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Decomposition of first-order hybrid Petri nets for hierarchical control of manufacturing systems
Abstract
Although hybrid Petri net (HPN) is a popular formalism in modelling hybrid production systems, the HPN model of large scale systems gets substantially complicated for analysis and control due to large dimensionality of such systems. To overcome this problem, a typical approach is to decompose the net into subnets and then control the plant through hierarchical or decentralized structures. Although this concept has been widely discussed in the literature for discrete PNs, there is a lack of research for HPNs. In this paper, a new method of decomposition of first-order hybrid Petri nets (FOHPNs) is proposed first and then the hierarchical control of the subnets through a coordinator is introduced. The advantage of using the proposed approach is validated by an existing example. A sugar milling case study is analysed by using a decomposed FOHPN model and the optimization results are compared against the results of the approaches presented in other papers. Simulation results show not only an improvement in production rate, but also show the ability to control the plant online. In addition, by using the hierarchical control structure for an FOHPN model, it is possible to reduce the cost of communication links, improve the reliability of the system, maintain the plant locally, and partially redesign the system.
... Many advanced Petri net approaches have been developed to improve the limitations of the original model. For example, the hierarchical Petri net is suitable for industrial production systems, simplifying complicated systems into hierarchical subnetwork structures, thus controlling the functional units [41]. Modular Petri net can efectively resolve the issues such as state space explosion due to the advantages of easy scalability and better maintainability [42]. ...
The implementation of the urban underground logistics system (ULS) can effectively mitigate the contradiction between the surging logistics demand and the increased negativity of urban logistics. The widespread implementation of ULS still suffers from a lack of research into its operation in the marketplace, although the research on ULS system technology and network design appears to be sufficient. A new supply chain for logistics service based on ULS (ULS-SSC) was proposed, as ULS embedded in the urban logistics system could lead to the evolution of the role of supply chain participants. This article analyzed the organizational structure and operation characteristics of ULS-SSC and designed a top-down ULS-SSC operation process model based on the designed functional structure and subsystems relationship using the hierarchical colored Petri net (HCPN). The simulation results show that the integrated information management platform based on ULS can integrate urban logistics service supply chain resources and operate effectively under the two main service modes designed. The high-time delay intermediate links can be upgraded by system optimization, and the links with initial pickup and terminal distribution can be improved through outsourcing and supply chain collaboration. The findings provide new insights into the feasibility of the operation of ULS in the market and help stimulate the implementation of ULS.
... Ye et al. [16] presented a two-phase decomposition algorithm to divide a large-size controller. Other typical applications of the decomposition algorithm using PN in industrial fields can be found in references [17][18][19][20]. Although various decomposition algorithms have been proposed to overcome the state explosion issue of PN and gained fruitful results, the existing literature did not analyze the proposed algorithms own the ability to keep the consistency of dynamic properties between the original PN and the obtained sub-PN models. ...
Recently, it is difficult to simulate, analyze and control a real knowledge-based system using the correspondence Petri net (PN) when there exist many current states. To overcome the state explosion problem of PN, an efficient decomposition algorithm is presented to divide a large-scale PN into a series of corresponding sub-PNs by keeping the consistency of dynamic properties. In this novel decomposition approach, an index function is defined to judge the subnet needs to be decomposed or not. Furthermore, an exhaustive analysis on the consistency of related dynamic properties is also discussed between the original PN and the corresponding sub-PNs. Finally, a case study is carried out to illustrate the feasibility and validity of the proposed approach.
... Broadly, a Petri net is a compact representation of the system under study, the scheduling environment, and of each of its possible states including its initial and a possible final state [see for instance 53,56]. This representation, together with a set of rules to describe transformations between states, denoted as transition firings, provides a general formalism in which a schedule corresponds to an ordered set of transition firings that transform the initial state into the final state. ...
In this work, we focus on general multi-objective scheduling problems that can be modeled using a Petri net framework. Due to their generality, Petri nets are a useful abstraction that captures multiple characteristics of real-life processes.
To provide a general solution procedure for the abstraction, we propose three alternative approaches using an indirect scheme to represent the solution: (1) a genetic algorithm that combines two objectives through a weighted fitness function, (2) a non dominated sorting genetic algorithm (NSGA-II) that explicitly addresses the multi-objective nature of the problem and (3) a multi-objective local search approach that simultaneously explores multiple candidate solutions. These algorithms are tested in an extensive computational experiment showing the applicability of this general framework to obtain quality solutions.
