Abstract
The concept of a cybernetical action is defined as an action leading to a certain goal, subject to some constraints, by choosing the most appropriate (optimal) way. It is shown that cybernetical actions play a fundamental role not only in organisms (synaptic events, O2 transport system hierarchy, etc.), but also in biological populations (neuron populations, bacterial populations, social populations of insects, etc.). They lead to new orderly structures (states) in the population under consideration, according to the pursued goal, by using informations conveyed by the so calledactive messages defined in a previous paper (Teodorescu, 1976c). When stored (or generated) in a subsystem these active messages lead tocybernetical models, implicated in the muscle control phenomena, as well as in the optimal adaptive models of motion. Thus, mathematical models of the active messages are defined, namely themessage operators and an axiomatic theory is developed, emphasizing their main properties. They may be regarded as operators in a wider sense, involving an optimization. Moreover, message operators are comparable by using the concept ofstrength. Thus, the concepts ofcodex andmetacodex (as fundamental sets of message operators) are defined. It is shown that message operators involved by the codex (Ω) are always able to perform transitions from a given orderly state (F 0), to a new orderly state (F), whereF's are elements of a particular metric space, ℱ, satisfying someconditional metric properties. (“Distances” are conditioned by the states of the initial random process.) This fact emphasizes the central role played by the intrinsic features, i.e. “aptitudes”, of the biological population, in performing a cybernetical action. Hence, a cybernetical action may be defined as a tripletA =(Ω, ℱ, S) involving the codex Ω, the space ℱ as well as the domainS of the possible states of the initial random process (real numbers associated to the possible outcomes). A mathematical model of the cybernetical action is, thus, obtained which leads to a deeper understanding of the transformations performed by active messages in biological populations, as well as to new investigation tools in biology.
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References
Ashby Ross, W.: An introduction to cybernetics. London:Chapman and Hall 1961
Attinger, E.O., Attinger, F.: Hierarchy levels in the control of blood flow. Kybernetik13, 195–214 (1973)
Capocelli, R.M., Ricciardi, L.M.: Growth with regulation in random environment. Kybernetik15, 147–157 (1974)
Inbar, G.F.: Muscle spindles in muscle control. Analysis of an adaptive system model. Kybernetik11, 130–141 (1972)
Kawabata, N.: Dynamics of the electroencephalogram during performance of a mental task. Kybernetik15, 237–242 (1974)
Goodwin, B.C.: Temporal organization in cells. New York: Academic Press 1963
Himmelblau, D.: Process analysis by statistical methods. New York: Wiley 1970
Mesarovic, M.D., Macko, D., Takahara, Y.: Theory of hierarchical, multilevel systems. New York: Academic Press 1970
Matsuyama, Y., Shirai, K., Akizuki, K.: On some properties of stochastic information processes in neurons and neuron populations. Kybernetik15, 127–145 (1974)
Mood, A.M., Graybill, F.A., Boes, D.C.: Introduction to the theory of statistics. New York: McGraw Hill 1974
Rosen, R.: Is there a unified mathematical biology? In: Foundations of mathematical biology. New York: Academic Press 1973
Teodorescu, D.: Entwurf nichtlinearer Regelsysteme mittels Abtastmatrizen, Heidelberg: Hüthig 1973
Teodorescu, D.: Optimized statistical models: a new means for stochastic process estimation. Proc. IEE122, 856–857 (1975)
Teodorescu, D.: Sampled data vectors: a new means for biological model identification. Biol. Cybernetics21, 41–45 (1976a)
Teodorescu, D.: An analysis of biological random processes via optimized statistical models. Biol. Cybernetics22, 189–201 (1976b)
Teodorescu, D.: Message operators: a new expression of the information. Biol. Cybernetics24, 199–209 (1976c)
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Teodorescu, D. Cybernetical actions—Constraints and orderliness in biological populations. Biol. Cybernetics 26, 63–72 (1977). https://doi.org/10.1007/BF00801210
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DOI: https://doi.org/10.1007/BF00801210