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  • Articles  (82,348)
  • Springer  (82,348)
  • 1980-1984  (43,709)
  • 1960-1964  (38,639)
  • 1981  (43,709)
  • 1964  (20,569)
  • 1962  (18,070)
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  • 1980-1984  (43,709)
  • 1960-1964  (38,639)
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  • 1
    Electronic Resource
    Electronic Resource
    Tissue blood flow and the sympathomimetic amines (1964)
    Springer
    Bulletin of mathematical biology 26 (1964), S. 1-7 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the arteries, blood flow and blood pressure are pulsatile in nature (Roston, 1962a; Roston 1962b). The patterns of blood movement and mural distension in the arteries are important because they may be associated with life-threatening degenerative changes in the arterial walls. As the vascular channels narrow, the pulsation decreases. At the level of the capillaries, almost no pulsation exists (Best and Taylor, 1961). The tissues are affected by the direct flow in the capillaries and not by the pulsation in the arteries. Thus, such quantities as pulse pressure, systolic pressure, and diastolic pressure which characterize blood movement in the arteries are not important as far as the tissues are concerned. Rather, the average pressure and flow in the capillaries are the quantities significant for tissue blood flow. The present study analyzes the local blood circulation in a typical tissue. Logical extension of this analysis results in insights into the physiological behavior of the circulation which integrate a considerable body of experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476615
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  • 2
    Electronic Resource
    Electronic Resource
    Multibreath tracer species dynamics in the lung (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 1-19 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460935
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  • 3
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    Global stability of population models (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 47-58 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460938
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  • 4
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    The logistic equation with a diffusionally coupled delay (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 125-140 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Layapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopf's bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.
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    URL: http://dx.doi.org/10.1007/BF02459438
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  • 5
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    Uncertainty in physiology and physics (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 141-149 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It was hypothesized in an earlier work that sensory perception can occur only when the perceiving system is uncertain about the nature of the event being perceived. In the absence of any uncertainty, perception will not take place. The response of the sensory afferent neuron (impulse transmission rate) was calculated using Shannon's measure of uncertainty or entropy. It will now be shown that when the event being perceived is the position and momentum of a particle, Shannon's measure of uncertainty leads to the Heisenberg Uncertainty relationship.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459439
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  • 6
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    Consensusn-trees (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 239-244 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is not unusual for several classifications to be given for the same collection of objects. We present a method, called majority rule, which can be used to define a consensus of these classifications. We also discuss some mathematical properties of this consensus tree.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459446
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  • 7
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    Morphogen pattern formation and development in growth (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 259-270 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The dependence of the spatial concentration profiles of morphogens on a characteristic dimension is obtained by continuation techniques for Gierer and Meinhardt's activator-inhibitor model of morphogenesis. The study of the behaviour of the system during growth, where the linear and exponential increase of the characteristic dimension is considered, revealed that more complex patterns of morphogen spatial concentrations appear regularly in a reproducible way.
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    URL: http://dx.doi.org/10.1007/BF02462200
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  • 8
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    Simulation experiments with a model for cellular growth (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 271-278 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Computer models have been used by various authors to simulate both the growth of normal cellular tissue and the development of cancerous cells within normal tissue. As these models were the result of considerable idealization, the purpose of the present paper is to propose a model in which the degree of simplification is relaxed: the features of simultaneous growth, and cell growth whose rate depends on the free absorbing periphery of the cell are introduced. Simulation experiments have been conducted using the model, and the results are presented.
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    URL: http://dx.doi.org/10.1007/BF02462201
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  • 9
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    Complementary extremum principles for a nonlinear model of heat conduction in the human head (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 341-346 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for a nonlinear model of heat conduction in the human head. Accurate variational solutions are obtained in illustrative calculations. The effect of nonlinearity is seen to be significant from a comparison with the linearized model.
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    URL: http://dx.doi.org/10.1007/BF02462204
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  • 10
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    On Zeeman's equations for the nerve impulse (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 279-325 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.
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    URL: http://dx.doi.org/10.1007/BF02462202
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  • 11
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    Asymptotic analysis of the Michaelis-Menten reaction equations (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 375-388 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The irreversible Michaelis-Menten reaction is studied by the use of the method of multiple scales. Three stages of the reaction are identified, one of which is studied in detail. The results are compared with those of two earlier analyses.
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    URL: http://dx.doi.org/10.1007/BF02459428
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  • 12
    Electronic Resource
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    Pulse evolution on coupled nerve fibres (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 389-400 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A numerical study of the coupled nerve fibre problem is given which verifies and extends the perturbation theory of Luzader. Pulses on adjacent fibres can couple together with two possible stable pulse separations.
