Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

New and Emerging Challenges of the ICT-Mediated Health and Well-Being Services

This monograph dissertation looks into the field of ICT-mediated health and well-being services. Through six chapters that extend the work done in the reviewed and published articles, the dissertation focuses on new and emerging technologies, and to impact of their use on the beneficiary; the individual who eventually derives advantage from the services. As the field is currently going through major changes particularly in the OECD countries, the focus is on shortterm developments in the field and the analysis on the long term developments is cursory by nature. The dissertation includes theoretical and empirical elements. Most of the empirical elements are linked to product development and conceptualization performed in the national MyWellbeing project that ended in 2010. In the project, the emphasis was on conceptualization of a personal aid for the beneficiary that could be used for managing information and services in the field of health and well-being services. This work continued the theme of developing individual-centric solutions for the field; a work that started in the InnoElli Senior program in 2006. The nature of this thesis is foremost a conceptual elaboration based on a literature review, illustrated in empirical work performed in different projects. As a theoretical contribution, this dissertation elaborates the role of a mediator, i.e. an intermediary, and it is used as an overarching theme. The role acts as a ‘lens’ through which a number of technology-related phenomena are looked at, pinned down and addressed to a degree. This includes introduction of solutions, ranging from anthropomorphic artefacts to decision support systems that may change the way individuals experience clinical encounters in the near-future. Due to the complex and multiform nature of the field, it is impractical and effectively impossible to cover all aspects that are related to mediation in a single work. Issues such as legislation, financing and privacy are all of equal importance. Consideration of all these issues is beyond the scope of this dissertation and their investigation is left to other work. It follows from this that the investigation on the role is not intended as inclusive one. The role of the mediator is also used to highlight some of the ethical issues related to personal health information management, and to mediating health and well-being related issues on behalf of another individual, such as an elderly relative or a fellow member of a small unit in the armed forces. The dissertation concludes in a summary about the use and functions of the mediator, describing some potential avenues for implementing such support mechanisms to the changing field of ICT-mediated health and well-being services. The conclusions also describe some of the limitations of this dissertation, including remarks on methodology and content.

Social class as a factor for the construction of a musician’s identity : The Musician’s social background and identity questionnaire (MSBIQ) – a cross-sectional comparative quantitative online survey research study of music students at two higher education institutions in Finland

There is currently little empirical knowledge regarding the construction of a musician’s identity and social class. With a theoretical framework based on Bourdieu’s (1984) distinction theory, Bronfenbrenner’s (1979) theory of ecological systems, and the identity theories of Erikson (1950; 1968) and Marcia (1966), a survey called the Musician’s Social Background and Identity Questionnaire (MSBIQ) is developed to test three research hypotheses related to the construction of a musician’s identity, social class and ecological systems of development. The MSBIQ is administered to the music students at Sibelius Academy of the University of Arts Helsinki and Helsinki Metropolia University of Applied Sciences, representing the ’highbrow’ and the ’middlebrow’ samples in the field of music education in Finland. Acquired responses (N = 253) are analyzed and compared with quantitative methods including Pearson’s chi-square test, factor analysis and an adjusted analysis of variance (ANOVA). The study revealed that (1) the music students at Sibelius Academy and Metropolia construct their subjective musician’s identity differently, but (2) social class does not affect this identity construction process significantly. In turn, (3) the ecological systems of development, especially the individual’s residential location, do significantly affect the construction of a musician’s identity, as well as the age at which one starts to play one’s first musical instrument. Furthermore, a novel finding related to the structure of a musician’s identity was the tripartite model of musical identity consisting of the three dimensions of a musician’s identity: (I) ’the subjective dimension of a musician’s identity’, (II) ’the occupational dimension of a musician’s identity’ and, (III) ’the conservative-liberal dimension of a musician’s identity’. According to this finding, a musician’s identity is not a uniform, coherent entity, but a structure consisting of different elements continuously working in parallel within different dimensions. The results and limitations related to the study are discussed, as well as the objectives related to future studies using the MSBIQ to research the identity construction and social backgrounds of a musician or other performing artists.

A new & accurate map of the North Pole with all the countries hitherto discovered situated near or adjacent to it as well as some others more remote. Drawn from the latest and best authorities and regulated by astronom.l observat.ns by Eman. Bowen.

0-meridiaani: Lontoo. - Koordinaattiasteikko: N90°-55°[50°].

