Portal:Complex Systems Digital Campus/E-Department on Reconstruction of Multi-level Dynamics: from multi-scale to multi-level dynamics

Portal:Complex_Systems_Digital_Campus/E-Department_on_Reconstruction of Multi-level Dynamics: from multi-scale to multi-level dynamics Reconstruction of multi-level dynamics: from multi-scale to multi-level dynamics through emergence and immergence processes

The data related to complex systems are most often incomplete and difficult to exploit because they are limited to a single level, i.e. refer to observations made on particular scales of space and time. Gathering data effectively first requires the definition of common concepts and pertinent variables for models at each level. Another important problem is obtaining unified and coherent representations for integrating different levels of organization as to predict the dynamics of the complete system. This goal can be achieved by defining pertinent variables at each level of organization, i.e. at different time (slow/fast) and spatial (macro/micro) scales, their relationships, and how they are coupled together in models that describe the dynamics at each level. The challenge is to make explicit integration functions from micro to macro levels (emergence functions) and from micro to macro levels (immergence functions).

Grand challenges: 1.	Building common and pertinent references in the life sciences. 2.	Achieving coherence in the modeling of complex systems. 3.	Development of mathematical and computer formalisms for modeling multi-level and multiscales systems. 1. Building common and pertinent references in the life sciences The data relating to complex systems are often incomplete and therefore difficult to exploit. A main challenge is to find common methods to collect data at different levels of observation, which are coherent and compatible in the sense that they can be used in order to integrate a multi-level (multiscale) system. Thus, it is necessary to find multiscale models that allow researches to define pertinent experimental variables at each level and to achieve a common reference frame with data reproducibility in the different levels of organization of the complete system. 2. Achieving coherence in the modeling of complex systems The goal is to find coherence in the definition of variables and models used at each level of the hierarchical system and to make compatible the models that are used to describe the dynamics at each hierarchical level of organization at given time and space scales.

As a first step, one must ensure that natural constraints are taken into account and that fundamental laws are verified at each level of description (definition of pertinent species, symmetry laws, physical laws, conservation laws and so on). The next step is to connect the description and models used at each level to those at other levels: (i) Modeling the dynamics at microscopic levels can be useful for defining boundaries for global variables and even to obtain correct interpretations for global variables. (ii) Modeling the dynamics at macroscopic levels can be helpful for defining local functions and variables governing microscopic dynamics. 3. Development of mathematical and computer formalisms for modeling multi-level and multiscale systems. The complexity of natural and social systems stems from the existence of several levels of organization corresponding to different time and space scales. A major challenge of complex systems science is to develop formalisms and modeling methods in order to rebuild the complete system by integration of its hierarchical multiscale levels. This goal can be achieved by defining emergence and immergence functions and integrating intra-level (horizontal) and inter-level (vertical) couplings.

Mathematical models used to describe the dynamics of natural and social systems involve a large number of coupled variables at different space and time scales. These models are in general nonlinear and difficult to handle analytically. Therefore, it is crucial to develop mathematical methods that allow one to build a reduced system governing a few global variables at a macroscopic level, i.e. at a slow time scales and long spatial scales.

Among open questions, we mention the definition of pertinent variables at each level of organization and their relationships. It is also necessary to obtain emergence (resp. immergence) functions that allow analysis to jump from a microscopic (resp. macroscopic) level to a macroscopic (resp. microscopic) level, to study the coupling between the different levels and therefore the effects of a change at one level of a hierarchy on the dynamics at others.

Methods based on the separation of time scales already allow the aggregation of variables and are used in mathematical modeling for integrating different hierarchical levels. However, such multi-level modeling methods need to be extended to computer modeling and particularly to IBM (Individual Based Models) and constitute a very promising research theme. Also, the comparison of multi-level models to experimental data obtained at different levels remains also a major challenge which has to be investigated in parallel to the development of mathematical and computer modeling methodologies for multi-level systems.