During last decade, multi-level agent-based modeling has received significant and dramatically increasing interest. In this article we conduct a comprehensive and structured review of literature on this emerging research domain that aims at extending the classical agent-based modeling paradigm to overcome some of its limitations. We present the main theoretical contributions and applications with an emphasis on social, flow, biological and biomedical models.

Introduction 1.Agent-based modeling

Agent-based modeling (ABM) is a computational modeling paradigm that allow to simulate the interactions of autonomous agents in an environment. It has been widely used to study complex systems in various domains [START_REF] Epstein | Generative social science: Studies in agentbased computational modeling[END_REF][START_REF] Ferber | Multi-Agent Systems: An Introduction to Distributed Artificial Intelligence[END_REF][START_REF] Gilbert | Agent-Based Models[END_REF][START_REF] Railsback | Agent-Based and Individual-Based Modeling: A Practical Introduction[END_REF][START_REF] Resnick | Turtles, termites, and traffic jams: Explorations in massively parallel microworlds[END_REF][START_REF] Treuil | Modélisation et simulation à base d'agents[END_REF].

However, it suffers from important known limitations that reduce its scope [START_REF] Drogoul | Multi-agent based simulation: Where are the agents?[END_REF][START_REF] Scerri | An architecture for modular distributed simulation with agent-based models[END_REF]. First, ABM is purely bottom-up: a microscopic knowledge, i.e., related to system components, is used to construct models while a macroscopic knowledge, i.e., related to global system properties, is used to validate models.Therefore, it is not straightforward to explicitly introduce bidirectional relations between these two points of view in the general case. It becomes even harder when different spatial or temporal scales or domains of interest are involved in a same simulation. Moreover, agent-based models do not scale easily and generally require large computational resources since many agents are simulated. Finally, most agentbased simulation platforms lack tools to reify complex singular emergent properties: human observation often remains the most efficient way to capture multi-level pattern formation or crowd behavior.

Multi-level agent-based modeling 1.2.1 Definitions

The works surveyed in this paper aim at extending the classical ABM paradigm to overcome these limitations. While they can be very different (in terms of goals, technical approaches or application domains), these woks share a common idea: introducing more levels of description in agent-based models. Therefore, we group them under a common term: Multi-Level Agent-based Modeling (ML-ABM). In the following we propose definitions of the concepts of level and multi-level agent-based model that seem broad enough to encompass the different surveyed approaches (see section 1.3).

Definition 1 A level is a point of view on a system, integrated in a model as a specific abstraction.

The name refers to the familiar expressions levels of organization, observation, analysis, etc.

Definition 2 A multi-level agent-based model integrates heterogenous (agent-based) models, representing complementary points of view, so called levels, of the same system.

In this definition, three concepts are highlighted and should themselves be defined formally.

Definition 3 Integration means that the ABMs within a ML-ABM can interact and share entities such as environments and agents.

Definition 4 Heterogeneity means that the ABMs integrated in a ML-ABM can be based on different modeling paradigms (differential equations, cellular automata, etc.), use different time representation (discrete events, step-wise) and represent processes at different spatio-temporal scales.

Definition 5 Points of view are complementary for a given problem since they can not be taken in isolation to address it.

This idea is very important in the literature on complex systems [START_REF] Morin | Method: Towards a Study of Humankind[END_REF]. Indeed, as [START_REF] Müller | L'ontologie pour construire une représentation multi-niveau de et par les systèmes sociaux[END_REF] note, "the global behavior of a complex system cannot be understood without letting a set of points of view interact".

1.2.2 Types of problems solved using multi-level agent-based approaches ML-ABM is mainly used to solve three types of modeling problems:

• the modeling of cross-level interactions, e.g., an explicit top-down feedback control,

• the coupling of heterogeneous models,

• the (dynamic) adaptation of the level of detail of simulations, e.g., to save computational resources or use the best available model in a given context.

In the first case, the different points of view always co-exist, as they integrate interdependent models, while in the last ones, levels are (de)activated at run-time according to the context, as they represent independent models designed for specific situations. For instance, in flow hybrid models areas with simple topologies are handled with an equation-based model (EBM) while others are handled with an ABM.

Terminology issues

Different terms have been used to describe what we call here a level: e.g., perspective, interaction, layer or view [START_REF] Desmeulles | In virtuo experiments based on the multi-interaction system framework: the réiscop metamodel[END_REF][START_REF] Parunak | Multilayer simulation for analyzing IED threats[END_REF][START_REF] Torii | Layering social interaction scenarios on environmental simulation[END_REF][START_REF] White | On interpreting scale (or view) and emergence in complex systems engineering[END_REF]. Some are domain-specific; thus, in the flow modeling domain, when two levels with static relations are considered, models are often described as hybrid as shown in the section 3.2 [START_REF] Burghout | Hybrid mesoscopic-microscopic traffic simulation[END_REF][START_REF] El Hmam | Contribution à la modélisation et la simulation du flux de trafic: approche hybride basée sur les systèmes multiagents[END_REF]El hmam et al., , 2006a,b,c;,b,c;[START_REF] Marino | A hybrid multi-compartment model of granuloma formation and t cell priming in tuberculosis[END_REF]Mathieu et al., 2007a;Nguyen et al., 2012b;[START_REF] Rejniak | Hybrid models of tumor growth[END_REF][START_REF] Wakeland | A hybrid simulation model for studying acute inflammatory response[END_REF].

The term multi-scale -or multi-resolution [START_REF] Jeschke | Multi-resolution spatial simulation for molecular crowding[END_REF]Zhang et al., 2009a[START_REF] Zhang | Developing a multiscale, multiresolution agent-based brain tumor model by graphics processing units[END_REF] -is often used but has a more restrictive meaning as it focuses on the spatial and temporal extents of levels and not on their interactions and organization. Gil-Quijano et al. (2012, p. 622-623) pointed that the term multi-scale can be misleading and advocated for using multi-level instead. Let take as an example the Simpop3 model, described by their authors as multi-scale [START_REF] Pumain | Interaction des ontologies informatique et géographique pour simuler les dynamiques multiscalaires[END_REF]. Two levels are considered: the city level, representing the internal dynamics of a city, and the system of cities level, representing the interactions between cities. However, the idea of scale does not fit to describe the relation between them: one can easily figure a city bigger (in terms of population, spatial extent, economic exchanges, etc.) than a system of cities. In contrast, the idea of levels of organization in interaction seems more appropriate. Furthermore, to extend the definitions 1 and 2 such models could be more precisely denoted as nested or hierarchical multi-level agent-based models.

Bibliography

During last decade, ML-ABM has received significant and dramatically increasing interest (fig. 1). In this article we present a comprehensive and structured review of literature on the subject1 .

Another survey on the subject has been previously conducted by Gil-Quijano et al. and published in different versions2 . While the present article aims at providing an overview of the literature, Gil-Quijano et al. performed a comparative study of three models [START_REF] Gil-Quijano | Social Simulation: Technologies, Advances and New Discoveries, chapter Mechanisms of Automated Formation and Evolution of Social-Groups: A Multi-Agent System to Model the Intra-Urban Mobilities of Bogota City[END_REF][START_REF] Lepagnot | A multiscale agentbased model for the simulation of avascular tumour growth[END_REF] and [START_REF] Pumain | Interaction des ontologies informatique et géographique pour simuler les dynamiques multiscalaires[END_REF]. A similar survey, comparing four models, can be found in Vo (2012, p. 28-34). The paper is structured as follows. Section 2 introduces the main theoretical contributions and section 3 presents the different application domains of ML-ABM, with an emphasis on social, flow, biological and biomedical models. In section 4, some issues about ML-ABM are discussed. Finally, the remaining sections conclude this paper by an analysis of the benefits, drawbacks and current limitations of the existing approaches.

Theoretical issues

In the surveyed literature, three main theoretical issues have been addressed so far:

• the definition and implementation of meta-models and simulation engines,

• the detection and reification of emergent phenomena,

• and the definition of generic representations for aggregated entities.

They are described in the following sections.

Meta-models, simulation engines and platforms

Many meta-models and simulation engines dedicated to ML-ABM have been proposed in the literature. They are are briefly presented in the following, in a chronological order.

Approaches based on DEVS have also been included [START_REF] Zeigler | Theory of Modeling and Simulation[END_REF]. Indeed, DEVS, as a generic event-based simulation framework, has been extended to support ABM [START_REF] Duboz | Intégration de modèles hétèrogenes pour la modélisation et la simulation de systèmes complexes[END_REF][START_REF] Duboz | Scale transfer modeling: using emergent computation for coupling an ordinary differential equation system with a reactive agent model[END_REF][START_REF] Müller | Towards a formal semantics of eventbased multi-agent simulations[END_REF]. A comprehensive survey of the literature on multi-level DEVS extensions can be found in [START_REF] Duhail | DEVS et ses extensions pour des simulations multi-modèles en interaction multi-échelles[END_REF].

GEAMAS (Marcenac et al., 1998a,b;[START_REF] Marcenac | Geamas: A generic architecture for agent-oriented simulations of complex processes[END_REF]) (GEneric Architecture for MultiAgent Simulation) is a pioneering ML-ABM framework integrating three levels of description (micro, meso, macro). Micro and macro levels represent respectively agent and system points of view while the meso (or middle) level represents an aggregation of agents in a specific context. Communication between levels is asynchronous. GEAMAS-NG is a newer version of the framework providing tools to detect and reify emergent phenomena [START_REF] David | Réification de zones urbaines émergentes dans un modèle simulant l'évolution de la population à la réunion[END_REF].

tMans3 [START_REF] Scheutz | tMANSthe multi-scale agent-based networked simulation for the study of multi-scale, multi-level biological and social phenomena[END_REF]) is a multi-scale agent-based meta-model and platform. Unfortunately, the project seems to have died in the bud.

ML-DEVS [START_REF] Steiniger | Modeling agents and their environment in multi-level-DEVS[END_REF][START_REF] Uhrmacher | Combining micro and macro-modeling in DEVS for computational biology[END_REF] is an extension of DEVS that allows the simulation of multi-scale models (and not only coupled models in which the behavior of a model is determined by the behaviors of its sub-models). Two types of relation between levels are defined: information propagation and event activation. However, ML-DEVS focuses on multi-scale modeling and therefore, only supports pure hierarchies of models: interaction graphs are viewed as trees [START_REF] Maus | Hierarchical modeling for computational biology[END_REF].

CRIO (Gaud, 2007;Gaud et al., 2008a,b) (Capacity Role Interaction Organization) is an organizational meta-model dedicated to ML-ABM based on the concept of holon [START_REF] Koestler | The Ghost in the Machine[END_REF][START_REF] Koestler | [END_REF]. It has been used to develop multi-scale simulations of pedestrian flows (cf. section 3.2).

