Gröbnerbasen in Ore-Algebren

In dieser Arbeit werden grundlegende Algorithmen für Ore-Algebren in Mathematica realisiert. Dabei entsteht eine Plattform um die speziellen Beschränkungen und Möglichkeiten dieser Algebren insbesondere im Zusammenhang mit Gröbnerbasen an praktischen Beispielen auszuloten. Im Gegensatz zu den existierenden Paketen wird dabei explizit die Struktur der Ore-Algebra benutzt. Kandri-Rody und Weispfenning untersuchten 1990 Verallgemeinerungen von Gröbnerbasen auf Algebren ordnungserhaltender Art (``algebras of solvable type''). Diese verhalten sich so, dass Buchbergers Algorithmus stets eine Gröbnerbasis findet. Es wird ein Beispiel gezeigt, an dem klar wird, dass es mehr Ore-Algebren ordnungserhaltender Art gibt als die in der Literatur stets betrachteten Operator-Algebren. Für Ore-Algebren ordnungserhaltender Art werden Algorithmen zu Gröbnerbasen implementiert. Anschließend wird der Gröbner-Walk für Ore-Algebren untersucht. Der Gröbner-Walk im kommutativen Fall wird mit einem instruktiven Beispiel vorgestellt. Dann wird zum nichtkommutativen Fall übergegangen. Es wird gezeigt, dass die Eigenschaft ordnungserhaltender Art zu sein, auf der Strecke zwischen zwei Ordnungen erhalten bleibt. Eine leichte Modifikation des Walks für Ore-Algebren wird implementiert, die im Erfolgsfall die Basis konvertiert und ansonsten abbricht. Es werden Beispiele angegeben, in denen der modifizierte Walk funktioniert sowie ein Beispiel analysiert, in dem er versagt.

Biohöfe als Ausgangspunkte informeller Lernprozesse

Die Arbeit befasst sich mit der Frage nach dem Einfluss von Biohöfen auf die Menschen, die in ihrem Umfeld leben. Sie bietet Einblicke in die Zusammenhänge, in denen Nachbarn, Kollegen, Freunde oder Kunden einen Biohof gezielt oder eher zufällig nutzen, um hier informell Erfahrungen zu sammeln, die zu nachhaltigen Lebennstilen und Wirtschaftsweisen beitragen können. Im Rahmen von sechs Fallstudien wurden hierfür ökologisch wirtschaftende Landwirtschaftsbetriebe in Brandenburg im Hinblick auf die informelle Vermittlung von Wissen und Erfahrungen qualitativ untersucht. Mit Hilfe der Grounded Theory wird die Entstehung von informellen Lernprozessen im sozialen Umfeld der Höfe rekonstruiert. Neben dem empirischen Ausgangsmaterial erwiesen sich die handlungstheoretischen Konstrukte Lebenswelt, Habitus, Lebensstil und Lebensführung als hilfreicher Interpretationshintergrund. Mit diesen theoretischen Ansätzen werden die soziokulturellen Einflussfaktoren für Erfahren, Lernen und Vermitteln betont. Informelles Lernen wird so als ein sozial eingebetteter Prozess verstanden. Aus dieser, weniger subjektorientierten Perspektive treten dann Faktoren wie z.B. die Atmosphäre der Beziehung zwischen einer Person und dem Biohof, die sinnliche Wahrnehmung und die Art der Kommunikation in das Blickfeld der Analyse. In der Untersuchung wird eine Vielzahl von Verhaltensänderungen, Denkanstößen und Anregungen benannt, die im Zusammenhang mit den untersuchten Biohöfen geschildert wurden und die im Hinblick auf eine nachhaltige Entwicklung als förderlich eingeschätzt werden. Sie basieren, so der Ansatz der Arbeit, auf informellen Lernprozessen. Das zentrale Ergebnis der Fallanalysen ist eine strukturierte Zusammenstellung der im Untersuchungskontext relevanten Einflussfaktoren für erfolgreiches informelles Lernen. Als wesentliche erscheinen hierbei insbesondere zwei Variablen: zum einen hat sich das „wohlwollende Interesse“ als förderlich für das Zustandekommen und den Verlauf von informellen Lernprozessen herausgestellt. Mit diesem Begriff wird eine Einstellung dem Biohof gegenüber beschrieben, die ein Wohlgesonnensein, das Vertrauen und die Neugierde am Hof beinhaltet. Zum anderen scheint die „Erlebbarkeit“ der Angebote zur Wissensvermittlung für das informelle, habitus- und lebensstilbezogene Lernen bedeutsam zu sein. Ergänzend zu dem auf die lernenden Subjekte gerichteten Fokus wurden in der Forschungsarbeit auch Beweggründe der Betriebsleiter, für die jeweils praktizierte Wissens- und Erfahrungsvermittlung herausgearbeitet. Die Betrachtung wird durch die Zusammenstellung von Schwierigkeiten und Hindernissen abgerundet, die dem informellen Lernen vom Biohof entgegen stehen können. Ausgehend von den fallbezogenen Ergebnissen liefert die Arbeit damit eine Grundlage, um über die Bedeutung von Lernfeldern, die durch Biolandwirte, aber auch andere Akteursgruppen bereit gestellt werden, nachzudenken und um ihre gesellschaftliche Relevanz zu diskutieren.