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    URL: http://dx.doi.org/10.1007/BF02459429
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  • 13
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    Field-induced forces at dielectric interfaces as a possible mechanism of RF hearing effects (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 401-413 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A possible mechanism for effects of microwave radiation on the auditory system is the generation of field-induced forces at interfaces that divide materials of dissimilar electrical properties. A general expression for these “Maxwell stresses” is derived and then used to calculate the approximate magnitude of field-induced force within the organ of Corti during microwave exposure. Comparison of the results with data on the force needed to excite cochlear hair cells indicates auditory responses could be evoked by this mechanism at power densities near the threshold of rf hearing sensations.
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    URL: http://dx.doi.org/10.1007/BF02459430
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  • 14
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    The construction of homogeneous nets (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 415-426 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A definition of homogeneity for neural networks is given which permits their construction as group quotients. The significance of this for neural dynamics is discussed.
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    URL: http://dx.doi.org/10.1007/BF02459431
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  • 15
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    Contractile analysis and kinetic energy of the myocardium (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 447-461 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The left ventricle is represented as a cylinder contracting both radially and longitudinally. A simple method is indicated to derive an expression for the rate of change of the kinetic energy of this three-dimensional model, which quantity can be used as an index for the study of the contractile behaviour of the myocardium. An application to the study of muscle mechanics is also indicated.
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    URL: http://dx.doi.org/10.1007/BF02459433
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  • 16
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    Limit cycles in periodically perturbed population systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 463-485 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.
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    URL: http://dx.doi.org/10.1007/BF02459434
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  • 17
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    On a unified approach to pattern generation (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 513-516 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02459437
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  • 18
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    On the possibilities of error-detecting codes in nucleic acid molecules (1964)
    Springer
    Bulletin of mathematical biology 26 (1964), S. 25-29 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Error-detecting codes have been known to mathematicians and to electrical engineers for over ten years. In general, such codes utilize an additional orparity bit for purposes of detecting errors by the addition of all positive binary bits or “1’s” occurring in any code word. However, since the process of addition is required for such code detection, it is not surprising that these codes have not been applied to the nucleic acid molecule. In 1962, P. I. Hershberg (Trans. I.R.E., CS-10, 280–4, 1962) outlined a categorical constraint which permitted the realization of a class of error-detecting codes which did not require parity bits. This class of codes is applied to the nucleic acid molecule in the present paper.
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    URL: http://dx.doi.org/10.1007/BF02476617
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  • 19
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    On some topological properties of the systems of compartments (1964)
    Springer
    Bulletin of mathematical biology 26 (1964), S. 31-38 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Compartment systems are often used as models for tracer and drug kinetics. The structure of a compartment system is here analyzed by means of theory of graphs methods. In particular the precursor-successor relationship between any two compartments is classified according to the structure of the graph of the system and to the values of the elements of the matrix associated with it.
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    URL: http://dx.doi.org/10.1007/BF02476618
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  • 20
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    The equations of growth (1964)
    Springer
    Bulletin of mathematical biology 26 (1964), S. 39-43 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An application of a bifurcation theorem shows the existence of periodic solutions of a system of differential equation used to describe competition between two species. It is then shown that the results are more general than those previously established.
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    URL: http://dx.doi.org/10.1007/BF02476619
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  • 21
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    An analysis of the 2o and 10o field color-matching functions (1964)
    Springer
    Bulletin of mathematical biology 26 (1964), S. 9-24 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The 2o and 10o field color-matching functions are independent: one specification is not a linear transformation of the other, even after correcting for macular pigment effects. Therefore, the “true” color-matching functions which directly describe the linear responses of the eye must be different for the two field sizes. This means that a given stimulus will, in general, have a different chromaticity depending upon the field size, regardless of the choice of any one colorimetric co-ordinate system for all field sizes. However, in spite of these chromaticity differences, a large uniform field usually appears nearly uniform. Such color uniformity implies that even though chromatic differences occur as a function of retinal position or field size, these differences are small. If this is the case, then the underling “true” color-matching functions determining the observed color-matching functions must be nearly, but not quite, identical. These differences vanish as identity between the sets of color-matching functions is approached. This property suggests a method of calculating the “true” color-matching functions. The “true” color-matching functions must approximate those obtained by minimizing the chromaticity differences between two independent sets of data. This can be done by assuming that the coefficients of transformation should be adjusted so as to produce as nearly identical chromaticities for spectrum stimuli as possible. In this paper, it is also assumed that the “true” color-matching functions have no negative values, as if they were based on actual absorption spectra. This article describes the calculation of the “true” 2o and 10o field color-matching functions satisfying these two conditions. For both field sizes, the maxima of the three functions are near 435, 540, and 585 mμ, after correcting for the filtering effects of the ocular media and macular pigment.
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    URL: http://dx.doi.org/10.1007/BF02476616
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  • 22
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    A note on the elementary α-perceptron (1964)
    Springer
    Bulletin of mathematical biology 26 (1964), S. 45-47 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this note the principal convergence theorem (F. Rosenblatt,Principles of Neurodynamics, Spartan Books, Washington D.C., 1962, 111–116) is proved by a new method.