SPARK4 [START_REF] Solovyev | SPARK: A framework for multi-scale agentbased biomedical modeling[END_REF] (Simple Platform for Agent-based Representation of Knowledge) is a framework for multi-scale ABM, dedicated to biomedical research.

Scerri et al. proposed a technical architecture to distribute the simulation of complex agent-based models [START_REF] Scerri | An architecture for modular distributed simulation with agent-based models[END_REF]. This approach aims at integrating multiple ABMs in a single simulation, each ABM representing a specific aspect of the problem. In their article, authors focus on the management of time in such simulations. Therefore, the proposed platform provides two main technical services that ensure the consistency of simulations: (1) a time manager that ensures that integrated ABMs advance in time in a consistent way and (2) a conflict resolver that manages the problematic interactions between agents and shared data (such as the environment). Authors evaluate their approach on a modified version of Repast5 and show it can scale large-scale models easily.

IRM4MLS6 [START_REF] Morvan | Multi-level agent-based modeling with the Influence Reaction principle[END_REF][START_REF] Morvan | IRM4MLS: the influence reaction model for multi-level simulation[END_REF] (Influence Reaction Model for Multi-Level Simulation) is a multi-level extension of IRM4S (Influence Reaction Model for Simulation) [START_REF] Michel | The IRM4S model: the influence/reaction principle for multiagent based simulation[END_REF], an ABM meta-model based on the Influence Reaction model which views action as a two step process: (1) agents produce "influences", i.e., individual decisions, according to their internal state and perceptions, (2) the system "reacts", i.e., computes the consequences of influences, according to the state of the world [START_REF] Ferber | Influences and reaction: a model of situated multiagent systems[END_REF]. The relations of perception and influence between levels are specified with digraphs. IRM4MLS relies on a generic vision of multi-level modeling (see section 1). Therefore, interactions between levels are not constrained. It has been applied to simulate and control intelligent transportation systems composed of autonomous intelligent vehicles (Morvan et al., 2012[START_REF] Morvan | Modélisation et conception multiniveau de systèmes complexes : stratégie d'agentification des organisations[END_REF][START_REF] Soyez | A methodology to engineer and validate dynamic multi-level multi-agent based simulations[END_REF][START_REF] Soyez | Multi-agent multi-level modeling -a methodology to simulate complex systems[END_REF] (see section 3.2).

ML-Rules [START_REF] Maus | Rulebased multi-level modeling of cell biological systems[END_REF]) is a rule-based multi-scale modeling language dedicated to cell biological systems. Rules, describing system dynamics, are described in a similar way as in chemical reaction equations. ML-Rules has been implemented within the simulation framework JAMES II7 . This approach does not refer explicitly to ABM; however, multi-level rule-based languages seem a promising way to engineer complex individual-based models.

Müller et al. developed an approach that consists in decomposing a problem according to the complementary points of view involved in the modeling [START_REF] Müller | L'ontologie pour construire une représentation multi-niveau de et par les systèmes sociaux[END_REF][START_REF] Müller | Vers une méthode multi-point de vue de modélisation multi-agent[END_REF]Müller et al., 2011). For instance in their case study the problem is the relation between residential and scholar segregation. Three points of view are considered: the geographer, the sociologist and the economist. Then, independent conceptual agent-based models are defined for each point of view. As models share agents and concepts, the conceptual models cannot be merged without some processing. Indeed, a same concept can have different meanings according to the point of view. To solve this issue, Müller et al. adapt a technique described in the modular ontology literature: defining bridge rules that explicit the relations between concepts.

PADAWAN [START_REF] Picault | An interaction-oriented model for multi-scale simulation[END_REF] (Pattern for Accurate Design of Agent Worlds in Agent Nests) is a multi-scale ABM meta-model based on a compact matricial representation of interactions, leading to a simple and elegant simulation framework. This representation is based on the meta-model of IODA (Interaction-Oriented Design of Agent simulations) dedicated to classical (1-level) ABM [START_REF] Kubera | Interactionoriented agent simulations: From theory to implementation[END_REF].

GAMA8 [START_REF] Drogoul | GAMA: A spatially explicit, multi-level, agent-based modeling and simulation platform[END_REF][START_REF] Taillandier | GAMA: bringing GIS and multi-level capabilities to multi-agent simulation[END_REF][START_REF] Taillandier | GAMA: A simulation platform that integrates geographical information data, agent-based modeling and multi-scale control[END_REF]) is an ABM platform with a dedicated modeling language, GAML, that offers multi-level capabilities. Moreover, it includes a framework (a set of predefined GAML commands) to Multi-perspective modelling of complex phenomena Now if the phenomena we try to model are complex, a reductionist formal system can only be partially successful in describing the natural system (Agazzi 1991;Mikulecky 2001). By describing a natural system as a collection of perspectives, though, where each perspective is associated with a unique formal system (having a unique decomposition) as shown in Fig. 2, we can model a system in an inherently 'richer' way by having multiple non-isomorphic decompositions that may influence each other. Such multi-perspective models can indeed capture the tangledness of the systems that result when we observe the world from different perspectives. As Morin puts it (Morin 1990), "we must found the idea of a complex system on a nonhierarchical concept of the whole" (Morin 1990). In a similar way, Levins (2006) proposes the robustness methodology, which, in a sort of triangulation, invites to analyze and model systems with multiple conceptually independent tools, thus improving accuracy of the models by relating the outcomes obtained from different perspectives.

The relation between complexity and multiple perspectives has been acknowledged by various authors. Kaufmann has stated that the number of possible theo- 2012) approach agentify emerging structures (Vo et al., 2012b). It is certainly the most advanced platform, from an end-user point of view, that integrates a multi-level approach. The multi-scale meta-model focuses on the notion of situated agent and therefore, top class abstractions include geometry and topology of simulated entities (Vo et al., 2012a). The notion of level does not appear explicitly but the concept of species defines attributes and behaviors of a class of same type agents and the multi-scale structure of the model, i.e., how species can be nested within each other.

Seck and Honig developed an extension of DEVS that allows the simulation of multi-level (i.e., non hierarchically coupled) models [START_REF] Seck | Multi-perspective modelling of complex phenomena[END_REF]. The coupling between levels is done through regular DEVS models, named bridge models (fig. 2).

AA4MM [START_REF] Camus | Multilevel modeling as a society of interacting models[END_REF][START_REF] Camus | Modélisation multi-niveaux dans AA4MM[END_REF][START_REF] Siebert | Approche multi-agent pour la multimodélisation et le couplage de simulations[END_REF][START_REF] Siebert | Agents and artefacts for multiple models co-evolution. building complex system simulation as a set of interacting models[END_REF] (Agent and Artifact for Multi-Modeling) is a multi-modeling (or model coupling) meta-model applied to ML-ABM. Levels are reified by agents that interact trough artifacts. This meta-model extends existing ones, see e.g., [START_REF] Bonneaud | Des agents-modèles pour la modélisation et la simulation de systèmes complexes: application à l'écosystémique des pêches[END_REF]; [START_REF] Bonneaud | Pattern oriented agent-based multi-modeling of exploited ecosystems[END_REF], distributing the scheduling between levels.

Observation, detection and agentification of emergent phenomena

An important issue concerning ML-ABM is to observe, detect and possibly reify (or more precisely agentity) phenomena emerging from agent interactions. Of course, the question is not to detect any emergent phenomenon but those of interest, in order to e.g., adapt the level of detail of simulations, model cross-level interactions or observe multi-level behaviors.

Very different approaches have been proposed to solve this problem. The first ones were of course exploratory. Therefore, they rely on dedicated methods related to specific models. Newer works focus on generic methodologies and frameworks. They are briefly presented in a chronological order.

Dedicated clustering methods

The pioneering RIVAGE project [START_REF] Servat | Modélisation de dynamiques de flux par agents. Application aux processus de ruissellement[END_REF]Servat et al., 1998a,b) aimed "at modeling runoff, erosion and infiltration on heterogeneous soil surfaces" (Servat et al., 1998a, p. 184). At the microscopic level, water is viewed as a set of interacting waterballs. An indicator characterizes waterball movements to detect two types of remarkable situations: straight trajectories (corresponding to the formation of ravines) and stationary particles (corresponding to the formation of ponds). Close agents sharing such properties are aggregated in ravine or pond macroscopic agents. [START_REF] Bertelle | Dynamic clustering for autoorganized structures in complex fluid flows[END_REF]; [START_REF] Tranouez | Contribution à la modélisation et à la prise en compte informatique de niveaux de descriptions multiples[END_REF]; [START_REF] Tranouez | Changing the level of description of a fluid flow in agent-based simulation[END_REF][START_REF] Tranouez | Emergent properties in natural and artificial dynamical systems, chapter Changing levels of description in a fluid flow simulation[END_REF]; [START_REF] Tranouez | Different goals in multiscale simulations and how to reach them[END_REF]; [START_REF] Tranouez | Contribution à la représentation multi-échelle des écosystèmes aquatiques[END_REF] aimed at changing the level of detail of fluid flow simulations using the vortex method [START_REF] Leonard | Vortex methods for flow simulation[END_REF]. The goal was, as in the RIVAGE model, to detect complex structures, i.e., clusters of particles sharing common properties, and aggregate them. However, the detection of emergent phenomena relies on graph-based clustering methods. [START_REF] Moncion | Automatic characterization of emergent phenomena in complex systems[END_REF] used a similar approach to detect aggregations of agents in flocking simulations.

Gil-Quijano (2007); Gil-Quijano and Piron ( 2007) and Gil-Quijano et al. ( 2008) used various clustering algorithms such as self-organizing maps, K-Means and particle swarm algorithms, to detect group formations.

Generic frameworks

Chen (2009,2013); Chen et al. (2010); [START_REF] Chen | Learning from multilevel behaviours in agent-based simulations: a systems biology application[END_REF]; Chen et al. (2008aChen et al. ( ,b, 2009) ) proposed a formalism, named complex event types to describe multi-level behaviors in ABMs. "Conceptually, complex events are a configuration of simple events where each component event can be located in a region or point in a hyperspace that includes time, physical space and any other dimensions" (Chen et al., 2008b, p. 4). Using this approach, it is then possible to formally define and observe complex phenomena at different levels. David andCourdier (2008, 2009) developed a conceptual and technical framework to handle emergence reification. It is implemented in the GEAMAS-NG platform (cf. GEAMAS paragraph in the previous section) and has been used in a population model of the Reunion Island, to detect and reify new urban areas [START_REF] David | Reification of emergent urban areas in a land-use simulation model in reunion island[END_REF][START_REF] David | Réification de zones urbaines émergentes dans un modèle simulant l'évolution de la population à la réunion[END_REF].

