virus (hrHPV). Other associated risk factors include low socioeconomic status, smoking, sexually transmitted infections, and high number of sexual partners, and these risk factors can predispose to some other cancers, excess mortality, and reproductive health complications as well. The aim was to study long-term cancer incidence, mortality, and reproductive health outcomes among women treated for CIN. Based on the results, we could evaluate the efficacy and safety of CIN treatment practices and estimate the role of the risk factors of CIN patients for cancer incidence, mortality, and reproductive health. We collected a cohort of 7 599 women treated for CIN at Helsinki University Central Hospital from 1974 to 2001. Information about their cancer incidence, cause of death, birth of children and other reproductive endpoints, and socio-economic status were gathered through registerlinkages to the Finnish Cancer Registry, Finnish Population Registry, and Statistics Finland. Depending on the endpoints in question, the women treated were compared to the general population, to themselves, or to an age- and municipality-matched reference cohort. Cervical cancer incidence was increased after treatment of CIN for at least 20 years, regardless of the grade of histology at treatment. Compared to all of the colposcopically guided methods, cold knife conization (CKC) was the least effective method of treatment in terms of later CIN 3 or cervical cancer incidence. In addition to cervical cancer, incidence of other HPV-related anogenital cancers was increased among those treated, as was the incidence of lung cancer and other smoking-related cancers. Mortality from cervical cancer among the women treated was not statistically significantly elevated, and after adjustment for socio-economic status, the hazard ratio (HR) was 1.0. In fact, the excess mortality among those treated was mainly due to increased mortality from other cancers, especially from lung cancer. In terms of post-treatment fertility, the CIN treatments seem to be safe: The women had more deliveries, and their incidence of pregnancy was similar before and after treatment. Incidence of extra-uterine pregnancies and induced abortions was elevated among the treated both before and after treatment. Thus this elevation did not occur because they were treated rather to a great extent was due to the other known risk factors these women had in excess, i.e. sexually transmitted infections. The purpose of any cancer preventive activity is to reduce cancer incidence and mortality. In Finland, cervical cancer is a rare disease and death from it even rarer, mostly due to the effective screening program. Despite this, the women treated are at increased risk for cancer; not just for cervical cancer. They must be followed up carefully and for a long period of time; general health education, especially cessation of smoking, is crucial in the management process, as well as interventions towards proper use of birth control such as condoms.

Generalised regression estimation for domain class frequencies

This study examines the properties of Generalised Regression (GREG) estimators for domain class frequencies and proportions. The family of GREG estimators forms the class of design-based model-assisted estimators. All GREG estimators utilise auxiliary information via modelling. The classic GREG estimator with a linear fixed effects assisting model (GREG-lin) is one example. But when estimating class frequencies, the study variable is binary or polytomous. Therefore logistic-type assisting models (e.g. logistic or probit model) should be preferred over the linear one. However, other GREG estimators than GREG-lin are rarely used, and knowledge about their properties is limited. This study examines the properties of L-GREG estimators, which are GREG estimators with fixed-effects logistic-type models. Three research questions are addressed. First, I study whether and when L-GREG estimators are more accurate than GREG-lin. Theoretical results and Monte Carlo experiments which cover both equal and unequal probability sampling designs and a wide variety of model formulations show that in standard situations, the difference between L-GREG and GREG-lin is small. But in the case of a strong assisting model, two interesting situations arise: if the domain sample size is reasonably large, L-GREG is more accurate than GREG-lin, and if the domain sample size is very small, estimation of assisting model parameters may be inaccurate, resulting in bias for L-GREG. Second, I study variance estimation for the L-GREG estimators. The standard variance estimator (S) for all GREG estimators resembles the Sen-Yates-Grundy variance estimator, but it is a double sum of prediction errors, not of the observed values of the study variable. Monte Carlo experiments show that S underestimates the variance of L-GREG especially if the domain sample size is minor, or if the assisting model is strong. Third, since the standard variance estimator S often fails for the L-GREG estimators, I propose a new augmented variance estimator (A). The difference between S and the new estimator A is that the latter takes into account the difference between the sample fit model and the census fit model. In Monte Carlo experiments, the new estimator A outperformed the standard estimator S in terms of bias, root mean square error and coverage rate. Thus the new estimator provides a good alternative to the standard estimator.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

Drug cultures in Estonia : contexts, meanings and patterns of illicit drug use.