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    URL: http://dx.doi.org/10.1007/BF02476620
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  • 23
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    On the adsorption of ions at charged sites in an electric field: I (1964)
    Springer
    Bulletin of mathematical biology 26 (1964), S. 49-55 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Considering only nearest neighbor interactions, an expression is obtained for the grand partition function for the adsorption of two kinds of monovalent positive ions at a long chain of one type of monovalent negative fixed sites in an electric field. Expressions are obtained for the fractions of sites which are occupied by each kind of ion as well as of those which are unoccupied as a function of the potential of the electric field.
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    URL: http://dx.doi.org/10.1007/BF02476621
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  • 24
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    Two remarks on the mathematical biology of automobile driving (1964)
    Springer
    Bulletin of mathematical biology 26 (1964), S. 57-61 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In connection with a series of previous papers by this author (Bulletin of Mathematical Biophysics,21, 299–308, 375–385;22, 257–262, 263–267;23, 19–29;24, 319–325) results obtained by A. Crawford (Economics 5, 417–428) on the effects of irrelevant lights on reaction times toward a given light stimulus are discussed. The conclusions from a previous paper of this author (Bulletin of Mathematical Biophysics,23, 19–29) are elaborated.
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  • 25
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    Analysis of a simple avoidance situation. II. A model (1964)
    Springer
    Bulletin of mathematical biology 26 (1964), S. 77-81 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model has been constructed to describe experimental data recorded in a study of a simple avoidance situation. The theoretical description makes use of the concept of the effective number of shocks. The model explains the existence of oscillations encountered in previous experiments.
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    URL: http://dx.doi.org/10.1007/BF02476624
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  • 26
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    Studies in stochastic learning theory: II. Interpretation of response probabilities (1964)
    Springer
    Bulletin of mathematical biology 26 (1964), S. 63-75 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Response probabilities are interpreted from two points of view. One corresponds to fluctuations in physical parameters suggestive of a neurological basis, and the other corresponds to fluctuations in stimulus sample constitution. The two interpretations are shown to be equivalent under rather general conditions, giving the same type of relation between response and training states. This relation is different from that obtained via the response strength concept used in Part I. As a step toward evaluating the difference in predicted behavior for these different response-training relations, a general functional-difference equation is derived that describes the moments of the corresponding stochastic process in experimenter-subject controlled experiments. As an immediate application, it is used to obtain the continuity condition for the solution of the functional equation treated in Part I, and to justify the differentiability conditions assumed in establishing asymptotic properties of the solution as a function of the reinforcement parameter.
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    URL: http://dx.doi.org/10.1007/BF02476623
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  • 27
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    An avoidance learning situation. A neural net model (1964)
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    Bulletin of mathematical biology 26 (1964), S. 83-89 
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    Notes: Abstract A simple avoidance situation is considered in terms of a neural net learning model. Data for the control situation can be represented by an expression having three parameters which determine the initial and the steady state activities together with the transient aspects. The introduction of a learning parameter then allows one to calculate satisfactorily the results obtained in the experimental situation in which shock is applied.
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    URL: http://dx.doi.org/10.1007/BF02476625
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  • 28
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    Comparison of two models for a simple avoidance learning situation (1964)
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    Bulletin of mathematical biology 26 (1964), S. 101-101 
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    URL: http://dx.doi.org/10.1007/BF02476627
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  • 29
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    Group representation of genetic recombinations (1964)
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    Bulletin of mathematical biology 26 (1964), S. 91-100 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract An algebraic representation of operations of genetic recombinations is illustrated. It is shown that the recombinations between chromosomes in the two-strand model can be represented by groups, in the sense of the theory of groups. Recombinations between chromosomes with inversions and a translocation are considered as well as cases without them. It is found that the groups derived from such cases are Abelianp-groups (p=2) and that the types of the Abelian groups for the various pairs of chromosomes are different from each other. Differences among those recombination groups are illustrated by showing the sets of generators of the various groups, which generate the corresponding recombination groups by multiplication.
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  • 30
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    Abstract biological systems as sequential machines (1964)
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    Bulletin of mathematical biology 26 (1964), S. 103-111 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract It is shown that a rather close relationship exists between the (ℳ,ℛ)-systems, defined previously as prototypes of abstract biological systems, and the sequential machines which have been studied by various authors. The theory of sequential machines is reformulated in a way suitable for its application to the study of the intertransformability of (ℳ,ℛ)-systems as a result of environmental alteration. The important concept of strong connectedness is most useful in this direction, and is used to derive a number of results on intertransformability. Some suggestions are made for further studies along these lines.
