AbstractCellpresentation summary objectives and scientific challenges working schedule affiliated events members and frequent collaborators publications |
AbstractCell
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Firstly, we will deal with formal foundations of differential and stochastic semantics. The goals are first to extend the definition of differential semantics to the case when the dimension (the number of distinct chemical species) is infinite and then to relate the stochastic and differential semantics of rule-based models. This will explain which information can be obtained in the differential semantics and in which context numerical integration of the differential system can be used.
Then we will design sound approximations for the differential semantics (which deals with ordinary differential equations systems) and the stochastic semantics (which is based on continuous time Markov chains). We propose to use the abstract interpretation framework to design sound and exact approximations of these semantics. Abstract interpretation is a unifying framework for the approximation of semantics. Semantics can be designed at various levels of observation. The abstract interpretation framework formalizes the comparison between more concrete and more abstract semantics. By using this formal framework, we know, by design, that the approximations that are used preserve the dynamics of the modelled systems. More precisely, the trajectories of the approximate differential semantics will be projections of the trajectories of the original differential semantics. The same way, the distribution of traces of the reduced stochastic semantics will be projection of the distribution of traces of the initial stochastic semantics. We have already achieved some preliminary results for the approximation of differential semantics, thus we are going to extend this framework in order to increase the reduction factor and get scalable differential systems. As far as the approximations of stochastic semantics are concerned, our contribution will be two-fold: First we will collaborate with researchers in applied-mathematics in order to evaluate existing approaches for the approximation of stochastic semantics. We aim to show that existing approaches do not preserve the dynamics of the systems that we are interested in. Then we will strengthen our framework for the reduction of differential semantics so that it can also be applied with stochastic semantics. Our goal, for the stochastic semantics, is more to show the limitation of this approach in term of scalability rather than to obtain scalable solutions.
Finally, we will build tools for integrating (reduced, or not) differential and stochastic semantics. For the integration of differential semantics, we will collaborate with people that have skills in numerical integrations in order to emit a C program featuring both an internal encoding of a differential system and the embedded implementation of a numerical integration algorithm. We will focus on memory management in order to get scalable integration tools. For the simulation of stochastic trajectories, we will use hybrid approaches between an agent-based and a specie-based representation. Moreover, we will use a time advance scheme mixing event-based simulation (for low concentration chemical species) and tau-leaping procedures (for high concentration chemical species).
Tools will be integrated to the OpenKappa platform (which is currently under development).