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.

Nitrogen use efficiency and optimization of nitrogen fertilizer application for stable yields and high quality of cereals grown in conservation agriculture

In most agroecosystems, nitrogen (N) is the most important nutrient limiting plant growth. One management strategy that affects N cycling and N use efficiency (NUE) is conservation agriculture (CA), an agricultural system based on a combination of minimum tillage, crop residue retention and crop rotation. Available results on the optimization of NUE in CA are inconsistent and studies that cover all three components of CA are scarce. Presently, CA is promoted in the Yaqui Valley in Northern Mexico, the country´s major wheat-producing area in which from 1968 to 1995, fertilizer application rates for the cultivation of irrigated durum wheat (Triticum durum L.) at 6 t ha-1 increased from 80 to 250 kg ha-1, demonstrating the high intensification potential in this region. Given major knowledge gaps on N availability in CA this thesis summarizes the current knowledge of N management in CA and provides insights in the effects of tillage practice, residue management and crop rotation on wheat grain quality and N cycling. Major aims of the study were to identify N fertilizer application strategies that improve N use efficiency and reduce N immobilization in CA with the ultimate goal to stabilize cereal yields, maintain grain quality, minimize N losses into the environment and reduce farmers’ input costs. Soil physical and chemical properties in CA were measured and compared with those in conventional systems and permanent beds with residue burning focusing on their relationship to plant N uptake and N cycling in the soil and how they are affected by tillage and N fertilizer timing, method and doses. For N fertilizer management, we analyzed how placement, time and amount of N fertilizer influenced yield and quality parameters of durum and bread wheat in CA systems. Overall, grain quality parameters, in particular grain protein concentration decreased with zero-tillage and increasing amount of residues left on the field compared with conventional systems. The second part of the dissertation provides an overview of applied methodologies to measure NUE and its components. We evaluated the methodology of ion exchange resin cartridges under irrigated, intensive agricultural cropping systems on Vertisols to measure nitrate leaching losses which through drainage channels ultimately end up in the Sea of Cortez where they lead to algae blooming. A throughout analysis of N inputs and outputs was conducted to calculate N balances in three different tillage-straw systems. As fertilizer inputs are high, N balances were positive in all treatments indicating the risk of N leaching or volatilization during or in subsequent cropping seasons and during heavy rain fall in summer. Contrary to common belief, we did not find negative effects of residue burning on soil nutrient status, yield or N uptake. A labeled fertilizer experiment with urea 15N was implemented in micro-plots to measure N fertilizer recovery and the effects of residual fertilizer N in the soil from summer maize on the following winter crop wheat. Obtained N fertilizer recovery rates for maize grain were with an average of 11% very low for all treatments.