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

A Process Modelling Framework Based on Point Interval Temporal Logic with an Application to Modelling Patient Flows

This thesis considers an application of a temporal theory to describe and model the patient journey in the hospital accident and emergency (A&E) department. The aim is to introduce a generic but dynamic method applied to any setting, including healthcare. Constructing a consistent process model can be instrumental in streamlining healthcare issues. Current process modelling techniques used in healthcare such as flowcharts, unified modelling language activity diagram (UML AD), and business process modelling notation (BPMN) are intuitive and imprecise. They cannot fully capture the complexities of the types of activities and the full extent of temporal constraints to an extent where one could reason about the flows. Formal approaches such as Petri have also been reviewed to investigate their applicability to the healthcare domain to model processes. Additionally, to schedule patient flows, current modelling standards do not offer any formal mechanism, so healthcare relies on critical path method (CPM) and program evaluation review technique (PERT), that also have limitations, i.e. finish-start barrier. It is imperative to specify the temporal constraints between the start and/or end of a process, e.g., the beginning of a process A precedes the start (or end) of a process B. However, these approaches failed to provide us with a mechanism for handling these temporal situations. If provided, a formal representation can assist in effective knowledge representation and quality enhancement concerning a process. Also, it would help in uncovering complexities of a system and assist in modelling it in a consistent way which is not possible with the existing modelling techniques. The above issues are addressed in this thesis by proposing a framework that would provide a knowledge base to model patient flows for accurate representation based on point interval temporal logic (PITL) that treats point and interval as primitives. These objects would constitute the knowledge base for the formal description of a system. With the aid of the inference mechanism of the temporal theory presented here, exhaustive temporal constraints derived from the proposed axiomatic system’ components serves as a knowledge base. The proposed methodological framework would adopt a model-theoretic approach in which a theory is developed and considered as a model while the corresponding instance is considered as its application. Using this approach would assist in identifying core components of the system and their precise operation representing a real-life domain deemed suitable to the process modelling issues specified in this thesis. Thus, I have evaluated the modelling standards for their most-used terminologies and constructs to identify their key components. It will also assist in the generalisation of the critical terms (of process modelling standards) based on their ontology. A set of generalised terms proposed would serve as an enumeration of the theory and subsume the core modelling elements of the process modelling standards. The catalogue presents a knowledge base for the business and healthcare domains, and its components are formally defined (semantics). Furthermore, a resolution theorem-proof is used to show the structural features of the theory (model) to establish it is sound and complete. After establishing that the theory is sound and complete, the next step is to provide the instantiation of the theory. This is achieved by mapping the core components of the theory to their corresponding instances. Additionally, a formal graphical tool termed as point graph (PG) is used to visualise the cases of the proposed axiomatic system. PG facilitates in modelling, and scheduling patient flows and enables analysing existing models for possible inaccuracies and inconsistencies supported by a reasoning mechanism based on PITL. Following that, a transformation is developed to map the core modelling components of the standards into the extended PG (PG*) based on the semantics presented by the axiomatic system. A real-life case (from the King’s College hospital accident and emergency (A&E) department’s trauma patient pathway) is considered to validate the framework. It is divided into three patient flows to depict the journey of a patient with significant trauma, arriving at A&E, undergoing a procedure and subsequently discharged. Their staff relied upon the UML-AD and BPMN to model the patient flows. An evaluation of their representation is presented to show the shortfalls of the modelling standards to model patient flows. The last step is to model these patient flows using the developed approach, which is supported by enhanced reasoning and scheduling

Sixth Workshop and Tutorial on Practical Use of Coloured Petri Nets and the CPN Tools Aarhus, Denmark, October 24-26, 2005

This booklet contains the proceedings of the Sixth Workshop on Practical Use of Coloured Petri Nets and the CPN Tools, October 24-26, 2005. The workshop is organised by the CPN group at the Department of Computer Science, University of Aarhus, Denmark. The papers are also available in electronic form via the web pages: http://www.daimi.au.dk/CPnets/workshop0