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  • 31
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    The arterial circulation of the heart (1964)
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    Bulletin of mathematical biology 26 (1964), S. 113-120 
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    ISSN: 1522-9602
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    Notes: Abstract Blood flows into the aorta and its branches during left ventricular systole. Most of the arterial walls in the body stretch during systole in accordance with their elastic properties (Roston, 1962a, b). During diastole, the rebound of the distended walls supplies an additional propulsive force pushing the blood forward. Since the metabolic exchange between most of the tissues in the body and their blood vessels is ordinarily the same throughout the cardiac cycle, it makes little difference whether or not the blood flow occurs during systole or diastole. The circulation in the coronary arteries behaves in a quite different way. Because the muscle fibers of the heart contract during systole and relax during diastole, different conditions for blood flow and metabolic exchange exist during the phases of the cardiac cycle. As a result, specification of whether blood flows in the coronary arteries during systole or diastole may be important. Such specification complicates the study of the coronary artery circulation. For example, because of the arterial elasticity, some of the blood which enters the coronary arteries during diastole comes in contact with the muscle fibers during systole. The present work contains a theoretical study of the coronary artery circulation.
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    On the adsorption of ions at charged sites in an electric field: II (1964)
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    Bulletin of mathematical biology 26 (1964), S. 139-146 
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    Notes: Abstract A study is made of the adsorption of one kind of monovalent positive ion at a long chain of alternating monovalent negative fixed charged (“lattice”) and uncharged (“interstitial”) sites both of one type in an electric field. Considering only nearest neighbor interactions an expression is obtained for the grand partition function. The fractions of sites of both types which are occupied and unoccupied are determined. It is shown that an equilibrium constant can be defined for the adsorption of ions at oppositely charged sites.
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    Color perception using a single cone type with distributed maximum sensitivity (1964)
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    Bulletin of mathematical biology 26 (1964), S. 121-138 
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    Notes: Abstract This paper proposes a model for color perception which accounts for variations in the dimension of the space of perceived colors. The model assumes that there is only one type of cone with only one shape of response curve, but that different cone's response curves differ by translation. It also assumes that the final discrimination system, learned from originally random connections, maximizes discrimination in the normal visual environment. Learning mechanisms are discussed, and the form which the final discrimination system ought to take is plausibly derived. An algorithm for the tristimulus curves is obtained from this model, and it is shown that a good fit of the empirical data can be obtained.
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    Some remarks on Rosen's quantum-mechanical approach to genetics (1964)
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    Bulletin of mathematical biology 26 (1964), S. 187-191 
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    Notes: Abstract It has been suggested by Robert Rosen (Bull. Math. Biophysics,22, 227–255, 1960) that multiple alleles or pseudoalleles correspond to multiple cites of degenerate states of some quantum mechanical observable which acts as a source of primary genetic information. It is pointed out here that if the quantum mechanical states are determined by the different sequences of the purine and pyrimidine bases in the DNA molecule, the expected number of pseudoalleles would be much too large. The expected number is considerably reduced if we assume that a quantum mechanical state determines the coupling between a molecule of transfer RNA and the corresponding amino acid.
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    A mathematical model of the human thermal system (1964)
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    Bulletin of mathematical biology 26 (1964), S. 147-166 
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    Notes: Abstract This paper describes a mathematical model developed to simulate the physical characteristics of the human thermal system in the transient state. Physiological parameters, such as local metabolic heat generation rates, local blood flow rates, and rates of sweating, must be specified as input data. Automatic computation of these parameters will be built into the model at a later date when it is used to study thermal regulation in the human. Finite-difference techniques have been used to solve the heat conduction equation on a Control Data Corporation 1604 computer. Since numerical techniques were used, it was possible to include many more factors in this model than in previous ones. The body was divided into 15 geometric regions, which were the head, the thorax, the abdomen, and the proximal, medial, and distal segments of the arms and legs. Axial gradients in a given segment were neglected. In each segment, the large arteries and veins were approximated by an arterial pool and a venous pool which were distributed radially throughout the segment. Accumulation of heat in the blood of the large arteries and veins, and heat transfer from the large arteries and veins to the surrounding tissue were taken into account. The venous streams were collected together at the heart before flowing into the capillaries of the lungs. Each of the segments was subdivided into 15 radial sections, thereby allowing considerable freedom in the assignment of physical properties such as thermal conductivity and rate of blood flow to the capillaries. The program has been carefully checked for errors, and it is now being used to analyze some problems of current interest.
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    A physicomathematical model of sodium balance (1964)
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    Bulletin of mathematical biology 26 (1964), S. 193-198 
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    Notes: Abstract A model is introduced in which the reabsorption of sodium is governed by an enzymatic process. This process is in turn assumed to be influenced by the extracellular volume which depends on the amount of sodium in the body at a given time. The model allows for damped oscillations when the sodium intake lies within range of values and thus can account for observed oscillations.