Knowledge Building in Landscape Architecture

The objective of this study was to develop an internet-based seminar framework applicable for landscape architecture education. This process was accompanied by various aims. The basic expectation was to keep the main characteristics of landscape architecture education also in the online format. On top of that, four further objectives were anticipated: (1) training of competences for virtual team work, (2) fostering intercultural competence, (3) creation of equal opportunities for education through internet-based open access and (4) synergy effects and learning processes across institutional boundaries. This work started with the hypothesis that these four expected advantages would compensate for additional organisational efforts caused by the online delivery of the seminars and thus lead to a sustainable integration of this new learning mode into landscape architecture curricula. This rationale was followed by a presentation of four areas of knowledge to which the seminar development was directly related (1) landscape architecture as a subject and its pedagogy, (2) general learning theories, (3) developments in the ICT sector and (4) wider societal driving forces such as global citizenship and the increase of open educational resources. The research design took the shape of a pedagogical action research cycle. This approach was constructive: The author herself is teaching international landscape architecture students so that the model could directly be applied in practice. Seven online seminars were implemented in the period from 2008 to 2013 and this experience represents the core of this study. The seminars were conducted with varying themes while its pedagogy, organisation and the technological tools remained widely identical. The research design is further based on three levels of observation: (1) the seminar design on the basis of theory and methods from the learning sciences, in particular educational constructivism, (2) the seminar evaluation and (3) the evaluation of the seminars’ long term impact. The seminar model itself basically consists of four elements: (1) the taxonomy of learning objectives, (2) ICT tools and their application and pedagogy, (3) process models and (4) the case study framework. The seminar framework was followed by the presentation of the evaluation findings. The major findings of this study can be summed up as follows: Implementing online seminars across educational and national boundaries was possible both in term of organisation and technology. In particular, a high level of cultural diversity among the seminar participants has definitively been achieved. However, there were also obvious obstacles. These were primarily competing study commitments and incompatible schedules among the students attending from different academic programmes, partly even in different time zones. Both factors had negative impact on the individual and working group performances. With respect to the technical framework it can be concluded that the majority of the participants were able to use the tools either directly without any problem or after overcoming some smaller problems. Also the seminar wiki was intensively used for completing the seminar assignments. However, too less truly collaborative text production was observed which could be improved by changing the requirements for the collaborative task. Two different process models have been applied for guiding the collaboration of the small groups and both were in general successful. However, it needs to be said that even if the students were able to follow the collaborative task and to co-construct and compare case studies, most of them were not able to synthesize the knowledge they had compiled. This means that the area of consideration often remained on the level of the case and further reflections, generalisations and critique were largely missing. This shows that the seminar model needs to find better ways for triggering knowledge building and critical reflection. It was also suggested to have a more differentiated group building strategy in future seminars. A comparison of pre- and post seminar concept maps showed that an increase of factual and conceptual knowledge on the individual level was widely recognizable. Also the evaluation of the case studies (the major seminar output) revealed that the students have undergone developments of both the factual and the conceptual knowledge domain. Also their self-assessment with respect to individual learning development showed that the highest consensus was achieved in the field of subject-specific knowledge. The participants were much more doubtful with regard to the progress of generic competences such as analysis, communication and organisation. However, 50% of the participants confirmed that they perceived individual development on all competence areas the survey had asked for. Have the additional four targets been met? Concerning the competences for working in a virtual team it can be concluded that the vast majority was able to use the internet-based tools and to work with them in a target-oriented way. However, there were obvious differences regarding the intensity and activity of participation, both because of external and personal factors. A very positive aspect is the achievement of a high cultural diversity supporting the participants’ intercultural competence. Learning from group members was obviously a success factor for the working groups. Regarding the possibilities for better accessibility of educational opportunities it became clear that a significant number of participants were not able to go abroad during their studies because of financial or personal reasons. They confirmed that the online seminar was to some extent a compensation for not having been abroad for studying. Inter-institutional learning and synergy was achieved in so far that many teachers from different countries contributed with individual lectures. However, those teachers hardly ever followed more than one session. Therefore, the learning effect remained largely within the seminar learning group. Looking back at the research design it can be said that the pedagogical action research cycle was an appropriate and valuable approach allowing for strong interaction between theory and practice. However, some more external evaluation from peers in particular regarding the participants’ products would have been valuable.

