We are concerned with the probability that a standard Brownian motion W(t) crosses a curved boundary c(t) on a finite interval [0, T]. Let this probability be denoted by Q(c(t); T). Due to recent advances in research a new way of estimating Q(c(t); T) seems feasible: Monte Carlo Simulation. Wang and Pötzelberger (1997) derived an explicit formula for the boundary crossing probability of piecewise linear functions which has the form of an expectation. Based on this formula we proceed as follows: First we approximate the general boundary c(t) by a piecewise linear function cm(t) on a uniform partition. Then we simulate Brownian sample paths in order to evaluate the expectation in the formula of the authors for cm(t). The bias resulting when estimating Q(c_m(t); T) rather than Q(c(t); T) can be bounded by a formula of Borovkov and Novikov (2005). Here the standard deviation - or the variance respectively - is the main limiting factor when increasing the accuracy. The main goal of this dissertation is to find and evaluate variance reducing techniques in order to enhance the quality of the Monte Carlo estimator for Q(c(t); T). Among the techniques we discuss are: Antithetic Sampling, Stratified Sampling, Importance Sampling, Control Variates, Transforming the original problem. We analyze each of these techniques thoroughly from a theoretical point of view. Further, we test each technique empirically through simulation experiments on several carefully chosen boundaries. In order to asses our results we set them in relation to a previously established benchmark. As a result of this dissertation we derive some very potent techniques that yield a substantial improvement in terms of accuracy. Further, we provide a detailed record of our simulation experiments. (author's abstract)

As a paradigm of a wounded healer, parentified therapists may be gifted with therapeutic talents, but also with related vulnerabilities that may have a significant influence on their therapeutic practice. Therefore, the aim of the current study was to explore the impact of parentification on therapeutic practice, especially on the therapeutic skills of empathy and boundary settings. For this purpose, a mixed method design was employed in which 38 trainee psychologists provided self-report data on the constructs of parentification measured by parentification questionnaire (Jurkovic, 1997), empathy, measured by Interpersonal Reactivity Index (Davis, 1980), and boundary settings, measured by Exploitation Index (Epstein, 1990) in a survey study, while 4 trainee psychologists were interviewed in a separate study. First, the quantitative data were analysed to assess the existence of possible relationships among the variables of parentification, empathy and boundary transgressions by a regression analysis. The results offered significant suggestions for the predictive power of parentification in regard to empathy and boundary transgressions. Following this, a qualitative study analysed the interviews with the 4 trainees using thematic analysis to explore the above relationships and provided a deeper insight, especially for their therapeutic utility. Combining the findings, the current study supported that parentification may first of all catalyse the choice of a psychologist's profession, well as the choice of the psychotherapeutic approach. In regard to the interpersonal skills, parentification may positively impact the development of enhanced levels of empathy, boundary flexibility, and creativity. On the other hand, parentification may also negatively impact on practitioners by making them more vulnerable to enmeshed therapeutic relationships. Especially in the case of destructive parentification, professional support may be needed to minimise the risk for enmeshed relationships, by increasing self-care and self-other differentiation. Clinical implications for parentified therapists were also discussed.

This thesis consists of two novel contributions to the computation of first passage time distribution for Brownian motion. First, we extend the known formula for boundary crossing probabilities for Brownian motion to the discontinuous piecewise linear boundary. Second, we derive explicit formula for the first passage time density of Brownian motion crossing piecewise linear boundary. Further, we demonstrate how to approximate the boundary crossing probabilities and density for general nonlinear boundaries. Moreover, we use Monte Carlo simulation method and develop algorithms for the numerical computation. This method allows one to assess the accuracy of the numerical approximation. Our approach can be further extended to compute two-sided boundary crossing probabilities.

This thesis is concerned with boundary crossing probabilities and first crossing time densities for stochastic processes. This is a classical problem in probability that goes back to the famous ballot problem (first studied by W. A. Whitworth (1878) and J. Bertrand (1887)) and has numerous applications in diverse areas including mathematical statistics and financial mathematics. Our main objective is the study of approximation methods and control of the resulting approximation error for boundary crossing probabilities where a closed-form solution is unavailable. This leads to the study of bounds for the density of the first crossing time of the boundary, which in turn leads to the derivation of some analytic properties of the densities. This thesis presents a whole suite of closely related new results obtained when working on the outlined research program. (For complete abstract open document).

