First, as we have seen, almost every set theoretically defined mathematical structure with the appropriate notion of homomorphism yields a category.
Such rudimentary methods are used either because there has historically been no suitable mathematical structure with which to represent the relevant grain boundary information, or, where there are existing methods they are extremely unintuitive and cumbersome to use.
Sharing the same mathematical structure with the original (reduced) systems, their numerical solution, is likewise efficiently performed.
This crucial step provides the mathematical structure with the capacity to reproduce a given data set, make predictions and discriminate among different model candidates.
The next step is to propose a mathematical structure with the necessary level of detail, which will in general include a number of unknown, non-measurable parameters.
Large scale metabolic network of the glycolysis, the pentose-phosphate-pathway, and the phosphotransferase system of E. coli K-12 W3110 [ 40] consists of a complex mathematical structure with 18 dynamic mass balance equations, (5) to (22) presented below, 7 additional algebraic equations, (A.1) to (A.7), and 30 kinetic rate expressions, (A.8) to (A.37) [ 2].
In this study, we maintain the important physical requirements by employing a strategy based on the key concept that mathematical structures associated with conservative and nonconservative equations are preserved, even at the discrete level.
Take fractals, mathematical structures or sets with intermediate dimensionality.
Individual components are linked with mathematical structures that enable computational analysis of the network as an integrated system.
These four areas need to be modelled in a unitary way in order to capture formally (with mathematical structures) the context of the human behaviour and its variability.
