Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.

Aspects of Arminian Soteriology in Methodist-Lutheran Ecumenical Dialogues in 20th and 21st Century

The aim of this thesis is to analyse the key ecumenical dialogues between Methodists and Lutherans from the perspective of Arminian soteriology and Methodist theology in general. The primary research question is defined as: "To what extent do the dialogues under analysis relate to Arminian soteriology?" By seeking an answer to this question, new knowledge is sought on the current soteriological position of the Methodist-Lutheran dialogues, the contemporary Methodist theology and the commonalities between the Lutheran and Arminian understanding of soteriology. This way the soteriological picture of the Methodist-Lutheran discussions is clarified. The dialogues under analysis were selected on the basis of versatility. Firstly, the sole world organisation level dialogue was chosen: The Church – Community of Grace. Additionally, the document World Methodist Council and the Joint Declaration on the Doctrine of Justification is analysed as a supporting document. Secondly, a document concerning the discussions between two main-line churches in the United States of America was selected: Confessing Our Faith Together. Thirdly, two dialogues between non-main-line Methodist churches and main-line Lutheran national churches in Europe were chosen: Fellowship of Grace from Norway and Kristuksesta osalliset from Finland. The theoretical approach to the research conducted in this thesis is systematic analysis. The Remonstrant articles of Arminian soteriology are utilised as an analysis tool to examine the soteriological positions of the dialogues. New knowledge is sought by analysing the stances of the dialogues concerning the doctrines of partial depravity, conditional election, universal atonement, resistible grace and conditional perseverance of saints. This way information is also provided for approaching the Calvinist-Arminian controversy from new perspectives. The results of this thesis show that the current soteriological position of the Methodist-Lutheran dialogues is closer to Arminianism than Calvinism. The dialogues relate to Arminian soteriology especially concerning the doctrines of universal atonement, resistible grace and conditional perseverance of saints. The commonalities between the Lutheran and Arminian understanding of soteriology exist mainly in these three doctrines as they are uniformly favoured in the dialogues. The most discussed area of soteriology is human depravity, in which the largest diversity of stances occurs as well. On the other hand, divine election is the least discussed topic. The overall perspective, which the results of the analysis provide, indicates that the Lutherans could approach the Calvinist churches together with the Methodists with a wider theological perspective and understanding when the soteriological issues are considered as principal. Human depravity is discovered as the area of soteriology which requires most work in future ecumenical dialogues. However, the detected Lutheran hybrid notion on depravity (a Calvinist-Arminian mixture) appears to provide a useful new perspective for Calvinist-Arminian ecumenism and offers potentially fruitful considerations to future ecumenical dialogues.

Living Poetically in the Modern Age : The Situational Aspects of Kierkegaard's Thought

How did Søren Kierkegaard (1813 1855) situate the human subject into historical and social actuality? How did he take into consideration his own situatedness? As key for understanding these questions the research takes the ideal of living poetically that Kierkegaard outlined in his dissertation. In The Concept of Irony (1841) Kierkegaard took up this ideal of the Romantic ironists and made it into an ethical-religious ideal. For him the ideal of living poetically came to mean 1) becoming brought up by God, while 2) assuming ethical-religiously one s role and place in the historical actuality. Through an exegesis of Kierkegaard s texts from 1843 to 1851 it is shown how this ideal governed Kierkegaard s thought and action throughout his work. The analysis of Kierkegaard s ideal of living poetically not only a) shows how the Kierkegaardian subject is situated in its historical context. It also b) sheds light on Kierkegaard s social and political thought, c) helps to understand Kierkegaard s character as a religious thinker, and d) pits his ethical-religious orientation in life against its scientific and commonsense alternatives. The research evaluates the rationality of the way of life championed by Kierkegaard by comparing it with ways of life dominated by reflection and reasoning. It uses Kierkegaard s ideal of living poetically in trying to understand the tensions between religious and unreligious ways of life.