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    A neurobiophysical model of schizophrenias and of their possible treatment (1964)
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    Bulletin of mathematical biology 26 (1964), S. 167-185 
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    Notes: Abstract A neurobiophysical model is proposed for the explanation of some characteristics of schizophrenic behavior. The normal reactions to exogenous stimuli are mediated through a set of centers, while some endogenous stimuli result in abnormal reactions removed from reality, such as dreamlike states, paranoias, hallucinations, etc. The two sets of centers are cross-inhibited and the usual equations for such cross-inhibited systems are applied. In normal life exogenous stimuli as a rule result preponderantly in pleasant reactions, and the corresponding pathways are therefore reinforced. This results in an inhibition of the abnormal reactions. If the life history of an individual is such that a sufficiently large number of ordinarily experienced stimuli leads to unpleasant reactions and, therefore, the corresponding pathways are inhibited, the endogenously stimulated centers for abnormal reactions prevail and various schizophrenic symptoms occur. The same result may be achieved with a normal life history but through organic changes in the system, which differentially affect various thresholds and excitation parameters. The model thus leads to the conclusion that what appears now to be a large array of contradictory findings in the “organic” versus the “psychological” controversy is actually not a contradiction, but is a result of the dependence of normal and abnormal behaviors on a large number of neurobiophysical parameters. Some general comparisons between the conclusions drawn from the model and some known facts are made. The model also provides a first step toward a neurobiophysical interpretation of the mechanism of psychotherapy.
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    Limits on the computing power of biological systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 59-67 
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    Notes: Abstract The theory of computational complexity and certain explicitly-stated hypotheses imply limitations on the information processing power of biological systems. Parallelism, special purpose organization, and analog mechanisms may provide speedup critical for life processes, but have little power in the face of exponential growth. We show that “polynomially simulatable” biological systems cannot exhibit dynamic behavior which produces the solution of an intractable problem. The argument implies that parallelism does not allow biological systems to defeat the exponential explosion, but rather is important because it allows polynomial time algorithms to be used more efficiently.
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    A topological study of the base sequences of MS2 and ϕX174 genoma (1981)
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    Bulletin of mathematical biology 43 (1981), S. 81-88 
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    Notes: Abstract A correlation matrix analysis is applied to the base sequence of MS2 and ϕX174 in comparison with sets of simulated sequences with different degrees of constaint Significant differences between a codified sequence, and a statistical one in terms of the “correlation matrix” for sets of different length cannot be found. This result is analysed in terms of nucleotide sequences with different levels of informational content.
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    Volume of the conducting airways calculated from morphometric parameters (1981)
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    Bulletin of mathematical biology 43 (1981), S. 101-109 
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    Notes: Abstract A method of calculating the volume of a tree distal to a cut at the origin of a branch, using branching, diameter and length ratios, has been developed. The method was applied to bronchial tree casts from human, dog, sheep, hamster, and rat lungs. It was found that the exponenta in the equation weight=k×diameter a is approximately equal to 3.0 in sheep lung casts, as found by Hooper (1977), but it is greater than 3.0 in casts from the other four species.
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    Variability in a single compartment system: A note on S. R. Bernard's model (1981)
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    Bulletin of mathematical biology 43 (1981), S. 111-116 
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    Notes: Abstract In this note we examine a continuous time version of a compartmental model introduced in a discrete time setting by S. R. Bernard. The model allows for more than one particle to leave the system at any time. This introduces additional randomness into the system, over the pure death system and this is reflected in the variance function.
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    The diffusion transit time; A simple derivation (1981)
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    Bulletin of mathematical biology 43 (1981), S. 89-99 
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    Notes: Abstract The mean first passage time for free diffusion can be derived directly by solving a simple analogue steady state problem. In this problem the diffusion starting region is considered as a time independent source of diffusing particles and the diffusion target assumes the behaviour of a perfectly absorbing sink. It is shown here that the transit time between the source and the sink, which in this particular problem is equal to the ratio between the holdup of the system and the total flux, is identical to the Brownian movement concept of the mean first passage time for free diffusion. This established identity considerably facilitates the derivation and investigation of the timing of diffusion in complicated structures such as those commonly found in living organisms.
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    Nonlinear oscillations in biology (1981)
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    Bulletin of mathematical biology 43 (1981), S. 121-123 
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    A comment on Lin's paper on nonlinear diffusion in biological systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 117-120 
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    On the stochastic theory of compartments: The leaving process of the two-compartment systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 201-211 
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    Notes: Abstract In this paper three stochastic models are developed for a class of two-compartment systems to analyse the randomness of the leaving process of the particles in the system. Results in closed form for the distribution of the leaving process of the particles in the system are given both for general and exponential sojourn time distributions and also in association with forward recurrence time distributions with and without Poisson input.
