The models developed in these publications ranged from simple rules and equations to more complex first-order and mechanistic models.
The suggested model however has been designed to be flexible and to be implemented in a way which allows these rules and equations to be further modified if required to reflect any new quantitative information on the biology that might reasonably be expected to emerge in the future.
We have tried to work out how the model is set up and what the parameters, rules and equations are (as shown in the first paragraph), but have not succeeded.
We describe and analyze the variety of approaches to symbolic generalizations, syntactic rules and equation solving and the many solution strategies pursued successfully by the students.
The approach is based on the conventional optimization algorithms, FE simulations of industrial production process and knowledge base, containing both theoretical and practical data in form of rules, facts and equations.
To try to reconcile these into an easily visualized 3D model of wound healing amenable for experimentation by cell biologists, a multiscale model of the formation of a 3D skin epithelium was established with TGF-β1 literature derived rule sets and equations embedded within it.
Let us note that the following formula results from composition rules (9) and equation (31): I π, − 1 − α p ( x ) C D 0, + α y λ ( x ) = − I π, − 1 Y λ ( y ) + ξ 2. For a continuous function y λ, we obtain the following values at the ends: I π, − 1 − α p ( x ) C D 0, + α y λ ( x ) | x = 0 = − ∫ 0 π Y λ ( y ) d x + ξ 2, (32).
The first-order Chapman Kolmogorov differential equations are developed with the use of mnemonic rule and these equations are solved with Runga Kutta fourth-order method.
Assuming the functions to be differentiable, we may rewrite this conservation law via the chain rule and the equation (4) as ∇ d σ ( d ) div x f ( d ) = div x ϕ ( d ), (10).
We suggest to capture the modelling process including the definition of the topology of the model, the balances, transfer laws, kinetics, the required constitutive equations, and the compilation into a hierarchical set of ontologies that capture all these elements in the form of logical rules, basic equations and other objects.
His account of the experience is entertaining and informative.Human beings like to think of themselves as possessing unique capabilities such as being able to use tools, employ a language with syntactic rules and process complex mathematical equations.
