Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Finding Spaces for Urban Food Production – Matching Spatial and Stakeholder Analysis with Urban Agriculture Approaches in the Urban Renewal Area of Dortmund-Hörde, Germany

Using the case of an economically declined neighbourhood in the post-industrial German Ruhr Area (sometimes characterized as Germany’s “Rust Belt”), we analyse, describe and conclude how urban agriculture can be used as a catalyst to stimulate and support urban renewal and regeneration, especially from a socio-cultural perspective. Using the methodological framework of participatory action research, and linking bottom-up and top-down planning approaches, a project path was developed to include the population affected and foster individual responsibility for their district, as well as to strengthen inhabitants and stakeholder groups in a permanent collective stewardship for the individual forms of urban agriculture developed and implemented. On a more abstract level, the research carried out can be characterized as a form of action research with an intended transgression of the boundaries between research, planning, design, and implementation. We conclude that by synchronously combining those four domains with intense feedback loops, synergies for the academic knowledge on the potential performance of urban agriculture in terms of sustainable development, as well as the benefits for the case-study area and the interests of individual urban gardeners can be achieved.