We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.

We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.

Under många år har det pratats om ämnesintegrering i den svenska skolan. Detta skulle enligt forskare, Skolverket och Skolinspektionen vara ett sätt att öka engagemanget för matematik och förhoppningsvis öka kunskapsnivån i matematik hos Sveriges skolungdomar. Vår studie undersöker om elever på gymnasiets Restaurang- och livsmedelsprogram angriper matematikproblem olika beroende på graden av ämnesintegrering av programmets karaktärsämnen. Hela matematikkursen har präglats av denna typ av uppgifter för att sätta matematiken i en kontext som eleverna möter i sina karaktärsämnen och kommande yrkesliv.   Genom att både observera elever, då de löst större karaktärsämnesnära matematikuppgifter, och genomföra före-efter-diagnoser studerar vi hur eleverna formar sina lösningar men även hur deras kunskapsnivå i matematik påverkats av att kursen integrerats med karaktärsämnen.   Observationerna har analyserats med hjälp av boundary objects och boundary crossings mellan matematik och karaktärsämne. Dessa har tagits fram med hjälp av Engeströms (2005; 2015) aktivitetsteori samt Star och Griesemers (1989) utveckling av boundary crossing-teori.   Vi har i våra observationer sett att om uppgifter ligger nära elevernas kunskaper i karaktärsämnen har de lättare att hitta alternativa lösningsmetoder för matematikproblemen. Uppgifter kan vara färgade av karaktärsämnet men det är elevernas trygghet i sina karaktärsämneskunskaper som spelar störst roll huruvida de löser uppgiften med en traditionellt matematisk metod eller om de prövar alternativa metoder.   Elevernas kunskapsnivå i matematik förändras till största delen positivt, men inte så markant att det går att dra slutsatsen att ämnesintegrerad undervisning kan revolutionera svensk matematikundervisning.   Denna studie kan vara av intresse för fortsatt forskning kring ämnesintegrering samt för matematikkollegor som undervisar yrkeselever.

