Solving Partial Differential Equations with Chaotic Asynchronous Schemes in Multi- Interaction Systems

International audienceWithin the framework of multi-interaction systems (MIS), we aim at proposing algorithms for solving some partial differential equations (PDE), that are commonly used for modeling phenomena like transport or diffusion, as they often occur in a complex system involving natural phenomena. Unlike classical synchronous ones, schemes for MIS have to be compatible with chaotic asynchronous iterations, which enable multi-model/scale, interactive and real-time simulations. In our context, the notion of asynchronous iteration expresses the fact that activities, each modeling a phenomenon, have their own lifetime and are processed one after the other. These activations are processed by cycles, in a random order -to avoid computation bias-, what we name chaotic iterations. We provide MIS-compatible schemes to simulate transport phenomena, thermal diffusion phenomena and the spreading phenomenon of a wave packet. Our schemes are based on interactions that represent sorts of Maxwell daemons: transfers of flows between several separate environments given by a spatial resolution grid. We establish formal proofs of convergence for our transport methods. We experiment an efficient asynchronous diffusion scheme, and couple both schemes for solving the advection-diffusion problem. We finally illustrate a multi-interaction method for the spreading of a wave packet described by the Schrödinger equation. Results are compared to classical numerical methods and they show that our methods are as accurate as classical ones, whilst respecting MIS constraints

Common metrics for cellular automata models of complex systems

The creation and use of models is critical not only to the scientific process, but also to life in general. Selected features of a system are abstracted into a model that can then be used to gain knowledge of the workings of the observed system and even anticipate its future behaviour. A key feature of the modelling process is the identification of commonality. This allows previous experience of one model to be used in a new or unfamiliar situation. This recognition of commonality between models allows standards to be formed, especially in areas such as measurement. How everyday physical objects are measured is built on an ingrained acceptance of their underlying commonality. Complex systems, often with their layers of interwoven interactions, are harder to model and, therefore, to measure and predict. Indeed, the inability to compute and model a complex system, except at a localised and temporal level, can be seen as one of its defining attributes. The establishing of commonality between complex systems provides the opportunity to find common metrics. This work looks at two dimensional cellular automata, which are widely used as a simple modelling tool for a variety of systems. This has led to a very diverse range of systems using a common modelling environment based on a lattice of cells. This provides a possible common link between systems using cellular automata that could be exploited to find a common metric that provided information on a diverse range of systems. An enhancement of a categorisation of cellular automata model types used for biological studies is proposed and expanded to include other disciplines. The thesis outlines a new metric, the C-Value, created by the author. This metric, based on the connectedness of the active elements on the cellular automata grid, is then tested with three models built to represent three of the four categories of cellular automata model types. The results show that the new C-Value provides a good indicator of the gathering of active cells on a grid into a single, compact cluster and of indicating, when correlated with the mean density of active cells on the lattice, that their distribution is random. This provides a range to define the disordered and ordered state of a grid. The use of the C-Value in a localised context shows potential for identifying patterns of clusters on the grid

TOWARD A PLATFORM FOR MULTI-LAYERED MULTI-AGENT SITUATED SYSTEM (MMASS)-BASED SIMULATIONS: FOCUSING ON FIELD DIFFUSION

The paper introduces some issues and related solutions adopted in order to realize the MMASS platform. This is a framework to specify and execute simulation applications based on the multilayered multi-agent situated system model (MMASS). MMASS is a model for multi-agent systems (MAS) situated in an environment whose structure is explicitly defined. The behavior and interaction models of MMASS agents are strongly related to the spatial structure of their environment. The MMASS model is the result of a long-term research that has its roots and motivations on application domains and problems that require spatial features to be considered. Our experiences with these problems have concerned the design of domain models and their implementations, according to the MAS approach for simulation purposes. This activity has revealed that currently available tools do not support the management of spatial features of agent environment and interaction mechanisms defined by the MMASS model and thus they are not suitable for our purposes. The paper focuses on the MMASS platform that aims to support the specification and development of applications (mainly, simulations) based on MMASS. Design issues and related solutions that have been adopted in order to manage those aspects that characterize the MMASS model will be shown. After a description of the conceptual model that underlies the MMASS platform and its general architecture, we will overview how the platform supports the specification of agent structured environment, behavior and interaction, and how it supports the execution of agent actions and interactions. Then we will describe issues and adopted solutions (both algorithmic and implementative ones) to manage at-a-distance interaction among MMASS agents

