Abstract.Learning from interpretation transition (LFIT) automatically constructs a model of the dynamics of a system from the observation of its state transitions. So far, the systems that LFIT handles are restricted to synchronous deterministic dynamics, i.e., all variables update their values at the same time and, for each state of the system, there is only one possible next state. However, other dynamics exist in the field of logical modeling, in particular the asynchronous semantics which is widely used to model biological systems. In this paper, we focus on a method that learns the dynamics of the system independently of its semantics. For this purpose, we propose a modeling of multi-valued systems as logic programs in which a rule represents what can occurs rather than what will occurs. This modeling allows us to represent nondeterminism and to propose an extension of LFIT in the form of a semantics free algorithm to learn from discrete multi-valued transitions, regardless of their update schemes. We show through theoretical results that synchronous, asynchronous and general semantics are all captured by this method. Practical evaluation is performed on randomly generated systems and benchmarks from biological literature to study the scalability of this new algorithm regarding the three aforementioned semantics.Keywords: Dynamical semantics, learning from interpretation transition, dynamical systems, Inductive Logic Programming IntroductionLearning the dynamics of systems with many interactive components becomes more and more important due to many applications, e.g., multi-agent systems, robotics and bioinformatics. Knowledge of a system dynamics can be used by agents and robots for planning and scheduling. In bioinformatics, learning the dynamics of biological systems can correspond to the identification of the influence of genes and can help to understand their interactions. While building a model, the choice of a relevant semantics associated to the studied system represents a major issue with regard to the kind of dynamical properties to analyze. The differences and common features of different semantics w.r.t. properties of interest (attractors, oscillators, etc.) constitutes an area of research per itself, especially in the field of Boolean networks. In [8], the author exhibits the translation from Boolean networks into logic programs and discusses the point attractors in both synchronous and asynchronous semantics. In [6], A. Garg et al. address the differences and complementarity of synchronous and asynchronous semantics to model biological networks and identify attractors. The benefits of the synchronous model are to be computationally tractable, while classical state space exploration algorithms fail on asynchronous ones. For some applications, like the biological ones, asynchronous semantics is said to capture more realistic behaviors: at a given time, a single gene can change its expression level. This results in a potential combinatorial explosion of the number of reachable states. To illustr...

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Accepted at CS2Bio'13. http://cs2bio13.di.unito.it/International audienceThe Process Hitting is a recently introduced framework designed for the modelling of concurrent systems. Its originality lies in a compact representation of both components of the model and its corresponding actions: each action can modify the status of a component, and is conditioned by the status of at most one other component. This allowed to define very efficient static analysis based on local causality to compute reachability properties. However, in the case of cooperations between components (for example, when two components are supposed to interact with a third one only when they are in a given configuration), the approach leads to an over-approximated interleaving between actions, because of the pure asynchronous semantics of the model. To address this issue, we propose an extended definition of the framework, including priority classes for actions. In this paper, we focus on a restriction of the Process Hitting with two classes of priorities and a specific behaviour of the components, that is sufficient to tackle the aforementioned problem of cooperations. We show that this class of Process Hitting models allows to represent any Asynchronous Discrete Networks, either Boolean or multivalued. Then we develop a new refinement for the under-approximation of the static analysis to give accurate results for this class of Process Hitting models. Our method thus allows to efficiently under-approximate reachability properties in Asynchronous Discrete Networks; it is in particular conclusive on reachability properties in a 94 components Boolean network, which is unprecedented

An extended set of statistical tests, aimed at assessing the quality of the magnetic reconstructions in JET, obtained with the code EFIT using the external magnetic measurements, is described and the results reported in detail. In addition to the traditional analysis of the global distributions of the residuals (the difference between the actual measurements and their reconstructions from the equilibrium), to determine to what extent they approximate a Gaussian, more sophisticated correlation tests have been performed. Since EFIT solves a highly non-linear equation, tests adequate for multi-input multi-output, non-linear systems have been implemented. Not only the reconstruction of the pickup coil signals but also the accuracy of the plasma boundary has been investigated. The results indicate quite clearly that the errors in the reconstruction of the pickup coils are not negligible. The coils, whose residuals present skewed monomodal distributions (distributions asymmetric with respect to their maximum value), are affected by average errors of the order of more than one millitesla and multimodal distributions of the residuals (distributions presenting more than one local maximum) are quite common. Also the correlation of the residuals is typically outside the 95% limits for a good model in typically more than 70% of the cases. With regard to the plasma boundary, the situation is better since the errors in the distances of the plasma from the wall are typically of the order of 1 cm. On the other hand, in this case the autocorrelations of the residuals are also well outside the 95% confidence interval for random residuals. A detailed analysis of the correlations indicates that the main reasons for the imperfections in the magnetic reconstructions do not reside in the measurements, since there is no evidence of systematic errors or problems with the calibrations. Therefore, the main improvements are to be expected by refinements in the used equilibrium code EFIT, whose constraints and boundary conditions are probably not the most appropriate to model H mode plasmas.