Methicillin-resistant Staphylococcus aureus in Finland: recent changes in the epidemiology, long-term facility aspects, and phenotypic and molecular detection of isolates

Staphylococcus aureus is one of the most important bacteria that cause disease in humans, and methicillin-resistant S. aureus (MRSA) has become the most commonly identified antibiotic-resistant pathogen in many parts of the world. MRSA rates have been stable for many years in the Nordic countries and the Netherlands with a low MRSA prevalence in Europe, but in the recent decades, MRSA rates have increased in those low-prevalence countries as well. MRSA has been established as a major hospital pathogen, but has also been found increasingly in long-term facilities (LTF) and in communities of persons with no connections to the health-care setting. In Finland, the annual number of MRSA isolates reported to the National Infectious Disease Register (NIDR) has constantly increased, especially outside the Helsinki metropolitan area. Molecular typing has revealed numerous outbreak strains of MRSA, some of which have previously been associated with community acquisition. In this work, data on MRSA cases notified to the NIDR and on MRSA strain types identified with pulsed-field gel electrophoresis (PFGE), multilocus sequence typing (MLST), and staphylococcal cassette chromosome mec (SCCmec) typing at the National Reference Laboratory (NRL) in Finland from 1997 to 2004 were analyzed. An increasing trend in MRSA incidence in Finland from 1997 to 2004 was shown. In addition, non-multi-drug resistant (NMDR) MRSA isolates, especially those resistant only to methicillin/oxacillin, showed an emerging trend. The predominant MRSA strains changed over time and place, but two internationally spread epidemic strains of MRSA, FIN-16 and FIN-21, were related to the increase detected most recently. Those strains were also one cause of the strikingly increasing invasive MRSA findings. The rise of MRSA strains with SCCmec types IV or V, possible community-acquired MRSA was also detected. With questionnaires, the diagnostic methods used for MRSA identification in Finnish microbiology laboratories and the number of MRSA screening specimens studied were reviewed. Surveys, which focused on the MRSA situation in long-term facilities in 2001 and on the background information of MRSA-positive persons in 2001-2003, were also carried out. The rates of MRSA and screening practices varied widely across geographic regions. Part of the NMDR MRSA strains could remain undetected in some laboratories because of insufficient diagnostic techniques used. The increasing proportion of elderly population carrying MRSA suggests that MRSA is an emerging problem in Finnish long-term facilities. Among the patients, 50% of the specimens were taken on a clinical basis, 43% on a screening basis after exposure to MRSA, 3% on a screening basis because of hospital contact abroad, and 4% for other reasons. In response to an outbreak of MRSA possessing a new genotype that occurred in a health care ward and in an associated nursing home of a small municipality in Northern Finland in autumn 2003, a point-prevalence survey was performed six months later. In the same study, the molecular epidemiology of MRSA and methicillin-sensitive S. aureus (MSSA) strains were also assessed, the results to the national strain collection compared, and the difficulties of MRSA screening with low-level oxacillin-resistant isolates encountered. The original MRSA outbreak in LTF, which consisted of isolates possessing a nationally new PFGE profile (FIN-22) and internationally rare MLST type (ST-27), was confined. Another previously unrecognized MRSA strain was found with additional screening, possibly indicating that current routine MRSA screening methods may be insufficiently sensitive for strains possessing low-level oxacillin resistance. Most of the MSSA strains found were genotypically related to the epidemic MRSA strains, but only a few of them had received the SCCmec element, and all those strains possessed the new SCCmec type V. In the second largest nursing home in Finland, the colonization of S. aureus and MRSA, and the role of screening sites along with broth enrichment culture on the sensitivity to detect S. aureus were studied. Combining the use of enrichment broth and perineal swabbing, in addition to nostrils and skin lesions swabbing, may be an alternative for throat swabs in the nursing home setting, especially when residents are uncooperative. Finally, in order to evaluate adequate phenotypic and genotypic methods needed for reliable laboratory diagnostics of MRSA, oxacillin disk diffusion and MIC tests to the cefoxitin disk diffusion method at both +35°C and +30°C, both with or without an addition of sodium chloride (NaCl) to the Müller Hinton test medium, and in-house PCR to two commercial molecular methods (the GenoType® MRSA test and the EVIGENETM MRSA Detection test) with different bacterial species in addition to S. aureus were compared. The cefoxitin disk diffusion method was superior to that of oxacillin disk diffusion and to the MIC tests in predicting mecA-mediated resistance in S. aureus when incubating at +35°C with or without the addition of NaCl to the test medium. Both the Geno Type® MRSA and EVIGENETM MRSA Detection tests are usable, accurate, cost-effective, and sufficiently fast methods for rapid MRSA confirmation from a pure culture.