... Hybrid Petri Nets are an excellent choice for supervision manufacturing system. This tools enjoys wide applications in fields such as modeling and control [1][2][3], monitoring [4] and decision making [5], [6]. ...
This article proposes the establishment of monitoring and diagnosis tools in order to implement an automated system. The purpose of monitoring task is to preserve the production equipments quality and personnel safety. The study proposed in this paper consists in developing algorithms, based on Hybrid Signal Interpreted Petri Nets (HSIPN) for monitoring the quality of bobbins obtained by a winding machine. This monitoring approach is integrated into maintenance decision process.
... Liu and Barkaoui (2016) surveyed the state-of-the-art siphon theory of Petri nets including basic concepts, computation of siphons, controllability conditions, and deadlock control policies based on siphons. Vatani and Doustmohammadi (2015) proposed a new method of decomposition of first-order hybrid Petri nets (FOHPNs) and introduced the hierarchical control of the subnets through a coordinator. Motallebi et al. defined parametric multisingular hybrid Petri nets (P-MSHPNs), as a parametric extension of MSHPNs (Motallebi & Azgomi, 2015). ...
The cold-chain information has characterized by the loss and dispersion according to the different collecting methods. The description for the quality decay factors of aquatic products can be defined as the multidimensional information. A series of nodes with multidimensional information are assembled to be hierarchies aiming at describing the environment conditions and locations in the supply chain. Each of the single hierarchy levels constitutes a sequence of node information in a network, which is applied as internal information analysis. The cross-layer information structure is defined as “bridge” information which is able to record the information transmissions among every hierarchy from the point of view of the whole chain. The study has established a novel structured modeling to describe the cold chain of aquatic products based on a network-hierarchy framework. An organized and sustainable transmission process can be built and recorded by the multidimensional attributes for the whole course of cold chain of aquatic products. In addition, seamless connections among every hierarchy are attainable by the environmental information records continuously to monitor the quality of aquatic products. The quality assessments and shelf life predictions are estimated properly as the risk control in order to monitor and trace the safety of aquatic products under the supply chain perspective.
... Nowadays, one of major issues is that how to capture users' frequently changing needs and expectations and to support those with dynamic business processes. Moreover, analytical systems design must take into consideration that there are multiple channels of data that may need to be accessed and incorporated for further exploration [10]. One of key characteristics of cloud is ondemand and secure access to scalable data exploration resources. ...
The paper deals with the design of data analysis systems for business process automation. A general scheme of decision support system was developed in which one of the modules is based on Petri Nets. The way of implementation of Petri Net model in optimization problem regarding service-oriented decision support system was shown. The Petri Net model of distribution workflow was presented and simulation experiments was completed. As a result the optimal solution as a set of parameters was emerged.
... The common modularization methodologies are Lagrange methodology [20][21][22][23][24][25], meta methodology [26,34], SCOR methodology [27][28][29][30], UML methodology [31][32][33] and Petir network methodology [35][36][37][38][39][40][41][42][43][44]. Under some circumstances, The regular UML modeling methodology supplies necessary supports for some of fields. ...
The supply chain of perishable products is a combination of information organization, sharing and integration. The information modeling of supply chain is constructed to abstract key quality information including environment information, processing procedures and product quality assessments based on principle of quality safety factors and property of decay rate. The coloured Petri Net is applied for integrated description of independent information classification, aiming at risk identification and risk management framework. Well, according to the quality deterioration tendency, risk grades management and decision-making system are established. Practically, the circulation system of aquatic products is studied in this paper for full processing description. The simulation experiments are manipulated on environmental information, processing information and product quality information by the coloured Petri Net. Eventually, the conclusion turns out precisely as such that the coloured Petri Net conclusive for information classification and information transmission while integrated information management is available of efficient risk identification and decision-making system in supply chain of perishable products. Meanwhile, the validity of evaluating management and shelf-life estimation of perishable products are technically feasible.