BackgroundThis paper addresses the problem of finding attractors in biological regulatory networks. We focus here on non-deterministic synchronous and asynchronous multi-valued networks, modeled using automata networks (AN). AN is a general and well-suited formalism to study complex interactions between different components (genes, proteins,...). An attractor is a minimal trap domain, that is, a part of the state-transition graph that cannot be escaped. Such structures are terminal components of the dynamics and take the form of steady states (singleton) or complex compositions of cycles (non-singleton). Studying the effect of a disease or a mutation on an organism requires finding the attractors in the model to understand the long-term behaviors.ResultsWe present a computational logical method based on answer set programming (ASP) to identify all attractors. Performed without any network reduction, the method can be applied on any dynamical semantics. In this paper, we present the two most widespread non-deterministic semantics: the asynchronous and the synchronous updating modes. The logical approach goes through a complete enumeration of the states of the network in order to find the attractors without the necessity to construct the whole state-transition graph. We realize extensive computational experiments which show good performance and fit the expected theoretical results in the literature.ConclusionThe originality of our approach lies on the exhaustive enumeration of all possible (sets of) states verifying the properties of an attractor thanks to the use of ASP. Our method is applied to non-deterministic semantics in two different schemes (asynchronous and synchronous). The merits of our methods are illustrated by applying them to biological examples of various sizes and comparing the results with some existing approaches. It turns out that our approach succeeds to exhaustively enumerate on a desktop computer, in a large model (100 components), all existing attractors up to a given size (20 states). This size is only limited by memory and computation time.

Abstract. The Process Hitting (PH) is a recently introduced framework to model concurrent processes. Its major originality lies in a specific restriction on the causality of actions, which makes the formal analysis of very large systems tractable. PH is suitable to model Biological Regulatory Networks (BRNs) with complete or partial knowledge of cooperations between regulators by defining the most permissive dynamics with respect to these constraints.On the other hand, the qualitative modeling of BRNs has been widely addressed using René Thomas' formalism, leading to numerous theoretical work and practical tools to understand emerging behaviors.Given a PH model of a BRN, we first tackle the inference of the underlying Interaction Graph between components. Then the inference of corresponding Thomas' models is provided using Answer Set Programming, which allows notably an efficient enumeration of (possibly numerous) compatible parametrizations.In addition to giving a formal link between different approaches for qualitative BRNs modeling, this work emphasizes the ability of PH to deal with large BRNs with incomplete knowledge on cooperations, where Thomas' approach fails because of the combinatorics of parameters. IntroductionAs regulatory phenomena play a crucial role in biological systems, they need to be studied accurately. Biological Regulatory Networks (BRNs) consist in sets of either positive or negative mutual effects between the components. With the purpose of analyzing these systems, they are often modeled as graphs which make it possible to determine the possible evolutions of all the interacting components of the system. Indeed, besides continuous models of physicists, often designed through systems of ordinary differential equations, a discrete modeling approach was initiated by René Thomas in 1973 [1].In this approach, the different levels of a component, such as concentration or expression levels, are abstractly represented by (positive) integer values and transitions between these levels may be considered as instantaneous. Hence, qualitative state graphs may be derived from which we are able to formally find out all the possible behaviors expressed as sequences of transitions between these states. Nevertheless, these dynamics can be precisely established only with regard to some discrete parameters which stand for a kind of "focal points", i.e. the evolutionary tendency from each state and depending of the set of resources in this very state, that is, the set of the other currently interacting components. Hereafter, we refer to these discrete parameters as Thomas' parameters.Thomas' modeling has motivated numerous works around the link between the Interaction Graph (IG) (summarizing the global influences between components) and the possible dynamics (e.g., [2,3]), model reduction (e.g., [4]), formal checking of dynamics (e.g., [5,6]), and the incorporation of time (e.g., [7,8]) and probability (e.g., [9]) dimensions, to name but a few. While the formal checking of dynamical properties is often limite...

The modeling challenge Regulation is a key aspect of biological systems, all the way from the molecular scale to the ecological one. Gaining a precise understanding of regulation is one of the main goals of systems biology. This discipline has emerged from the synergy between cell biology and cybernetics [WIE 48], from the collaboration of biologists, physicists and computer scientists [IDE 01]. The modeling approach presented in this chapter derives from this heritage by studying the interactions of components of a biological system and analyzing how these interactions impact the function and behavior of the system as a whole. Here, we will focus on applications to genetics, but the potential field of the approach is broader: the Process Hitting framework is relevant to any interactive system, whether it is a biological regulatory network, a logistic scheme or an embedded system. The recent progress in molecular biology has made it possible to obtain a comprehensive map of the genomes of many living organisms. Simultaneously, the development of DNA micro array technology has given access to time series data of the expression of several thousands of genes. One of the main challenges now is to Chapter written by Loïc PAULEVÉ and Courtney CHANCELLOR and Maxime FOLSCHETTE and Morgan MAGNIN and Olivier ROUX.