As the demand for distance learning increases, traditional campus-based universities continue to struggle in supporting working distance students. This has resulted in the increased phenomena of students using social media within their ecosystems of learning support. The use of formal and informal tools such as social media gives rise to boundaries which students need to cross for effective support. How social media facilitates the crossing of boundaries within ecosystems of learning support remains an unfamiliar area of research. This study employed a predominately qualitative research methods, with a small element being a quantitative method to view and investigate postgraduate distance students' ecosystem of learning support holistically. The findings of this study revealed that participants used a combination of formal and informal tools to support their learning, including social media. In particular WhatsApp, which enables the crossing of transitional, formal and informal learning contexts, hierarchical and, time and space boundaries. Recognizing social media as an important part of students' learning support ecosystem, allowed an expanded view on learning support. As such, the study highlighted a range of different learning mechanisms which occur when students cross these boundaries, with coordination being the dominant learning mechanism. In conclusion, social media (such as WhatsApp) does indeed enhance the crossing of various boundaries to support learning. However, some students do not necessarily perceive their interaction on social media as learning, which speaks to the need of legitimising social media as learning tools by institutions. This study then recommends the need for institutions to recognize and nurture the use of social media as one element of a distance learning support ecosystem for cost-effective student support strategies guided by institutional guidelines and policies.

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Studien bidrar med fördjupad kunskap om en partsintermediärs, ett bransch- och arbetsgivarförbund, möjligheter till parts- och arbetsgivarsamverkan kring kompetensförsörjningsåtgärder för medlemsföretag och regional utveckling på en lokal arbetsmarknad. Fokus ligger på intermediärens villkor som samordnare av utbildning för maskinförares etablering på arbetsmarknaden. Studiens teoretiska referensram tar sin grund i tidigare forskning om intermediärer och de teoretiska utgångspunkterna från ett boundary-crossing perspektiv och omsluts av lärandemekanismer och dialektiska lärandeprocesser. Det empiriska materialet baseras på 12 intervjuer och två fokusgrupper. Slutsatserna som dras är att partsintermediären verkar i en dualistisk samverkansstruktur i tre nivåer i och mellan två praktikgemenskaper: organisatorisk, interpersonell och intrapersonell. Det som möjliggör samverkan gällande kompetensförsörjning för samordning av utbildning är de formella kunskapsråd mellan parterna på nationell och regional nivå samt juridiska stödstrukturer genom yrkesutbildningsavtal. Begränsningen för överskridande samordning är omfattande matchningsproblem mellan utbildning och medlemsföretag, genom frånvaron av ekonomiska och pedagogiska stödfunktioner för den lokala arbetsmarknaden. / The study provides in-depth knowledge of an intermediary, an industry and employers' federation, opportunities for party and employer cooperation on competence-providing measures for member companies and regional development in a local labor market. The focus is on the intermediary's conditions as coordinator of education for machine operators' establishment in the labor market. The theoretical reference framework of the study is based on previous research on intermediates and the theoretical starting points from a boundary-crossing perspective, and is encompassed by learning mechanisms and dialectical learning processes. The empirical material is based on 12 interviews and two focus groups. The conclusions drawn are that the intermediary acts in a dual-level collaboration structure in three levels in and between two communities of practice: organizational, interpersonal and intrapersonal. What allows co-operation on the provision of skills for coordination of education is the formal knowledge council between the parties at national and regional level and legal support structures through vocational training agreements. The overriding coordination constraints are extensive matching problems between education and member companies, due to the absence of financial and educational support for the local labor market.