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    Models on prebiotic polymer competition: A deterministic approach (1981)
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    Bulletin of mathematical biology 43 (1981), S. 213-232 
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    Notes: Abstract Two simple models are proposed and analysed, in which it is shown that the formation of a new polymer, resulting from an “error” in the template action mechanism of production of an old polymer, may compromise the stability of the initial system under specific conditions, in the context of prebiotic evolution. Autocatalysis is shown to be a “selective advantage”, enabling the “mutant” to dominate in concentration and even replace the initial polymer. The addition of a third molecule playing the role of a catalyst causes hysteresis effects.
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    Extinction probabilities in microbial predation: A birth and death approach (1981)
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    Bulletin of mathematical biology 43 (1981), S. 165-181 
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    Notes: Abstract The problem of extinction of the prey population in a microbial predator-prey interaction in a chemostat has been examined. Usual deterministic lumped parameter models were used for the dynamics of the chemostat for large numbers of the two populations; the generalized birth and death stochastic process was employed for the description of the random variations at small prey numbers. Extinction probabilities of the prey population were calculated for different holding times and chemostat volumes, and their dependence upon the growth parameters of the two populations was studied. It was found that extinction was possible when the Monod model was used for the specific growth rate of the predators as a function of the prey number density. On the other hand, the decrease of the feeding activity of the predators at low prey densities predicted by the multiple saturation model acts as a regulatory factor that prevents extinction of the prey. In view of the fact that extinction of the prey has never been observed in the laboratory, the latter model seems more appropriate to describe the dynamics of microbial predation.
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    Prediction of the effect of the choroidal circulation on the retinal temperature during illumination (1981)
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    Bulletin of mathematical biology 43 (1981), S. 233-238 
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    Notes: Abstract During exposures of the eye to light, the choroidal circulation may have a regulatory influence on the retinal temperature. This is investigated using a mathematical model and a finite-difference technique. It is predicted that the choroidal blood flow a small effect on retinal temperature, which may be important.
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    Spatially localized interactive neural populations—I. A mathematical model (1981)
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    Bulletin of mathematical biology 43 (1981), S. 427-446 
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    Notes: Abstract A probabilistic model of a spatially localized, mutually exitatory (inhibitory) population of neurons is formulated to help explain average evoked potential and post-stimulus time histogram measurements. The model is based on the stochastic activity of single neurons within interactive masses of neurons which exhibit co-operative behavior. Macrostate variables corresponding to the above measurements are related through the model to features of neural operation at the individual and ensemble level. Steady-state solution are obtained and their physiological implications are discussed.
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    A one-compartment model with stochastic parameter (1981)
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    Bulletin of mathematical biology 43 (1981), S. 503-512 
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    Notes: Abstract We consider a one-compartment system with stochastic transfer rate characterized either by Gaussian or by two-level jump process and study the time evolution of the (statistical) moments of the (random) amount of the substance present in the system. The effect of the coloured as well as of the white noise is investigated and it is found that the presence of stochasticity in the transfer rate parameter increases the relaxation time of the system. Finally, we obtain the conditions for the stability of the system in the moment sense.
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    A dose-response model for estimating lifetime tumor risks when cell killing occurs (1981)
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    Bulletin of mathematical biology 43 (1981), S. 487-501 
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    Notes: Abstract A model is described in which damage to a single intracellular locus can lead to a tumorigenic transformation. Assuming a large number of independent intracellular loci to be at risk and assuming that damage to a locus sufficient to cause a tumorigenic transformation occurs with probability greater than zero for all doses greater than zero, leads to the use of the Weibull distribution to characterize the probability of a nonspontaneous tumorigenic cellular transformation occurring after exposure to a given dose of carcinogen. The excess lifetime tumor incidence (i.e., the proportion of tumor bearers) above the spontaneous incidence is used as an estimate of the non-spontaneous incidence and is characterized by a tumor incidence function that represents the probability of occurrence of one or more non-spontaneous tumorigenic cellular transformations amongN(D) independent surviving cells per individual, after exposure to a doseD of carcinogen. The tumor incidence function is fitted to published data for the excess tumor incidence after exposure of animals or humans to ionizing radiation and after exposure of animals to chemical carcinogens.
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    A stochastic model for then-compartment irreversible system (1981)
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    Bulletin of mathematical biology 43 (1981), S. 549-561 
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    Notes: Abstract This paper deals with a stochasticn-compartment irreversible system with a non-homogeneous Poisson input and arbitrary residence time for each of the compartments. Results relating to the number of particles present in each of the compartments as well as the total number of particles present in the system at any time are derived. Further, explicit expressions for the auto covariance function for each compartment and the cross-covariance function between any two compartments with a given time lag are obtained. As a particular case, then-compartment irreversible system is analyzed with homogeneous Poisson input and exponential residence time distribution for each of the compartments. The possible applications of the model are discussed.
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    Pulsatile blood flow in a rigid pulmonary alveolar sheet with porous walls (1981)
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    Bulletin of mathematical biology 43 (1981), S. 563-577 
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    Notes: Abstract This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.
