Ingredients of Locational Analysis (J. Krarup & P. Pruzan). The p-Median Problem and Generalizations (P. Mirchandani). The Uncapacitated Facility Location Problem (G. Cornuejols, et al.). Multiperiod Capacitated Location Models (S. Jacobsen). Decomposition Methods for Facility Location Problems (T. Magnanti & R. Wong). Covering Problems (A. Kolen & A. Tamir). p-Center Problems (G. Handler). Duality: Covering and Constraining p-Center Problems on Trees (B. Tansel, et al.). Locations with Spatial Interactions: The Quadratic Assignment Problem (R. Burkard). Locations with Spatial Interactions: Competitive Locations and Games (S. Hakimi). Equilibrium Analysis for Voting and Competitive Location Problems (P. Hansen, et al.). Location of Mobile Units in a Stochastic Environment (O. Berman, et al.). Index.

https://link.springer.com/content/pdf/10.1057%2Fjors.1991.208.pdf

Discrete location theory

Control of Discrete-event Systems provides a survey of the most important topics in the discrete-event systems theory with particular focus on finite-state automata, Petri nets and max-plus algebra. Coverage ranges from introductory material on the basic notions and definitions of discrete-event systems to more recent results. Special attention is given to results on supervisory control, state estimation and fault diagnosis of both centralized and distributed/decentralized systems developed in the framework of the Distributed Supervisory Control of Large Plants (DISC) project. Later parts of the text are devoted to the study of congested systems though fluidization, an over approximation allowing a much more efficient study of observation and control problems of timed Petri nets. Finally, the max-plus algebraic approach to the analysis and control of choice-free systems is also considered. Control of Discrete-event Systems provides an introduction to discrete-event systems for readers that are not familiar with this class of systems, but also provides an introduction to research problems and open issues of current interest to readers already familiar with them. Most of the material in this book has been presented during a Ph.D. school held in Cagliari, Italy, in June 2011. This book constitutes the refereed proceedings of the Third International Workshop on Tools and Algorithms for the Construction and Analysis of Systems, TACAS '97, held in Enschede, The Netherlands, in April 1997. The book presents 20 revised full papers and 5 tool demonstrations carefully selected out of 54 submissions; also included are two extended abstracts and a full paper corresponding to invited talks. The papers are organized in topical sections on space reduction techniques, tool demonstrations, logical techniques, verification support, specification and analysis, and theorem proving, model checking and applications. The refereed proceedings of the 24th International Conference on Applications and Theory of Petri Nets, ICATPN 2003, held in Eindhoven, The Netherlands, in June 2003. The 25 revised full papers presented together with 6 invited contributions were carefully reviewed and selected from 77 submissions. All current issues on research and development in the area of Petri nets are addressed, in particular concurrent systems design and analysis, model checking, networking, business process modeling, formal methods in software engineering, agent systems, systems specification, systems validation, discrete event systems, protocols, and prototyping. The contents of this volume are application oriented. The volume contains a de tailed presentation of 19 applications of CP-nets, covering a broad range of ap plication areas. Most of the projects have been carried out in an industrial set ting.

Coloured Petri Nets Basic Concepts, Analysis Methods and Practical Use

Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future.

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Modeling formalisms in Systems Biology

Sur le probléme des courbes gauches en Topologie

With the emergence of ride-sharing companies that offer transportation on demand at a large scale and the increasing availability of corresponding demand data sets, new challenges arise to develop ...

Online Vehicle Routing: The Edge of Optimization in Large-Scale Applications

The reconstruction of biochemical and genetic networks from experimental data is an important challenge in biology and medical basic research. We formalize this problem mathematically and present an exact algorithm for its solution. Our procedure yields either a complete list of all alternative network structures that explain the observed phenomena or proves that no solution exists using the given data set.

A mathematical approach to solve the network reconstruction problem

Petri nets are directed, weighted bipartite graphs that have successfully been applied to the systems biology of metabolic and signal transduction pathways in modeling both stochastic (discrete) and deterministic (continuous) processes Here we exemplify how molecular mechanisms, biochemical or genetic, can be consistently respresented in the form of place/transition Petri nets We then describe the application of Petri nets to the reconstruction of molecular and genetic networks from experimental data and their power to represent biological processes with arbitrary degree of resolution of the subprocesses at the cellular and the molecular level Petri nets are executable formal language models that permit the unambiguous visualization of regulatory mechanisms, and they can be used to encode the results of mathematical algorithms for the reconstruction of causal interaction networks from experimental time series data

Petri nets as a framework for the reconstruction and analysis of signal transduction pathways and regulatory networks

Webs and antiwebs are natural generalizations of odd holes and odd antiholes with circular symmetry of their maximum cliques and stable sets. Webs and antiwebs turned out to play a crucial role for describing the stable set polytopes for larger graph classes. In this short note we obtain, with the help of a result of Shepherd (1995), a complete description of the stable set polytopes for antiwebs showing that antiwebs are rank-perfect.

https://opus4.kobv.de/opus4-zib/files/674/ZR-02-07.pdf

Antiwebs are rank-perfect

Network inference methods reconstruct mathematical models of molecular or genetic networks directly from experimental data sets. We have previously reported a mathematical method which is exclusively data-driven, does not involve any heuristic decisions within the reconstruction process, and deliveres all possible alternative minimal networks in terms of simple place/transition Petri nets that are consistent with a given discrete time series data set. We fundamentally extended the previously published algorithm to consider catalysis and inhibition of the reactions that occur in the underlying network. The results of the reconstruction algorithm are encoded in the form of an extended Petri net involving control arcs. This allows the consideration of processes involving mass flow and/or regulatory interactions. As a non-trivial test case, the phosphate regulatory network of enterobacteria was reconstructed using in silico-generated time-series data sets on wild-type and in silico mutants. The new exact algorithm reconstructs extended Petri nets from time series data sets by finding all alternative minimal networks that are consistent with the data. It suggested alternative molecular mechanisms for certain reactions in the network. The algorithm is useful to combine data from wild-type and mutant cells and may potentially integrate physiological, biochemical, pharmacological, and genetic data in the form of a single model.

/pdf/reconstruction-of-extended-petri-nets-from-time-series-data-3i2papz92k.pdf

Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks.

We apply a mathematical algorithm which processes discrete time series data to generate a complete list of Petri net structures containing the minimal number of nodes required to reproduce the data set. The completeness of the list as guaranteed by a mathematical proof allows to define a minimal set of experiments required to discriminate between alternative network structures. This in principle allows to prove all possible minimal network structures by disproving all alternative candidate structures. The dynamic behaviour of the networks in terms of a switching rule for the transitions of the Petri net is part of the result. In addition to network reconstruction, the algorithm can be used to determine how many yet undetected components at least must be involved in a certain process. The algorithm also reveals all alternative structural modifications of a network that are required to generate a predefined behaviour.

Annegret Wagler

Papers

A mathematical approach to solve the network reconstruction problem

Petri nets as a framework for the reconstruction and analysis of signal transduction pathways and regulatory networks

Antiwebs are rank-perfect

Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks.

Automatic reconstruction of molecular and genetic networks from discrete time series data.