A Language-centered Approach to support environmental modeling with Cellular Automata

Die Anwendung von Methodiken und Technologien aus dem Bereich der Softwaretechnik auf den Bereich der Umweltmodellierung ist eine gemeinhin akzeptierte Vorgehensweise. Im Rahmen der "modellgetriebenen Entwicklung"(MDE, model-driven engineering) werden Technologien entwickelt, die darauf abzielen, Softwaresysteme vorwiegend auf Basis von im Vergleich zu Programmquelltexten relativ abstrakten Modellen zu entwickeln. Ein wesentlicher Bestandteil von MDE sind Techniken zur effizienten Entwicklung von "domänenspezifischen Sprachen"( DSL, domain-specific language), die auf Sprachmetamodellen beruhen. Die vorliegende Arbeit zeigt, wie modellgetriebene Entwicklung, und insbesondere die metamodellbasierte Beschreibung von DSLs, darüber hinaus Aspekte der Pragmatik unterstützen kann, deren Relevanz im erkenntnistheoretischen und kognitiven Hintergrund wissenschaftlichen Forschens begründet wird. Hierzu wird vor dem Hintergrund der Erkenntnisse des "modellbasierten Forschens"(model-based science und model-based reasoning) gezeigt, wie insbesondere durch Metamodelle beschriebene DSLs Möglichkeiten bieten, entsprechende pragmatische Aspekte besonders zu berücksichtigen, indem sie als Werkzeug zur Erkenntnisgewinnung aufgefasst werden. Dies ist v.a. im Kontext großer Unsicherheiten, wie sie für weite Teile der Umweltmodellierung charakterisierend sind, von grundsätzlicher Bedeutung. Die Formulierung eines sprachzentrierten Ansatzes (LCA, language-centered approach) für die Werkzeugunterstützung konkretisiert die genannten Aspekte und bildet die Basis für eine beispielhafte Implementierung eines Werkzeuges mit einer DSL für die Beschreibung von Zellulären Automaten (ZA) für die Umweltmodellierung. Anwendungsfälle belegen die Verwendbarkeit von ECAL und der entsprechenden metamodellbasierten Werkzeugimplementierung.The application of methods and technologies of software engineering to environmental modeling and simulation (EMS) is common, since both areas share basic issues of software development and digital simulation. Recent developments within the context of "Model-driven Engineering" (MDE) aim at supporting the development of software systems at the base of relatively abstract models as opposed to programming language code. A basic ingredient of MDE is the development of methods that allow the efficient development of "domain-specific languages" (DSL), in particular at the base of language metamodels. This thesis shows how MDE and language metamodeling in particular, may support pragmatic aspects that reflect epistemic and cognitive aspects of scientific investigations. For this, DSLs and language metamodeling in particular are set into the context of "model-based science" and "model-based reasoning". It is shown that the specific properties of metamodel-based DSLs may be used to support those properties, in particular transparency, which are of particular relevance against the background of uncertainty, that is a characterizing property of EMS. The findings are the base for the formulation of an corresponding specific metamodel- based approach for the provision of modeling tools for EMS (Language-centered Approach, LCA), which has been implemented (modeling tool ECA-EMS), including a new DSL for CA modeling for EMS (ECAL). At the base of this implementation, the applicability of this approach is shown

Recent advances in petri nets and concurrency

CEUR Workshop Proceeding

Architecting system of systems: artificial life analysis of financial market behavior

This research study focuses on developing a framework that can be utilized by system architects to understand the emergent behavior of system architectures. The objective is to design a framework that is modular and flexible in providing different ways of modeling sub-systems of System of Systems. At the same time, the framework should capture the adaptive behavior of the system since evolution is one of the key characteristics of System of Systems. Another objective is to design the framework so that humans can be incorporated into the analysis. The framework should help system architects understand the behavior as well as promoters or inhibitors of change in human systems. Computational intelligence tools have been successfully used in analysis of Complex Adaptive Systems. Since a System of Systems is a collection of Complex Adaptive Systems, a framework utilizing combination of these tools can be developed. Financial markets are selected to demonstrate the various architectures developed from the analysis framework --Introduction, page 3