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By J Cruz

Evaluating the foremost positive aspects of biophysical inadequacy was once comparable with the illustration of differential equations. procedure dynamics is frequently modeled with the expressive energy of the present period constraints framework. it truly is transparent that an important version was once via differential equations yet there has been no manner of expressing a differential equation as a constraint and combine it in the constraints framework. as a result, the objective of this paintings is concentrated at the integration of standard differential equations in the period constraints framework, which for this function is prolonged with the recent formalism of Constraint pride Differential difficulties. Such framework permits the specification of standard differential equations, including similar details, through constraints, and gives effective propagation recommendations for pruning the domain names in their variables. This enabled the mixing of all such info in one constraint whose variables may perhaps hence be utilized in different constraints of the version. the categorical procedure used for pruning its variable domain names can then be mixed with the pruning equipment linked to the opposite constraints in an total propagation set of rules for lowering the limits of all version variables.

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Constraint Reasoning for Differential Models

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Several approaches are devised for enforcing Global Hull-consistency. A suggested approach ((n+1)B-consistency) is based on existing higher order consistency criteria and the corresponding generic enforcing algorithm. Four different alternative approaches (BS0, BS1, BS2, and BS3) are proposed based on backtrack search over the space of possibilities. Two additional approaches (OS1 and OS3) are derived from the modification of the backtrack search into an ordered search of the space of possibilities.

In chapter 10 we present our proposal of Constraint Satisfaction Differential Problems (CSDPs) for integrating differential equations within the interval constraints framework. Chapter 11 describes the procedure that is proposed for solving CSDPs. Chapter 12 tests our proposal on several biomedical problems for decision support with ODEs. In chapter 13 conclusions are discussed and future work is suggested. Chapter 9: Ordinary Differential Equations Ordinary differential equations and initial value problems (IVPs) are presented.

16 Chapter 2. 2-1 (Numeric Constraint Satisfaction Problem). A NCSP is a CSP P=(X,D,C) where i) DiD DiŽѐ › DiŽъ ii) (s,U)C U is defined as a numeric relation between the variables of s ‰ Further restrictions, either on the allowed variable domains or on the kind of numeric expressions used for specifying the numeric relations, may be imposed to address subclasses of problems and eventually to take advantage of their specific properties. For example, if only linear equations over the real numbers are allowed then the subclass of linear constraint satisfaction problems could be considered and some particular methods for solving systems of linear equations would be used.

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