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.

Influence of farmers educational level on comprehending, acting-upon and sharing of agro advisories

Although short messaging service (SMS) through mobile phones has quickly gained popularity among most other sectors in India, its potential is not fully realised in the agriculture sector as a cost effective service to reach farmers and elicit desirable action. Despite the cost effectiveness, mobile messaging has remained a challenge in the farming sector in terms of its end use and action as far as extension systems are concerned. While there could be many influencing factors affecting the utility of mobile messages, this study assumed that educational level of farmers could be a major factor. A telephone survey was conducted to ascertain the influence of farmers’ education on the level of utilisation of mobile-based advisories. Farmers with higher education level showed better comprehension of advisories, actedupon the advisories more promptly and shared the information with fellow farmers more often than those with lower education level. There was a significant association between comprehending, sharing and acting upon advisories. This has implications to achieve enhanced extension reach with higher efficiency in terms of cost and time.