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

Hybrid performance modelling of opportunistic networks

We demonstrate the modelling of opportunistic networks using the process algebra stochastic HYPE. Network traffic is modelled as continuous flows, contact between nodes in the network is modelled stochastically, and instantaneous decisions are modelled as discrete events. Our model describes a network of stationary video sensors with a mobile ferry which collects data from the sensors and delivers it to the base station. We consider different mobility models and different buffer sizes for the ferries. This case study illustrates the flexibility and expressive power of stochastic HYPE. We also discuss the software that enables us to describe stochastic HYPE models and simulate them.Comment: In Proceedings QAPL 2012, arXiv:1207.055

Modeling by Petri Nets

One specific model of a digital system in different types of Petri nets is presented. The formal definitions of the basic (black-and-white) Petri net, a place/transition net (P/T net), an arc-constant coloured Petri net (ac-CPN) and a coloured Petri net (CPN) are presented and explained on the basis of this example. Real models of dining philosophers, a producer-consumer system and railway tracks are described

On functional module detection in metabolic networks

Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models

Translating synchronous Petri Nets into PROMELA for verifying behavioural properties

For developing embedded systems, the design process may benefit in some contexts from the usage of formal methods, namely to find critical errors and flaws, before final design and implementation decisions are taken. The Synchronous and Interpreted Petri Net (SIP-net) modelling language is considered in this article to model embedded systems. This model of computation is based on safe Petri nets with guarded transitions and synchronous transitions firing, and also includes enabling and inhibitor arcs. The Spin tool, whose input language is PROMELA, is a verification system based on model checking techniques. This article presents a program to translate SIP-net models into PROMELA code and discusses in detail the adequacy of the created PROMELA specification for verification through model checking techniques.Fundação para a Ciência e a Tecnologia (FCT) - bolsa SFRH/BD/19718/200

Computing Optimal Coverability Costs in Priced Timed Petri Nets

We consider timed Petri nets, i.e., unbounded Petri nets where each token carries a real-valued clock. Transition arcs are labeled with time intervals, which specify constraints on the ages of tokens. Our cost model assigns token storage costs per time unit to places, and firing costs to transitions. We study the cost to reach a given control-state. In general, a cost-optimal run may not exist. However, we show that the infimum of the costs is computable.Comment: 26 pages. Contribution to LICS 201

Modelling- and Simulation-Based Design of Multi-tier Systems

This paper introduces a domain-specific language for modelling andsimulation-based design of multi-tier systems.  Multi-tier systems are complexand very few general models have been developed. Rather, models are alwaysdedicated to a specific architecture. Our approach allows for rapidexperimentation with different multi-tier alternatives. Not only parameters,but also structure can be drastically varied.  Using graph transformation,multi-tier systems models are translated into Queueing Petri Nets (QPNs) in asystematic way for analysis with the SimQPN simulator.  We describe QPN, ourmulti-tier architecture visual language, as well as the transformation between them.  A case study demonstrates the power of the approach for design-space exploration

Designing, Building, and Modeling Maneuverable Applications within Shared Computing Resources

Extending the military principle of maneuver into war-fighting domain of cyberspace, academic and military researchers have produced many theoretical and strategic works, though few have focused on researching actual applications and systems that apply this principle. We present our research in designing, building and modeling maneuverable applications in order to gain the system advantages of resource provisioning, application optimization, and cybersecurity improvement. We have coined the phrase “Maneuverable Applications” to be defined as distributed and parallel application that take advantage of the modification, relocation, addition or removal of computing resources, giving the perception of movement. Our work with maneuverable applications has been within shared computing resources, such as the Clemson University Palmetto cluster, where multiple users share access and time to a collection of inter-networked computers and servers. In this dissertation, we describe our implementation and analytic modeling of environments and systems to maneuver computational nodes, network capabilities, and security enhancements for overcoming challenges to a cyberspace platform. Specifically we describe our work to create a system to provision a big data computational resource within academic environments. We also present a computing testbed built to allow researchers to study network optimizations of data centers. We discuss our Petri Net model of an adaptable system, which increases its cybersecurity posture in the face of varying levels of threat from malicious actors. Lastly, we present work and investigation into integrating these technologies into a prototype resource manager for maneuverable applications and validating our model using this implementation

Modelling- and Simulation-Based Design of Multi-tier Systems

This paper introduces a domain-specific language for modelling andsimulation-based design of multi-tier systems.  Multi-tier systems are complexand very few general models have been developed. Rather, models are alwaysdedicated to a specific architecture. Our approach allows for rapidexperimentation with different multi-tier alternatives. Not only parameters,but also structure can be drastically varied.  Using graph transformation,multi-tier systems models are translated into Queueing Petri Nets (QPNs) in asystematic way for analysis with the SimQPN simulator.  We describe QPN, ourmulti-tier architecture visual language, as well as the transformation between them.  A case study demonstrates the power of the approach for design-space exploration