... This study utilises a timed Petri net (TPN) model with elements of a coloured Petri net (CPN). In this context it is a hybrid Petri net (HPN) [19], adapted to the modelling and simulation of workflow-type systems. ...
Proper selection of personnel constitutes a frequent challenge for the management of many enterprises. In this paper the above problem has been defined using three objective functions which required simultaneous optimisation. To solve this problem, computer modelling based on Petri nets was proposed. The model was subjected to iterative computer simulation, during which various variants of workstation assignment were tested. This resulted in the emergence of a variant which best fulfilled the assumed optimisation criteria.
The continuous and stable operations of equipment are the crucial factor for the safety of process industries. Risk assessment has demonstrated its capabilities as a practical method to analyze and prevent process equipment failure. Since the status of equipment is mainly determined by its components and the coupling relationship is complex, a systematical and practicable method is needed to help risk assessment. Petri nets provide a graphical and mathematical representation for risk modelling and reasoning. With the complexity of equipment, there could be lots of diagnosis rules, which makes the network complicated and huge. In order to describe the coupling relationship clearly and make the computational process flexible, a layered Petri nets method is presented in this context to conduct complex rule-based risk analysis and assessment. Moreover, The fuzzy logic is introduced to represent expert knowledge in a semi-quantitative way. The method presented was applied for assessing the risk of reciprocating compressor failure, which is the supercharging equipment widely used in the natural gas transportation process.
A tutorial introduction is provided to the relatively new subject of hybrid systems. The modelling of hybrid systems is assuming ever greater importance for systems where the combination of continuous control and with logical decision making is required. This arises in some of the most critical operating regions where systems are under start-up, shutdown or are undergoing major planned changes. There is recognition that separate independent design of these functions will reduce achievable performance and cause unpredictable behaviour in some of the most safety critical areas of operation. The introduction provided is not exhaustive but it introduces some of the main concepts and motivates the use in applications of this relatively new area of control design. The theoretical results are illustrated using engineering examples.
A supply chain (SC) is a network of independent manufacturing and logistics companies that perform the critical functions in the order fulfillment process. This paper proposes an effective and modular model to describe material, financial and information flow of SCs at the operational level based on first-order hybrid Petri nets (PNs), i.e., PNs that make use of first-order fluid approximation. The proposed formalism enables the SC designer to choose suitable production rates of facilities in order to optimize the chosen objective function. The optimal mode of operation is performed based on the state knowledge of the obtained linear discrete-time, time-varying state variable model in order to react to unpredictable events such as the blocking of a supply or an accident in a transportation facility. A case study is modeled in the proposed framework and is simulated under three different closed-loop control strategies.
The paper proposes a model for real time control of urban traffic networks. A modular framework based on first order hybrid Petri nets models the vehicle flows by a first order fluid approximation. Moreover, the lane interruptions and the signal timing plan controlling the area are described by the discrete event dynamics using timed Petri nets. The proposed model is applied to a real intersection located in Bari, Italy. Simulation of different scenarios shows the technique efficiency: validation is performed by comparison with a previously proposed alternative approach employing colored Petri nets.
In this paper we consider Hybrid Petri Nets (HPNs), a particular formalism that combines fluid and discrete event dynamics. We first provide a survey of the main HPN models that have been presented in the literature in the last decades. Then, we focus on a particular HPN model, namely the First-Order Hybrid Petri Net (FOHPN) model, whose continuous dynamics are piece-wise constant. Here the problem of designing an optimal controller simply requires solving on-line an appropriate linear integer programming problem. In this paper we show how FOHPNs can efficiently represent the concurrent activities of Distributed Manufacturing Systems (DMS), and some interesting optimization problems are also solved via numerical simulation.
Workflow model analysis is performed at logic, temporal, and performance levels. This paper mainly deals with the performance level issues. Workflow net (WF-net) is extended with time information to the timing workflow net (TWF-net). To provide a formal framework for modeling and analyzing workflow, this paper proposes a multidimension workflow net (MWF-net) that include multiple TWF-nets and the organization and resource information. The algorithm to decompose a free-choice and acyclic Petri nets (PN) into a set of T-components is extended to a TWF-net containing iteration structures. Then, resource availability and workload analysis is performed. A method for computing the lower bound of average turnaround time of transaction instances processed in a MWF-net is proposed. Finally a case study is used to show that the proposed method can be effectively utilized in practice.