Abstract Speed of information, uncertainty and complexity are increasing in the work-life of the knowledge worker. In addition, solving complex and wicked global problems require cooperation skills as well as ability to learn in collaboration across the disciplines, meaning skills in crossing boundaries. These requirements set new challenges for educating knowledge workers in higher education. Metaskills, such as learning by utilising networks, communication and critical thinking, have become as essential as discipline-specific skills. Metaskills combined with discipline-specific skills are called T-shaped skills. Individuals possessing these skills, so-called T-shaped professionals, are exposed to the experience and the knowledge of other disciplines and thus are recognised as carrying the skills for crossing boundaries. This dissertation examines how a Finnish studio-based pedagogical approach to bachelor education, the LAB Studio Model (LSM), contributes to the education of boundary crossing competence. This qualitative dissertation utilises exploratory as well as design research as its research approach and contains four original publications. First, the characteristics of LSM and the utilisation of studio-based practices in higher education are studied by conducting literature reviews. Second, the internal and external boundary crossing activities are studied by performing case studies, where the new knowledge creation and establishment of learning networks are in focus. Empirical data has been collected by conducting web-based surveys, theme-based student and student team interviews, direct observation, and participative observation. The outcome of this dissertation suggests that LSM offers a potential educational model for learning the skills of boundary crossing, resulting in a T-shaped skill base. The results of this dissertation include new findings on how commonly studio-based education is utilised world wide in higher education, how LSM differs from the existing configurations that utilise the studio-based model in higher education, as well as active internal and external boundary crossing among students. This dissertation contributes to the discussion of university-society collaboration by the new learning configurations, and to the interdisciplinary education of knowledge workers. The results of this dissertation can be utilised in the development of studio-based configurations in higher education. / Tiivistelmä Tiedonvälittämisen nopeus, epävarmuus ja monimutkaisuus lisääntyvät tietotyöläisten työssä. Lisäksi yleismaailmallisten ja monimutkaisten ongelmien ratkaisemisen vaatima monialainen yhteistyö, sekä yhdessä oppiminen edellyttävät taitoja erilaisten rajojen ylittämiseen. Nämä vaatimukset asettavat uusia haasteita tietotyöläisten korkeakoulutukselle. Metataidot, kuten vuorovaikutustaidot, verkostojen avulla oppiminen ja kriittinen ajattelu, ovat tulleet yhtä tärkeiksi kuin alakohtaiset taidot. Metataidot yhdistettyinä alakohtaisiin taitoihin muodostavat niin kutsutut T-malliset taidot. T-mallisia taitoja omaavat ammattilaiset ovat altistuneet muiden alojen ammattilaisten kokemuksille ja tietotaidolle, ja siten omaavat taitoja rajojen ylittämiseen monialaisissa työryhmissä. Tämä väitöskirja pyrkii vastaamaan kuinka suomalaisessa korkeakoulussa kehitetty, studiomallinen ja monialainen tietotyöläisten koulutusmalli, LAB-malli, vastaa rajojen ylittämisen taitojen kouluttamisen haasteeseen. Tutkimus toteuttaa laadullista tutkimusstrategiaa käyttäen eksploratiivista ja kehittämistutkimuksen lähestymistapaa tutkimusprosessissaan. Alkuperäiset julkaisut keskittyvät studiomallin hyödyntämisen yleisyyteen korkeakoulutuksessa maailmanlaajuisesti, LAB-mallin ominaisuuksiin studiomallina ja opiskelijoiden rajojen ylittämiseen monialaisen koulutuksen aikana. Ensimmäinen julkaisu keskittyy LAB-mallin ominaisuuksien analyysiin ja toinen studiomallin hyödyntämisen selvittämiseen kirjallisuuskatsauksien avulla. Kolmas julkaisu keskittyy rajojen ylittämiseen koulutuksen sisällä uuden tiedon tuottamisen teorian kautta ja neljäs koulutuksen ulkopuolisten rajojen ylittämiseen oppimisverkostojen muodostamisen kautta. Tutkimus tehtiin keräämällä tietoa kyselyillä, teemapohjaisilla opiskelija- ja tiimihaastatteluilla, sekä suoralla, että osallistuvalla tarkkailemisella. Tämä väitöskirja osoittaa, että LAB-malli tarjoaa koulutusmallin rajojen ylittämisen oppimiseen ja siten T-mallisten taitojen oppimiseen. Tulokset osoittavat, että studiomallin hyödyntäminen on lisääntynyt korkeakoulutuksessa, LAB-malli on omaleimainen verrattuna muihin studiomallia noudattaviin korkeakoulutuksiin ja että koulutuksen aikana opiskelijat ylittävät rajoja aktiivisesti. Tämä väitöskirja osallistuu keskusteluun korkeakoulujen yhteiskunnallisesta yhteistyöstä, sekä monialaisen ja studiomallisen oppimisen mahdollisuuksista tietotyöläisten kouluttamisessa. Tämän väitöskirjan tuloksia voidaan hyödyntää edelleen kehitettäessä studiomallisia korkeakoulujen oppimisympäristöjä.

The author deals with the phenomenon of dumpster diving. Being focused on those divers who are used to dumpster dive not being pressed to it by their financial situation, she concentrates on their definition of purity and their way of dealing with symbolic boundaries of clean and unclean. After summarising social-environmental and social scientific background of the phenomenon in context of the theoretical frame based on Mary Douglas and her book about purity and danger the author presents a qualitative analysis of participant observation and in- depth interviews with informants who dumpster dive voluntarily. Based on quantitatively and representatively tested public opinion on dumpster diving she points both the colourful composition of dumpster divers' motives and ideological believes and their reflection and norm- based boundaries categorization that is connected to food they are used to eat. In connection with informants' conception of food value the author argues that through inspiring power of the first dumpster diving experience informants' understanding and dealing with those boundaries have changed. Nevertheless, she stresses that despite being convinced their way of consumption is right and thus pure the informants tend to apply and present themselves by pattern of conduct that...

