ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Graph properties of biological interaction networks

This thesis considers two modelling frameworks for interaction networks in biology. The first models the interacting species qualitatively as discrete variables, with the regulatory graphs expressing their mutual influence. Circuits in the regulatory structure are known to be indicative of some asymptotic behaviours. We investigate the relationship between local negative circuits and sustained oscillations, presenting new examples of Boolean networks without local negative circuits and admitting a cyclic attractor. We then show how regulatory properties of Boolean networks can be investigated via satisfiability problems, and use the technique to examine the role of local negative circuits in networks of small dimension. To enable the application of Boolean techniques to the study of multivalued networks, a mapping of discrete networks to Boolean can be considered. The Boolean version, however, is defined only on a subset of the Boolean states. We propose a method for extending the Boolean version that preserves both the attractors and the regulatory structure of the network. Chemical reaction network theory models the dynamics of species concentrations via systems of ordinary differential equations, establishing connections between the network structure and the dynamics. Some results assume mass action kinetics, whereas biochemical models often adopt other rate forms. We propose algorithms for elimination of intermediate species, that can be used to find whether a mass action network simplifies to a given chemical system. We then consider the problem of identification of generalised mass action networks that give rise to a given mass action dynamics, while displaying useful structural properties, such as weak reversibility. In particular, we investigate systems obtained by preserving the reaction vectors of the mass action network, and outline a new algorithmic approach

Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984

There is an increasing awareness of the important and persuasive role that instability and random, chaotic motion play in the dynamics of macrosystems. Further research in the field should aim at providing useful tools, and therefore the motivation should come from important questions arising in specific macrosystems. Such systems include biochemical networks, genetic mechanisms, biological communities, neutral networks, cognitive processes and economic structures. This list may seem heterogeneous, but there are similarities between evolution in the different fields. It is not surprising that mathematical methods devised in one field can also be used to describe the dynamics of another. IIASA is attempting to make progress in this direction. With this aim in view this workshop was held at Laxenburg over the period 3-7 September 1984. These Proceedings cover a broad canvas, ranging from specific biological and economic problems to general aspects of dynamical systems and evolutionary theory

Studies related to the process of program development

The submitted work consists of a collection of publications arising from research carried out at Rhodes University (1970-1980) and at Heriot-Watt University (1980-1992). The theme of this research is the process of program development, i.e. the process of creating a computer program to solve some particular problem. The papers presented cover a number of different topics which relate to this process, viz. (a) Programming methodology programming. (b) Properties of programming languages. aspects of structured. (c) Formal specification of programming languages. (d) Compiler techniques. (e) Declarative programming languages. (f) Program development aids. (g) Automatic program generation. (h) Databases. (i) Algorithms and applications