A similar framework has been integrated in the GAMA platform (see GAMA paragraph in the previous section). It includes various clustering methods developed in the literature (Vo et al., 2012b).

SimAnalyzer is a general-purpose tool, to detect and describe group dynamics in simulations (Caillou and Gil-Quijano, 2012;Caillou et al., 2012).

Representation of aggregated entities

While developing generic representations for aggregated entities (also called group abstractions) seems an important issue, to the best of our knowledge a few publications are available on the subject. The common idea in these works is to delegate the computation of agent behavioral functions to less detailed agents, representing groups of aggregated agents, in other levels in order to reduce the complexity of interaction computing. Sharpanskykh and Treur (2011a,b) proposed two approaches to group abstraction dedicated to models where agent state are represented by variables taking values in {0, 1} or [0, 1]:

• weighting averaging: an aggregated state of a group is estimated by averaging agent states, with a weighting factor related to the strength of influence of an agent in the group (the stronger, the more important).

• invariant-based abstraction: this approach consists in determining an invariant in a group of agents, i.e., a property that does not change in time and using it as a conservation law.

Sharpanskykh and Treur applied these methods to a collective decision making model of social diffusion. They performed a comparative study of the methods, focusing on computational efficiency and approximation error. [START_REF] Parunak | Between agents and mean fields[END_REF] introduced the notion of pheromone field (refering to the concept of mean field in statistical physics) that "gives the probability of encountering an agent of the type represented by the field at a given location" (Parunak, 2012, p. 115). In this approach, agents act according to their perceptions of pheromone fields (but not of agents). [START_REF] Navarro | Mesoscopic level: A new representation level for large scale agent-based simulations[END_REF] proposed a generic approach based on the notion of mesoscopic representation: agents sharing common properties (related to their physical or mental states) delegate the computation of behavioral functions to a mesoscopic agent. Authors developed this approach to reduce the computational cost of simulations while guaranteeing accurate results.

Application domains

ML-ABM has been used in various fields such as

• biomedical research cancer modeling [START_REF] Andasari | Integrating intracellular dynamics using compucell3d and bionetsolver: Applications to multiscale modelling of cancer cell growth and invasion[END_REF][START_REF] Brown | Applying multi-agent techniques to cancer modeling[END_REF][START_REF] Deisboeck | Multiscale cancer modeling[END_REF][START_REF] Lepagnot | A multiscale agentbased model for the simulation of avascular tumour growth[END_REF][START_REF] Olsen | Multiscale agent-based model of tumor angiogenesis[END_REF][START_REF] Paiva | A multiscale mathematical model for oncolytic virotherapy[END_REF][START_REF] Rejniak | Hybrid models of tumor growth[END_REF][START_REF] Sun | Multi-scale agent-based brain cancer modeling and prediction of tki treatment response: Incorporating egfr signaling pathway and angiogenesis[END_REF][START_REF] Wang | Multi-scale agentbased modeling on melanoma and its related angiogenesis analysis[END_REF]Wang et al., , 2008;;Wang and Deisboeck, 2008;[START_REF] Wang | Simulating non-small cell lung cancer with a multiscale agent-based model[END_REF][START_REF] Zhang | Development of a three-dimensional multiscale agent-based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer[END_REF]Zhang et al., , 2009a[START_REF] Zhang | Developing a multiscale, multiresolution agent-based brain tumor model by graphics processing units[END_REF][START_REF] Zhang | Multiscale agent-based cancer modeling[END_REF],

inflammation modeling (An, 2008;[START_REF] An | Agentbased modeling approaches to multi-scale systems biology: An example agent-based model of acute pulmonary inflammation[END_REF][START_REF] Wilensky | Artificial life models in software[END_REF][START_REF] Kim | A multi-scale agent-based model of necrotizing enterocolitis integrating oxidative stress, inflammation, and microvascular thrombosis[END_REF][START_REF] Scheff | A multiscale modeling approach to inflammation: A case study in human endotoxemia[END_REF][START_REF] Vodovotz | Translational systems biology of inflammation[END_REF][START_REF] Wakeland | A hybrid simulation model for studying acute inflammatory response[END_REF],

arterial adaptation [START_REF] Hayenga | Ensuring congruency in multiscale modeling: towards linking agent based and continuum biomechanical models of arterial adaptation[END_REF][START_REF] Thorne | Toward a multi-scale computational model of arterial adaptation in hypertension: verification of a multi-cell agent based model[END_REF],

stent design [START_REF] Tahir | Multi-scale simulations of the dynamics of in-stent restenosis: impact of stent deployment and design[END_REF],

vascular tissue engineering [START_REF] Zahedmanesh | A multiscale mechanobiological modelling framework using agentbased models and finite element analysis: application to vascular tissue engineering[END_REF],

bone remodeling [START_REF] Cacciagrano | Bone remodelling: A complex automata-based model running in bioshape[END_REF],

• flow modeling of walking (and running) (Gaud et al., 2008a;[START_REF] Navarro | Dynamic level of detail for large scale agent-based urban simulations[END_REF][START_REF] Nguyen | Hybrid equation-based and agentbased modeling of crowd evacuation on road network[END_REF]Nguyen et al., , 2012b;;[START_REF] Xi | Two-level modeling framework for pedestrian route choice and walking behaviors[END_REF], driving [START_REF] Bourrel | Modélisation dynamique de l'écoulement du trafic routier : du macroscopique au microscopique[END_REF][START_REF] Bourrel | Mixing micro and macro representations of traffic flow: a first theoretical step[END_REF][START_REF] Bourrel | Mixing micro and macro representations of traffic flow: a hybrid model based on the LWR theory[END_REF][START_REF] Burghout | Hybrid mesoscopic-microscopic traffic simulation[END_REF][START_REF] El Hmam | Contribution à la modélisation et la simulation du flux de trafic: approche hybride basée sur les systèmes multiagents[END_REF]El hmam et al., , 2006a,b,c;,b,c;[START_REF] Espié | Hybrid traffic model coupling macro-and behavioral microsimulation[END_REF][START_REF] Magne | Towards an hybrid macro-micro traffic flow simulation model[END_REF][START_REF] Mammar | Hybrid model based on second-order traffic model[END_REF]Morvan et al., 2012[START_REF] Morvan | Modélisation et conception multiniveau de systèmes complexes : stratégie d'agentification des organisations[END_REF][START_REF] Poschinger | Coupling of concurrent macroscopic and microscopic traffic flow models using hybrid stochastic and deterministic disaggregation[END_REF][START_REF] Sewall | Interactive hybrid simulation of large-scale traffic[END_REF][START_REF] Soyez | A methodology to engineer and validate dynamic multi-level multi-agent based simulations[END_REF][START_REF] Soyez | Multi-agent multi-level modeling -a methodology to simulate complex systems[END_REF][START_REF] Wedde | 2-way evaluation of the distributed BeeJamA vehicle routing approach[END_REF] or streaming (Servat et al., 1998a,b;[START_REF] Tranouez | Emergent properties in natural and artificial dynamical systems, chapter Changing levels of description in a fluid flow simulation[END_REF] agents,

• biology [START_REF] Adra | Development of a three dimensional multiscale computational model of the human epidermis[END_REF][START_REF] Biggs | Novel multiscale modeling tool applied to pseudomonas aeruginosa biofilm formation[END_REF]Christley et al., 2007a,b;[START_REF] Jeschke | Multi-resolution spatial simulation for molecular crowding[END_REF][START_REF] Marino | A hybrid multi-compartment model of granuloma formation and t cell priming in tuberculosis[END_REF]Montagna et al., 2010a,b;[START_REF] Seal | Agent-based dynamic knowledge representation of pseudomonas aeruginosa virulence activation in the stressed gut: Towards characterizing host-pathogen interactions in gut-derived sepsis[END_REF][START_REF] Shimoni | Multi-scale stochastic simulation of diffusioncoupled agents and its application to cell culture simulation[END_REF][START_REF] Smallwood | Multiscale, multi-paradigm modelling of tissues: embedding development in tissue behaviour[END_REF][START_REF] Smallwood | The epitheliome project: multiscale agent-based modeling of epithelial cells[END_REF][START_REF] Stiegelmeyer | Agentbased modeling of competence phenotype switching in bacillus subtilis[END_REF][START_REF] Sun | Exploring hypotheses of the actions of tgf-β1 in epidermal wound healing using a 3d computational multiscale model of the human epidermis[END_REF],

• social simulation [START_REF] Conte | Emergent and immergent effects in complex social systems[END_REF][START_REF] Conte | Simulating multiagent interdependencies. a two-way approach to the micro-macro link[END_REF][START_REF] Dascalu | Multilevel simulator for artificial societies[END_REF][START_REF] Dascalu | Applications of multilevel cellular automata in epidemiology[END_REF][START_REF] Gil-Quijano | Social Simulation: Technologies, Advances and New Discoveries, chapter Mechanisms of Automated Formation and Evolution of Social-Groups: A Multi-Agent System to Model the Intra-Urban Mobilities of Bogota City[END_REF][START_REF] Hassoumi | Toward a spatially-centered approach to integrate heterogeneous and multi-scales urban component models[END_REF][START_REF] Laperrière | Un cadre de modélisation dynamique multiniveau pour la peste bubonique des hautes terres de madagascar[END_REF][START_REF] Louail | Comparer les morphogénèses urbaines en Europe et aux États-Unis par la simulation à base d'agents -Approches multi-niveaux et environnements de simulation spatiale[END_REF][START_REF] North | Multiscale agent-based consumer market modeling[END_REF][START_REF] Ozik | Modeling dynamic multiscale social processes in agent-based models[END_REF][START_REF] Parry | Agent-based models of geographical systems, chapter Large scale agent-based modelling: A review and guidelines for model scaling[END_REF][START_REF] Pumain | Interaction des ontologies informatique et géographique pour simuler les dynamiques multiscalaires[END_REF][START_REF] Sawyer | Simulating emergence and downward causation in small groups[END_REF][START_REF] Sawyer | Artificial societies, multiagent systems and the micro-macro link in sociological theory[END_REF][START_REF] Schaller | Combining farmers' decision rules and landscape stochastic regularities for landscape modelling[END_REF][START_REF] Schillo | The micromacro link in DAI and sociology[END_REF][START_REF] Seck | Multi-perspective modelling of complex phenomena[END_REF][START_REF] Squazzoni | The micro-macro link in social simulation[END_REF],