Genetic aspects of outcome in kidney transplantation: cytokine and thrombosis associated candidate genes and gene expression biomarkers

Kidney transplantation (Tx) is the treatment of choice for end stage renal disease. Immunosuppressive medications are given to prevent an immunological rejection of the transplant. However, immunosuppressive drugs increase e.g. the risk of infection, cancer or nephrotoxicity. A major genetic contributors to immunological acceptance of the graft are human leukocyte antigen (HLA) genes. Also other non-HLA gene polymorphisms may predict the future risk of complications before Tx, possibly enabling individualised immunotherapy. Graft function after Tx is monitored using non-specific clinical symptoms and laboratory markers. The definitive diagnosis of graft rejection however relies on a biopsy of the graft. In the acute rejection (AR) diagnostics there is a need for an alternative to biopsy that would be an easily repeatable and simple method for regular use. Frequent surveillance of acute or subclinical rejection (SCR) may improve long-term function. In this thesis, associations between cytokine and thrombosis associated candidate genes and the outcome of kidney Tx were studied. Cytotoxic and co-stimulatory T lymphocyte molecule gene expression biomarkers for the diagnosis of the AR and the SCR were also investigated. We found that polymorphisms in the cytokine genes tumor necrosis factor and interleukin 10 (IL10) of the recipients were associated with AR. In addition, certain IL10 gene polymorphisms of the donors were associated with the incidence of cytomegalovirus infection and occurrence of later infection in a subpopulation of recipients. Further, polymorphisms in genes related to the risk of thrombosis and those of certain cytokines were not associated with the occurrence of thrombosis, infarction, AR or graft survival. In the study of biomarkers for AR, whole blood samples were prospectively collected from adult kidney Tx patients. With real-time quantitative PCR (RT-QPCR) gene expression quantities of CD154 and ICOS differentiated the patients with AR from those without, but not from the patients with other causes of graft dysfunction. Biomarkers for SCR were studied in paediatric kidney Tx patients. We used RT-QPCR to quantify the gene expression of immunological candidate genes in a low-density array format. In addition, we used RT-QPCR to validate the results of the microarray analysis. No gene marker differentiated patients with SCR from those without SCR. This research demonstrates the lack of robust markers among polymorphisms or biomarkers in investigated genes that could be included in routine analysis in a clinical laboratory. In genetic studies, kidney Tx can be regarded as a complex trait, i.e. several environmental and genetic factors may determine its outcome. A number of currently unknown genetic factors probably influence the results of Tx.

Clinical aspects of exhaled nitric oxide in adults : Associations with atopy, bronchial hyperresponsiveness, smoking and chronic obstruction

Measurement of fractional exhaled nitric oxide (FENO) has proven useful in assessment of patients with respiratory symptoms, especially in predicting steroid response. The objective of these studies was to clarify issues relevant for the clinical use of FENO. The influence of allergic sensitization per se on FENO in healthy asymptomatic subjects was studied, the association between airway inflammation and bronchial hyperresponsiveness (BHR) in steroid-naive subjects with symptoms suggesting asthma was examined, as well as the possible difference in this association between atopic and nonatopic subjects. Influence of smoking on FENO was compared between atopic and nonatopic steroid-naive asthmatics and healthy subjects. The short-term repeatability of FENO in COPD patients was examined in order to assess whether the degree of chronic obstruction influences the repeatability. For these purposes, we studied a random sample of 248 citizens of Helsinki, 227 army conscripts with current symptoms suggesting asthma, 19 COPD patients, and 39 healthy subjects. FENO measurement, spirometry and bronchodilatation test, structured interview. skin prick tests, and histamine and exercise challenges were performed. Among healthy subjects with no signs of airway diseases, median FENO was similar in skin prick test-positive and –negative subjects, and the upper normal limit of FENO was 30 ppb. In atopic and nonatopic subjects with symptoms suggesting asthma, FENO associated with severity of exercise- or histamine-induced BHR only in atopic patients. FENO in smokers with steroid-naive asthma was significantly higher than in healthy smokers and nonsmokers. Among atopic asthmatics, FENO was significantly lower in smokers than in nonsmokers, whereas no difference appeared among nonatopic asthmatics. The 24-h repeatability of FENO was equally good in COPD patients as in healthy subjects. These findings indicate that allergic sensitization per se does not influence FENO, supporting the view that elevated FENO indicates NO-producing airway inflammation, and that same reference range can be applied to both skin prick test-positive and -negative subjects. The significant correlation between FENO and degree of BHR only in atopic steroid-naive subjects with current asthmatic symptoms supports the view that pathogenesis of BHR in atopic asthma is strongly involved in NO-producing airway inflammation, whereas in development of BHR in nonatopic asthma other mechanisms may dominate. Attenuation of FENO only in atopic but not in nonatopic smokers with steroid-naive asthma may result from differences in mechanisms of FENO formation as well as in sensitivity of these mechanisms to smoking in atopic and nonatopic asthma. The results suggest, however, that in young adult smokers, FENO measurement may prove useful in assessment of airway inflammation. The short-term repeatability of FENO in COPD patients with moderate to very severe disease and in healthy subjects was equally good.

