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.

A contextual-logic extension of TOSCANA

The aim of this paper is to indicate how TOSCANA may be extended to allow graphical representations not only of concept lattices but also of concept graphs in the sense of Contextual Logic. The contextual-logic extension of TOSCANA requires the logical scaling of conceptual and relatioal scales for which we propose the Peircean Algebraic Logic as reconstructed by R. W. Burch. As graphical representations we recommend, besides labelled line diagrams of concept lattices and Sowa's diagrams of conceptual graphs, particular information maps for utilizing background knowledge as much as possible. Our considerations are illustrated by a small information system about the domestic flights in Austria.

Conceptual information systems discussed through an IT-security tool

Conceptual Information Systems are based on a formalization of the concept of "concept" as it is discussed in traditional philosophical logic. This formalization supports a human-centered approach to the development of Information Systems. We discuss this approach by means of an implemented Conceptual Information System for supporting IT security management in companies and organizations.

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

Information needs for a purchase of fairtrade coffee

This research investigates what information German Fairtrade coffee consumers search for during pre-purchase information seeking and to what extent information is retrieved. Furthermore, the sequence of the information search as well as the degree of cognitive involvement is highlighted. The role of labeling, the importance of additional ethical information and its quality in terms of concreteness as well as the importance of product price and organic origin are addressed. A set of information relevant to Fairtrade consumers was tested by means of the Information Display Matrix (IDM) method with 389 Fairtrade consumers. Results show that prior to purchase, information on product packages plays an important role and is retrieved rather extensively, but search strategies that reduce the information processing effort are applied as well. Furthermore, general information is preferred over specific information. Results of two regression analyses indicate that purchase decisions are related to search behavior variables rather than to socio-demographic variables and purchase motives. In order to match product information with consumers’ needs, marketers should offer information that is reduced to the central aspects of Fairtrade.