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The applications of computers to biological and biomedical problem solving go back to the very beginnings of computer science, automata theory [1], and mathematical biology [2]. With the advent of more versatile and powerful computers, biological and biomedical applications of computers have proliferated so rapidly that it would be virtually impossible to compile a comprehensive review of all developments in this field. Limitations of computer simulations in biology have also come under close scrutiny, and claims have been made that biological systems have limited information processing power [3]. Such general conjectures do not, however, deter biologists and biomedical researchers from developing new computer applications in biology and medicine. Microprocessors are being widely employed in biological laboratories both for automatic data acquisition/processing and modeling; one particular area, which is of great biomedical interest, involves fast digital image processing and is already established for routine clinical examinations in radiological and nuclear medicine centers, Powerful techniques for biological research are routinely employing dedicated, online microprocessors or array processors; among such techniques are: Fouriertransform nuclear magnetic resonance (NMR), NMR imaging (or tomography),
xray tomography, xray diffraction, high performance liquid chromatography, differential scanning calorimetry and mass spectrometry. Networking of laboratory microprocessors linked to a central, large memory computer is the next logical step in laboratory automation. Previously unapproachable problems, such as molecular dynamics of solutions, manybody interaction calculations and statistical mechanics of biological processes are all likely to benefit from the increasing access to the new generation of "supercomputers". In view of the large number, diversity and complexity of computer applications in biology and medicine, we could not review in any degree of detail all computer applications in these fields; instead, we shall be selective and focus our discussion on suggestive computer models of biological systems and those fundamental aspects of computer applications that are likely to continue to make an impact on biological and biomedical research. Thus, we shall consider unifying trends in mathematics, mathematical logics and computer science that are relevant to computer modeling of biological and biomedical systems. The latter are pitched at a more formal, abstract level than the applications and, therefore, encompass a number of concepts drawn from the abstract theory of sets and relations, network theory, automata theory, Boolean and nvalued logics, abstract algebra, topology and category theory. The present analysis of relational theories in biology and computer simulation has also inspired a number of new results which are presented here as "Conjectures" since their proofs are too lengthy and too technical to be included in this review. In order to maintain a selfcontained presentationthe definitions of the main concepts are given, with the exception of a minimum of simple mathematical concepts.
The purpose of these theoretical sections is to provide the basis for approaching a number of basic biological questions:
(1) What are the essential characteristics of a biological organism as opposed to an automaton?
(2) Are biological systems recursively computable?
(3) What is the structure of the simplest (primordial) organism?
(4) What are the basic structures of neural and genetic networks?
(5) What are the common properties of classes of biological organisms?
(6) Which system representations are adequate for biodynamics?
(7) What is the optimal strategy for modifying an organism through genetic engineering? (8) What is the optimal simulation of a biological system with a digital or analog computer?
(9) What is life?

Baianu
I. C.
Professor
icb
"Math

Witten
Matthew
Professor
pub
Computer Models in Biology; Cellular Automata Models in Biology and Medicine; Relational Biology of MetabolicRepairReplication Systems in Categories; Lukasiewicz Logic Algebras of Nonlinear Dynamics in Genetic Networks; Neural Network Dynamics; the Enzymatic Neuron Network model; Cell Interactomics; Computability questions for models of Biosystems; Evolution of organisms and the principles of relational biology; computer modelling of the human cardiovascular system; computer modeling of lung vascularization; optimal control of the cardiovascular system; Medical Diagnosis models in Lukasiewicz Logic Algebras with nvalues; Adjoint and analogous models of Organisms; quantum computation and natural transformations of organic structures; Cellular automata models of carcinogenesis; optimal chemotherapy of cancer designed by computer models of Cancer; theoretical models in Medicine and biomedical research.
This review article covers a wide range of models in theoretical biology and mathematical biophysics of interest to applied mathematicians, dynamic systems theorists, theoretical biologists, complex system analysts, topologists and algebraists.
15131986
TRUE
Mathematical Modelling, vol.7.
Pergamon Press, Ltd.
TRUE
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17. Bourbaki, N. 1958. Elements de Mathematique, Paris: Hermann & Cle, Editeurs.
18. Carnap. R. 1938. "'The Logical Syntax of Language" New York: Harcourt, Brace and Co.
19. Cazanescu, D. 1967. On the Category of Abstract Sequential Machines. Ann. Univ. Buch., Maths & Mech. series, 16 (1):3137.
20. Comorozan, S. and Baianu, I.C. 1969. Abstract Representations of Biological Systems in Supercategories. Bull. Math. Biophys., 31: 5971.
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27. Lawvere, F. W. 1963. "Functional Semantics of Algebraic Theories." Proc. Natl.Acad. Sci., 50, 869872.
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Proc. Conf. Categorical .AlgebraLa Jolla 1965, Eilenberg, S., et al. eds., Berlin, Heidelberg and New York: SpringerVerlag, pp. 120.
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 biotheory
COMPUTER MODELS AND AUTOMATA THEORY
IN BIOLOGY AND MEDICINE
published
1987
This review article covers a wide range of models in theoretical biology and mathematical biophysics of interest to applied mathematicians, dynamic systems theorists, theoretical biologists, complex system analysts, topologists and algebraists.
public