• ecology [START_REF] Belem | A conceptual model for multipoints of view analysis of complex systems[END_REF][START_REF] Belem | Toward a conceptual framework for multi-points of view analysis in complex system modeling: Orea model[END_REF][START_REF] Belem | An organizational model for multi-scale and multi-formalism simulation: Application in carbon dynamics simulation in westafrican savanna[END_REF][START_REF] Cheong | Mixed methods in land change research: towards integration[END_REF][START_REF] Duboz | Intégration de modèles hétèrogenes pour la modélisation et la simulation de systèmes complexes[END_REF][START_REF] Duboz | Scale transfer modeling: using emergent computation for coupling an ordinary differential equation system with a reactive agent model[END_REF][START_REF] Le | Feedback loops and types of adaptation in the modelling of land-use decisions in an agent-based simulation[END_REF][START_REF] Marilleau | Multiscale mas modelling to simulate the soil environment: Application to soil ecology[END_REF][START_REF] Morvan | Vers une méthode de modélisation multi-niveaux[END_REF][START_REF] Morvan | Modélisation et conception multiniveau de systèmes complexes : stratégie d'agentification des organisations[END_REF][START_REF] Prévost | Ecosystem complexity described with ontological tool for a multi-scale, multi-model approaches in distributed environment[END_REF][START_REF] Ratzé | Simulation modelling of ecological hierarchies in constructive dynamical systems[END_REF][START_REF] Rounsevell | Challenges for land system science[END_REF][START_REF] Schmidt | A multiscale agent-based distributed simulation framework for groundwater pollution management[END_REF][START_REF] Seidl | An individual-based process model to simulate landscape-scale forest ecosystem dynamics[END_REF][START_REF] Seidl | A mechanistic, individual-based approach to modeling complexity and dynamics of forest ecosystems across scales[END_REF][START_REF] Semeniuk | Biodiversity, chapter Integrating Spatial Behavioral Ecology in Agent-Based Models for Species Conservation[END_REF][START_REF] Vincenot | Theoretical considerations on the combined use of system dynamics and individual-based modeling in ecology[END_REF],

• military simulation (Mathieu et al., 2007a,b;[START_REF] Parunak | Multilayer simulation for analyzing IED threats[END_REF]).

An interesting comparative analysis of three of these models can be found in Gil-Quijano et al. (2009,2010); [START_REF] Gil-Quijano | From biological to urban cells: Lessons from three multilevel agent-based models[END_REF] and Louail (2010, p. 185-204).

Social simulation

Social simulation is defined by Squazzoni (2008, p. 4) as "the study of social outcomes, let us say a macro regularity, by means of computer simulation where agents' behavior, interactions among agents and the environment are explicitly modeled to explore those micro-based assumptions that explain the macro regularity of interest".

Major social theories developed in the second half of the twentieth century, e.g., structuration [START_REF] Giddens | La constitution de la société: éléments de la théorie de la structuration[END_REF] and habitus [START_REF] Bourdieu | Raisons pratiques: sur la théorie de l'action[END_REF] theories 9 , share a common ambition: solving the micro/macro (so called agency/structure) problem that can be summarized by the following question: To understand social systems, should we observe agent interactions (micro level) or structures emerging from these interactions (macro level)? Such theories tend to consider altogether agent positions in the social space (objective facts) and goals (subjective facts) to explain their beliefs and actions. Their answer to the previous question could be: social systems can only be understood by considering simultaneously agent interactions and structures in which they occur: social structures agent interactions.

social practices

A key concept used by social theorists and modelers to understand downward (or top-down) causation in social systems, i.e., how social structures influence agents, is reflexivity. It can be defined as the "regular exercise of the mental ability, shared by all normal people, to consider themselves in relation to their (social) contexts and vice versa" (Archer, 2007, p. 4). Thus, social systems differ from other types of systems, by the reflexive control that agents have on their actions: "The reflexive capacities of the human actor are characteristically involved in a continuous manner with the flow of day-to-day conduct in the contexts of social activity" (Giddens, 1987, p. 22). Two very different approaches, both from technical and methodological perspectives, can be considered to simulate systems composed of reflexive agents:

• a purely emergentist approach, only based on the cognitive capabilities of agents to represent and consider themselves in relation to the structures emerging from their interactions -e.g., [START_REF] Conte | Reputation in Artificial Societies[END_REF]; [START_REF] Gilbert | Varieties of emergence[END_REF],

• a multi-level approach based on the cognitive capabilities of agents and the dynamic reification of interactions between social structures and agents, i.e., processes that underlie social practices -e.g., Gil-Quijano et al. ( 2009); Pumain et al. (2009).

According to [START_REF] Giddens | La constitution de la société: éléments de la théorie de la structuration[END_REF], two forms of reflexivity can be distinguished: practical (agents are not conscious of their reflexive capabilities, and therefore, are not able to resonate about them) and discursive (agents are conscious of their reflexive capabilities) reflexivity. These two forms are respectively related to the ideas of immergence in which agent interactions produce emergent properties that modify the way they produce them [START_REF] Conte | Emergent and immergent effects in complex social systems[END_REF] and second order emergence in which agent interactions produce emergent properties that are recognized (incorporated) by agents and influence their actions [START_REF] Gilbert | Varieties of emergence[END_REF]. ML-ABM can also be viewed as a way to link independent social theories (and therefore concepts) defined at different levels (fig. 3) [START_REF] Sawyer | Simulating emergence and downward causation in small groups[END_REF][START_REF] Sawyer | Artificial societies, multiagent systems and the micro-macro link in sociological theory[END_REF][START_REF] Seck | Multi-perspective modelling of complex phenomena[END_REF]. Thus, [START_REF] Seck | Multi-perspective modelling of complex phenomena[END_REF] proposed a model of social conflicts integrating agent behaviors and social laws. [START_REF] Gil-Quijano | Modèles d'auto-organisation pour l'émergence de formes urbaines à partir de comportements individuels à Bogota[END_REF]Gil-Quijano et al. (2007, 2008) developed a multi-scale model of intra-urban mobility. The microscopic level represents households and housing-units, the mesoscopic one, groups of microagents and urban-sectors and the macroscopic one, the city itself. A clustering algorithm is applied to detect and reify groups of households and housing-units. [START_REF] Pumain | Interaction des ontologies informatique et géographique pour simuler les dynamiques multiscalaires[END_REF] developed Simpop3, a multi-scale model based on two previously developed single-scale models: Simpop nano, simulating the internal dynamics of a city and Simpop2, simulating city interactions.

Readers interested in a more comprehensive presentation of these questions may refer to [START_REF] Sawyer | Artificial societies, multiagent systems and the micro-macro link in sociological theory[END_REF]; [START_REF] Schillo | The micromacro link in DAI and sociology[END_REF]; [START_REF] Squazzoni | The micro-macro link in social simulation[END_REF] and [START_REF] Raub | Micro-macro links and microfoundations in sociology[END_REF] .

Flow modeling

A flow of moving agents can be observed at different scales. Thus, in traffic modeling, three levels are generally considered: the micro, meso and macro levels, representing respectively the interactions between vehicles, groups of vehicles sharing common properties (such as a common destination or a common localisation) and flows of vehicles. Each approach is useful in a given context: micro and meso models allow to simulate road networks with complex topologies such as urban area, while macro microsociology mesosociology macrosociology agent community organization large-scale social structures Figure 3: ML-ABM in social simulation as a link between concepts defined at different levels models allow to develop control strategies to prevent congestion in highways. However, to simulate large-scale road networks, it can be interesting to integrate these different representations (fig. 4). The main problem is to determine an appropriate coupling between the different representations, i.e., that preserves the consistency of simulations [START_REF] Davis | Families of models that cross levels of resolution: issues for design, calibration and management[END_REF].

Micro-macro models

An interesting comparison of existing micro-macro traffic models can be found in El hmam (2006, p. 31-44) (table 1). The coupling methods rely on the following idea: creating a virtual section which is both macro and micro at level connections. This virtual section is used as a buffer to generate appropriate micro or macro data according to the type of connection. On this basis, El hmam (2006); El hmam et al. (2008, 2006a,b,c) proposed a generic coupling method between agent-based microscopic models and widely used macroscopic models such as LWR, ARZ and Payne. While micro-macro flow models were essentially developed in the traffic domain, other applications such as crowd simulation emerged in recent years [START_REF] Nguyen | Hybrid equation-based and agentbased modeling of crowd evacuation on road network[END_REF](Nguyen et al., , 2012b)).

However, all the surveyed hybrid models share the same limitation: connections between levels are fixed a priori and cannot be changed at runtime. Therefore, to be able to observe some emerging phenomena such as congestion formation or to find the exact location of a jam in a large macro section, a dynamic hybrid modeling approach is needed [START_REF] Sewall | Interactive hybrid simulation of large-scale traffic[END_REF]

Micro-meso models

This kind of models is often used to reduce the complexity of agent interactions. Agents sharing common properties can be aggregated to form up a higher level (mesoscopic) agent and then, save computer resources or describe group dynamics such as in the already mentioned RIVAGE [START_REF] Servat | Modélisation de dynamiques de flux par agents. Application aux processus de ruissellement[END_REF]Servat et al., 1998a,b) and DS [START_REF] David | Réification de zones urbaines émergentes dans un modèle simulant l'évolution de la population à la réunion[END_REF]) models (cf. section 2.2). Conversely, mesoscopic agents can be broken up into lower level agents if related structures vanish. Morvan et al. (2012[START_REF] Morvan | Modélisation et conception multiniveau de systèmes complexes : stratégie d'agentification des organisations[END_REF] introduced an multi-level approach to solve the deadlock problem in field-driven autonomous intelligent vehicle systems. These systems generally rely on self-organization to achieve their goals, but AIVs can remain trapped into dead-locks. When such a situation is detected (using a similar approach than [START_REF] Servat | Modélisation de dynamiques de flux par agents. Application aux processus de ruissellement[END_REF]; Servat et al. (1998a,b)), it is agentified to solve the problem using hierarchical control. [START_REF] Flacher | Multiagent simulation system[END_REF]; [START_REF] Navarro | Mesoscopic level: A new representation level for large scale agent-based simulations[END_REF][START_REF] Navarro | A flexible approach to multi-level agent-based simulation with the mesoscopic representation[END_REF][START_REF] Navarro | Dynamic level of detail for large scale agent-based urban simulations[END_REF] proposed an innovative framework for such models: (de)aggregation functions rely not only on the observable state of simulations (the environment) but also on the internal state of agents. It has been applied to pedestrian flow simulation. The proximity between agent states (external and internal) is computed by an affinity function. [START_REF] Soyez | A methodology to engineer and validate dynamic multi-level multi-agent based simulations[END_REF][START_REF] Soyez | Multi-agent multi-level modeling -a methodology to simulate complex systems[END_REF] extended this framework on the basis of IRM4MLS. Agents are "cut" into a a set of physical parts (bodies), situated in different levels, and a non-situated part (mind) (see fig. 5). Therefore, these different parts can be (de)aggregated independently. This approach has been applied to dynamically adapt the level of detail in a port operations simulator. Each research area has developed its own ontologies and models to describe the same reality observed at different levels. However, this reductionist approach fails when addressing complex issues [START_REF] Schnell | Multiscale modeling in biology. new insights into cancer illustrate how mathematical tools are enhancing the understanding of life from the smallest scale to the grandest[END_REF]. Thus, it has been shown that living systems are co-produced by processes at different levels of organization [START_REF] Maturana | Autopoiesis and Cognition The Realization of the Living[END_REF]. Therefore, an explanatory model of such systems should account for the interactions between levels.