We consider in this paper first-order hybrid Petri nets, a model
that consists of continuous places holding fluid, discrete places
containing a nonnegative integer number of tokens, and transitions,
either discrete or continuous. We set up a linear algebraic formalism to
study the first-order continuous behavior of this model and show how its
control can be framed as a conflict resolution policy that aims at
optimizing a given objective function. The use of linear algebra leads
to sensitivity analysis that allows one to study of how changes in the
structure of the model influence the optimal behavior. As an example of
application, we show how the proposed formalism can be applied to
flexible manufacturing systems with arbitrary layout and different
classes of products
With a combinatorial nature and hybrid characteristics, it is very challenging to schedule crude oil operations in a refinery and, up to now, there is no software tool for practical use in this field. To solve this problem, based on the two-level architecture in our previous work, for cases where crude oil mixing is required, this paper investigates the refining scheduling problem at the upper level. Based on the schedulability conditions, a threestage approach is proposed. First, a linear programming model is developed to maximize productivity. Second, another linear programming model is built and solved to optimally obtain the mixed crude oil types and their amounts, and assign them into the distillers. Finally, this paper simply sequences and merges the oil parcels obtained at the second stage to form a desired schedule. Because the proposed approach mainly solves two linear programming problems, it is very efficient. An industrial case study is presented to illustrate the proposed approach.
Hybrid supervisory systems integrate and exchange information between discrete- and continuous-data-based controllers and subsystems. Application areas include process, manufacturing and service industries, healthcare, telecommunication, transportation and logistics, among others.
From the hardware point of view, the rapid progress of information-processing power and its commercial availability has made possible the development of complex supervisory systems. Many barriers that restrained the evolution of supervisory systems in the past have been removed by the recent popularisation of the open-system paradigm. On the other hand, software has not followed the evolution in hardware and both the industrial and scientific communities have pointed out the need for a generic approach that guides the development of hybrid supervisory systems.
Modelling and Analysis of Hybrid Supervisory Systems introduces a modelling formalism that merges Petri nets, differential equation systems and object-oriented methods; a formalism that is adequate for modelling complex and large-scale systems. To guide the designer and conduct hybrid modelling, the book describes a method that starts from the requirements of a supervisory system and results in a proposal for such a system. The method is mainly based on Unified Modelling Language diagrams, well-known tools in both academia and industry. In order to ensure that the supervisory system will behave as expected under any operational circumstances, a validation procedure that allows verification of the formal properties of the hybrid model is presented.
In building a bridge between what is developed in academic research and what is available to the industrial professional, this monograph places particular emphasis on the description of real-world examples; three of these – an HVAC management system, a landing system and a cane-sugar factory – are discussed at length. It will interest academic researchers working with hybrid systems and their applications and will answer the need of industry-based engineers to unify their control of continuous- and discrete-event systems.
Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.
In this paper, we propose a Lagrangian relaxation method for solving routing problems for multiple AGVs by decomposition of timed Petri nets. The AGV routing problem is represented by an optimal transition firing sequence problem for timed Petri nets. The timed Petri net is decomposed into several subnets in which the subproblem for each subnet can be easily solved by Dijkstra's algorithm. We show that each subproblem generated by each subnet is polynomially solvable. The optimality of the solution can be evaluated by the duality gap derived by the Lagrangian relaxation method. The performance of the proposed method is compared with a conventional optimisation algorithm with the penalty function method. The effectiveness of the proposed method is demonstrated.
First-order hybrid Petri nets are models that consist of continuous places holding fluid, discrete places containing a non-negative integer number of tokens, and transitions, either discrete or continuous. In the first part of the paper, we provide a framework to describe the overall hybrid net behaviour that combines both time-driven and event-driven dynamics. The resulting model is a linear discrete-time, time-varying state variable model that can be directly used by an efficient simulation tool. In the second part of the paper, we focus on manufacturing systems. Manufacturing systems are discrete-event dynamic systems whose number of reachable states is typically very large, hence approximating fluid models have often been used in this context. We describe the net models of the elementary components of a flexible manufacturing system (machines and buffers) and we show in a final example how these modules can be put together in a bottom-up fashion.