In this dissertation, I investigate the implications of libertarian morality in relation to the problem of climate change. This problem is explicated in the first chapter, where preliminary clarifications are also made. In the second chapter, I briefly explain the characteristics of libertarianism relevant to the subsequent study, including the central non-aggression principle. In chapter three, I examine whether our individual emissions of greenhouse gases, which together give rise to climate change, meet this principle. I do this based on the assumption that we are the legitimate owners of the resources we use in those activities. In the fourth chapter, I question this assumption and scrutinize libertarianism’s restrictions on appropriations of climate-relevant resources, which leads me to distinguish between some different versions of the libertarian view. Toward the end of the chapter, I also examine libertarianism’s answer to the political question regarding how emission rights should be distributed. The fifth chapter investigates libertarianism’s verdicts for mere risks of infringement, as stemming from people’s emissions and acts of appropriations. In chapter six, I investigate the libertarian right to self-defense against both the effects of climate change and other people’s climate-relevant activities. In chapter seven, I discuss two intergenerational issues related to climate change: what libertarianism says concerning future generations and how libertarianism might deal with the problem of historical emissions. The eighth chapter explores the implications of libertarianism regarding collective moral wrongdoing in connection to climate change. In chapter nine, I take a look at the libertarian room for governmental responses for tackling climate change. The tenth and final chapter is a summary. The overall conclusion of the dissertation is that libertarianism recommends that we reduce our emissions and decrease our extraction of natural resources such as forests and fossil fuels. Furthermore, governments are permitted to undertake some quite substantial actions in order to fight the causes of climate change. I end with some bottom-up reflections on what these conclusions might say about the plausibility of libertarianism. I claim that although libertarianism after all manages to explain some of our moral intuitions regarding climate change, it is questionable whether libertarianism’s explanation is better than those offered by alternative moral theories.

The aim of this dissertation is to describe and analyze how discourse as a theoretical and didactical concept can help in advancing knowledge about the teaching of mathematics in school. The dissertation has been written within a socio-cultural perspective where active participation and support from artefacts and mediation are viewed as important contributions to the development of understanding. Discourse analysis was used as a theoretical point of departure to grasp language use, knowledge construction and mathematical content in the teaching practises. The collection of empirical data was made up of video and audio tape recordings of the interaction of teachers and pupils in mathematics classrooms when they deal with problem-solving tasks, as well as discussions between student teachers as they engage in planning a teaching situation in mathematics. Discourse analysis was used as a tool to shed light upon how pupils learn and develop understanding of mathematics. The results of my studies demonstrate that discussions very often are located in either a mathematical or in an every-day discourse. Furthermore, the results demonstrate how change between every-day and mathematical language often takes place unknowingly. Also the results underline that a specific and precise dialogue can contribute towards teachers’ and pupils’ conscious participation in the learning process. Translated into common vocabulary such as speak, think, write, listen and read teachers and pupils would be able to interact over concepts, signs, words, symbols, situations and phenomena in every-day discourse and its mathematical counterpart. When teachers and pupils become aware of discursive boundary crossing in mathematics an understanding of mathematical phenomena can start to develop. Teachers and pupils can construct a meta-language leading to new knowledge and new learning in mathematics. / Syftet med avhandlingen är att beskriva och analysera hur diskurs som teoretiskt- didaktiskt begrepp kan bidra till att utveckla kunskap i och om matematik i skolan. Avhandlingen skrivs utifrån ett sociokulturellt perspektiv där aktivt deltagande med hjälp av artefakter och mediering är viktiga bidrag till förståelsen. För att få syn på språket, kunskapen och matematiken i matematikundervisningen används diskursanalys som teoretisk utgångspunkt och metod. Data insamlingen består av video- och ljudbandsinspelningar av lärares och elevers samtal i ett matematikklassrum då de arbetar med problemlösning och lärarstudenters samtal när de planerar en undervisningssituation i matematik. Diskusanalys har använts som ett redskap för att upptäcka hur elever lär och utvecklar sin förståelse av matematik. Resultaten visar att i mina studier befinner sig samtalet ofta antingen i en matematisk eller i en vardaglig diskurs. Växlingen mellan vardagligt och matematiskt språk sker ofta omedvetet. I avhandlingen understryks att ett specifikt och precist samtal i matematik underlättar ömsesidig förståelse och kan bidra till att lärare och elever blir delaktiga i lärandet. Med hjälp av orden tala, tänka, skriva, lyssna och läsa skulle lärare och elever kunna interagera kring begrepp, tecken, ord, symboler, situationer och företeelser i den vardagliga och den matematiska diskursen och förståelse skulle lättare kunna äga rum i matematik. Genom att lärare och elever blir medvetna om hur de passerar diskursiva gränser både i matematiken och mellan matematik och vardag kan förståelse klargöras. Lärare och elever skulle kunna utveckla ett metaspråk som leder till ny kunskap och nytt lärande inom matematiken i skolan.