Biological and biomedical models

Cell biology

At least two levels are explicitly represented in cell biology models: the macroscopic one, representing the extracellular environment and the interactions between cells, and the microscopic one, representing the intracellular environment and the interactions between cell components such as signaling pathways and gene regulatory networks. A major modeling issue is that these two levels continuously influence each other. It leaded to the development of multi-scale models. Montagna et al. (2010a,b) developed a model of morphogenesis in biological systems, in particular for the Drosophila Melanogaster species. [START_REF] Maus | Rulebased multi-level modeling of cell biological systems[END_REF] proposed a model of Schizosaccharomyces pombe (a species of yeast) cell division and mating type switching based on the ML-Rules approach (cf. section 2.1).

Cancer modeling

Cancer is a complex spatialized multi-scale process, starting from genetic mutations and potentially leading to metastasis. Moreover, it has multi-scale (from from genetic to environmental) causes. Therefore, it can be studied from various perspectives from the intracellular (molecular) to the population levels.

ML-ABM is a promising paradigm to model cancer development (Wang and Deisboeck, 2008). Indeed, as Schnell et al. (2007, p. 140) note, "a multi-scale model would allow us to explore the effect of combination therapies, approaches that attempt to stop cancer in its tracks by barricading multiple pathways. Most present models, focusing on processes at a single scale, cannot provide this comprehensive view."

Zhang et al. developed an ML-ABM of a brain tumor named Glioblastoma Multiforme (GBM) [START_REF] Zhang | Development of a three-dimensional multiscale agent-based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer[END_REF](Zhang et al., , 2009a[START_REF] Zhang | Developing a multiscale, multiresolution agent-based brain tumor model by graphics processing units[END_REF][START_REF] Zhang | Multiscale agent-based cancer modeling[END_REF]. This model explicitly defines the relations between scales and uses different modeling approaches: ordinary differential equations (ODE) at the intracellular level, discrete rules typically found in ABM at the cellular level and partial differential equations (PDE) at the tissue level (see fig. 6).

Moreover, this model also relies on a multi-resolution approach: heterogenous clusters, i.e., composed of migrating and proliferating cells are simulated at a high resolution while homogenous clusters of dead cells are simulated at a lower resolution. In short, "more computational resource is allocated to heterogenous regions of the cancer and less to homogenous regions" (Zhang et al., 2011, p. 6). This model has been implemented on graphics processing units (GPU), leading to an efficient parallel simulator [START_REF] Zhang | Developing a multiscale, multiresolution agent-based brain tumor model by graphics processing units[END_REF]. [START_REF] Zhang | Development of a three-dimensional multiscale agent-based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer[END_REF](Zhang et al., , 2009a[START_REF] Zhang | Developing a multiscale, multiresolution agent-based brain tumor model by graphics processing units[END_REF][START_REF] Zhang | Multiscale agent-based cancer modeling[END_REF]) [START_REF] Sun | Multi-scale agent-based brain cancer modeling and prediction of tki treatment response: Incorporating egfr signaling pathway and angiogenesis[END_REF] also developed a brain tumor ML-ABM available as a MATLAB library called ABM-TKI10 . It is based on a 4 level architecture (tissue, microenvironmental, cellular, modelcular). [START_REF] Lepagnot | A multiscale agentbased model for the simulation of avascular tumour growth[END_REF] model the growth of avascular tumors to study the impact of PAI-1 molecules on metastasis. To deal with the problem complexity (a tumor may be composed of millions of cells) two levels are introduced: the cell and the tumor's core levels (fig. 7). Indeed, such cancers are generally structured as a kernel of necrosed or quiescent cells surrounded by living tumor cells. As necrosed and quiescent cells are mostly inactive, tumor's core is reified as a single upper-level agent, interacting with cells and PAI-1 molecules at its boundary. A more comprehensive analysis of this model can be found in [START_REF] Gil-Quijano | From biological to urban cells: Lessons from three multilevel agent-based models[END_REF].

Ecology

Ecologists study processes that can have very different spatio-temporal dynamics. Then, characterizing their interactions is a complicated problem and traditional bottom-up or top-down approaches do not seem relevant: ABMs tend to be too complex, requiring a lot of computational resources11 while EBMs cannot deal with complex heterogenous environments [START_REF] Shnerb | The importance of being discrete: Life always wins on the surface[END_REF]. Ecological systems are generally described as hierarchies [START_REF] Müller | Modeling and simulating hierarchies using an agentbased approach[END_REF][START_REF] Ratzé | Simulation modelling of ecological hierarchies in constructive dynamical systems[END_REF]. Thus the hierarchy theory is "a view of ecological systems, which takes the scales of observation explicitly into account and which tries to conceptualize the phenomena at their proper scale" (Ratzé et al., 2007, p. 14). ML-ABM seems a interesting way to implement this concept. Different modeling issues in Ecology have been solved by ML-ABM. [START_REF] Duboz | Intégration de modèles hétèrogenes pour la modélisation et la simulation de systèmes complexes[END_REF]; [START_REF] Duboz | Scale transfer modeling: using emergent computation for coupling an ordinary differential equation system with a reactive agent model[END_REF] proposed the scale transfer approach to link microscopic and macroscopic models: the state of the system is computed by an ABM and is used to parametrize an EBM describing population dynamics. This EBM can then be used to parametrize the ABM environment (fig. 8).

ABM EBM emergent computation environment parametrization

Figure 8: The scale transfer approach [START_REF] Duboz | Intégration de modèles hétèrogenes pour la modélisation et la simulation de systèmes complexes[END_REF][START_REF] Duboz | Scale transfer modeling: using emergent computation for coupling an ordinary differential equation system with a reactive agent model[END_REF] Marilleau et al. ( 2008) introduced a efficient method to represent complex soils, named APSF (Agent, Pores, Solid and fractal). Traditionally, the environment is viewed as a regular grid, discretized into cells. A cell can represent a pore, i.e., a part of a soil cavity, a solid or a fractal. The idea is that a cell is not necessarily an atomic element describing an homogenous area but can be fractal, i.e., composed of smaller pore, solid or fractal cells with a self similar structure. Fractal cells are instantiated at run time, generating finer representations of the environment when it is needed. Thus, this approach based on self-generation allows to represent complex multi-scale environments at a minimal computational cost. It has been used in the SWORM (Simulated WORMS) model that studies the relation between earthworm activity and soil structure [START_REF] Blanchart | SWORM: an agent-based model to simulate the effect of earthworms on soil structure[END_REF][START_REF] Laville | Using gpu for multi-agent multiscale simulations[END_REF].

Diptera larvae have a complex gregarious behavior that lead to the formation of large groups in which individuals regulate the temperature to optimize their development speed. This phenomenon can be described by a mesoscopic equation-based model (knowing the mass of the group and and the external temperature), while the crowding behavior of larvae can be modeled by an ABM. Moreover, the thermal dynamics of the cadaver can be modeled by a Cellular Automaton (CA). [START_REF] Morvan | Vers une méthode de modélisation multi-niveaux[END_REF][START_REF] Morvan | Modélisation et conception multiniveau de systèmes complexes : stratégie d'agentification des organisations[END_REF]) integrated these different models in a ML-ABM to perform more accurate forensic entomology expertises. In this model, the EBM is parametrized according to the ABM state. It computes the increase of temperature caused by Diptera interactions at the group level and send it to the CA model that is used as an environment for the ABM (fig. 9). The environment can thus be viewed as an artifact, used to synchronize the different models. Figure 9: Levels of organization in a ML-ABM of necrophagous Diptera development [START_REF] Morvan | Vers une méthode de modélisation multi-niveaux[END_REF][START_REF] Morvan | Modélisation et conception multiniveau de systèmes complexes : stratégie d'agentification des organisations[END_REF] 4 Discussion

In this section two issues are discussed:

• the different forms of level integration,

• the use of ML-ABM to solve technical problems.

Level integration

In the introduction, ML-ABM has been defined as integrating heterogenous ABMs in a single model. Following the approach of [START_REF] Michel | Weak interaction and strong interaction in agent based simulations[END_REF] on interaction, one can distinguish at least two forms of integration:

• weak integration: levels share objects, e.g., environment properties, but not agents,

• strong integration: levels share objects and agents.

Weak integration can be regarded as a form of multi-modeling (or model coupling) where levels represent different models interacting through shared variables called artifacts [START_REF] Camus | Modélisation multi-niveaux dans AA4MM[END_REF][START_REF] Seck | Multi-perspective modelling of complex phenomena[END_REF][START_REF] Siebert | Agents and artefacts for multiple models co-evolution. building complex system simulation as a set of interacting models[END_REF].

Weaker forms of integration are not regarded as multi-level modeling. Thus, in the SWARM platform [START_REF] Minar | The swarm simulation system: A toolkit for building multi-agent simulations[END_REF], integration can be described as bottom-up or isotropic (information flows in one direction). An agent is designed as a russian doll and its behavior at a given level depends on the lower ones.

An simple example of strong integration is given by Picault and Mathieu (2011, p. 334): "a membrane protein, which has an end inside the cell, and the other end outside".

In the meta-models presented in section 2.1, IRM4MLS and PADAWAN are, to the best of our knowledge, the only ones able to simulate strongly integrated levels. It is not surprising as they are based on formal interaction models (respectively IRM4S and IODA) that differentiate between agent influences and level reaction and therefore, are able to represent strong interaction [START_REF] Michel | Weak interaction and strong interaction in agent based simulations[END_REF]. In short, agents are strongly interacting if the interaction output depends on the influences of each agent. Thus, STRIPS-like action models (i.e., that view action as a change of the state of the world), used in most of agent-based simulation platforms, are unable to represent such interactions. Yet, [START_REF] Michel | Weak interaction and strong interaction in agent based simulations[END_REF] showed that modeling a strong interaction as a weak one leads to arbitrary implementation choices and result interpretation issues.

