The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Model checking
Beyond HYTECH: Hybrid Systems Analysis Using Interval Numerical Methods
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Level Set Methods for Computation in Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Symbolic Techniques for Parametric Reasoning about Counter and Clock Systems
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Overapproximating Reachable Sets by Hamilton-Jacobi Projections
Journal of Scientific Computing
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
A Counterexample-Guided Approach to Parameter Synthesis for Linear Hybrid Automata
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Parameter Synthesis for Hybrid Systems with an Application to Simulink Models
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Model checking genetic regulatory networks with parameter uncertainty
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Systematic simulation using sensitivity analysis
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
The image computation problem in hybrid systems model checking
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Model checking liveness properties of genetic regulatory networks
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Efficient representation and computation of reachable sets for hybrid systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Robust sampling for MITL specifications
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
Reconstruction of switching thresholds in piecewise-affine models of genetic regulatory networks
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Computing Reachable States for Nonlinear Biological Models
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Computing reachable states for nonlinear biological models
Theoretical Computer Science
On Parameter Synthesis by Parallel Model Checking
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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The dynamics of biological processes are often modeled as systems of nonlinear ordinary differential equations (ODE). An important feature of nonlinear ODEs is that seemingly minor changes in initial conditions or parameters can lead to radically different behaviors. This is problematic because in general it is never possible to know/measure the precise state of any biological system due to measurement errors. The parameter synthesis problem is to identify sets of parameters (including initial conditions) for which a given system of nonlinear ODEs does not reach a given set of undesirable states. We present an efficient algorithm for solving this problem that combines sensitivity analysis with an efficient search over initial conditions. It scales to high-dimensional models and is exact if the given model is affine. We demonstrate our method on a model of the acute inflammatory response to bacterial infection, and identify initial conditions consistent with 3 biologically relevant outcomes.