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    Dynamic structure theory: A structural approach to social and biological systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 579-591 
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    Notes: Abstract The relationships that define the structure of a given ecosystem, social system, or even a physiological function can only exist if certain parameters are confined to a certain range of values. As the values change and exceed this given range the relationships are forced to change, and so produce a new pattern of relationships. The concept of a dynamic structure captures this potential for structural change in relation to a set of parameters. The precise definition of structure and allowable transformation constitutes the definition of a category. The total range of parameters associated with all the relevant structures provides a parameter space which is assumed to be a manifold. Maps with extra structure from the manifold to the category define dynamic structures. The domain of differential dynamic systems is the manifold, and a flow or movement across the manifold is associated with a series of structural transformations in the category. In some cases a structure outruns its parameter range, to be faced with an obstruction—an absence of possible transformations. Ways of studying such “obstructions” are considered along with the related problem of extending a dynamic structure beyond a previously given set of parameters. The cost or resistance of transformations is also studied. The concepts of dynamic structures are illustrated by the structural change of food webs and they are used in a necessarily qualitative fashion to study dominance structures of social orders and finally to speculate on the qualitative nature of evolutionary change of functional aspects of organisms.
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    Peak drug levels in linear pharmacokinetic systems—II. Conditions for a paradoxical injection rate effect with rectangular input (1981)
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    Bulletin of mathematical biology 43 (1981), S. 705-715 
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    Notes: Abstract The preceding paper (Thorn, 1981) has shown that in a linear pharmacokinetic system with a multimodal impulse response the peak drug level may sometimes be smaller with slower rates of injection. This paper presents two theorems on this paradoxical injection rate effect where the injection is a constant infusion of finite duration. The first theorem establishes a graphical method for determining whether a given impulse response will give a paradoxical injection rate effect; and the second establishes that the maximum paradoxical increase in peak drug level is by a factor of two. It is further shown that in order to approach this maximum paradoxical increase the impulse response must contain two isolated, sharp, narrow pulses of approximately equal area. Some examples of bimodal arterial dye-dilution curves from the literature are discussed as impulse responses; and there is also a discussion of the behavior of drug level maxima and minima at different injection rates.
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    Peak drug levels in linear pharmacokinetic systems—I. Effect of rate of injection (1981)
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    Bulletin of mathematical biology 43 (1981), S. 693-703 
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    Notes: Abstract This paper presents three theorems on the peak drug levels that result from injection into a linear pharmacokinetic system. As a preliminary, the “rate of injection” is defined in terms of time expansion or time contraction of the injection function (input). The first theorem then states that the peak drug level will not be greater when the rate of injection is slow than when it is fast, if the impulse response is unimodal. The second theorem sets limits for the time of the maximum drug level, in relation to the time of the maximum of the (unimodal) impulse response and the duration of the input. The third theorem defines conditions which assure a definitely lower peak drug level if the rate of injection is slower. A graphical method is suggested for determining the times and magnitudes of the peak drug levels that result from constant infusions of a fixed dose at different rates. An example is provided to show that if the impulse response is multimodal then the peak drug level may sometimes increase with a decrease in the injection rate.
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    Journal of applied probability (1964)
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    Bulletin of mathematical biology 26 (1964), S. 199-199 
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    Training program in computer use for biomedical scientists (1964)
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    Bulletin of mathematical biology 26 (1964), S. 201-201 
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    1964 International Congress for Logic, Methodology, and Philosophy of Science (1964)
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    Bulletin of mathematical biology 26 (1964), S. 203-203 
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    On a two urn model of Polya-type (1981)
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    Bulletin of mathematical biology 43 (1981), S. 33-45 
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    Notes: Abstract A two urn Polya-type scheme is considered in whichr black balls (corresponding to the stable form of an element) are added to urn one at every stage and the same number of balls are removed at random at every stage from the same urn. In between these two operations, which form a stage or iteration, a fixed number of balls is exchanged at random between urns one and two. Urn one has a given initial number of white balls (corresponding to a radioactive form of the same element). The problem of interest is to study the stochastic aspect of the number of white balls remaining in urn one (and/or urn two) aftern iterations.
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    Nonlinear biological oscillators: Action-angle variable approach with an application to Cowan's model of neuroelectric activity (1981)
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    Bulletin of mathematical biology 43 (1981), S. 21-32 
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    Notes: Abstract We obtain within the action-angle variable approach new expressions, involving the Dirac delta function, for time periods and time averages of dynamical variables which are useful for nonlinear biological oscillator problems. We combine these with Laplace transformation techniques for evaluating the required perturbation expansions. The radii of convergence of these series are determined through a complex variable approach. The method is powerful enough to yield explicit results for such systems as the two species Volterra model, Goodwin's model of protein synthesis etc. and as an illustration, is applied here to Cowan's model of neuroelectric activity. We also point out the usefulness of the action integral in the case where parameters occurring in dynamics have slow time variations.