Bridging Perspectives

People’s ability to change their social and economic circumstances may be constrained by various forms of social, cultural and political domination. Thus to consider a social actor’s particular lifeworld in which the research is embedded assists in the understanding of how and why different trajectories of change occur or are hindered and how those changes fundamentally affect livelihood opportunities and constraints. In seeking to fulfill this condition this thesis adopted an actor-oriented approach to the study of rural livelihoods. A comprehensive livelihoods study requires grasping how social reality is being historically constituted. That means to understand how the interaction of modes of production and symbolical reproduction produces the socio-space. Research is here integrated to action through the facilitation of farmer groups. The overall aim of the groups was to prompt agency, as essential conditions to build more resilient livelihoods. The smallholder farmers in the Mabalane District of Mozambique are located in a remote semi-arid area. Their livelihoods customarily depend at least as much on livestock as on (mostly) rain-fed food crops. Increased climate variability exerts pressure on the already vulnerable production system. An extensive 10-month duration of participant observation divided into 3 periods of fieldwork structured the situated multi-method approach that drew on a set of interview categories. The actor-oriented appraisal of livelihoods worked in building a mutually shared definition of the situation. This reflection process was taken up by the facilitation of the farmer groups, one in Mabomo and one in Mungazi, which used an inquiry iteratively combining individual interviews and facilitated group meetings. Integration of action and reflection was fundamental for group constitution as spaces for communicative action. They needed to be self-organized and to achieve understanding intersubjectively, as well as to base action on cooperation and coordination. Results from this approach focus on how learning as collaboratively generated was enabled, or at times hindered, in (a) selecting meaningful options to test; (b) in developing mechanisms for group functioning; and (c) in learning from steering the testing of options. The study of livelihoods looked at how the different assets composing livelihoods are intertwined and how the increased severity of dry spells is contributing to escalated food insecurity. The reorganization of the social space, as households moved from scattered homesteads to form settlements, further exerts pressure on the already scarce natural resource-based livelihoods. Moreover, this process disrupted a normative base substantiating the way that the use of resources is governed. Hence, actual livelihood strategies and response mechanisms turn to diversification through income-generating activities that further increase pressure on the resource-base in a rather unsustainable way. These response mechanisms are, for example, the increase in small-livestock keeping, which has easier conversion to cash, and charcoal production. The latter results in ever more precarious living and working conditions. In the majority of the cases such responses are short-term and reduce future opportunities in a downward spiral of continuously decreasing assets. Thus, by indicating the failure of institutions in the mediation of smallholders’ adaptive capabilities, the livelihood assessment in Mabomo and Mungazi sheds light on the complex underlying structure of present day social vulnerability, linking the macro-context to the actual situation. To assist in breaking this state of “subordination”, shaped by historical processes, weak institutions and food insecurity, the chosen approach to facilitation of farmer groups puts farmer knowledge at the center of an evolving process of intersubjective co-construction of knowledge towards emancipation.

Learning analysis by reduction from positive data

Analysis by reduction is a linguistically motivated method for checking correctness of a sentence. It can be modelled by restarting automata. In this paper we propose a method for learning restarting automata which are strictly locally testable (SLT-R-automata). The method is based on the concept of identification in the limit from positive examples only. Also we characterize the class of languages accepted by SLT-R-automata with respect to the Chomsky hierarchy.