In ML-ABM, the problem is similar since levels can be seen are strongly interacting entities. Thus, we can conclude that a modeling formalism capable of representing strong interaction12 can be extended to a multi-level one.

Multi-level technical tools

Although considering cross-level interactions is usually related to the application domain as shown previously in this article, it can also be viewed as a technical tool:

• an ABM (microscopic level) can be used to parametrize an equation based model (macroscopic level) [START_REF] Duboz | Intégration de modèles hétèrogenes pour la modélisation et la simulation de systèmes complexes[END_REF][START_REF] Duboz | Scale transfer modeling: using emergent computation for coupling an ordinary differential equation system with a reactive agent model[END_REF]Nguyen et al., 2012a),

• levels can be created at run-time by other levels to generate fractal environments [START_REF] Marilleau | Multiscale mas modelling to simulate the soil environment: Application to soil ecology[END_REF],

• a mesoscopic level can be viewed as a controller (in the control theory meaning) of group-related properties [START_REF] Morvan | Multi-level agent-based modeling with the Influence Reaction principle[END_REF].

• automated observation and analysis tools can be introduced at levels not explicitly present in the model to detect and study (multi-level) emergent phenomena13 (cf. section 2.2). However, reified emergent phenomena cannot be considered as model entities since they are not re-injected in the simulation (see fig. 10),

• a radical interpretation of ML-ABM is the concept of multi-future (Parunak et al., 2010;Parunak and Brueckner, 2010). The possible trajectories of agent actions are computed by "ghosts" as a pheromone field and agents act according to it, selecting the most probable one.

As these ideas are domain-independent, they could be implemented as a generic library, providing such services to a classical ABM or ML-ABM framework or platform.

Conclusion

An important challenge for the scientific community is to find ways to deal with the complexity of natural and artificial complex systems. This issue led to the development of dedicated modeling paradigms and engineering principles that focus on interaction and organization. We strongly believe that such techniques will play an important role in the future.

In this article, we conducted a comprehensive analysis of the bibliography available on one of them: multi-level agent-based modeling.

As we shown, many papers focus on the application of this technique and then, are published in domain-related journals and conferences. However, a dedicated venue for theoretical or methodological papers is lacking. Such forum would allow to unify the vocabulary and concept definitions, discuss the main issues of this approach and more generally, share ideas with the interested communities.

Figure 1 :

 1 Figure 1: Bibliographical statistics on ML-ABM computed from author's bibliographic database and google scholar data on the Nov. 15, 2013

Fig. 1 Fig. 2

 12 Fig. 1 Modelling simple phenomena

Figure 2 :

 2 Figure 2: The Seck and Honig (2012) approach

Figure 4 :

 4 Figure 4: ML-ABM and control in traffic simulation

AFigure 5 :

 5 Figure 5: Mind/bodies separation in the Soyez et al. (2013) model

  Figure6: ML-ABM in brain tumor modeling[START_REF] Zhang | Development of a three-dimensional multiscale agent-based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer[END_REF](Zhang et al., , 2009a[START_REF] Zhang | Developing a multiscale, multiresolution agent-based brain tumor model by graphics processing units[END_REF][START_REF] Zhang | Multiscale agent-based cancer modeling[END_REF]

Figure 7 :

 7 Figure7: ML-ABM in avascular tumor growth modeling[START_REF] Lepagnot | A multiscale agentbased model for the simulation of avascular tumour growth[END_REF]

Figure 10 :

 10 Figure 10: Two main uses of detected emergent phenomena: visualization or reinjection in the simulation as agents

Table 1 :

 1 . Main micro-macro traffic flow models, adapted from El hmam(2006, p. 42)

	model	micro model	macro model
	Magne et al. (2000)	SITRA-B+	SIMRES
	Poschinger et al. (2002)	IDM	Payne
	Bourrel and Lesort (2003) Mammar and Haj-Salem (2006)	optimal velocity	LWR ARZ
	Espié et al. (2006)	ARCHISM	SSMT
	El hmam (2006) Sewall et al. (2011)	generic ABM	LWR, ARZ, Payne ARZ

The bibliographic database is available at the following URL: http://www.lgi2a.univ-artois. fr/~morvan/Gildas_Morvan/ML-ABM_files/mlbib.bib.

This work was first published in french[START_REF] Gil-Quijano | De la cellule biologique à la cellule urbaine : retour sur trois expériences de modélisation multi-échelles à base d'agents[END_REF], then extended[START_REF] Gil-Quijano | Accroche-toi au niveau, j'enlève l'échelle: Éléments d'analyse des aspects multiniveaux dans la simulation à base d'agents[END_REF],(Louail, 2010, p. 185-204) and finally translated into english[START_REF] Gil-Quijano | From biological to urban cells: Lessons from three multilevel agent-based models[END_REF]

http://tmans.sourceforge.net/

http://www.pitt.edu/~cirm/spark/

http://repast.sourceforge.net

http://www.lgi2a.univ-artois.fr/~morvan/Gildas_Morvan/IRM4MLS.html

http://www.jamesii.org

http://code.google.com/p/gama-platform/

These theories are described by some sociologists as hybrid[START_REF] Sawyer | Simulating emergence and downward causation in small groups[END_REF].

https://sites.google.com/site/agentbasedtumormodeling/home

An interesting solution to this problem is to reduce the complexity of agent interactions using estimation algorithms such as the fast multipole method[START_REF] Razavi | Multi-agent based simulations using fast multipole method: application to large scale simulations of flocking dynamical systems[END_REF].

Some authors described these approaches as "interaction-based modeling", by opposition to the term "individual-based modeling", as that they focus on interactions rather than on individual behaviors[START_REF] Desmeulles | In virtuo experiments based on the multi-interaction system framework: the réiscop metamodel[END_REF][START_REF] Kubera | Interactionoriented agent simulations: From theory to implementation[END_REF].

13 Indeed, asAn (2008, p. 4) notes about ABM, "since the models rely on an ill-defined principle of 'emergence' in order to transcend the epistemological boundaries represented by the multiple hierarchies of system organization, their behavior is difficult to characterize analytically".

Acknowledgments

I am particularly grateful to my colleagues Shahin Gelareh, Yoann Kubera and Jean-Baptiste Soyez for their help and support. I also would like to thank Chih-Chun Chen, Jean-Pierre Müller and Sebastian Senge for suggesting new entries in the bibliographical database.


Gildas Morvan
email: gildas.morvan@univ-artois.fr

Yoann Kubera

On time and consistency in multi-level agent-based simulations

Keywords:

The integration of multiple viewpoints became an increasingly popular approach to deal with agent-based simulations. Despite their disparities, recent approaches successfully manage to run such multi-level simulations. Yet, are they doing it appropriately?

This paper tries to answer that question, with an analysis based on a generic model of the temporal dynamics of multi-level simulations. This generic model is then used to build an orthogonal approach to multi-level simulation called SIMI-LAR. In this approach, most time-related issues are explicitly modeled, owing to an implementation-oriented approach based on the influence/reaction principle.

Introduction

Simulating complex systems often requires the integration of knowledge coming from different viewpoints (e.g. different application fields, different focus points) to obtain relevant results. Yet, the representations of the agents, the environment and the temporal dynamics in regular multi-agent based simulation meta-models are designed to support a single viewpoint. Therefore, they lack the structure to manage the integration of such systems, called multi-level simulations.

Managing multiple viewpoints on the same phenomenon induces the use of heterogeneous time models, thus raising issues related to time and consistency. Multi-Level Agent-based Modeling (ML-ABM) is a recent approach that aims at extending the classical single-viewpoint agent-based modeling paradigm to cope with these issues and create multiple-viewpoints based simulations [START_REF] Camus | Considering a multi-level model as a society of interacting models: Application to a collective motion example[END_REF][START_REF] David | See emergence as a metaknowledge. a way to reify emergent phenomena in multiagent simulations[END_REF][START_REF] Gil-Quijano | From biological to urban cells: Lessons from three multilevel agent-based models[END_REF][START_REF] Hjorth | Levelspace netlogo extension[END_REF][START_REF] Huraux | A multi-level model for multi-agent based simulation[END_REF][START_REF] Morvan | Multi-level agent-based modeling -a literature survey[END_REF][START_REF] Picault | An interaction-oriented model for multi-scale simulation[END_REF][START_REF] Vo | An operational architecture to handle multiple levels of representation in agent-based models[END_REF]. Considering the disparities between the various ML-ABM approaches, a natural question comes to mind: is there a "right" way to do ML-ABM?

In this context, the aim of this paper is double. We first aim at eliciting the issues and simulation choices underlying such simulations, with an analysis based on a generic model of the temporal dynamics of a multi-level simulation. Then, we present SIMILAR, a ML-ABM approach using the influence/reaction principle to manage explicitly the issues related to the simultaneous actions of agents in multiple levels [START_REF] Ferber | Influences and reaction: a model of situated multiagent systems[END_REF][START_REF] Michel | The IRM4S model: the influence/reaction principle for multiagent based simulation[END_REF][START_REF] Morvan | IRM4MLS: the influence reaction model for multi-level simulation[END_REF].

Temporal dynamics in Multi-level simulations

In this section some issues related to multi-level simulation are emphasized using a generic model describing the temporal dynamics of a multi-level simulation.

General case

From a coarse grain viewpoint, simulation is a process transforming the data about a phenomenon from initial values into a sequence of intermediate values, until a final state is reached. This evolution is characterized by: 1) A dynamic state δ(t ) ∈ ∆ modeling the data of the simulation at time t ; 2) A time model representing the moments when each state of the discrete evolution was obtained; 3) A behavior model describing the evolution process of the dynamic state between two consecutive moments of the time model.

The exact content of the time model, dynamic state, as well as the behavior model of a simulation depends on the simulation approach being used. Yet, despite their disparities, many common points can be identified among them.

First, since real time can be seen as a continuous value, most simulation assume that ⊂ . Moreover, we can assume that a simulation eventually ends. Thus, contains an ordered, finite and discrete set of time values t ∈ . Then, the dynamic state contains data related to the agents and the environment1 .

Multi-level case

In multi-level simulations, each level embodies a specific viewpoint on the studied phenomenon. Since these viewpoints can evolve using very different time scales, each level l ∈ (where is the set of all levels) has to define its own time model l .

The interaction of the levels is possible only by defining when and under which circumstances interaction is possible. For this purpose, we introduce a multi-level specific terminology to the temporal dynamics.

Local information

We consider that agents can lie in more than one level at a time.

(t , l ) ∈ l denotes the set of agents of the level l ∈ at time t ∈ l . Since levels can have very different temporal dynamics, this point has various implications on the structure of the simulation: 1) Agents have a local state2 φ a (t , l ) ∈ Φ a,l in each level l ∈ where they lie; 2) Agents perform decisions differently depending on the level from which the decisions originates; 3) A level l can only trigger the local behavior of the agents lying in l .