Obstetric and gynaecological aspects of HIV infection

The purpose of the present study was to examine the outcome of pregnancies among HIV-infected women in Helsinki, use of the levonorgestrel-releasing intrauterine system (LNG-IUS) among HIV-infected women and the prevalence and risk factors of cytological and histologically proven cervical lesions in this population. Between 1993 and 2003 a total of 45 HIV-infected women delivered 52 singleton infants. HIV infection was diagnosed during pregnancy in 40% of the mothers. Seventeen of the mothers received antiretroviral (ARV) medication prior to pregnancy and in 34 cases, the medication was started during pregnancy. A good virological response (i.e. HIV RNA load <1000/mL during the last trimester) to ARV medication was achieved in 36/40 (90%) of the patients in whom HI viral load measurements were performed. Of the infants, 92% were born at term, and their mean (±SD) birth weight was 3350±395 g. The Caesarean section rate was low, 25%. All newborns received ARV medication and none of the infants born to mothers with pre-delivery diagnosis of maternal HIV infection were infected. The safety and advantages of the LNG-IUS were studied prospectively (n=12) and retrospectively (n=6). The LNG-IUS was well tolerated and no cases of PID or pregnancy were noted. Menstrual bleeding was reduced significantly during use of the LNG-IUS; this was associated with a slight increase in haemoglobin levels. Serum oestradiol concentrations remained in the follicular range in all subjects. The key finding was that genital shedding of HIV RNA did not change after the insertion of the LNG-IUS. The mean annual prevalence of low-grade squamous intraepithelial lesions (SIL) was 15% and that of high-grade SIL was 5% among 108 systematically followed HIV-infected women during 1989 2003. A reduced CD4 lymphocyte count was associated with an increased prevalence of SIL, whereas duration of HIV infection, use of ARV medication and HI viral load were not. The cumulative risk of any type of SIL was 17% after one year and 48% after five years among patients with initially normal Pap smears. The risk of developing SIL was associated with young age and a high initial HI viral load. During the follow-up 51 subjects (n=153) displayed cervical intraepithelial neoplasia (CIN), (16% CIN1 and 18% CIN 2-3). Only one case of cancer of the uterine cervix was detected. Pap smears were reliable in screening for CIN. Both nulliparity (p<0.01) and bacterial vaginosis (p<0.04) emerged as significant risk factors of CIN. In conclusion, a combination of universal antenatal screening and multidisciplinary management allows individualized treatment and prevents vertical transmission of HIV. Use of the LNG-IUS is safe among HIV-infected women and cervicovaginal shedding of HIV RNA is not affected by use of the LNG-IUS. The risk of cervical pre-malignant lesions is high among HIV-infected women despite systematic follow-up.