This paper introduces a new approach for the modelling of hybrid productive systems. This approach is based on Petri nets to represent the discrete part, differential equations to describe the continuous part and Object-Oriented paradigm to deal with the complexity problem in real systems. During the modelling process, the Unified Modelling Language (UML) is used in order to support the description of different aspects and identify different hybrid characteristics of the system. The proposed approach is illustrated using as an example the design of supervisory systems for air-conditioning systems.
In this paper we consider a software tool for the simulation and analysis of discrete, continuous and hybrid Petri nets, called HYPENS. It is an open source tool we have recently developed in Matlab. The main contribution of this paper is that of demonstrating the efficiency of HYPENS via real several non trivial examples. In particular, we consider a family of purely discrete event systems modeling a queueing network, and a job shop system with finite capacity buffers and unreliable multi-class machines. A detailed analysis of the computational times and of the accuracy of the results is proposed. In particular, in the first case example, that is modeled using discrete Petri nets, the correctness of the results is proved using well known analytical results from the queueing theory.
Because of the complexity of a short-term scheduling problem for crude oil operations, some constraints are ignored in modeling the system by the existing approaches, leading to an infeasible solution. To avoid this, the short-term scheduling problem can be studied in control theory perspective by viewing an operation decision in the schedule as a control. With this idea, this paper conducts the schedulability analysis for systems with two and more than two distillers, and the schedulability conditions are presented with the help of Petri net theory. It shows that the number of charging tanks and their capacity, the amount of crude oil of different types in the charging tanks, the oil transportation rate of the pipeline, and the production rate of the system affect the safeness of the system. It also presents the conditions under which the system can reach its maximal production rate. With the safeness conditions and proved results presented in this paper, if a refining schedule is realizable, a feasible detailed schedule for the refining schedule can be easily obtained by creating the operation decisions for the schedule one by one. In the schedule obtained, the starting time of each operation decision can be at any continuous time point, and the schedule is certainly feasible, which overcomes the difficulty faced by techniques that are based on mathematical programming methods.
Hybrid Petri Net is a popular formalism in modelling hybrid production systems. Due to their hybrid nature, scheduling and throughput optimization of these systems are complex problems. A notable amount of researches have been done on different methods for scheduling of either continuous or batch chemical plants, however there is a lack of research in the scheduling of mixed batch/continuous systems. In this paper, First-Order Hybrid Petri Net (FOHPN) is used to model a mixed batch/continuous chemical plant. A sugar milling case study is analyzed using FOHPN and the optimization results are compared with those of integrated Timed Arc Hybrid Petri Nets (TAHPN) and Genetic Algorithm (GA) approach, and Mixed Integer Linear Programming (MILP) approach presented in other papers. Simulation results not only show an improvement in production rates, but they also show considerable reduction in computation time. This reduction in computational time enables one to control the plant in real time through a supervisory control scheme.
There are varieties of constraints for a short-term scheduling problem of crude oil operations in a refinery. These constraints are difficult to model and complicate the short-term scheduling problem. Among them, oil residency time and high fusion point crude oil transportation constraints are the challenging ones. With high setup cost for high fusion point oil transportation, it is desired that the volume of high fusion point oil can be transported as much as possible by a single setup. This may result in late transportation of other types of crude oil, leading to the violation of crude oil residency time constraint. These constraints are ignored by existing methods in the literature. To solve this problem, this paper studies the problem in a control theory perspective by viewing an operation decision in the schedule as a control. With this idea, the system is modeled by a hybrid Petri net. With this model and tank grouping strategy, schedulability analysis is carried out and schedulability conditions are presented with tank charging and discharging costs being taken into consideration. These conditions are necessary for determining a refining schedule and can be used to check whether a target-refining schedule is realizable or not. If so, a feasible detailed schedule for the refining schedule can be easily obtained by creating the operation decisions one by one.