Emerging markets are fraught with uncertainty, diverse global players, rapid technological change, wide-spread price wars, and seemingly endless reorganization (Ilinitch, 1996). These changes have presented challenges to organizations in the form of shorter product cycles, increased segment fragmentation, blurring industry boundaries, breaking corporate hierarchies, and increased interdependence of world markets (Ozsomer et. al., 1991). Organizations are responding to competition by capitalizing on global policies and adopting self-directed teams and horizontal structures that enhance external activities. To do this organizations are getting conscious of the boundaries they are operating in. With hyper competition and globalization organizations blur boundaries to gain maximum business opportunity from other geographic boundaries. For this to happen organizations must engage in boundary crossing behaviour. Competition is also managed by focussing on bringing out new products to the market. Product development (PD) is critical because new products are becoming the nexus of competition for firms (Clark and Fujimoto, 1991). They are the means by which members of organizations diversify, adapt, and even reinvent their firms to match evolving market and technological conditions (Schoonhoven et. al., 1990). This calls for a closer look at boundary crossing behaviour as part of the external activity during PD. The studies carried out in the process of PD identify external activity orientation as important criteria for success (Brown and Eisenhardt, 1995). PD processes involve project management activity. Unlike other processes of an organization, PD is a knowledge intensive activity, which brings together individuals having different skill sets and mindsets. These individuals need to interact regularly to understand and coordinate their activities. The non-routine nature of the process makes boundary-crossing activity more critical for successful PD. This thesis focuses on the boundary crossing behaviours performed by PD teams. Literature review showed that external activities play a crucial role in PD (Calantoue and Di Benedetto 1990a, b; Griffin and Hauser 1992; Olson et. al., 1995; Song et al., 2000; Souder 1987). The importance of external activities for successful project development was shown by Allen (1971, 1977) based on his seminal work on communication and organizations. He showed that R&D team’s frequency of communication within the team has no relationship to performance, while increased communication between teams and other parts of the laboratory was strongly related to project performance. Teams carrying out complex tasks in uncertain environments were found to perform higher levels of external activities (Ancona and Caldwell 1992). External activity was found to result in high percentages of successful projects and sales derived from new products (Cooper 1984; Dougherty 1987; Ancona and Caldwell, 1992; Ancona, 1990; Sheremata 2002). PD is an activity with high uncertainty. The external activities that are performed by PD teams and their nature of relationships shared are variously classified as interactive and collaborative behaviour (Kahn 1996). Underlying this classification is a dichotomous behaviour where in the former embodies presence of informal behaviour between partners, while the latter embodies formal behaviour. Further research on these behaviours have shown that informal type of external activity also known as collaborative behaviour plays an important role in the successful development of products. Collaboration represents the unstructured, affective nature of interdepartmental relationships. They were found to result in improved product development. A study on software product development teams by Kraut and Streeter(1995) also showed the importance of informal behaviour. He found that product development requires personal communication across functional boundaries to cope with uncertainty. The external activities performed by PD teams were also found to be influenced by variables like product development life cycle (Brodbeck, 2001; Sawyer & Guinan, 1998; Boehm, 1987), informal groups (Hirschhorn and Gilmore, 1992), awareness, (Pinto and Slevin, 1987), and open climate (Ashkenas et. al., 1990). After identifying the missing gaps in gaps were the objectives of the study was defined. The objectives of the study are as follows: To understand the interactive and collaborative boundary crossing behaviour of product development teams To study the difference in boundary crossing behaviour of horizontal, geographic and value chain boundaries of product development teams To understand the relationship of variables influencing boundary crossing behaviour of product development teams To give suggestions to better understand management of boundary crossing behaviour in product development teams A combination of qualitative and quantitative techniques was adopted to study these objectives. Based on the past literature a conceptual framework was developed. It consisted of defining the role of collaborative and interactive boundary crossing behaviours across product development teams and certain variables influencing this behaviour. The model was validated through preliminary interviews. These interviews were conducted across team members, team leaders and knowledge management experts. A few more variables were identified that were considered to influence the collaborative behaviour performed by PD teams. These variables are sharing behaviour and confidence with the time available for developing the product. The variables were operationally defined and measurement instrument, namely a questionnaire, was developed. The questionnaire was administered to team leaders and team members. The measurement instrument was tested for its psychometric properties namely, reliability and validity. Cronbach alphas are reported. For the main study, data was collected