Similarly, the environment has a local state φ ω (t , l ) ∈ Φ ω in each level of the simulation. Yet, contrary to the agents, the environment is present in each level of the simulation. Each local state embodies any agent-independent information like a topology or a state (e.g. an ambient temperature).

Global information

The coherence of agent behaviors in each level can require information like cross-level plans or any other level-independent information. Therefore, we consider that agents have a global state3 µ a (t ) ∈ a , which is independent from any level.

Content of a dynamic state

Owing to the abovementioned information, the dynamic state δ(t ) ∈ ∆ of a multilevel simulation at time t can be defined as the sum of the local dynamic state δ(t , l ) ∈ ∆ l of each level l ∈ and the global dynamic state δ G (t ) ∈ ∆ G containing the global state of the agents.

∆ = ∆ G × l ∈ ∆ l (1) ∀δ(t ) ∈ ∆, δ(t ) = δ G (t ), δ(t , l ) l ∈ with δ G (t ) ∈ ∆ G ∧∀l ∈ , δ(t , l ) ∈ ∆ l (2)

Time model of the simulation

The interaction between levels is possible only if their time models are somehow correlated. Since the time model of each level is a discrete ordered set, it is possible to build an order between their elements. The time model of a multi-level simulation is defined as the union of the time models of all the levels: = l ∈ l . For consistency reasons, the time models and l must have the same bounds. Since and l are ordered, we also define s + d t (resp. s + d t l ) as the successor of s ∈ (resp. s ∈ l ).

Consistent and transitory states

In the case where t ∈ l , the level l ∈ is in a transitory state. No guarantee can be provided on such a state, since it corresponds to a temporary value used by l to compute its future consistent dynamic state. On the opposite, the data contained in the dynamic state of a level l ∈ can be safely read or perceived at times in l , where this state is considered as consistent. From a global viewpoint, the dynamic state of the simulation is consistent (resp. transitory) if all of its levels are consistent (resp. transitory). It can also be in an intermediate situation called half-consistent state, if a level is in a consistent and another level is in a transitory state. These concepts are illustrated in Figure 1.

To clarify our speech, we write δ(t ) the consistent (or half-consistent) dynamic state of the simulation at time t ∈ and δ(]t , t [) the transitory dynamic state of the simulation between the times t ∈ and t ∈ .

Multi-level inherent issues

When a simulation is in a transitory phase, each level performs operations in parallel to determine the next consistent value of their dynamic state. The transitory periods of the levels are not necessarily in sync. Therefore, each level can be at a different step of its transitory operations when an interaction occurs. This point raises the following time-related issues: 1) Determine on which dynamic states is based the decision in a level to interact with another level; 2) Determine when to take into consideration the modifications in a level resulting from an action initiated in another level; 3) Determine how to preserve the consistency of the global state of the agents despite having its update occurring after the level-dependent perceptions. This section illustrates these issues on an example containing two levels "A" and "B", presented in Figure 2 Figure 2: Illustration of a subset of a time model containing two levels "A" and "B".

Level interaction through perception

The first issue is related to the perception of the dynamic state of the other levels. It happens for instance at the time t 2 (see fig. 2), when an agent from the level "B" tries to read information from the level "A". Indeed, since "A" is in a transitory state at that time, the data being read by the agent might have arbitrary values. Therefore, a heuristic has to be used to disambiguate that value. For instance using the last consistent dynamic state of the level (in this case the dynamic state of "A" at the time t 1 ), using the arbitrary values from the transitory state at t 2 or anticipating the modifications that might have occurred in "A" between t 1 and t 2 .

Level interaction through actions

The second issue is related to the side effects of an interaction between two levels. It happens for instance during the transitory period ]t 1 , t 3 [ (see fig. 2) of the level "A", if an agent from "A" tries to interact with the level "B". Indeed, since both levels have a different time scale, it is difficult to determine when the actions of "A" have to be taken for account into the computation of the dynamic state of "B". It can be during the transitory phases ]t 1 , t 2 [, ]t 2 , t 3 [ or a later one.

A generic answer to that problem might be "the next time both levels are in sync" (t 3 in this case). Yet, this leads to aberrations like taking into consideration these actions at the end of the simulation (for instance in fig 1, if an agent from the level "A" interacts with "B" during the transitory period ]t 3 , t 5 [).

Global state update

The third issue is related to the read and write access of the global state of an agent and the update of that value. Indeed, during the transitory phase of each level, the agent has to read and possibly update the value of the global states, to take into account the information that were perceived. Yet, since the perception is relative to each level, the global state is the subject of the same issues than the interactions between levels.

For instance, in figure 2, the ]t 1 , t 2 [ of the simulation is a transitory period for the level "B" and a subset of the transitory period for the level "A". The latter raises the question of whether if the global state of the agent at the time t 2 has to take into consideration the data being perceived by the agent from "A" or not. Indeed, perception might not be complete at that time in "A".

Differences between multi-level approaches

There is no universal answer to the issues presented in this section, since the coherence between heterogeneous time scales is itself an ill-defined notion. The main differences between existing ML-ABM approaches are the way these issues are handled, through the answer of the following questions about the operations performed during a transitory phase ]t , t + d t [: 1) Which agents can perform a decision during a transitory period of a level? 2) How many actions can be performed by the decision process of an agent? 3) How are committed the results of the action to the future dynamic state of a level? 4) When are performed these operations during the transitory state? 5) Which dynamic state of a level k is read by a level l initiating an interaction with k? A consistent one? A transitory one? Which ones ? 6) When is taken into account the interaction initiated by a level l with a level k? 7) How is managed the consistency of the global state of agents?

In the next section, we present an agent-based approach called SIMILAR, that aims at addressing these issues.

SIMILAR

Many meta-models and simulation engines dedicated to ML-ABM have been proposed in the literature such as IRM4MLS [START_REF] Morvan | IRM4MLS: the influence reaction model for multi-level simulation[END_REF], PADAWAN [START_REF] Picault | An interaction-oriented model for multi-scale simulation[END_REF], GAMA [START_REF] Grignard | GAMA 1.6: Advancing the art of complex agent-based modeling and simulation[END_REF] or NETLOGO LEVELSPACE [START_REF] Hjorth | Levelspace netlogo extension[END_REF]. All these approaches provide a different and yet valid answer to the multi-level simulation issues. In this paper, we do not aim at detailing precisely their differences: a comprehensive survey of the different approaches can be found in [START_REF] Morvan | Multi-level agent-based modeling -a literature survey[END_REF].

Existing approaches like GAMA or PADAWAN (Pattern for Accurate Design of Agent Worlds in Agent Nests) are complete approaches providing various interesting features respectively including the agentification of emerging structures or the elicitation of interactions between agents. However, these approaches rely on a time model where the management of the potentially simultaneous actions is strongly constrained by the sequential execution of agent actions.

In this paper, we investigate another approach where agent actions are separated from their consequences in the dynamic state of the simulation, using the influence/reaction principle [START_REF] Ferber | Influences and reaction: a model of situated multiagent systems[END_REF]. The resulting approach, called SIMILAR (SImulations with MultI-Level Agents and Reactions), is deeply inspired by IRM4MLS [START_REF] Morvan | IRM4MLS: the influence reaction model for multi-level simulation[END_REF], a multi-level extension of IRM4S [START_REF] Michel | The IRM4S model: the influence/reaction principle for multiagent based simulation[END_REF]. The main differences between SIMILAR and IRM4MLS are the more precise and less misleading terminology and simulation algorithms, as well as a more precise and implementation-oriented model for the reaction phase (the latter is not described in this paper due to the lack of space).

Core concepts

SIMILAR revolves around five core concepts: 1) Levels, modeling different viewpoints on the simulated phenomenon; 2) Agents lying in one or more levels. From each level where they lie, they perceive the state of one or more levels to decide how they wish to influence the evolution of the system; 3) the Environment modeling the topology, the local information (e.g. temperature) and the natural evolution 4 of each level; 4) Influences modeling actions which effect has yet to be committed to the state of the simulation; 5) Reactions modeling how the changes depicted by the influences are committed to the state of the simulation.

We note the levels defined for a simulation, the domain space of all the possible influences of the simulation and all possible agents of the simulation.

Heuristics

SIMILAR relies on the following heuristics and choices to manage the issues raised in the section 1.4. 1) During the transitory period ]t , t + d t l [ of a level l ∈ , the agents from (t , l ) decide once in parallel; 2) The number of influences produced by each decision is not constrained; 3) The result of the actions is committed to the future dynamic state of a level using a reaction mechanism [START_REF] Ferber | Influences and reaction: a model of situated multiagent systems[END_REF] ; 4) During the transitory period ]t , t + d t l [ of a level l ∈ , the behavior of the agents is triggered slightly after t and the reaction occurs slightly before t + d t l ; 5) The dynamic state being read by the behavior of an agent (or of the environment) is always the most recent consistent state of the level5 ; 6) The actions emitted by an agent from a level l to a level k during a transitory period ]t , t +d t l [ are taken into account in the next reaction of k after the time t (i.e. the reaction occurring during the transitory period containing or starting with the time t ); 7) The consistency of agent global states is attained by: i) Computing the revised global state of the agents at the beginning of the transitory period of a level (i.e. before any reaction); ii) Computing the revised global state of an agent once for all the levels starting a new transitory period at the same time; iii) Use this revised global state as the global state of the agent for the next half-consistent state of the simulation. This approach is summarized in Figure 3 2

.3 Dynamic state

In SIMILAR, we consider that each point of view on a phenomenon has to be embodied in a level l ∈ . As a consequence, the dynamic state δ(t ) of the simulation is divided in level-specific dynamic states δ(t , l ). Two kind of data can be obtained from the dynamic state of a level l ∈ : a state valuation σ(t , l ), defining a valuation of the level-related properties of the agents (e.g. their location or their temperature) or the environment (e.g. an ambient temperature) and the state dynamics γ (t , l ), defining the actions that were still being performed 6 in that level during the observation. and joint for all the levels (rectangles) during a simulation. The letters describe the type of the operation: Perception (P), Global state revision (M), Decision (D) and Reaction (R). Any arrow starting on a consistent dynamic state at a time t points to the revised global state used as the new global state of the agents in the half-consistent dynamic state of the time t . This example focuses on the operations performed in a simulation containing one agent lying in three levels.

∀l ∈ , ∀t ∈ l , δ(t , l ) =< σ(t , l ), γ (t , l ) > (3)

State valuation

The state valuation σ(t , l ) of a level l ∈ is the union of the local state of the environment φ ω (t , l ) ∈ Φ ω , containing agent-unrelated information and a local state7 φ a (t , l ) ∈ Φ a,l for each agent a ∈ contained in the level.

