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.

Rural households’ social capital and welfare: A case study of Msinga, KwaZulu-Natal, South Africa

In a household or nations production system, social capital has been recognized as an input having major implications for project design as well as policy development. Using a structured questionnaire, household level data was obtained from a representative sample of 300 rural households in Msinga, KwaZulu-Natal. This study employed the conventional household economic behaviour model under constrained utility maximisation to examine the effect of social capital on the welfare of household, testing the hypothesis that the possession of social capital improves household welfare. The result shows that social capital endowments have a statistically significant positive effect on household welfare, in addition to the some household’s demographic and socio-economic characteristics. The study concluded that, access to social capital among other factors, is very crucial for improved rural household welfare and poverty reduction. It is therefore important for government to have knowledge of existing social groups and networks as this will improve the effectiveness of the present strategies aimed at reducing poverty.

Innovation, Creativity, and Positive Psychological Capital: Examining the Relationships in Adolescents, Employees and Entrepreneurs

Innovation ist für das Überleben von Firmen und die Entwicklung von Ländern wesentlich, weil sie entscheidend für einen erhöhten Marktanteil und wettbewerbsfähigen Vorsprung ist (Baer & Frese, 2003; Dodgson, Gann & Salter; George & Zhou, 2011; Kleysen & Street, 2001). Gleichzeitig steht Innovation in engem Zusammenhang mit Erkenntnisfortschritten (West & Altink, 1996). Konzepte, die mit Innovation zu tun haben, beinhalten innovatives Verhalten und Kreativität. Kreativität ist die Produktion von neuen und nützlichen Ideen (Amabile, 1998), und Innovation ist die Umsetzung dieser neuen und nützlichen Ideen (Amabile, 1998; West, 2002). Diese Dissertation besteht aus fünf Abhandlungen, die sich mit den beiden Bereichen des Managements und der positiven Psychologie beschäftigen. Im Einzelnen verbindet die Dissertation Forschungen aus dem Bereich der positiven Psychologie mit Forschungen der Innovation, wie auch der pädagogischen Psychologie, um Antworten auf Forschungsfragen zu finden, die sich damit beschäftigen, was es ist, das die Kreativität von Mitarbeitern, Unternehmern und Jugendlichen und ihr positives psychologisches Kapital steigert (PsyCap). Luthans und seine Kollegen (2007, S.3) definieren das psychologische Kapital oder PsyCap als „den positiven psychologischen Entwicklungszustand einer Einzelperson, welcher wie folgt beschrieben wird: (1) Selbstvertrauen haben (Selbstwirksamkeit), um sich Herausforderungen zu stellen und den notwendigen Aufwand aufzubringen; (2) Eine positive Attribution (Optimismus) in Bezug auf gegenwärtigen und zukünftigen Erfolg; (3) Ziele anstreben und, wenn notwendig, die Wege zu den Zielen ändern, um Erfolg zu erreichen (Hoffnung); (4) Im Falle von Problemen und Missgeschicken standhalten und wieder zurückkommen (Widerstandsfähigkeit), um Erfolg zu erreichen.“