Title page -- Table of Contents -- Introduction -- Contributions -- Interval Constraints for Differential Equations -- Global Hull-consistency - A Strong Consistency Criterion -- Local Search for Interval Constraint Reasoning -- Prototype Implementation: Applications to Biophysical Modelling -- Guide to the Dissertation -- Interval Constraints -- Constraint Satisfaction Problems -- Solving a Constraint Satisfaction Problem -- Pruning -- Branching -- Stopping -- Constraint Satisfaction Problems With Continuous Domains -- Intervals Representing Unidimensional Continuous Domains -- Interval Operations and Basic Functions -- Interval Approximations -- Boxes Representing Multidimensional Continuous Domains -- Solving Continuous Constraint Satisfaction Problems -- Summary -- Interval Analysis -- Interval Arithmetic -- Extended Interval Arithmetic -- Interval Functions -- Interval Extensions -- Interval Methods -- Univariate Interval Newton Method -- Multivariate Interval Newton Method -- Summary -- Constraint Propagation -- The Propagation Algorithm -- Associating Narrowing Functions to Constraints -- Constraint Decomposition Method -- Constraint Newton Method -- Complementary Approaches -- Summary -- Partial Consistencies -- Local Consistency -- Higher Order Consistency -- Summary -- Global Hull-Consistency -- The Higher Order Consistency Approach -- The (n+1)B-consistency Algorithm -- Backtrack Search Approaches -- The BS0 Algorithm -- The BS1 Algorithm -- The BS2 Algorithm -- The BS3 Algorithm -- Ordered Search Approaches -- The OS1 Algorithm -- The OS3 Algorithm -- The Tree Structured Approach -- The Data Structures -- The Actions -- The TSA Algorithm -- Summary -- Local Search -- The Line Search Approach -- Obtaining a Multidimensional Vector - the Newton-Raphson Method -- Obtaining a New Point -- Alternative Local Search Approaches.

Integration of Local Search with Global Hull-Consistency Algorithms -- Summary -- Experimental Results -- A simple example -- The Census Problem -- Protein Structure -- Local Search -- Summary -- Interval Constraints for Differential Equations -- Ordinary Differential Equations -- Numerical Approaches -- Taylor Series Methods -- Errors and Step Control -- Interval Approaches -- Interval Taylor Series Methods -- Validation and Enclosure of Solutions Between two Discrete Points -- Computation of a Tight Enclosure of Solutions at a Discrete Point -- Constraint Approaches -- Older's Constraint Approach -- Hickey's Constraint Approach -- Jansen, Deville and Van Hentenryck's Constraint Approach -- Summary -- Constraint Satisfaction Differential Problems -- CSDPs are CSPs -- Value Restrictions -- Maximum and Minimum Restrictions -- Time and Area Restrictions -- First and Last Value Restrictions -- First and Last Maximum and Minimum Restrictions -- Integration of a CSDP within an Extended CCSP -- Canonical Solutions for Extended CCSPs -- Local Search for Extended CCSPs -- Modelling with Extended CCSPs -- Modelling Parametric ODEs -- Representing Interval Valued Properties -- Combining ODE Solution Components -- Summary -- Solving a CSDP -- The ODE Trajectory -- Narrowing Functions for Enforcing the ODE Restrictions -- Value Narrowing Functions -- Maximum and Minimum Narrowing Functions -- Time and Area Narrowing Functions -- First and Last Value Narrowing Functions -- First and Last Maximum and Minimum Narrowing Functions -- Narrowing Functions for the Uncertainty of the ODE Trajectory -- Propagate Narrowing Function -- Link Narrowing Function -- Improve Narrowing Functions -- The Constraint Propagation Algorithm for CSDPs -- Summary -- Biomedical Decision Support with ODEs -- A Differential Model for Diagnosing Diabetes.

Representing the Model and its Constraints with an Extended CCSP -- Using the Extended CCSP for Diagnosing Diabetes -- A Differential Model for Drug Design -- Representing the Model and its Constraints with an Extended CCSP -- Using the Extended CCSP for Parameter Tuning -- The SIR Model of Epidemics -- Using the Extended CCSP for Predicting the Epidemic Behaviour -- Summary -- Conclusions and Future Work -- Interval Constraints for Differential Equations -- Global Hull-consistency -- Local Search for Interval Constraint Reasoning -- Prototype Implementation: Applications to Biophysical Modelling -- Conclusions -- References -- Appendix A: Interval Analysis Theorems -- Appendix B: Constraint Propagation Theorems.