O-Minimal Hybrid Reachability Games

In this paper, we consider reachability games over general hybrid systems, and distinguish between two possible observation frameworks for those games: either the precise dynamics of the system is seen by the players (this is the perfect observation framework), or only the starting point and the delays are known by the players (this is the partial observation framework). In the first more classical framework, we show that time-abstract bisimulation is not adequate for solving this problem, although it is sufficient in the case of timed automata . That is why we consider an other equivalence, namely the suffix equivalence based on the encoding of trajectories through words. We show that this suffix equivalence is in general a correct abstraction for games. We apply this result to o-minimal hybrid systems, and get decidability and computability results in this framework. For the second framework which assumes a partial observation of the dynamics of the system, we propose another abstraction, called the superword encoding, which is suitable to solve the games under that assumption. In that framework, we also provide decidability and computability results

Analysis of signalling pathways using the prism model checker

We describe a new modelling and analysis approach for signal transduction networks in the presence of incomplete data. We illustrate the approach with an example, the RKIP inhibited ERK pathway [1]. Our models are based on high level descriptions of continuous time Markov chains: reactions are modelled as synchronous processes and concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis of queries such as if a concentration reaches a certain level, will it remain at that level thereafter? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable

LNCS

Despite researchers’ efforts in the last couple of decades, reachability analysis is still a challenging problem even for linear hybrid systems. Among the existing approaches, the most practical ones are mainly based on bounded-time reachable set over-approximations. For the purpose of unbounded-time analysis, one important strategy is to abstract the original system and find an invariant for the abstraction. In this paper, we propose an approach to constructing a new kind of abstraction called conic abstraction for affine hybrid systems, and to computing reachable sets based on this abstraction. The essential feature of a conic abstraction is that it partitions the state space of a system into a set of convex polyhedral cones which is derived from a uniform conic partition of the derivative space. Such a set of polyhedral cones is able to cut all trajectories of the system into almost straight segments so that every segment of a reach pipe in a polyhedral cone tends to be straight as well, and hence can be over-approximated tightly by polyhedra using similar techniques as HyTech or PHAVer. In particular, for diagonalizable affine systems, our approach can guarantee to find an invariant for unbounded reachable sets, which is beyond the capability of bounded-time reachability analysis tools. We implemented the approach in a tool and experiments on benchmarks show that our approach is more powerful than SpaceEx and PHAVer in dealing with diagonalizable systems

The categorical limit of a sequence of dynamical systems

Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns out to be subject to ambiguity. Depending on the interpretation of the sequence, i.e. depending on how the behaviors of the systems in the sequence are related, it may vary what the limit should be. Topologies, and in particular metrics, define limits uniquely, if they exist. Thus they select one interpretation implicitly and leave no room for other interpretations. In this paper, we define limits using category theory, and use the mentioned relations between system behaviors explicitly. This resolves the problem of ambiguity in a more controlled way. We introduce a category of prefix orders on executions and partial history preserving maps between them to describe both discrete and continuous branching time dynamics. We prove that in this category all projective limits exist, and illustrate how ambiguity in the definition of limits is resolved using an example. Moreover, we show how various problems with known topological approaches are now resolved, and how the construction of projective limits enables us to approximate continuous time dynamics as a sequence of discrete time systems.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

User-centered visual analysis using a hybrid reasoning architecture for intensive care units

One problem pertaining to Intensive Care Unit information systems is that, in some cases, a very dense display of data can result. To ensure the overview and readability of the increasing volumes of data, some special features are required (e.g., data prioritization, clustering, and selection mechanisms) with the application of analytical methods (e.g., temporal data abstraction, principal component analysis, and detection of events). This paper addresses the problem of improving the integration of the visual and analytical methods applied to medical monitoring systems. We present a knowledge- and machine learning-based approach to support the knowledge discovery process with appropriate analytical and visual methods. Its potential benefit to the development of user interfaces for intelligent monitors that can assist with the detection and explanation of new, potentially threatening medical events. The proposed hybrid reasoning architecture provides an interactive graphical user interface to adjust the parameters of the analytical methods based on the users' task at hand. The action sequences performed on the graphical user interface by the user are consolidated in a dynamic knowledge base with specific hybrid reasoning that integrates symbolic and connectionist approaches. These sequences of expert knowledge acquisition can be very efficient for making easier knowledge emergence during a similar experience and positively impact the monitoring of critical situations. The provided graphical user interface incorporating a user-centered visual analysis is exploited to facilitate the natural and effective representation of clinical information for patient care