An efficient algorithm for the parallel solution of high-dimensional differential equations

The study of high-dimensional differential equations is challenging and difficult due to the analytical and computational intractability. Here, we improve the speed of waveform relaxation (WR), a method to simulate high-dimensional differential-algebraic equations. This new method termed adaptive waveform relaxation (AWR) is tested on a communication network example. Further we propose different heuristics for computing graph partitions tailored to adaptive waveform relaxation. We find that AWR coupled with appropriate graph partitioning methods provides a speedup by a factor between 3 and 16

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 bibliography on formal methods for system specification, design and validation

Literature on the specification, design, verification, testing, and evaluation of avionics systems was surveyed, providing 655 citations. Journal papers, conference papers, and technical reports are included. Manual and computer-based methods were employed. Keywords used in the online search are listed

Analysis of Petri Net Models through Stochastic Differential Equations

It is well known, mainly because of the work of Kurtz, that density dependent Markov chains can be approximated by sets of ordinary differential equations (ODEs) when their indexing parameter grows very large. This approximation cannot capture the stochastic nature of the process and, consequently, it can provide an erroneous view of the behavior of the Markov chain if the indexing parameter is not sufficiently high. Important phenomena that cannot be revealed include non-negligible variance and bi-modal population distributions. A less-known approximation proposed by Kurtz applies stochastic differential equations (SDEs) and provides information about the stochastic nature of the process. In this paper we apply and extend this diffusion approximation to study stochastic Petri nets. We identify a class of nets whose underlying stochastic process is a density dependent Markov chain whose indexing parameter is a multiplicative constant which identifies the population level expressed by the initial marking and we provide means to automatically construct the associated set of SDEs. Since the diffusion approximation of Kurtz considers the process only up to the time when it first exits an open interval, we extend the approximation by a machinery that mimics the behavior of the Markov chain at the boundary and allows thus to apply the approach to a wider set of problems. The resulting process is of the jump-diffusion type. We illustrate by examples that the jump-diffusion approximation which extends to bounded domains can be much more informative than that based on ODEs as it can provide accurate quantity distributions even when they are multi-modal and even for relatively small population levels. Moreover, we show that the method is faster than simulating the original Markov chain

A Taxonomy of Workflow Management Systems for Grid Computing

With the advent of Grid and application technologies, scientists and engineers are building more and more complex applications to manage and process large data sets, and execute scientific experiments on distributed resources. Such application scenarios require means for composing and executing complex workflows. Therefore, many efforts have been made towards the development of workflow management systems for Grid computing. In this paper, we propose a taxonomy that characterizes and classifies various approaches for building and executing workflows on Grids. We also survey several representative Grid workflow systems developed by various projects world-wide to demonstrate the comprehensiveness of the taxonomy. The taxonomy not only highlights the design and engineering similarities and differences of state-of-the-art in Grid workflow systems, but also identifies the areas that need further research.Comment: 29 pages, 15 figure

Under-approximating Cut Sets for Reachability in Large Scale Automata Networks

In the scope of discrete finite-state models of interacting components, we present a novel algorithm for identifying sets of local states of components whose activity is necessary for the reachability of a given local state. If all the local states from such a set are disabled in the model, the concerned reachability is impossible. Those sets are referred to as cut sets and are computed from a particular abstract causality structure, so-called Graph of Local Causality, inspired from previous work and generalised here to finite automata networks. The extracted sets of local states form an under-approximation of the complete minimal cut sets of the dynamics: there may exist smaller or additional cut sets for the given reachability. Applied to qualitative models of biological systems, such cut sets provide potential therapeutic targets that are proven to prevent molecules of interest to become active, up to the correctness of the model. Our new method makes tractable the formal analysis of very large scale networks, as illustrated by the computation of cut sets within a Boolean model of biological pathways interactions gathering more than 9000 components

Discovering Petri Net Models of Discrete-Event Processes by Computing T-Invariants

