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  • Springer  (207,872)
  • 1970-1974  (177,357)
  • 1930-1934
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  • 1
    Electronic Resource
    Electronic Resource
    Contributions to the theory of organismic sets, II: Aggressiveness and submissiveness (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 49-54 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the theory of organismic sets (Bull. Math. Biophysics,31, 159–198, 1969) we considered organisms as sets endowed with certain “activities,” the latter’s resulting in a set of “products.” Those products may be of a material nature, like a hormone secreted by a cell, or of a non-material nature, like a feeling or an attitude. In the present paper aggressiveness and submissiveness are considered as such non-material products of the activities of the brain cells. A general description of aggressiveness and submissiveness is given in terms of organismic sets. Cycles in “peck order” are thus naturally explained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476664
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  • 2
    Electronic Resource
    Electronic Resource
    Contribution to the theory of organismic sets, III (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 55-66 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In line with previous studies on organismic sets, the division of all organismic sets intogeneral autotrophic and heterotrophic is introduced. The first produce their food themselves from some external source of energy, which in general may be an energy of any kind. The others use other organismic sets as the source of their food and energy. On earth we know only one kind of generalgeneral autotrophic organismic sets, namely, the autotrophic plants which use solar radiation as their source of energy and for production of their own food. It is shown why autotrophic animals do not exist on earth except as microorganisms like, e.g.,Euglena. A rigorous proof of the previously derived theorem that in an organismic set of ordern〉1 no element can be completely specialized is given. It requires the introduction of new postulates. Finally, in considering the organic world as a whole, the notion of organismic sets ofmixed order is introduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476665
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  • 3
    Electronic Resource
    Electronic Resource
    “A stochastic solution of the 3-body problem in chemical kinetics. The termolecular stochastic process I” (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 67-81 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It appears to be axiomatic that termolecular and higher order reactions occur relatively rarely. The basis for this judgment seems to lie in the supposition that successful 3-Body collisions of 3 interactive species of molecules cannot occur frequently enought to account for chemical or biochemical transformation. In order to provide a more complete mathematical framework than now exists for examining this hypothesis the probability of effective termolecular “δ-collisions” as a function of time is derived. This amounts to adding to the class of reactions for which stochastic models are now available the termolecular reaction. In common with the unimolecular and bimolecular cases this process is seen to satisfy the criterion of consistency-in-the-mean with respect to deterministic formulations. It is planned next to use the termolecular process and the lower order processes in computer-assistedin numero experimental studies aimed at comparing alternative mechanisms of reaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476666
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  • 4
    Electronic Resource
    Electronic Resource
    Maximum likelihood estimation for stochastic first order reactions (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 83-96 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Small sample properties of the maximum likelihood estimator for the rate constant of a stochastic first order reaction are investigated. The approximate bias and variance of the maximum likelihood estimator are derived and tabulated. If observations of the system are made at timesiτ,i=1, 2, ...,N; τ〉0, the observational spacing τ which minimizes the approximate variance of the maximum likelihood estimator is found. The non-applicability of large sample theory to confidence interval derivation is demonstrated by examination of the relative likelihood. Bartlett’s method is employed to derive approximate confidence limits, and is illustrated by using simulated kinetic runs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476667
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  • 5
    Electronic Resource
    Electronic Resource
    Organismic supercategories and qualitative dynamics of systems (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 339-354 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The representation of biological systems by means of organismic supercategories, developed in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–71;32, 539–561), is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Băianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete result concerning dynamics of genetic system, development, fertilization, regeneration, analogies, and oncogenesis are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476778
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  • 6
    Electronic Resource
    Electronic Resource
    Some realizations of (M, R)-systems and their interpretation (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 303-319 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some years ago (Rosen 1958a, b; 1959) we described a class of metaphorical, relational paradigms for cellular activity which we termed (M, R)-systems. A sizable amount of subsequent work, to be itemized below, has been devoted to an exploration of some of the properties of these systems. The main purpose of the present paper is to put this class of paradigms into a general system-theoretic perspective, with a particular view to appraising the relation between the type of system description embodied in the (M, R)-system and other kinds of physical and mathematical descriptions of cellular systems. Thus, the principal aim is to establish the relationships and connections between the global relational formalism embodied in the (M, R)-systems and the empirical descriptions which still represent the bulk of our biological knowledge.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476776
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  • 7
    Electronic Resource
    Electronic Resource
    Relational forces and structures produced by them (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 321-338 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract After giving a brief review of the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967;31, 159–198, 1969), in which the concept of relational forces, introduced earlier (Bull. Math. Biophysics,28, 283–308, 1966a) plays a fundamental role, the author discusses examples of possible different structures produced by relational forces. For biological organisms the different structures found theoretically are in general agreement with observation. For societies, which are also organismic sets as discussed in the above references, the structures can be described only in an abstract space, the nature of which is discussed. Different isomorphisms between anatomical structures, as described in ordinary Euclidean space, and the sociological structures described in an abstract space are noted, as should be expected from the theory of organismic sets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476777
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  • 8
    Electronic Resource
    Electronic Resource
    Probabilistic and multiple regression modeling of the biologist’s decision processes and its implications for medical diagnosis (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 439-449 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Current psychological research into the inference (diagnostic) process is briefly reviewed, using as a vehicle an investigation of the prediction of the probability of success of hypothetical applicants to a graduate program in biology. Brunswik’s lens model and multiple regression analysis are used, as is a Bayesian approach. Four judges’ (biologists’) predictions are analyzed. Some general conclusions about inference, drawn from the current data in psychology, are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476785
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  • 9
    Electronic Resource
    Electronic Resource
    Anin numero study of glucose-insulin interaction (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 451-462 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model has been developed to simulate the glucose-insulin interaction following a glucose load such as occurs in an IVGTT. This model differs from earlier models in that the insulin response to glucose loading is a recurring all or none threshold response. The model has been simulated on a digital computer using the digital analog simulation language CSMP.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476786
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  • 10
    Electronic Resource
    Electronic Resource
    Wave propagation in bone media (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 463-479 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The composite nature of bone dictates the use of a model for bone which is transversely isotropic. We solve the associated sets of partial differential equations governing the dynamic elastic behavoor of a two-layered cylindrical-shaped bone. The solution is analyzed for long, short, and intermediate length waves. The special case of compact bone is treated for long and short wave lengths and a numerical example is worked out to determine the wave speeds (for short wave lengths) given a set of elastic constants, determined by ultrasonic methods, and the bone density, wave frequency, and radius.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476787
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