Real-world applications of artificial intelligence often require the decision-maker to choose between multiple optimal solutions at hand before making a final decision. Since there is no guarantee that an increase in the budget or several independent executions will yield different solutions, classic mechanisms are not suitable for identifying multiple solutions. In the context of sequential decision-making problems, Monte Carlo Tree Search (MCTS) is a state-of-the-art online planning algorithm. It is responsible for the improvement of many computer games but also for real-world problems involving continuous action spaces. MCTS has recently been successfully applied to the diverse planning problem in the discrete setting. In this work, we propose different diverse planners based on MCTS (DP-MCTS) to be relevant in the continuous setting. The solution to a diverse planning problem is a Pareto set between diversity and quality of plans. Therefore, we suggest considering a multi-objective setting in which the vectorial reward integrates the diversity measure as an additional objective. In addition, we propose two types of inhibition strategies disregarding the optimal plans to enforce the exploration of the search space during the tree construction. The three different contributions are assessed independently against a diverse multi-armed bandit policy, and the comparison is held on a real-world biological problem involving continuous action and state spaces.

When modelling a complex biological system, the bottleneck of the process is the determination of parameter values that lead to model dynamics that are compatible with observations. Even for discrete modelling frameworks, this step can be limiting. Here we introduce a representation of the whole family of discrete models that can be associated to a biological system, where states are shared by all models and transitions are labelled by constraints on dynamical parameters. A model checking procedure is defined to handle this new representation. This procedure extracts the conditions on parameter settings that are compatible with a given dynamical property expressed in a temporal logic. We prove the correctness of our model checking procedure and illustrate the advantage of such an approach on some different systems of biological interest.

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We present a new hybrid Hoare logic dedicated for a class of linear hybrid automata well suited to model gene regulatory networks. These automata rely on Thomas' discrete framework in which qualitative parameters have been replaced by continuous parameters called celerities. The identification of these parameters remains one of the keypoints of the modelling process, and is difficult especially because the modelling framework is based on a continuous time. We introduce Hoare triples which handle biological traces and pre/post-conditions. Observed chronometrical biological traces play the role of an imperative program for classical Hoare logic and our hybrid Hoare logic, defined by inference rules, is proved to be sound. Furthermore, we present a weakest precondition calculus (a la Dijkstra) which leads to constraints on dynamical parameters. Finally, we illustrate our "constraints generator" with a simplified circadian clock model describing the rhythmicity of cells in mammals on a 24-hour period.

BACKGROUND: Pseudomonas aeruginosa, an opportunistic pathogen, is often encountered in chronic lung diseases such as cystic fibrosis or chronic obstructive pneumonia, as well as acute settings like mechanical ventilation acquired pneumonia or neutropenic patients. It is a major cause of mortality and morbidity in these diseases. In lungs, P. aeruginosa settles in a biofilm mode of growth with the secretion of exopolysaccharides in which it is encapsulated, enhancing its antibiotic resistance and contributing to the respiratory deficiency of patients. However, bacteria must first multiply to a high density and display a cytotoxic phenotype to avoid the host's defences. A virulence determinant implicated in this step of infection is the type III secretion system (TTSS), allowing toxin injection directly into host cells. At the beginning of the infection, most strains isolated from patients' lungs possess an inducible TTSS allowing toxins injection or secretion upon in vivo or in vitro activation signals. As the infection persists most of the bacteria permanently loose this capacity, although no mutations have been evidenced. We name "non inducible" this phenotype. As suggested by the presence of a positive feedback circuit in the regulatory network controlling TTSS expression, it may be due to an epigenetic switch allowing heritable phenotypic modifications without genotype's mutations. RESULTS: Using the generalised logical method, we designed a minimal model of the TTSS regulatory network that could support the epigenetic hypothesis, and studied its dynamics which helped to define a discriminating experimental scenario sufficient to validate the epigenetic hypothesis. A mathematical framework based on formal methods from computer science allowed a rigorous validation and certification of parameters of this model leading to epigenetic behaviour. Then, we demonstrated that a non inducible strain of P. aeruginosa can stably acquire the capacity to be induced by calcium depletion for the TTSS after a short pulse of a regulatory protein. Finally, the increased cytotoxicity of a strain after this epigenetic switch was demonstrated in vivo in an acute pulmonary infection model. CONCLUSION: These results may offer new perspectives for therapeutic strategies to prevent lethal infections by P. aeruginosa by reverting the epigenetic inducibility of type III cytotoxicity.