Psychological well-being of the parents and child development, behavior, and quality of life in very low birth weight infants

The parents of premature infants, especially the mothers, are at increased risk for distress. Infants born prematurely are at risk for developmental problems. The aim of this study was to investigate whether the psychological well-being of both parents is associated with child development in very low birth weight (VLBW, ≤1500g) children. The burden of prematurity-related morbidity to the children and to the family was also assessed. A cohort of 201 VLBW infants born during 2001–2006 in the Turku University Hospital, Finland, and their parents were studied (I–IV). One study included a control group (n=166) of full-term infants (IV). The psychological well-being of the parents was evaluated by assessments of depressive symptoms, parenting stress, the sense of coherence and general family functioning. Cognitive, behavioral, and socio-emotional development, and the health-related quality of life (HRQoL) of the children were determined when the children were 2 to 8 years old. The psychological well-being of the parents was associated with the cognitive, behavioral and social development of the VLBW children. The VLBW infants with prematurity-related morbidities had a poorer HRQoL and the general functioning of the family was inferior compared to the control children and their families. 64.5% of the VLBW children survived without morbidities. Most of the VLBW children did not have significant behavior problems (93%), had normal social skills (63%), had no emotional problems (64%), and had no problems in executive functioning (62%). Only 3% of the surviving VLBW infants had significant cognitive delay. In conclusion, the depressive symptoms and stress of the parents can be risk factors for disadvantageous child development, while a strong sense of coherence can be protective. Parents of the premature children with developmental delays might also experience more depressive symptoms and stress than other parents. Prematurity-related morbidities were a burden to the VLBW child as well as to the family.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

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.

Ethical leadership as a way to promote work-related well-being

The purpose of this study was to clarify the connections of ethical leadership with the work-related well-being of employees. Additionally, the role of occupational health care in ethical leadership that promotes work-related well- being was analyzed. The objective of the study was to produce knowledge to support the development of ethical leadership and work-related well-being as well as to find ways for occupational health care to support organizations in these actions. The target groups of this study consisted of the managers (N=43) and employees (N=336) working in one organization in the Finnish energy industry. The population was studied in November 2014 using census. The data was gathered with two different web-based surveys containing structured and open questions. The survey for managers consisted of background questions and statements concerning ethical leadership, work-related well-being and occupational health care. The employee questionnaire consisted of questions about background and statements about work-related well-being and ethical leadership. The structured questions were analyzed with SPSS Statistical Program and the open questions using inductive content analysis. At least 80 % of the managers saw their actions as ethical in all but one part of ethical leadership. The work-related well-being of the employees was found best in the area of ability to work (91 % agreed) and lowest in the area of experience of ethical leadership (67 % agreed). The results showed a strong positive connection between ethical leadership and all the components of work- related well-being. The managers and employees were generally quite happy with the services of occupational health care but managers saw some problems with the collaboration with occupational health care. Several ways to improve work-related well-being and collaboration with occupational health care were found. One of the most important things was thought to be offering ways to maintain ability to work and making these actions visible. Investing in ethical leadership and work-related well-being is extremely important for the success of an organization and the societal benefits cannot be forgotten either. The role of occupational health care in promoting the health and well-being of employees is substantial. Occupational health care should offer managers more tools to recognize difficult situations and acting in them as well as encourage managers to seek help from occupational health care without hesitation in problematic situations of leadership.

Ethical leadership as a way to promote work-related well-being

The purpose of this study was to clarify the connections of ethical leadership with the work-related well-being of employees. Additionally, the role of occupational health care in ethical leadership that promotes work-related well- being was analyzed. The objective of the study was to produce knowledge to support the development of ethical leadership and work-related well-being as well as to find ways for occupational health care to support organizations in these actions. The target groups of this study consisted of the managers (N=43) and employees (N=336) working in one organization in the Finnish energy industry. The population was studied in November 2014 using census. The data was gathered with two different web-based surveys containing structured and open questions. The survey for managers consisted of background questions and statements concerning ethical leadership, work-related well-being and occupational health care. The employee questionnaire consisted of questions about background and statements about work-related well-being and ethical leadership. The structured questions were analyzed with SPSS Statistical Program and the open questions using inductive content analysis. At least 80 % of the managers saw their actions as ethical in all but one part of ethical leadership. The work-related well-being of the employees was found best in the area of ability to work (91 % agreed) and lowest in the area of experience of ethical leadership (67 % agreed). The results showed a strong positive connection between ethical leadership and all the components of work- related well-being. The managers and employees were generally quite happy with the services of occupational health care but managers saw some problems with the collaboration with occupational health care. Several ways to improve work-related well-being and collaboration with occupational health care were found. One of the most important things was thought to be offering ways to maintain ability to work and making these actions visible. Investing in ethical leadership and work-related well-being is extremely important for the success of an organization and the societal benefits cannot be forgotten either. The role of occupational health care in promoting the health and well-being of employees is substantial. Occupational health care should offer managers more tools to recognize difficult situations and acting in them as well as encourage managers to seek help from occupational health care without hesitation in problematic situations of leadership.