Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

An introduction to Biomodel engineering, illustrated for signal transduction pathways

BioModel Engineering is the science of designing, constructing and analyzing computational models of biological systems. It is inspired by concepts from software engineering and computing science. This paper illustrates a major theme in BioModel Engineering, namely that identifying a quantitative model of a dynamic system means building the structure, finding an initial state, and parameter fitting. In our approach, the structure is obtained by piecewise construction of models from modular parts, the initial state is obtained by analysis of the structure and parameter fitting comprises determining the rate parameters of the kinetic equations. We illustrate this with an example in the area of intracellular signalling pathways

Some analyses of the chemistry and diffusion of SST exhaust materials during phase 3 of the wake period

In the generally stably stratified lower stratosphere, SST exhaust plumes could spend a significant length of time in a relatively undispersed state. This effort has utilized invariant modeling techniques to simulate the separate and combined effects of atmospheric turbulence, turbulent diffusion, and chemical reactions of SST exhaust materials in the lower stratosphere. The primary results to date are: (1) The combination of relatively slow diffusive mixing and rapid chemical reactions during the Phase III wake period minimizes the effect of SST exhausts on O3 depletion by the so-called NOx catalytic cycle. While the SST-produced NO is substantially above background concentrations, it appears diffusive mixing of NO and O3 is simply too slow to produce the O3 depletions originally proposed. (2) The time required to dilute the SST exhaust plume may be a significant fraction of the total time these materials are resident in the lower stratosphere. If this is the case, then prior estimates of the environmental impact of these materials must be revised significantly downward

Explaining anomalous responses to treatment in the Intensive Care Unit

The Intensive Care Unit (ICU) provides treatment to critically ill patients. When a patient does not respond as expected to such treatment it can be challenging for clinicians, especially junior clinicians, as they may not have the relevant experience to understand the patient’s anomalous response. Datasets for 10 patients from Glasgow Royal Infirmary’s ICU have been made available to us. We asked several ICU clinicians to review these datasets and to suggest sequences which include anomalous or unusual reactions to treatment. Further, we then asked two ICU clinicians if they agreed with their colleagues’ assessments, and if they did to provide possible explanations for these anomalous sequences. Subsequently we have developed a system which is able to replicate the clinicians’ explanations based on the knowledge contained in its several ontologies; further the system can suggest additional explanations which will be evaluated by the senior consultant

N=2 Topological Yang-Mills Theory on Compact K\"{a}hler Surfaces

We study a topological Yang-Mills theory with $N=2$ fermionic symmetry. Our formalism is a field theoretical interpretation of the Donaldson polynomial invariants on compact K\"{a}hler surfaces. We also study an analogous theory on compact oriented Riemann surfaces and briefly discuss a possible application of the Witten's non-Abelian localization formula to the problems in the case of compact K\"{a}hler surfaces.Comment: ESENAT-93-01 & YUMS-93-10, 34pages: [Final Version] to appear in Comm. Math. Phy

Persistent inflammation and impaired chemotaxis of alveolar macrophages on cessation of dust exposure.

Rats were exposed by inhalation to coal mine dust, titanium dioxide, or quartz. The magnitude of the consequent inflammatory response was assessed by counting numbers and types of leukocytes in the bronchoalveolar lavage fluid. The magnitude of the inflammatory response reflected the toxicity of the dusts, with quartz eliciting the greatest recruitment of inflammatory leukocytes, coal mine dust less than quartz, and titanium dioxide eliciting no inflammation. To assess the persistence of the inflammation, groups of rats were maintained in room air for 30 or 60 days after cessation of dust exposure and then numbers of leukocytes were assessed. Bronchoalveolar leukocytes in rats exposed to coal mine dust were reduced after exposure, but in the quartz-exposed rats the numbers increased with time after exposure. The chemotactic responses of bronchoalveolar leukocytes from rats inhaling coal mine dust and quartz were reduced and remained so after a 30-day recovery period. Their reduced ability to chemotact did not fully prevent macrophages from leaving the bronchoalveolar region of dust-exposed rats. However, it is likely that the delayed removal of inflammatory leukocytes with the potential to injure the lung tissue may contribute to septal damage and so contribute to the pathogenesis of pneumoconiosis

The ADHM Construction of Instantons on Noncommutative Spaces

We present an account of the ADHM construction of instantons on Euclidean space-time $\mathbb{R}^4$ from the point of view of noncommutative geometry. We recall the main ingredients of the classical construction in a coordinate algebra format, which we then deform using a cocycle twisting procedure to obtain a method for constructing families of instantons on noncommutative space-time, parameterised by solutions to an appropriate set of ADHM equations. We illustrate the noncommutative construction in two special cases: the Moyal-Groenewold plane $\mathbb{R}^4_\hbar$ and the Connes-Landi plane $\mathbb{R}^4_\theta$.Comment: Latex, 40 page

On complex surfaces diffeomorphic to rational surfaces

In this paper we prove that no complex surface of general type is diffeomorphic to a rational surface, thereby completing the smooth classification of rational surfaces and the proof of the Van de Ven conjecture on the smooth invariance of Kodaira dimension.Comment: 34 pages, AMS-Te

State space c-reductions for concurrent systems in rewriting logic

We present c-reductions, a state space reduction technique. The rough idea is to exploit some equivalence relation on states (possibly capturing system regularities) that preserves behavioral properties, and explore the induced quotient system. This is done by means of a canonizer function, which maps each state into a (non necessarily unique) canonical representative of its equivalence class. The approach exploits the expressiveness of rewriting logic and its realization in Maude to enjoy several advantages over similar approaches: exibility and simplicity in the definition of the reductions (supporting not only traditional symmetry reductions, but also name reuse and name abstraction); reasoning support for checking and proving correctness of the reductions; and automatization of the reduction infrastructure via Maude's meta-programming features. The approach has been validated over a set of representative case studies, exhibiting comparable results with respect to other tools