Computer programming mathematical concepts

The term model is used to describe exposure including all the circumstances, the scenarios and their mathematical expressions. The term model is also used for computer programs to calculate exposure. In clinical pharmacology, a model characterizes the mathematical expression of the uptake, distribution and elimination of a drug from the body. WHO defines exposure model as a conceptual or mathematical representation of the exposure process (IPCS, 2004). This means that the model includes both concept and mathematical description of the exposure process. 

The mathematical model chosen as a basis is confined to constitutional chemistry. The formal concepts for the treatment of the stereochemical features of molecules and reactions have been given elsewhere10, and a computer program based on these ideas is being developed. For the initial phase of the development of a computer program for the design of syntheses, stereochemistry has temporarily been set aside to concentrate on the more important aspects of constitutional chemistry. 

Figure 3. This kinetic model for zinc in humans was based on averaged data obtained following oral and i.v. administration of Zn to 17 patients with abnormalities of taste and smell. The compartmental model used all kinetic data from Zn activity in plasma, red blood cells, urine, liver, and thigh as well as stable zinc parameters, including dietary intake, serum, and urinary concentration. The SAAM27 computer program was used to obtain the simplest set of mathematical relationships that would satisfy the data characteristics for each measurement time in the study and remain consistent with accepted concepts of zinc metabolism. Although the short physical half-life of Zn limited the data collection period, this model allowed for analysis of the rapid phases of zinc metabolism (about 10% of total body zinc) and derivation of a number of fundamental steady state...

Models, representations of real objects, have long been used to understand, explain, predict, and, ultimately, harness and exploit natural phenomena. They range from simple descriptions or drawings useful for conveying basic concepts to precise mathematical relationships that can be embodied in sophisticated computer programs. Whatever their form, all models are approximations with individual strengths and limitations that must be astutely applied to solve particular problems quickly and properly. 

With all the above said, it is natural to expect, that equations of motion, phase space, statistical ensemble, and other abstract mathematical concepts we spend so much effort describing in this and previous sections, do indeed have something to do with computer simulations. In fact, various simulation techniques are nothing else but methods for the numerical solution of the statistical mechanics given a Hamiltonian 7f(r). They allow for the realization of these abstract concepts. It is through the principles of statistical mechanics, which we have briefly described above, that the numbers produced by the computer simulation program are linked to the results of real-life experiments and to the properties of real materials. 

Genetic programming [137] is an evolutionary technique which uses the concepts of Darwinian selection to generate and optimise a desired computational function or mathematical expression. It has been comprehensively studied theoretically over the past few years, but applications to real laboratory data as a practical modelling tool are still rather rare. Unlike many simpler modelling methods, GP model variations that require the interaction of several measured nonlinear variables, rather than requiring that these variables be orthogonal. 

The mathematics of the subject are minimized, aaJ more emphasis is placed on examples that illustrate principles and concepts of great practical importance. Simulation programs (in FORTRAN) for a number of example processes are used to generate dynamic results. Plotting and analysis are accomplished using computer-aided software (MATLAB). 

---