Essential Thrombocythaemia : Diagnosis, Prognostic Aspects, and the Outcome of Finnish patients

Essential thrombocythaemia (ET) is a myeloproliferative disease (MPD) characterized by thrombocytosis, i.e. a constant elevation of platelet count. Thrombocytosis may appear in MPDs (ET, polycythaemia vera, chronic myeloid leukaemia, myelofibrosis) and as a reactive phenomenon. The differential diagnosis of thrombocytosis is important, because the clinical course, need of therapy, and prognosis are different in patients with MPDs and in those with reactive thrombocytosis. ET patients may remain asymptomatic for years, but serious thrombohaemorrhagic and pregnancy-related complications may occur. The complications are difficult to predict. The aims of the present study were to evaluate the diagnostic findings, clinical course, and prognostic factors of ET. The present retrospective study consists of 170 ET patients. Two thirds had a platelet count < 1000 x 109/l. The diagnosis was supported by an increased number of megakaryocytes with an abnormal morphology in a bone marrow aspirate, aggregation defects in platelet function studies, and the presence of spontaneous erythroid and/or megakaryocytic colony formation in in vitro cultures of haematopoietic progenitors. About 70 % of the patients had spontaneous colony formation, while about 30 % had a normal growth pattern. Only a fifth of the patients remained asymptomatic. Half had a major thrombohaemorrhagic complication. The proportion of the patients suffering from thrombosis was as high as 45 %. About a fifth had major bleedings. Half of the patients had microvascular symptoms. Age over 60 years increased the risk of major bleedings, but the occurrence of thrombotic complications was similar in all age groups. Male gender, smoking in female patients, the presence of any spontaneous colony formation, and the presence of spontaneous megakaryocytic colony formation in younger patients were identified as risk factors for thrombosis. Pregnant ET patients had an increased risk of complications. Forty-five per cent of the pregnancies were complicated and 38 % of them ended in stillbirth. Treatment with acetylsalicylic acid alone or in combination with platelet lowering drugs improved the outcome of the pregnancy. The present findings about risk factors in ET as well as treatment outcome in the pregnancies of ET patients should be taken into account when planning treatment strategies for Finnish patients.

Pathobiological Aspects of Nonreheumatic Aortic Valve Stenosis

Aortic valve stenosis (AS) is an active disease process akin to atherosclerosis, with chronic inflammation, lipid accumulation, extracellular matrix remodeling, fibrosis, and extensive calcification of the valves being characteristic features of the disease. The detailed mechanisms and pathogenesis of AS are still incompletely understood, however, and pharmacological treatments targeted toward components of the disease are not currently available. In this thesis project, my coworkers and I studied stenotic aortic valves obtained from 86 patients undergoing valve replacement for clinically significant AS. Non-stenotic control valves (n=17) were obtained from patients undergoing cardiac transplantation or from organ donors without cardiac disease. We identified a novel inflammatory factor, namely mast cell, in stenotic aortic valves and present evidence showing that this multipotent inflammatory cell may participate in the pathogenesis of AS. Using immunohistochemistry and double immunofluorescence stainings, we found that a considerable number of mast cells accumulate in stenotic valves and, in contrast to normal valves, the mast cells in diseased valves were in an activated state. Moreover, valvular mast cells contained two effective proteases, chymase and cathepsin G, which may participate in adverse remodeling of the valves either by inducing fibrosis (chymase and cathepsin G) or by degrading elastin fibers in the valves (cathepsin G). As chymase and cathepsin G are both capable of generating the profibrotic peptide angiotensin II, we also studied the expression and activity of angiotensin-converting enzyme (ACE) in the valves. Using RT-PCR, imunohistochemistry, and autoradiography, we observed a significant increase in the expression and activity of ACE in stenotic valves. Besides mast cell-derived cathepsin G, aortic valves contained other elastolytic cathepsins (S, K, and V). Using immunohistochemistry, RT-PCR, and fluorometric microassay, we showed that the expression and activity of these cathepsins were augmented in stenotic valves. Furthermore, in stenotic but not in normal valves, we observed a distinctive pattern of elastin fiber degradation and disorganization. Importantly, this characteristic elastin degradation observed in diseased valves could be mimicked by adding exogenous cathepsins to control valves, which initially contained intact elastin fibers. In stenotic leaflets, the collagen/elastin ratio was increased and correlated positively with smoking, a potent AS-accelerating factor. Indeed, cigarette smoke could also directly activate cultured mast cells and fibroblasts. Next, we analyzed the expression and activity of neutral endopeptidase (NEP), which parallels the actions of ACE in degrading bradykinin (BK) and thus inactivates antifibrotic mechanisms in tissues. Real-time RT-PCR and autoradiography revealed NEP expression and activity to be enhanced in stenotic valves compared to controls. Furthermore, both BK receptors (1 and 2) were present in aortic valves and upregulated in stenotic leaflets. Isolated valve myofibroblasts expressed NEP and BK receptors, and their upregulation occurred in response to inflammation. Finally, we observed that the complement system, a source of several proinflammatory mediators and also a potential activator of valvular mast cells, was activated in stenotic valves. Moreover, receptors for the complement-derived effectors C3a and C5a were expressed in aortic valves and in cultured aortic valve myofibroblasts, in which their expression was induced by inflammation as well as by cigarette smoke. In conclusion, our findings revealed several novel mechanisms of inflammation (mast cells and mast cell-derived mediators, complement activation), fibrosis (ACE, chymase, cathepsin G, NEP), and elastin fiber degradation (cathepsins) in stenotic aortic valves and highlighted these effectors as possible pathogenic contributors to AS. These results support the notion of AS as an active process with inflammation and extracellular matrix remodeling as its key features and identify possible new targets for medical therapy in AS.

