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The quantity of data and processes used in modeling projects has been dramatically increasing in recent years due to the progress in computation capability and to the popularity of new approaches such as open data. Modelers face an increasing di iculty in analyzing and modeling complex systems that consist of many heterogeneous entities. Adapting existing models is relevant to avoid dealing with the complexity of writing and studying a new model from scratch. ODD (Overview, Design concepts, Details) protocol has emerged as a solution to document Agent-Based Models (ABMs). It appears to be a convenient solution to address significant problems such as comprehension, replication, and dissemination. However, it lacks a standard that formalizes the use of data in empirical models. This paper tackles this issue by proposing a set of rules that outline the use of empirical data inside an ABM. We call this new protocol ODD+ D (ODD+Decision + Data). ODD+ D integrates a mapping diagram called DAMap (Data to Agent Mapping). This mapping model formalizes how data are processed and mapped to agent-based models. In this paper, we focus on the architecture of ODD+ D, and we illustrate it with a residential mobility model in Marrakesh. Figure :Describing data preprocessing (selecting and structuring) and analysis before using it in the model. Similar to machine learning algorithms, noisy, unreliable and unstructured data can lead to erroneous models..However, no standard or practice manual formalizes the use of models within a contextualized and empirical project (Smajgl & Barreteau ; Bruch & Atwell ). Neither protocol nor methodology gives a data point of view in the development of agent-based models. It is quite urgent to promote such an approach because of the growing popularity of empirical multi-agent models over the last few years (Geller ). The community needs more transparency in the use of theory and empirical data in modeling process (Barreteau & Smajgl )..Giving data point of view implies identifying and formalizing (i) the data preprocessing (selecting and structuring, see Figure ) and (ii) the mapping from empirical data to the model components (agents and environment). By mapping, we mean linking data structure, hidden rules and underlying patterns, to the ABM that they were used for its design and development.. We tackle this issue by proposing a set of rules that outline the use of empirical data inside a model. These rules are surrounded by a method that drives the development of multi-agent models according to available data and relevant theories/hypothesis. To meet this purpose, we adopt and extend the ODD+D (ODD+Decision) protocol (Müller et al. ) to describe and link data to the model. We call this extension ODD+ D (ODD+D+Data).. As a natural language description, this kind of protocol is simple and facilitates the comprehension and replication (Müller et al.). The choice of ODD+D instead of standard ODD is justified by the presence of human decision-making features. Showing that models are realistic enough...

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This work addresses a computational algorithm of terms of a center manifold for neutral functional differential equations. The Bogdanov᎐Takens and the Hopf singularities are considered. Finally, as an illustration of our scheme, we give an example where the second term of a center manifold is explicitly determined. Academic Press

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