Radio tomographic imaging (RTI) is a novel device-free localization technique which utilizes the changes in radio signals caused by obstruction to enable various sensing applications. However, the deployment of these applications is hindered by the energy-expensive radio sensing techniques employed in these systems. In this thesis, we tackle this issue by introducing a novel way to realize a battery-free RTI sensor. We go through the design process and produce and evaluate a working prototype that operates on minuscule amounts of energy. Our design reduces power consumption by orders of magnitude compared to traditional RTI sensors by eliminating the energy-expensive components used in current RTI systems, enabling battery-free operation of RTI sensors. We demonstrate the efficiency and accuracy of our system in a boundary crossing scenario. We Discuss its limitations and tackle some of the security threats correlated with the deployment of such a system. / Radiotomografisk avbildning (RTA) är en ny, anordningsfri lokaliseringstekniksom utnyttjar förändringarna i radiosignaler orsakat av obstruktioner för att möjliggöraolika avkänningsapplikationer. Utvecklingen av dessa applikationer hindrasemellertid av de energiineffektiva radioavkännande tekniker som användsi dessa system. I denna avhandling behandlar vi problemet genom att introduceraen ny metod för att skapa en batterifri RTA-sensor. Vi går igenom konstruktionsprocessenoch producerar och utvärderar en arbetsprototyp som kräver minusklermängder energi. Vår design minskar energiförbrukningen signifikantjämfört med traditionella RTA-sensorer, genom att eliminera de energiineffektivakomponenterna som används i dagens RTA-system, vilket möjliggör batterifridrift av RTA-sensorer. Vi demonstrerar effektiviteten och noggrannheten hos vårtsystem i ett gränsöverskridande scenario. Vi diskuterar begränsningarna och taritu med några av de säkerhetshot som är korrelerade med utplaceringen av ettsådant system.

This dissertation is cumulative and encompasses three self-contained research articles. These essays share one common theme: the probability that a given stochastic process crosses a certain boundary function, namely the boundary crossing probability, and the related financial and statistical applications. In the first paper, we propose a new Monte Carlo method to price a type of barrier option called the Parisian option by simulating the first and last hitting time of the barrier. This research work aims at filling the gap in the literature on pricing of Parisian options with general curved boundaries while providing accurate results compared to the other Monte Carlo techniques available in the literature. Some numerical examples are presented for illustration. The second paper proposes a Monte Carlo method for analyzing the sensitivity of boundary crossing probabilities of the Brownian motion to small changes of the boundary. Only for few boundaries the sensitivities can be computed in closed form. We propose an efficient Monte Carlo procedure for general boundaries and provide upper bounds for the bias and the simulation error. The third paper focuses on the inverse first-passage-times. The inverse first-passage-time problem deals with finding the boundary given the distribution of hitting times. Instead of a known distribution, we are given a sample of first hitting times and we propose and analyze estimators of the boundary. Firstly, we consider the empirical estimator and prove that it is strongly consistent and derive (an upper bound of) its asymptotic convergence rate. Secondly, we provide a Bayes estimator based on an approximate likelihood function. Monte Carlo experiments suggest that the empirical estimator is simple, computationally manageable and outperforms the alternative procedure considered in this paper.

