Systems theory, hierarchy

As far as an external aesthetic is concerned, we do have two important clues to help guide us (1) chaos theory, from which we learn that natural processes that appear complicated can often be well understood using relatively simple rules, and (2) complex systems theory, from which wc learn that interesting phenomena often emerge on higher levels from parts that are mutually interacting on the lower levels of a hierarchy. 

General systems theory is a set of related definitions, assumptions, and propositions which deal with reality as an integrated hierarchy of organizations of matter and energy. General living systems theory is concerned with a special subset of all systems, the living ones. 

The foundation of systems theory rests on two pairs of ideas (1) emergence and hierarchy and (2) communication and control [36],... 

The structure of an intent specification is based on the fundamental concept of hierarchy in systems theory (see chapter 3) where complex systems are modeled in terms of a hierarchy of levels of organization, each level imposing constraints on the degree of freedom of the components at the lower level. Different description languages may be appropriate at the different levels. Figure 10.1 shows the seven levels of an intent specification. 

Since these initial contributions, many works followed, which may be classified into three broad categories (1) Control structure development based mainly on process experience and engineering judgment [7], (2) Control structure development that follows the guidelines of the steady-state process design synthesis hierarchy [1], and (3) Control structure development that relies on a mathematical formulation based on dynamic system theory, optimization, and control-theoretic systems analysis. Some contributions can be classified in more than one category. 

Election nuclear dynamics theory is a direct nonadiababc dynamics approach to molecular processes and uses an electi onic basis of atomic orbitals attached to dynamical centers, whose positions and momenta are dynamical variables. Although computationally intensive, this approach is general and has a systematic hierarchy of approximations when applied in an ab initio fashion. It can also be applied with semiempirical treatment of electronic degrees of freedom [4]. It is important to recognize that the reactants in this approach are not forced to follow a certain reaction path but for a given set of initial conditions the entire system evolves in time in a completely dynamical manner dictated by the inteiparbcle interactions. 

Bogolubov3 developed a theory which allows the hierarchy to be cut and the evolution of in terms of fx itself to be expressed. To do this, he assumed that there are three stages in the evolution with time of a macroscopic gaseous system ... 

From these expressions, it is evident that the steep increase of the computational cost with X (the basis-set hierarchy) and m (the coupled-cluster hierarchy) severely restricts the levels of theory that can be routinely used for large systems or even explored for small systems. Nevertheless, we shall see that, with current computers, it is possible to arrange the calculations in such a manner that chemical accuracy (of the order of 1 kcal/mol 4 kJ/mol) can be achieved - at least for molecules containing not more than ten first-row atoms. 

The evolution of methods and models in technology and theory has brought drug research to its current state. But what is this current state We begin here with a brief answer by identifying the hierarchy of systems of interest to us in this activity and continue by describing the progress associated with each system. 

The Mpller-Plesset (MP) treatment of electron correlation [84] is based on perturbation theory, a very general approach used in physics to treat complex systems [85] this particular approach was described by M0ller and Plesset in 1934 [86] and developed into a practical molecular computational method by Binkley and Pople [87] in 1975. The basic idea behind perturbation theory is that if we know how to treat a simple (often idealized) system then a more complex (and often more realistic) version of this system, if it is not too different, can be treated mathematically as an altered (perturbed) version of the simple one. Mpller-Plesset calculations are denoted as MP, MPPT (M0ller-Plesset perturbation theory) or MBPT (many-body perturbation theory) calculations. The derivation of the Mpller-Plesset method [88] is somewhat involved, and only the flavor of the approach will be given here. There is a hierarchy of MP energy levels MPO, MP1 (these first two designations are not actually used), MP2, etc., which successively account more thoroughly for interelectronic repulsion. 

It is worth noting the way in which this account of prime matter can be integrated into Aristotle s theory of mathematics and his account of material substances. According to the interpretation I am offering, prime matter occupies a special position in both the mathematical hierarchy of objects and the material structure of substances. In fact, one interesting aspect of this interpretation is the way in which these two different parts of Aristodes system dovetail. 

We argue that the theory of the hyperspatial nature of superconductive bonds, and the experiment we devised to test that theory, yielded not only spectacular subjective results but also a modular wave-hierarchy theory of the nature of time that we have been able to construe, using a particular mathematical treatment of the / Ching, into a general theory of systems. 

---