Atrial remodeling in atrial fibrillation : Epidemiological, clinical and magnetocardiographic aspects

Atrial fibrillation is the most common arrhythmia requiring treatment. This Thesis investigated atrial fibrillation (AF) with a specific emphasis on atrial remodeling which was analysed from epidemiological, clinical and magnetocardiographic (MCG) perspectives. In the first study we evaluated in real-life clinical practice a population-based cohort of AF patients referred for their first elective cardioversion (CV). 183 consecutive patients were included of whom in 153 (84%) sinus rhythm (SR) was restored. Only 39 (25%) of those maintained SR for one year. Shorter duration of AF and the use of sotalol were the only characteristics associated with better restoration and maintenance of SR. During the one-year follow-up 40% of the patients ended up in permanent AF. Female gender and older age were associated with the acceptance of permanent AF. The LIFE-trial was a prospective, randomised, double-blinded study that evaluated losartan and atenolol in patients with hypertension and left ventricular hypertrophy (LVH). Of the 8,851 patients with SR at baseline and without a history of AF 371 patients developed new-onset AF during the study. Patients with new-onset AF had an increased risk of cardiac events, stroke, and increased rate of hospitalisation for heart failure. Younger age, female gender, lower systolic blood pressure, lesser LVH in ECG and randomisation to losartan therapy were independently associated with lower frequency of new-onset AF. The impact of AF on morbidity and mortality was evaluated in a post-hoc analysis of the OPTIMAAL trial that compared losartan with captopril in patients with acute myocardial infarction (AMI) and evidence of LV dysfunction. Of the 5,477 randomised patients 655 had AF at baseline, and 345 patients developed new AF during the follow-up period, median 3.0 years. Older patients and patients with signs of more serious heart disease had and developed AF more often. Patients with AF at baseline had an increased risk of mortality (hazard ratio (HR) of 1.32) and stroke (HR 1.77). New-onset AF was associated with increased mortality (HR 1.82) and stroke (HR of 2.29). In the fourth study we assessed the reproducibility of our MCG method. This method was used in the fifth study where 26 patients with persistent AF had immediately after the CV longer P-wave duration and higher energy of the last portion of atrial signal (RMS40) in MCG, increased P-wave dispersion in SAECG and decreased pump function of the atria as well as enlarged atrial diameter in echocardiography compared to age- and disease-matched controls. After one month in SR, P-wave duration in MCG still remained longer and left atrial (LA) diameter greater compared to the controls, while the other measurements had returned to the same level as in the control group. In conclusion is not a rare condition in either general population or patients with hypertension or AMI, and it is associated with increased risk of morbidity and mortality. Therefore, atrial remodeling that increases the likelihood of AF and also seems to be relatively stable has to be identified and prevented. MCG was found to be an encouraging new method to study electrical atrial remodeling and reverse remodeling. RAAS-suppressing medications appear to be the most promising method to prevent atrial remodeling and AF.