Effective scheduling of operations in the process industry has the potential to achieve high economic returns. Process plants containing both batch and continuous units present a difficult scheduling problem. When these processes are modelled with batch cycle times as decision variables, the complexity of the problem is increased significantly. These problems when modelled in the conventional MILP formulation are extremely difficult to solve as they are NP-hard. Many solution methods require unacceptable amounts of time/memory to solve even a simple problem. This paper considers an alternate way to represent the problem in an attempt to improve solution performance. This method is based on optimal control and the hierarchical splitting of the optimisation problem. Results are compared to the traditional MILP formulation. The motivation for this work is an existing scheduling problem in the sugar milling industry. A smaller problem, which has characteristics of the sugar milling problem is considered for performance comparison. A substantial reduction in the complexity required to solve several test-cases of this problem is achieved using the optimal control formulation, while maintaining good quality solutions.
This paper is devoted to the use of hybrid Petri nets (PNs) for modeling and control of hybrid dynamic systems (HDS). Modeling, analysis and control of HDS attract ever more of researchers’ attention and several works have been devoted to these topics. We consider in this paper the extensions of the PN formalism (initially conceived for modeling and analysis of discrete event systems) in the direction of hybrid modeling. We present, first, the continuous PN models. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Then, we present two hybrid PN models, which differ in the class of HDS they can deal with. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior.
Production scheduling in mixed batch/continuous plants, due to their hybrid nature, can become very complex. The main contribution of this paper is the presentation of a novel approach based on the integration of the Timed arc hybrid Petri net (TAHPN) and a genetic algorithm (GA) as a suitable tool for scheduling of hybrid systems. The major benefit of this approach is a significant reduction in complexity during problem formulation. The proposed method is explained through a sugar mill case study.
For short-term scheduling of crude oil operations, oil residency time and high fusion crude oil transportation constraints are difficult to model. With high setup cost for high fusion point oil transportation, it is desired that the volume of such oil should be transported as much as possible by a single setup. To do so and obtain a feasible schedule, charging tank cycling is an effective strategy. With a hybrid Petri net model, scheduling analysis is carried out and schedulability conditions under a charging tank cycling strategy are presented. They can be used for determining a refining schedule and checking if a target refining schedule is realizable. If so, a detailed feasible schedule can be easily obtained by creating the operation decisions one by one and put into immediate industrial use.
Scheduling of processes in mixed batch/continuous plants, due to their hybrid nature, can become very complex. This paper presents the Timed Hybrid Petri net (THPN) as a suitable tool for modelling and scheduling of hybrid systems. One of the major benefits over traditional methods is a significant reduction in complexity during problem formulation. A sugar milling plant containing both batch and continuous processing units is used to illustrate the application of the proposed scheduling algorithm.
This paper establishes equivalences among five classes of hybrid systems: mixed logical dynamical (MLD) systems, linear complementarity (LC) systems, extended linear complementarity (ELC) systems, piecewise affine (PWA) systems, and max-min-plus-scaling (MMPS) systems. Some of the equivalences are established under (rather mild) additional assumptions. These results are of paramount importance for transferring theoretical properties and tools from one class to another, with the consequence that for the study of a particular hybrid system that belongs to any of these classes, one can choose the most convenient hybrid modeling framework.
Fault monitoring plays an important role for safety and reliability of industrial systems. We present a novel on-line monitoring technique for automated manufacturing systems employing the first order hybrid Petri nets formalism, i.e., Petri nets making use of first order fluid approximation. The proposed fault analysis approach belongs to the class of event based methodologies, so that the state space explosion problem is avoided. Moreover, the presented technique relies on a modular framework: elementary monitors can be connected with other monitors to check complex systems. Timely and accurate detection of system failures is ensured, i.e., faults are detected before the maximum execution time assigned to each task. An application to an automated manufacturing system proposed in the related literature enlightens the simplicity and modularity of the technique.
This monograph presents a well written and clearly organized introduction in the standard methods of discrete, continuous and hybrid Petri Nets. Starting from the basics of Petri nets the book imparts an accurate understanding of continuous and hybrid Petri Nets. Preserving the consistency of basic concepts throughout the text it introduces a unified framework for all the models presented. The book is a scientific monograph as well as a didactic tutorial which is easy to understand due to many exercises with solutions, detailed figures and several case studies. It demonstrates that Petri nets are a deep, practical and alive field important for researchers, engineers and graduate students in engineering and computer science. Improvements and additions in this second edition have widely benefited from teaching, student questions, and various discussions with colleagues interested or involved in the topic. © 2010 Springer-Verlag Berlin Heidelberg. All rights are reserved.