International audienceThis paper addresses the problem of discovering a Petri Net (PN) from a long event sequence representing the behavior of discrete-event processes. A method for building a 1-bounded PN able to execute the events sequence S is presented; it is based on determining causality and concurrence relations between events and computing the t-invariants. This novel method determines the structure and the initial marking of an ordinary PN, which reproduces the behavior in S. The algorithms derived from the method are efficient and have been implemented and tested on numerous examples of diverse complexity. Note to Practitioners—Model discovery is useful to perform reverse engineering of ill-known systems. The algorithms proposed in this paper build 1-bounded PN models, which are enough powerful to describe many discrete-event processes from industry. The efficiency of the method allows processing very large sequences. Thus, an automated modeling tool can be developed for dealing with data issued from real systems

Checking Data-Flow Errors Based on The Guard-Driven Reachability Graph of WFD-Net

In order to guarantee the correctness of workflow systems, it is necessary to check their data-flow errors, e.g., missing data, inconsistent data, lost data and redundant data. The traditional Petri-net-based methods are usually based on the reachability graph. However, these methods have two flaws, i.e., the state space explosion and pseudo states. In order to solve these problems, we use WFD-nets to model workflow systems, and propose an algorithm for checking data-flow errors based on the guard-driven reachability graph (GRG) of WFD-net. Furthermore, a case study and some experiments are given to show the effectiveness and advantage of our method

Automated Process Discovery: A Literature Review and a Comparative Evaluation with Domain Experts

Äriprotsesside kaeve meetodi võimaldavad analüütikul kasutada logisid saamaks teadmisi protsessi tegeliku toimise kohta. Neist meetodist üks enim uuritud on automaatne äriprotsesside avastamine. Sündmuste logi võetakse kui sisend automaatse äriprotsesside avastamise meetodi poolt ning väljundina toodetakse äriprotsessi mudel, mis kujutab logis talletatud sündmuste kontrollvoogu. Viimase kahe kümnendi jooksul on väljapakutud mitmeidki automaatseid äriprotsessi avastamise meetodeid balansseerides erinevalt toodetavate mudelite skaleeruvuse, täpsuse ning keerukuse vahel. Siiani on automaatsed äriprotsesside avastamise meetodid testitud ad-hoc kombel, kus erinevad autorid kasutavad erinevaid andmestike, seadistusi, hindamismeetrikuid ning alustõdesid, mis viib tihti võrdlematute tulemusteni ning mõnikord ka mittetaastoodetavate tulemusteni suletud andmestike kasutamise tõttu. Eelpool toodu mõistes sooritatakse antud magistritöö raames süstemaatiline kirjanduse ülevaade automaatsete äriprotsesside avastamise meetoditest ja ka süstemaatiline hindav võrdlus üle nelja kvaliteedimeetriku olemasolevate automaatsete äriprotsesside avastamise meetodite kohta koostöös domeeniekspertidega ning kasutades reaalset logi rahvusvahelisest tarkvara firmast. Kirjanduse ülevaate ning hindamise tulemused tõstavad esile puudujääke ning seni uurimata kompromisse mudelite loomiseks nelja kvaliteedimeetriku kontekstis. Antud magistritöö tulemused võimaldavad teaduritel parandada puudujäägid meetodites. Samuti vastatakse küsimusele automaatsete äriprotsesside avastamise meetodite kasutamise kohta väljaspool akadeemilist maailma.Process mining methods allow analysts to use logs of historical executions of business processes in order to gain knowledge about the actual performance of these processes.One of the most widely studied process mining operations is automated process discovery.An event log is taken as input by an automated process discovery method and produces a business process model as output that captures the control-flow relations between tasks that are described by the event log.Several automated process discovery methods have been proposed in the past two decades, striking different tradeoffs between scalability, accuracy and complexity of the resulting models.So far, automated process discovery methods have been evaluated in an ad hoc manner, with different authors employing different datasets, experimental setups, evaluation measures and baselines, often leading to incomparable conclusions and sometimes unreproducible results due to the use of non-publicly available datasets.In this setting, this thesis provides a systematic review of automated process discovery methods and a systematic comparative evaluation of existing implementations of these methods with domain experts by using a real-life event log extracted from a international software engineering company and four quality metrics.The review and evaluation results highlight gaps and unexplored tradeoffs in the field in the context of four business process model quality metrics.The results of this master thesis allows researchers to improve the lacks in the automated process discovery methods and also answers question about the usability of process discovery techniques in industry