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  • Springer  (34,810)
  • Oxford University Press  (2,952)
  • Public Library of Science (PLoS)
  • 1950-1954  (37,762)
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Year
  • 11
    Electronic Resource
    Electronic Resource
    Spread of information through a population with socio-structural bias: II. Various models with partial transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 535-546 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The assumption of transitivity treated in part I is modified in various ways to describe an information-diffusion process, in which a certain amount of randomness of contact does occur. In one model a parameter is introduced which is indicative of a tendency to go beyond one's immediate vicinity to spread the information as the vicinity becomes saturated with knowers. In another model the randomness appears in the assumption that new knowers are uniformly distributed among the knowers. Two of the equations thus derived, each with two free parameters are in good agreement with experimental results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476441
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  • 12
    Electronic Resource
    Electronic Resource
    The transmission of excitation from the membrane to actomyosin (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 1-13 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The impressed field, “Window Field” (WF), due to a half-wave action potential on a muscle fiber, has been calculated on the basis of potential theory. It has been shown that in spite of the small intensity of the field, its integrated action can transfer the energy needed to induce, contraction from the membrane to the interior of the fiber. The energy of polarization has been found to be sufficient to exceed the energy of, thermal agitation on that length of fiber, which can be identified as the length of a sarcomere. The changes of ion concentration, caused by the WF, if calculated on the assumption of the semipermeability of theZ membranes, was found to be equal to the changes necessary to induce contraction of actomyosinin vitro.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476362
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  • 13
    Electronic Resource
    Electronic Resource
    Nonlinear diffusion in metabolic systems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 15-21 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some general properties of the solution of the diffusion equation are deduced for the steady-state, spherically symmetric system. On the basis of these developments some results of N. Rashevsky (Bull. Math. Biophysics,11, 15, 1949) are discussed and the results of a previous investigation (Hearon,Bull. Math. Biophysics,12, 135, 1950b) are extended to more general conditions. In particular these extensions apply to the flow of a soluteagainst its concentration gradient, the nonzero gradient of an inert metabolite, and theaccumulation or exclusion of an inert metabolite in a metabolic system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476363
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  • 14
    Electronic Resource
    Electronic Resource
    Comments on the approximate solution of the diffusion equation: I (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 23-31 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The approximation method of N. Rashevsky is discussed and reviewed. It is shown that in addition to theexplicit assumptions and approximations there is involved the assumption that the rate of metabolism is the same at every point in the cell and that theaverage rate of metabolism is different from zero. An expression is given for the error in the approximate method when the rate of metabolism is any function of the concentration. It is also shown that a solution in theform of that obtained by the approximate method is not possible if the generalized laws of diffusion are assumed to apply.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476364
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  • 15
    Electronic Resource
    Electronic Resource
    The kinetics of the succinoxidase (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 33-42 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Rate equations for the enzymatic oxidation of succinic acid are derived on the assumption that when a single molecule of substrate combines with an enzyme molecule, it can do so with either one or two sites on the enzyme, and that oxidation occurs only in the second case. In addition it is assumed that the product of the reaction, fumaric acid, combines reversibly with the enzyme. With certain enzyme preparations the data fitted such an equation satisfactorily. In others the rate was that of a first-order reaction, but addition of cytochrome changed it to the former type. It was concluded that the transfer of hydrogen to oxygen was a first-order reaction and dominated the whole rate when enzyme preparations were used which had been washed relatively free of cytochrome. When the limiting factor was succino-dehydrogenase the rates followed the new equation. Criteria for recognizing noncompetitive inhibition are given, and inhibition by di-tertiary butyl peroxide was shown to be of this type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476365
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  • 16
    Electronic Resource
    Electronic Resource
    The interpretation of exponential dose-effect curves (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 43-47 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper deals with the following question: Which distributions of radiosensitivity in a population can lead to an exponential survival curve? The problem is solved exactly, with statistical fluctuations in dose fully accounted for. It is shown that only an exponential distribution of sensitivities can give rise to an exponential survival curve.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476366
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  • 17
    Electronic Resource
    Electronic Resource
    An approximation method for the solution of diffusion and related problems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 49-61 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An approximation method is introduced which enables a number of diffusion-type problems to be solved in an approximate but simple manner. Many cases require only the solution of a simple first-order differential equation. The method is applied to a number of cases in which the exact solutions are available. A comparison shows that the method is quite satisfactory in these cases. The method is applied to diffusion problems with rate of consumption proportional to concentration or to the square of the concentration. In the latter case, the result obtained is essentially the same as that found by H. G. Landau (1950) after elaborate calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476367
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  • 18
    Electronic Resource
    Electronic Resource
    On spontaneous discharge obtained from a physicochemical model of excitation (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 83-91 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that a slight modification of a model of excitatory phenomena in irritable tissues, which has been treated before, exhibits spontaneous oscillations. The frequency of these oscillations and the time-course of the potential across the model membrane have been determined, together with the dependence of some of their characteristics on some important parameters, particularly (Ca++).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476370
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  • 19
    Electronic Resource
    Electronic Resource
    Cell division by swelling stresses (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 73-81 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is demonstrated that, if the variations of viscosity throughout a cell are considered, swelling stresses may produce elongation and division. To do this it is necessary to generalize Betti's theorem to cover systems containing viscosity gradients and such a generalization is presented. On the basis of two special assumptions it is shown that most of the results of the diffusion drag theory of cell division may be duplicated by the present theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476369
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  • 20
    Electronic Resource
    Electronic Resource
    Imitative behavior in nonuniformly spatially distributed populations (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 63-71 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The theory of imitative behavior, developed previously, is applied to the case of two social groups which are separated spatially. If the information of each group as to the behavior of the other is complete, the case reduces to that of a single group. When any information is lacking at all, the two groups are independent. If we have two mutually exclusive behaviorsA andB, all four combinationsAA, AB, BA, andBB are possible. If the mutual information gradually increases from zero, then for a certain value of it, the group which is more informed about the behavior of the other will change to that behavior if it did not already exhibit it. If for constant information the size of the group increases, then above a certain threshold value, the larger group imposes its behavior on the smaller.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476368
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