<p> The limited numbers of women in advanced mathematics courses is a critical factor hindering women’s academic and professional access to science, technology, engineering, and mathematics (STEM) fields. Informal learning environments have the potential to play a significant role in promoting the participation of girls and women in mathematics/STEM fields. However, research that addresses the intersection of informal education, mathematics education, and women’s studies is minimal. Specifically, little is known about informal educators’ lived experiences in facilitating girls’ learning. Based on four years of working alongside Laura, the founder of Girls Excelling in Math and Science (GEMS) clubs, I conducted a narrative inquiry that explored our boundary crossing experiences as we engaged in a GEMS collaboration. The exploration focused on Laura’s narratives of her past, present, and future experiences that shape her identity as an informal educator. During the exploration of Laura’s experiences, I reflected on and inquired about my own personal and professional experiences across multiple contexts that inform my evolving identity as an educator. The theoretical framework of this study is informed by feminist theory and boundary-crossing perspectives. Feminist theory guides me to perceive our narrative of experiences from a women’s perspective while the boundary-crossing framework provides an analytic lens to understand our interpersonal and intrapersonal boundary crossing experiences. Because of the nature of the narrative inquiry, data were co-constructed between Laura and me in various forms: interviews, field notes, family stories, autobiographical writing, documents, conversations, emails, etc. I employed Polkinghorne’s (1995) <em>narrative analysis </em>and <em>analysis of narrative</em> approaches to analyze data. First, I utilized a <em>narrative analysis </em>approach to generate three holistic plots: (1) narratives of becoming female educators, (2) boundary-crossing collaboration in the midst of GEMS, and (3) conceptualizing mathematics across multiple contexts. An<em> analysis of narrative</em> approach was used to generate themes that unfold the meanings of stories, moments, and events and configure the plot. In the findings, I portrayed the three plots which allowed me to rediscover and reconstruct our personal practical knowledge across the contexts. Building on the findings, I discuss how female educators’ narratives of experiences inform their personal practical knowledge, which empowers girls’ and women’s personal and social experiences in mathematics/STEM. Laura and I cross multiple boundaries engaging in collaboration which provides an example of the boundary crossing collaboration between mathematics education and informal education. Based on the findings, I describe how informal learning STEM environments provide potential spaces to implement alternative curricula to humanize mathematics. Two evolving mathematics-related tasks illustrate our experiences of humanizing mathematics in GEMS. This study is situated at the intersection of mathematics education, informal education, and women’s studies, which significantly impacted Laura, myself, and GEMS, the context in which this study took place. This study provides an example of the possibilities of building boundary-crossing collaborations between the mathematics education community and the informal education community to empower girls and women in mathematics/STEM. Drawing on this dissertation study, one future research direction focuses on implementing and further developing humanized mathematics curricula in informal learning environments. Another research direction is using intersectional feminist theory to understand women’s differences regarding multiple social constructs (e.g., race, gender, class, ethnicity) to explicate the dimensions of inequality women face in mathematics/STEM. The study also suggests future practical work for mathematics education to foster alternative ways of conceptualizing mathematics regarding curriculum and approach. Mathematics educators could contribute to creating a learning community and providing professional development opportunities to support informal educators. </p>

The purpose of this study was to evaluate a programme aimed at equipping adult mine workers in the North-West Province in computer-based skills. The study describes how the use of computers for learning has transformed some of the mine workers in an Own-Time learning environment, where computers were integrated in their learning activities, compared to the Full-Time adult learning environment, which did not present a similar opportunity. The perspective of using a combination of two teaching methodologies in the Adult Education and Training (AET) curriculum provided at this mine sought to minimise the conventional didactic instructional approaches, whereby the facilitator does most of the talking while learners become passive listeners. Activity theory (AT), in tandem with the reviewed literature, was well suited as a theoretical framework for this study, since it takes a developmental view of minds and technological interaction in context. The activity system was used to map how existing work-related practices fitted into each component, which includes the subject, object, rule, community and division of labour. A case study was applied as a guiding design in the study in which seventeen mine workers participated. The computer activity was illustrated from multiple perspectives, using a qualitative approach and associated epistemologies and beliefs regarding the engagement with mediational tools. Boundary crossings, the zone of proximal development, and the eight-step-model from activity theory were used to scrutinise the learners’ beliefs, attitudes, knowledge, practices and contradictions. These important aspects assisted in obtaining data through participant observation, interviews and field notes. To discover patterns, concepts, themes and meanings from the notes and transcripts, data analysis was blended with these aspects. This study demonstrated the use of the above-mentioned methods at appropriate times. Without ideal and effective research methods, the quality of evidence of this study would have suffered and elucidations of connections would have been inadequate. The findings revealed that the AET programme made an impact on the company and on the individual participants, in their homes, their place of work, and their communities. Change in the workers’ performance after attending AET computer-based programmes was noticeable especially regarding their literate and numerate knowledge and skills. Contradictions and disturbances in the AET programme were also identified, and an intervention was proposed to facilitate a computer programme that includes the curriculum components such as mouse skills, keyboarding, data manipulation and desktop publishing. The study proposes that the AET policy needs to cover Own-Time learners, even though their learning is not obligatory, in the same way as it covers the Full-Time learners. A modified activity theory, contextualised for a situation such as that in the mine in question, was contributed in the study. Furthermore, some limitations and recommendations for future research were identified from the findings. The proposed AT for adult learners suggests a new way of exploring the practices of mind and technology interaction for adult learners, incorporating cultural backgrounds, age, language, values and beliefs as well as reflective decision making. / Science and Technology Education / D. Ed. (Comparative Education)