In Estonia, illicit drug use hardly existed before the social changes of the 1990s when, as a result of economic and cultural transformations, the country became part of a world order centred in the West. On the one hand, this development is due to the spread of international youth culture, which many young people have perceived as being associated with drugs; on the other hand, it results from the marginalisation of a part of the population. The empirical part of the study is based mostly on in-depth interviews with different drug users conducted during between 1998 and 2002. Complementary material includes the results of participant observations, interviews with key experts, and the results of previous quantitative studies and statistics. The young people who started experimenting with illicit drugs from the 1990s and onwards perceived them as a part of an attractive lifestyle - a Western lifestyle, a point which is worth stressing in the case of Estonia. Although the reasons for initiation into drug use were similar for the majority of young people, their drug use habits and the impact of the drug use on their lives began to differ. I argue that the potential pleasure and harm which might accompany drug use is offset by the meanings attached to drugs and the sanctions and rituals regulating drug use. In the study both recreational and problem use have been analysed from different aspects in seven articles. I have investigated different types of drug users: new bohemians, cannabis users, in whose case partying and restrictive drug use is positively connected to their lives and goals within established society; stimulant-using party people for whom drugs are a means of having fun but who do not have the same restrictive norms regulating their drug use as the former and who may get into trouble under certain conditions; and heroin users for whom the drug rapidly progressed from a means of having fun to an obligation due to addiction. The research results point at the importance not only of the drug itself and the socio-economic situation of the user, but also of the cultural and social context within which the drug is used. The latter may on occasions be a crucial factor in whether or not initial drug use eventually leads to addiction.

Essays on the Modeling and Prediction of Volatility and Higher Moments of Stock Returns (summary section only)

One of the most fundamental and widely accepted ideas in finance is that investors are compensated through higher returns for taking on non-diversifiable risk. Hence the quantification, modeling and prediction of risk have been, and still are one of the most prolific research areas in financial economics. It was recognized early on that there are predictable patterns in the variance of speculative prices. Later research has shown that there may also be systematic variation in the skewness and kurtosis of financial returns. Lacking in the literature so far, is an out-of-sample forecast evaluation of the potential benefits of these new more complicated models with time-varying higher moments. Such an evaluation is the topic of this dissertation. Essay 1 investigates the forecast performance of the GARCH (1,1) model when estimated with 9 different error distributions on Standard and Poor’s 500 Index Future returns. By utilizing the theory of realized variance to construct an appropriate ex post measure of variance from intra-day data it is shown that allowing for a leptokurtic error distribution leads to significant improvements in variance forecasts compared to using the normal distribution. This result holds for daily, weekly as well as monthly forecast horizons. It is also found that allowing for skewness and time variation in the higher moments of the distribution does not further improve forecasts. In Essay 2, by using 20 years of daily Standard and Poor 500 index returns, it is found that density forecasts are much improved by allowing for constant excess kurtosis but not improved by allowing for skewness. By allowing the kurtosis and skewness to be time varying the density forecasts are not further improved but on the contrary made slightly worse. In Essay 3 a new model incorporating conditional variance, skewness and kurtosis based on the Normal Inverse Gaussian (NIG) distribution is proposed. The new model and two previously used NIG models are evaluated by their Value at Risk (VaR) forecasts on a long series of daily Standard and Poor’s 500 returns. The results show that only the new model produces satisfactory VaR forecasts for both 1% and 5% VaR Taken together the results of the thesis show that kurtosis appears not to exhibit predictable time variation, whereas there is found some predictability in the skewness. However, the dynamic properties of the skewness are not completely captured by any of the models.

