Stahl67D bmp

208 WALTER R. STAHL

are intrinsically partial models, as defined by certain particular similarity criteria. The naturę of these criteria varies within the three principal groups of models, namely physical analogs, numerical representations, and cybemetic-algorithmic models. In all cases, however, an objective computation procedurę (algorithm) can be used to define the specific naturę of similarity between model and prototype (or among related systems).

Considerable success has been achieved in making partial models of a large variety of biological systems, but only in very few instances have they allowed prediction of unknown quantitative data. The available simulations are commonly invariant under only a few of all possible pertinent similarity criteria, which is what makes them “models,” but not under a large enough set of such criteria to assure real physical or operational similarity in the generał sense.

Modeling is a synthetic method, contrasted with the purely analytical approach of conventional mathematics, and is freąuently able to provide insight into situations far morę complex than manageable, e.g., by use of differential calculus. Computer modeling of both physical and cyber-netic systems has added broad new capabilities to the synthetic simu-lation approach and promises to be of much value for biological simula-tion in all its varieties.

A model and prototype, or two similar systems, can be transformed or mapped into each other in some sense. During this transformation process some mathematical properties shall be found to be invariant and these properties are precisely those defining the extent of modeling. The mapping jnay be very “practical,” as in the case of numerical scale-up theory, or entirely abstract, as found in relational, topological, and algorithmfc representations of allegedly similar biological systems. In generał, any two systems which are “similar” to each other share at least one invariant of some sort. This may rangę for a ratio of Iengths of sides of triangles for Euclidean geometrie similarity, Reynolds number for ordinary fłow models, relative heart weight for two mammals, or intejli-gence ąuotient or “control score” for a young and an old human. The invariance is maintained during certain stated transformations of space, time, size, age, physiological state, location of functioning, etc.

A. VaLIDITY OF THE MODEL

In a volume on technological modeling theory Murphy (1950) distin-guishes the following types of models on the basis of invariance of pertinent criteria of similarity and quantitative validity of results obtained from the model.

Wyszukiwarka

Podobne podstrony:
MR293R19025 1 Unpicking COMPOSITION OF PART AS SUPPLIED BY PARTS DEPARTMENT Panel only The two cove
Stahl67 bmp 186 WALTER R. STAHL a very restricted modeling situation. Mannikins are also in use fo
Stahl67& bmp 190 WALTER R. STAHL sition of an allele in a genome. No physical constants other than
Stahl672 bmp 196 WALTER R. STAHL Function and regulation in the myocardium are the subject of sever
Stahl674 bmp 198 WALTER R. STAHL not all necessary numerical constants are available in vivo to val
Stahl67 bmp 166 WALTER R. STAHL 193 194 195 196 197 197 198 198 199 200 201 202 203 204
Stahl67 bmp 168 WALTER R. STAHL entire field of cybernetics. Westcott (1960) emphasizes the proble
Stahl67 bmp 170 WALTER R. STAHL Consider a small-scale test model of a new type of turbinę, which
Stahl67 bmp 172 WALTER R. STAHL TABLE I Mathematical Similaeitt Criteria for Variotjs Types of Mod
Stahl67 bmp 174 WALTER R. STAHL C. Mathematical Naturę of Modeling Invariants The different variet
Stahl67 bmp 178 WALTER R. STAHL a dimensionless criterion associated with the Poiseuille flow law.
Stahl67 bmp 180 WALTER R. STAHL of the entire cardiovascular system based on dozens of eąuations f
Stahl67 bmp 182 WALTER R. STAHL titative greenhouse studies on the effects of water, light intensi
Stahl67 bmp 184 WALTER R. STAHL B. Artificial Kidney The artificial kidney is very dissimilar in a
Stahl67$ bmp 188 WALTER R. STAHL Reeve and Bailey (1962) developed a rather complex differential eq
Stahl67( bmp 192 WALTER R. STAHL A rather different approach to ecological modeling has been chosen
Stahl670 bmp 194 WALTER R. STAHL a discussion of simulation of biological systems of all types by M
Stahl676 bmp 200 WALTER R. STAHL tempted to explain data in human coordinationdisturbances (Parkins

więcej podobnych podstron