Economic modelling using constraint logic programming

This paper investigates the use of constraint logic programming (CLP) in economic modelling through the design and implementation of two economic models. The first model, the Desai- Henry model contains only linear equations while the second model, constructed by the author, contains non-linear elements. In order to implement the second model, a non-linear constraint solver was constructed. This was necessary because, although CLP is a very powerful programming paradigm, currently available implementations lack any on-linear constraint solving mechanisms

The algebra of rewriting for presentations of inverse monoids

We describe a formalism, using groupoids, for the study of rewriting for presentations of inverse monoids, that is based on the Squier complex construction for monoid presentations. We introduce the class of pseudoregular groupoids, an example of which now arises as the fundamental groupoid of our version of the Squier complex. A further key ingredient is the factorisation of the presentation map from a free inverse monoid as the composition of an idempotent pure map and an idempotent separating map. The relation module of a presentation is then defined as the abelianised kernel of this idempotent separating map. We then use the properties of idempotent separating maps to derive a free presentation of the relation module. The construction of its kernel - the module of identities - uses further facts about pseudoregular groupoids.Comment: 22 page

Grid-enabled SIMAP utility: Motivation, integration technology and performance results

A biological system comprises large numbers of functionally diverse and frequently multifunctional sets of elements that interact selectively and nonlinearly to produce coherent behaviours. Such a system can be anything from an intracellular biological process (such as a biochemical reaction cycle, gene regulatory network or signal transduction pathway) to a cell, tissue, entire organism, or even an ecological web. Biochemical systems are responsible for processing environmental signals, inducing the appropriate cellular responses and sequence of internal events. However, such systems are not fully or even poorly understood. Systems biology is a scientific field that is concerned with the systematic study of biological and biochemical systems in terms of complex interactions rather than their individual molecular components. At the core of systems biology is computational modelling (also called mathematical modelling), which is the process of constructing and simulating an abstract model of a biological system for subsequent analysis. This methodology can be used to test hypotheses via insilico experiments, providing predictions that can be tested by in-vitro and in-vivo studies. For example, the ERbB1-4 receptor tyrosine kinases (RTKs) and the signalling pathways they activate, govern most core cellular processes such as cell division, motility and survival (Citri and Yarden, 2006) and are strongly linked to cancer when they malfunction due to mutations etc. An ODE (ordinary differential equation)-based mass action ErbB model has been constructed and analysed by Chen et al. (2009) in order to depict what roles of each protein plays and ascertain to how sets of proteins coordinate with each other to perform distinct physiological functions. The model comprises 499 species (molecules), 201 parameters and 828 reactions. These in silico experiments can often be computationally very expensive, e.g. when multiple biochemical factors are being considered or a variety of complex networks are being simulated simultaneously. Due to the size and complexity of the models and the requirement to perform comprehensive experiments it is often necessary to use high-performance computing (HPC) to keep the experimental time within tractable bounds. Based on this as part of an EC funded cancer research project, we have developed the SIMAP Utility that allows the SImulation modeling of the MAP kinase pathway (http://www.simap-project.org). In this paper we present experiences with Grid-enabling SIMAP using Condor

Exons, introns and DNA thermodynamics

The genes of eukaryotes are characterized by protein coding fragments, the exons, interrupted by introns, i.e. stretches of DNA which do not carry any useful information for the protein synthesis. We have analyzed the melting behavior of randomly selected human cDNA sequences obtained from the genomic DNA by removing all introns. A clear correspondence is observed between exons and melting domains. This finding may provide new insights in the physical mechanisms underlying the evolution of genes.Comment: 4 pages, 8 figures - Final version as published. See also Phys. Rev. Focus 15, story 1

Groupoids and the algebra of rewriting in group presentations

Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a $2$--complex -- the Squier complex -- whose fundamental groupoid then describes the derivation of consequences of the rewrite rules. We describe a reduced form of the Squier complex, investigate the structure of its fundamental groupoid, and show that key properties of the presentation are still encoded in the reduced form.Comment: 15 page