Modeling and Forecasting Implied Volatility: Implications for Trading, Pricing, and Risk Management

Modeling and forecasting of implied volatility (IV) is important to both practitioners and academics, especially in trading, pricing, hedging, and risk management activities, all of which require an accurate volatility. However, it has become challenging since the 1987 stock market crash, as implied volatilities (IVs) recovered from stock index options present two patterns: volatility smirk(skew) and volatility term-structure, if the two are examined at the same time, presents a rich implied volatility surface (IVS). This implies that the assumptions behind the Black-Scholes (1973) model do not hold empirically, as asset prices are mostly influenced by many underlying risk factors. This thesis, consists of four essays, is modeling and forecasting implied volatility in the presence of options markets’ empirical regularities. The first essay is modeling the dynamics IVS, it extends the Dumas, Fleming and Whaley (DFW) (1998) framework; for instance, using moneyness in the implied forward price and OTM put-call options on the FTSE100 index, a nonlinear optimization is used to estimate different models and thereby produce rich, smooth IVSs. Here, the constant-volatility model fails to explain the variations in the rich IVS. Next, it is found that three factors can explain about 69-88% of the variance in the IVS. Of this, on average, 56% is explained by the level factor, 15% by the term-structure factor, and the additional 7% by the jump-fear factor. The second essay proposes a quantile regression model for modeling contemporaneous asymmetric return-volatility relationship, which is the generalization of Hibbert et al. (2008) model. The results show strong negative asymmetric return-volatility relationship at various quantiles of IV distributions, it is monotonically increasing when moving from the median quantile to the uppermost quantile (i.e., 95%); therefore, OLS underestimates this relationship at upper quantiles. Additionally, the asymmetric relationship is more pronounced with the smirk (skew) adjusted volatility index measure in comparison to the old volatility index measure. Nonetheless, the volatility indices are ranked in terms of asymmetric volatility as follows: VIX, VSTOXX, VDAX, and VXN. The third essay examines the information content of the new-VDAX volatility index to forecast daily Value-at-Risk (VaR) estimates and compares its VaR forecasts with the forecasts of the Filtered Historical Simulation and RiskMetrics. All daily VaR models are then backtested from 1992-2009 using unconditional, independence, conditional coverage, and quadratic-score tests. It is found that the VDAX subsumes almost all information required for the volatility of daily VaR forecasts for a portfolio of the DAX30 index; implied-VaR models outperform all other VaR models. The fourth essay models the risk factors driving the swaption IVs. It is found that three factors can explain 94-97% of the variation in each of the EUR, USD, and GBP swaption IVs. There are significant linkages across factors, and bi-directional causality is at work between the factors implied by EUR and USD swaption IVs. Furthermore, the factors implied by EUR and USD IVs respond to each others’ shocks; however, surprisingly, GBP does not affect them. Second, the string market model calibration results show it can efficiently reproduce (or forecast) the volatility surface for each of the swaptions markets.

Essays on Market Microstructure: Price Discovery and Informed Trading

Market microstructure is “the study of the trading mechanisms used for financial securities” (Hasbrouck (2007)). It seeks to understand the sources of value and reasons for trade, in a setting with different types of traders, and different private and public information sets. The actual mechanisms of trade are a continually changing object of study. These include continuous markets, auctions, limit order books, dealer markets, or combinations of these operating as a hybrid market. Microstructure also has to allow for the possibility of multiple prices. At any given time an investor may be faced with a multitude of different prices, depending on whether he or she is buying or selling, the quantity he or she wishes to trade, and the required speed for the trade. The price may also depend on the relationship that the trader has with potential counterparties. In this research, I touch upon all of the above issues. I do this by studying three specific areas, all of which have both practical and policy implications. First, I study the role of information in trading and pricing securities in markets with a heterogeneous population of traders, some of whom are informed and some not, and who trade for different private or public reasons. Second, I study the price discovery of stocks in a setting where they are simultaneously traded in more than one market. Third, I make a contribution to the ongoing discussion about market design, i.e. the question of which trading systems and ways of organizing trading are most efficient. A common characteristic throughout my thesis is the use of high frequency datasets, i.e. tick data. These datasets include all trades and quotes in a given security, rather than just the daily closing prices, as in traditional asset pricing literature. This thesis consists of four separate essays. In the first essay I study price discovery for European companies cross-listed in the United States. I also study explanatory variables for differences in price discovery. In my second essay I contribute to earlier research on two issues of broad interest in market microstructure: market transparency and informed trading. I examine the effects of a change to an anonymous market at the OMX Helsinki Stock Exchange. I broaden my focus slightly in the third essay, to include releases of macroeconomic data in the United States. I analyze the effect of these releases on European cross-listed stocks. The fourth and last essay examines the uses of standard methodologies of price discovery analysis in a novel way. Specifically, I study price discovery within one market, between local and foreign traders.