State dynamics

SIMILAR relies on the influence/reaction principle to model the actions resulting from the decision of the agents, from the natural evolution of the environment and the actions still being performed at time t . Therefore, the state dynamics γ (t , l ) of a level l ∈ contains a set of influences.

∀l ∈ , ∀t ∈ l , γ (t , l ) ⊆ (4)
Since the data contained in an influence are mostly domain-dependent, no specific model is attached to them. They usually contain the subjects of the action (e.g. the physical state of one or more agents) as well as parameters (e.g. an amount of money to exchange).

General behavior model

The dynamic state of a simulation models a "photograph" of the simulation at time t . Motion is attained owing to the behavior of the agents, the natural action of the and the reaction of each level to influences.

Behavior of the agents

The behavior of an agent in a level l ∈ has three phases: 1) Perception: extract information from the dynamic state of the levels that can be perceived from l ; 2) Global state revision: use the newly perceived data to revise the content of the global state of the agent; 3) Decision: use the perceived data and the revised global state to create and send influences to the levels that can be influenced by l . Each influence models a modification request of the dynamic state of a level.

Natural action of the environment

The natural action of the environment is simpler than the behavior of agents: it only has one phase, where the dynamic state of the levels that can be perceived from l are used to create influences sent to one or more levels that can be influenced by l .

Reaction to the influences

As in IRM4MLS, in SIMILAR the reaction of a level l ∈ is a process computing the new consistent dynamic state of l . The reaction phase occurs at the end of a transitory period ]t , t + d t l [ of a level, and is computed using the value of the most recent consistent dynamic state of l and the influences that were sent to l during the transitory period ]t , t + d t l [; Yet, contrary to IRM4MLS, SIMILAR provides an explicit model to the generic influences that can be found in any simulation, like the addition/removal of an agent from the simulation/a level. Such influences are called system influences, in opposition to regular influences, which are user-defined. A model is also provided to their generic reaction. These points are not detailed in this paper.

Formal notations and simulation algorithm

Not all levels are able to interact. Therefore, the interactions between levels are constrained by two digraphs: A perception relation graph P (resp. influence relation graph I ) defines which levels can be perceived (resp. influenced) during the behavior of the agent/environment in a specific level. l 1 , l 2 ∈ P (resp. I ) ⇐⇒ An agent from l 1 can perceive (resp. influence) the dynamic state of l 2

The out neighborhood + P (l ) (resp.

+ I (l )) of a level l ∈ in the perception (resp. influence) relation graph defines the levels that can be perceived (resp. influenced) by l .

Agent behavior

Since the content of the dynamic state is not trustworthy during transitory periods, the natural action of the environment and the perception of the agents are based on the last consistent dynamic state of perceptible levels. This time is identified by the notation f l oo r l (]t , t [), which models the last time when the dynamic state of a level l was consistent for a perception occurring during a transitory period ]t , t [.

∀t , t ∈ 2 , ∀l ∈ , f l oo r l (]t , t [) = ma x {u ≤ t |u ∈ l } (6)
Based on these information, the perception phase of an agent a ∈ (t , l ) from a level l ∈ for the transitory period ]t , t +d t l [ is defined as an application p e r c e p t i on a,]t ,t +d t l [,l . This application reads the last consistent dynamic state of each perceptible level to produce the perceived data:

∀l ∈ , ∀t ∈ l \{ma x( l )}, ∀a ∈ (t , l ), p e r c e p t i on a,]t ,t +d t l [,l :

k∈ + P (l ) ∆ k -→ a,l δ f l oo r k (]t , t + d t l [), k k∈ + P (l ) -→ p a,l (]t , t + d t l [) (7)
In this notation, a models the domain space of the data that can be perceived by the agent a, from the perspective of the level l . It can contain raw data from the dynamic states, or an interpretation of these data. For instance, in a road traffic simulation, the drivers do not need to put the absolute position of the leading vehicle (i.e. raw data from the dynamic state) in their perceived data: the distance between the two vehicles is sufficient. The revision of the global state of an agent a ∈ (t , l ) for a transitory period starting at the time t is defined as an application g l o b a l Re v a,]t ,t +d t [ . This application reads the most recent consistent global state µ a t ) of the agent a and the perceived data p a,l (]t , t + d t l [), ∀l ∈ |t ∈ l of all the levels that started a transitory phase at the time t , in order to determine the value of the revised global state µ a (]t , t + d t [) of the agent during the transitory period.

∀t ∈ \{ma x( )}, ∀a ∈ (t ), g l o b a l Re v a,]t ,t +d t [ :

a × l ∈ |t ∈ l a,l -→ a µ a (t ), p a,l (]t , t + d t l [) l ∈ |t ∈ l -→ µ a (]t , t + d t [) (8)
Finally, the decision of an agent a ∈ (t , l ) from a level l ∈ for the transitory period ]t , t + d t l [ is defined as an application d e c i s i on a,]t ,t +d t l [,l . This application reads the revised global state µ a (]t , t +d t [) of a and the perceived data p a,l (]t , t +d t l [) computed for the level l to create the influences that will modify levels during their respective next reaction. ∀l ∈ , ∀t ∈ l \{ma x( l )}, ∀a ∈ (t , l ), d e c i s i on a,]t ,t +d t l [,l :

a × a,l -→ 2 µ a (]t , t + d t [), p a,l (]t , t + d t l [) -→ a,l (]t , t + d t l [) (9)
If we note l e v e l (i) the level at which the influence i ∈ is aimed, then the influence relation graph imposes the following constraint to the decision:

∀l ∈ , ∀t ∈ l \{ma x( l )}, i ∈ a,l (]t , t + d t l [) ⇒ l e v e l (i) ∈ + I (l ) (10)
a result to this phase, each created influence i ∈ a,l (]t , t + d t l [) is added to the transitory state dynamics of k = l e v e l (i), for the transitory period ] f l oo r

k (]t , t + d t l [), f l oo r k (]t , t + d t l [) + d t k [.

Natural action of the environment

The natural action of the environment from a level l ∈ for the transitory period ]t , t + d t l [ is defined as an application na t u ra l ]t ,t +d t l [,l . This application reads the last consistent dynamic state of each perceptible level to create the influences that will modify the dynamic state of the influenceable levels (during their reaction).

∀l ∈ , ∀t ∈ l \{ma x( l )}, na t u ra l ]t ,t +d t l [,l :

k∈ + P (l ) ∆ k -→ 2 δ f l oo r k (]t , t + d t l [), k k∈ + P (l ) -→ ω,l (]t , t + d t l [) (11)
The resulting influences are managed with the same process than the ones coming from the decisions of the agents.

Reaction of a level

reaction of a level l ∈ is computed at the end of each transitory period ]t , t + d t l [ where t ∈ l . It is defined as an application r eac t i on l ,]t ,t +d t l [ reading the transitory dynamic state δ(]t , t + d t l [, l ) of the level to determine the next consistent value of the dynamic state δ(t + d t l , l ). ∀l ∈ , ∀t ∈ l \{ma x( l )}, r eac t i on ]t ,t +d t l [,l :

∆ l -→ ∆ l δ ]t , t + d t l [, l -→ δ t + d t l , l (12)
The reaction has the following responsibilities:

Simulation algorithm

The simulation algorithm of SIMILAR is presented in Figure 4. It relies on the presented concepts and complies with the time constraints defined in [START_REF] Morvan | IRM4MLS: the influence reaction model for multi-level simulation[END_REF].

Conclusion and perspectives

In this paper, we elicited several issues about time and consistency raised in multi-level simulations. There is no clear solution to theme since the notion of time consistency among heterogeneous time models is itself ill-defined. Therefore, rather than distinguishing the "right" or "wrong" approaches, we defined a theoretical frame giving a better understanding of the choices underlying each approach. Then, it is up to modelers and domain specialists to tell if these choices are appropriate or not for the study of a given phenomenon.

To cope with the multi-level related issues, we introduced a meta-model named SIMILAR based on the influence/reaction principle. This model is designed to reify as much as possible the concepts involved in the abovementionned issues, thus providing a better support to the definition of explicit solutions to them. SIMILAR includes a generic and modular formal model, a methodology and a simulation API preserving the structure of the formal model. Thus, the design of simulations is in addition more robust to model revisions and relies on a structure fit to represent the intrinsic complexity of the simulated multi-level phenomena.

SIMILAR has been implemented in Java and is available under the CeCILL-B license.

Figure 1 :

 1 Figure 1: Illustration of a time model, for a simulation using two levels "A" and "B".The first line represents real time.The second and third line represent the time model of the levels "A" and "B". The last line represents the time model of the whole simulation. At t 1 , the state of the simulation is consistent. At t 4 , it is half-consistent.

Figure 3 :

 3 Figure 3: Illustration of the operation independently in each level (squares) and joint for all the levels (rectangles) during a simulation. The letters describe the type of the operation: Perception (P), Global state revision (M), Decision (D) and Reaction (R). Any arrow starting on a consistent dynamic state at a time t points to the revised global state used as the new global state of the agents in the half-consistent dynamic state of the time t . This example focuses on the operations performed in a simulation containing one agent lying in three levels.

tFigure 4 :

 4 Figure 4: The simulation algorithm used in SIMILAR

In this paper, we use a simplistic definition of these concepts: an agent is an entity that can perceive data about itself, the environment and the other agents, possibly memorize some of them and decide to perform actions

Also called "physical state" or "face" in the literature[START_REF] Ferber | Influences and reaction: a model of situated multiagent systems[END_REF][START_REF] Michel | The IRM4S model: the influence/reaction principle for multiagent based simulation[END_REF][START_REF] Morvan | IRM4MLS: the influence reaction model for multi-level simulation[END_REF][START_REF] Picault | An interaction-oriented model for multi-scale simulation[END_REF]

Also called "mind", "memory state" or "core" in the literature[START_REF] Ferber | Influences and reaction: a model of situated multiagent systems[END_REF][START_REF] Michel | The IRM4S model: the influence/reaction principle for multiagent based simulation[END_REF][START_REF] Morvan | IRM4MLS: the influence reaction model for multi-level simulation[END_REF][START_REF] Picault | An interaction-oriented model for multi-scale simulation[END_REF]

i.e. without the intervention of the behavior of an agent

Default heuristic of SIMILAR. SIMILAR also allows the definition of user-defined disambiguation heuristics

Actions that started before the time t and that will end after the time t

This replaces the term "physical state" from IRM4MLS, which was misleading, since that state also contains mental information like a desired speed.

is available at http://www.lgi2a.univ-artois.fr/~morvan/similar.html.