from 73 product development teams of IT organizations located in Bangalore. From the team leader the general characteristics of the PD team were understood, as well as the level of newness of the product developed. The latter was used as a measure of level of innovation. From team members, the interactive and collaborative behaviour of PD team members was studied. The statistical techniques that were used for analyzing the data are F-Test, t-test, Kruskall Wallis test, chi-square test , correlation and regression analyses. After the analysis it was found that the interactive and collaborative behaviour expressed by the teams across the three boundaries showed that as compared to collaborative behavior, product development teams more commonly used interactive behaviour. Interactive behaviours were also found to be used to the same extent across all the three boundaries. Since interactive behavior is formal and forced in organizations it is predominantly practiced although its efficiency may vary. The challenge for organizations hence is the collaborative behaviors. On the other hand, collaborative behaviour was seen used the most across horizontal boundary and the least across value chain boundary. Since the geographic distance across boundaries increases when moving from horizontal to value chain boundaries the chances of collaboration get decreased. Hence an influence of distance on boundary crossing behavior was sense influencing collaborative behaviour of product development teams. Hence further analysis focused on collaborative behaviors. The collaborative behaviour was further studied to understand its relationship with product development team behaviour, sharing behaviour of teams of outside the boundary, demographic variables and innovation level of product developed. Correlation analysis showed that the collaborative behaviour of teams were correlated with the sharing behaviour, informal groups, autonomous team leader behaviour, and open climate only. These variables were termed direct influencers of collaborative behavior.Innovation level did not play any significant role in influencing collaborative behavior.Collaboration behaviour was further studied to understand how they are causally related with these variables. Using regression analysis, the causal study considered collaboration behaviour of PD teams in general, as well as the collaboration behaviour across horizontal, geographical and value-chain boundary as the dependent variable. The independent variables studied are sharing behaviour, informal groups, open-climate behaviors, autonomous team leader behaviour. Regression results showed that open climate behaviours was causally related to overall collaboration behaviour of PD teams in all boundaries. With respect to collaboration across horizontal boundary, it was found that sharing behaviour, as well as autonomous team leader behaviour influenced them. Across geographical boundary, the open-climate was found causally related. Across value chain boundary sharing behaviour was found to influence collaborative behaviour. It was found that only some variables influence boundary crossing behavior namely, collaborative behavior, the most. These were open climate behaviors, sharing behaviour, and autonomous team leader behaviour. These were labeled direct influencers. The ones that did not show a direct influence were termed as indirect influencers. Since the role of direct influencers was clearly understood, the role of indirect influencers needed further analysis as these were variables selected from literature and expert interviews and expected to have influence on boundary crossing behaviour. Those variables that did not directly enter the regression analysis were further studied tounder stand if they had a relationship with the direct influencers independent of collaborative behaviors. It was assumed that if they did then they may indirectly influence collaborative behaviors. For this the indirect variables were correlated with the direct influencers. The results showed that open-climate was positively correlated with awareness of objectives, PD life cycle and the team’s confidence in time line of the project. Interestingly sharing behavior and autonomous behaviour of the team leader was not correlated with any potentially indirect influencer or variable. This meant that awareness of objectives, PD life cycle and the team’s confidence in time line of the project can influence collaborative behavior indirectly. In the next analysis the role of PD was understood deeper in the context of level of innovation and duration of projects vis-à-vis collaboration. This is specifically done as the poor influence of level of innovation and duration were a surprise since they were expected to have influence on boundary crossing behavior. Teams were classified into low, medium and high innovation level teams. The collaboration behaviour within these teams was then studied. The results showed that there was a pattern in the usage of collaboration behaviour across the different channels. Collaboration behaviour was used most across medium innovation level team as compared to low and high innovation level teams. This was the case of collaboration across horizontal and geographical boundary. In the case of value chain boundary, no such pattern was recognizable. Interestingly it meant that in low and high innovation collaborative behavior was lower and it increased only during medium innovation. Further to this, the influence of collaboration on duration of product developed was studied. The correlation study showed negative relation between the two only for horizontal boundaries. This meant that increase in collaborative behavior across horizontal boundaries result in lesser time taken to develop the product. The last chapter in this thesis describes the conclusions from this study and the managerial implications regarding nurturing and managing boundaries of PD teams.