A Paradigm for Decentralized Process Modeling presents a novel approach to decentralized process modeling that combines both trends and suggests a paradigm for decentralized PCEs, supporting concerted efforts among geographically-dispersed teams - each local individual or team with its own autonomous process - with emphasis on flexible control over the degree of collaboration versus autonomy provided. A key guideline in this approach is to supply abstraction mechanisms whereby pre-existing processes (or workflows) can be encapsulated and retain security of their internal artifacts and status data, while agreeing with other processes on formal interfaces through which all their interactions are conducted on intentionally shared information.
Using tools from mathematical kinetic theory and stochastic game theory, this work deals with the modeling of large complex systems in the applied sciences, particularly those comprised of several interacting individuals whose dynamics follow rules determined by some organized, or even "intelligent" ability. Traditionally, methods of mathematical kinetic theory have been applied to model the evolution of large systems of interacting classical or quantum particles. This book, on the other hand, examines the modeling of living systems as opposed to inert systems.
The author develops new mathematical methods and tools-hopefully a "new" mathematics-toward the modeling of living systems. Such tools need to be far more complex than those dealing with systems of inert matter. The first part of the book deals with deriving general evolution equations that can be customized to particular systems of interest in the applied sciences. The second part of the book deals with various models and applications.
The presentation unfolds using the following common approach in each chapter:
* Phenomenological interpretation of the physical system in the context of mathematical modeling
* Derivation of the mathematical model using methods from mathematical kinetic theory for active particles
* Simulations, parameter sensitivity analysis, and critical inspection of the derived model towards validation
* Overview of presented ideas to improve existing models, with special emphasis on applications
Specific topics covered include:
* Modeling of the competition between cells of an aggressive invasive agent and cells of the immune system
* Modeling of vehicular traffic flow
* Modeling of swarms and crowd dynamics in complex geometric environments
* Methodological aspects related to multiscale modeling of large systems viewed as interconnected subsystems
Modeling Complex Living Systems is a valuable resource for applied mathematicians, engineers, physicists, biologists, economists, and graduate students involved in modeling complex social systems and living matter in general.
This book is intended primarily as a handbook for engineers who must design practical systems.
Its primaryÂ goal is to discuss model development in sufficient detail so that the reader may design an estimator that meets all application requirements and is robust to modeling assumptions.Â Since it is sometimes difficult to a priori determine the best model structure, use of exploratory data analysis to define model structure is discussed.Â Methods for deciding on the ?best? model are also presented.Â
A second goal is to present little known extensions of least squares estimation or Kalman filtering that provide guidance on model structure and parameters, or make the estimator more robust to changes in real-world behavior.
A third goal is discussion of implementation issues that make the estimator more accurate or efficient, or that make it flexible so that model alternatives can be easily compared.
The fourth goal is to provide the designer/analyst with guidance in evaluating estimator performance and in determining/correcting problems.
The final goal is to provide a subroutine library that simplifies implementation, and flexible general purpose high-level drivers that allow both easy analysis of alternative models and access to extensions of the basic filtering.
Supplemental materials and up-to-date errata are downloadable at http://booksupport.wiley.com.
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