Syfte – Studien syftade till att undersöka den interna interaktionen i en liten, tillverkande ETO-verksamhets kundorderprocess samt hur boundary object underlättar dess gränsöverskridande interaktion. För att uppfylla studiens syfte kommer följande frågeställningar att besvaras: Vad kännetecknar den gränsöverskridande interaktionen i en liten, tillverkande ETO-verksamhets kundorderprocess? Hur kan boundary object underlätta den gränsöverskridande interaktionen i en liten, tillverkande ETO-verksamhet? Metod – För att uppfylla studiens syfte har en fallstudie genomförts hos Premould AB. Via intervjuer och dokumentstudier har deras kundorderprocess undersökts och interaktionsobjekt i processen identifierats. Insamlad data låg sedan till grund för hur det teoretiska ramverket upprättades. Med hjälp av den empiriska insamlingen och det teoretiska ramverket har en analys genomförts som i sin tur genererat studiens resultat. Resultat – Genom att undersöka kundorderprocessen, i en ETO-verksamhet, har olika kännetecken för den gränsöverskridande interaktionen kunnat urskiljas. Interaktionsobjekt, som belyses som boundary object, har identifierats i processen. Boundary object kan underlätta den interna interaktionen om de används utefter den nivå av komplexitet av kunskapsridning som finns i gränssnitten mellan funktioner. Implikationer – Resultatet att boundary object underlättar den gränsöverskridande interaktionen ger ett praktiskt bidrag till små, tillverkande ETO-verksamheter. Genom valet av boundary object ska det gå att förenkla kunskapsspridning och genom det effektivisera arbetsprocesser. Det ges även ett teoretiskt bidrag till vidare forskning om boundary object i ETO-kontexter. Begränsningar – En av begränsningarna i studien är att det kan vara svårt att generalisera utifrån resultatet eftersom studien var av enfallsdesign. Gränsöverskridande interaktion är dessutom komplext att undersöka med strukturella metoder och det saknades därför möjlighet att djupt undersöka de identifierade interaktionsobjekten. Nyckelord – Engineer to order (ETO), gränsöverskridande interaktion, kunskapsgränser, kunskapsspridning, boundary object. / Purpose – The purpose of the study was to investigate the internal interaction of a small, manufacturing ETO-business's customer order process, as well as how boundary objects facilitate its boundary-crossing interaction. In order to fulfill the purpose of the study the following questions will be answered: What characterizes boundary-crossing interaction in a small, manufacturing ETO-business's customer ordering process? How can boundary objects facilitate boundary-crossing interaction in a small, manufacturing ETO-business? Method – To fulfil the purpose of the study, a case study has been conducted at Premould AB. Through interviews and document studies, their customer order process has been investigated and interaction objects in the process been identified. The collected data then formed a base for the establishment of the theoretical framework. With the empirical collection and the theoretical framework, an analysis has been conducted which, in turn, generated the results of the study. Findings – By examining the customer ordering process, in an ETO-business, different characteristics of boundary-crossing interaction has been identified. Interaction objects, which are used according to the principles of boundary objects, have been identified in the process. Boundary objects can facilitate internal interaction if used at the proper level of complexity of knowledge sharing found in the interfaces. Implications – The result that boundary objects facilitate boundary-crossing interaction provides a practical contribution to small, manufacturing ETO-business. Through the choice of boundary object used, it is possible to simplify knowledge sharing and make more effective work processes. There is also a theoretical contribution to further research on boundary objects in ETO-contexts. Limitations – One of the limitations of the study is that it can be difficult to generalize from the result, due to the use of a single-case design. Moreover, boundary-crossing interaction is complex to investigate with structural methods, and it was therefore difficult to closely investigate the identified objects. Keywords – Engineer to order (ETO), boundary-crossing interaction, knowledge boundaries, boundary object.