Petri Net Modeling of Outpatient Waiting Time for MRI Examination

In Canada, access to magnetic resonance imaging (MRI) examination is limited with an outcome of long patient waiting time. It is reported that the current median waiting time for MRI examination in Saskatoon is almost double the target for waiting time, which may aggravate the disease. This research is towards reducing the waiting time of patients for MRI examination in Canada by applying an improved management. As a first step of this effort, a comprehensive model of MRI booking and serving system is needed. The city of Saskatoon was taken as an example and the MRI booking and serving system in the city was studied. The common tools (queuing theory, system dynamics (SD) and discrete event dynamics simulation (DES)) were compared and it is found that DES is more suitable, in particular Petri nets (PNs), deemed to be the best choice for the purpose of this thesis. The model in this research was constructed on the basis of Hierarchical Coloured Petri nets (HCPNs), a combination of two extended PNs: Coloured PNs (CPNs) and Hierarchical PNs (HPNs). The model is able to simulate and predict patients' waiting times. Given that the structure of the model developed by HCPNs is still too complex, two extensions to CPNs, Ordered CPNs (OCPNs) and Prioritized HCPNs (PHCPNs), were proposed in this study to reduce the complexity of the model. Validation of the model was performed using the data of Saskatoon Health Region - Royal University Hospital. The results have shown that the proposed model can effectively describe the real system. The model has potential applications in decision-making for the selection of an optimal booking strategy to shorten waiting time and in the prediction of possible waiting time of the system in the future, which may assist MRI administrators in the management of medical resources and may greatly improve the quality of MRI service

A SysML profile for smart city applications

A smart city is an urban center that integrates a variety of solutions to enhance infrastructure performance and achieve sustainable urban development. Urban roads are a critical infrastructure highly demanded by citizens and organizations interested in their deployment, performance, and safety. Urban traffic signal control is a major and challenging problem in the real world, which aims to monitor and enhance traffic congestion. Therefore, the deployment of traffic signals for vehicles or pedestrians at a junction is a complex activity, as it is necessary to establish rules to control the flow of vehicles and pedestrians. Also, traffic flow at intersections changes constantly, depending on weather conditions, day of the week, and period of the year, as well as road works and accidents that further influence complexity and performance. This thesis first describes SmartCitySysML, a proposed profile that adapts SysML with special elements that are specific to smart cities. In addition, an extension of the SmartCitySysML profile to the design of the dimensions of smart cities is proposed. Finally, integration of models is performed, that is, the integration of the SmartCitySysML profile with Petri Net to separately model the basic architectural elements (sensor, controller, and actuator) of an urban traffic control system as sub-models to describe the behavior of each element, and the integration of the SmartCitySysML profile with Timed Coloured Petri Nets (TCPN) for modeling, simulation, and verification of properties of an urban traffic signal control system. CPN tools allow the evaluation of the model behavior through simulation and property verification and perform a simulation-based performance. Model simulation allows observing the behavior of the system under conditions that would be difficult to organize in a truly controlled environment. Consequently, a preliminary evaluation can be performed in the early stages of system development, significantly reducing costs of improvements and increasing quality of the final product.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESUma cidade inteligente é um centro urbano que integra uma variedade de soluções para melhorar o desempenho da infraestrutura e alcançar um desenvolvimento urbano sustentável. As estradas urbanas são uma infraestrutura crucial altamente exigida pelos cidadãos e organizações interessadas em sua implantação, desempenho e segurança. O controle de sinais de trânsito urbano é um problema importante e desafiador no mundo real, que visa monitorar e melhorar o congestionamento de trânsito. Portanto, a implantação de semáforos para veículos ou pedestres em um cruzamento é uma atividade complexa, pois é necessário estabelecer regras para controlar o fluxo de veículos e pedestres. O fluxo de tráfego no cruzamento muda constantemente, dependendo das condições climáticas, dia da semana e período do ano, assim como obras e acidentes rodoviários que influenciam ainda mais a complexidade e o desempenho. Esta dissertação descreve primeiro o SmartCitySysML, um perfil proposto que adapta a SysML com elementos especiais que são específicos para cidades inteligentes. Depois, é elaborada uma extensão do perfil SmartCitySysML para o design das dimensões das cidades inteligentes. Em seguida, é realizada a integração de modelos, ou seja, a integração do perfil SmartCitySysML com Redes de Petri para modelar separadamente os elementos arquiteturais básicos (sensor, controlador e atuador) de um sistema de controle de tráfego urbano como sub-modelos para demonstrar o comportamento de cada elemento, e a integração do perfil SmartCitySysML com Redes de Petri Colorida Temporizada (TCPN) para modelagem, simulação e verificação de propriedades do sistema de controle de sinais de trânsito urbano. As ferramentas CPN permitem avaliar o comportamento do modelo por meio de simulação e verificação de propriedades e realizar um desempenho baseado em simulação. A simulação de modelos permite observar o comportamento do sistema sob condições que seriam difíceis de organizar em um ambiente realmente controlado. Consequentemente, uma avaliação preliminar pode ser realizada nos estágios iniciais de desenvolvimento do sistema, reduzindo significativamente os custos de melhorias e aumentando a qualidade do produto final.São Cristóvão, S