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    A generalized Fokker-Planck equation in the case of the Volterra model (1981)
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    Bulletin of mathematical biology 43 (1981), S. 69-79 
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    Notes: Abstract Zwanzig and Mori's projection-operator method is used in order to derive a generalized nonlinear Fokker-Planck equation for one “relevant” species in the many species conservative Volterra model. The deterministic, autonomous, Markovian equations of motion, when averaged over a suitable ensemble of initial conditions in general give rise to a non-autonomous, non-Markovian stochastic process for the evolution of this relevant species. Moreover, this relevant species may show irreversible damping, although self-interaction terms are absent in the many species model.
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    A hydrodynamical study of the flow in renal tubules (1981)
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    Bulletin of mathematical biology 43 (1981), S. 151-163 
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    Notes: Abstract The hydrodynamical problem of flow in proximal renal tubule is investigated by considering axisymmetric flow of a viscous, incompressible fluid through a long narrow tube of varying cross-section with reabsorption at the wall. Two cases for reabsorption have been studied (i) when the bulk flow,Q, decays exponentially with the axial distancex, and (ii) whenQ is an arbitrary function ofx such thatQ-Q 0 can be expressed as a Fourier integral (whereQ 0 is the flux atx=0). The analytic expressions for flow variables have been obtained by applying perturbation method in terms of wall parameter ε. The effects of ε on pressure drop across the tube, radial velocity and wall shear have been studied in the case of exponentially decaying bulk flow and it has been found that the results are in agreement with the existing ones for the renal tubules.
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    Some comments on the conductance of slow inward current in cardiac muscle (1981)
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    Bulletin of mathematical biology 43 (1981), S. 183-199 
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    Notes: Abstract Voltage clamp experiments, which determine the kinetic parameters of calcium conductance of cardiac muscle, (d ∞,f ∞, τ d and τ f ) are analyzed with a generally accepted expression for slow inward currentI s=g sdf (E-E R). Activation (d) and inactivation (f) reach the final valuesd ∞ andf ∞ with time constants τ d and τ f respectively. The analysis indicates that the measuredf ∞ agrees with the theoreticalf ∞, but the measuredd ∞ differs from the theoreticald ∞ by a factor which depends on τ d . The peak tension can be made to correlate closely with the theoreticald ∞ after a correction factor is applied to the raw measurements of activation. It can be shown that experiments designed to measure τ f can also be used to determine τ d with greater accuracy.
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    On the relevance of stochastic compartmental models to pharmacokinetic systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 245-247 
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    Identification of silent infections in SIR epidemics (1981)
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    Bulletin of mathematical biology 43 (1981), S. 249-257 
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    Notes: Abstract A deterministic model for an SIR epidemic with silent infections is investigated. It is shown for the model studied that the extent to which silent infections are present may be determined from data concerning only those individuals with symptomatic infection.
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    A reinforcement-depletion urn problem—I. Basic theory (1981)
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    Bulletin of mathematical biology 43 (1981), S. 327-340 
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    Notes: Abstract An urn contains balls of different colors. Specified numbers of each color are added and form a reinforcement. The total reinforcement is randomly removed, forming a depletion. The process, not necessarily with the same reinforcements, is performed a number of times. The factorial moment generating function of the urn configurations at any stage is given in terms of multivariate difference operators. Cases when the reinforcement vector is defined as a stochastic variable are considered. The problem is a generalization of an urn model associated with radioactive atoms and stable atoms proposed by S. R. Bernard. The solutions given here have a definite application to the problem of modelling tracers in compartmental systems.
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    Stochastic compartmental model with branching particles (1981)
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    Bulletin of mathematical biology 43 (1981), S. 347-360 
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    Notes: Abstract A multi-compartmental model with particles producing offspring according to the Markov branching process has been studied. Explicit results are given for the two-compartmental system and for irreversible general multicompartmental systems. The known models in stochastic compartmental analysis are shown to be particular cases of this model and applications are cited.
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    On Wei's fundamental equation for nerve excitation (1981)
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    Bulletin of mathematical biology 43 (1981), S. 371-372 
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    Phase-plane analyses of the Michaelis-Menten reaction equations (1981)
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    Bulletin of mathematical biology 43 (1981), S. 361-370 
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    Notes: Abstract The irreversible Michaelis-Menten scheme may be reduced to a pair of autonomous first-order differential equations. The phase-plane behaviour of these is investigated.
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    Reply to Chyuan-Yih Lee (1981)
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    Bulletin of mathematical biology 43 (1981), S. 372-373 
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    Further considerations in a theoretical description of gas transport in lung airways (1981)
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    Bulletin of mathematical biology 43 (1981), S. 517-548 
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    Notes: Abstract A discrete one-dimensional model of convection-diffusion in branching alveolar ducts is described and it is shown that, for a suitable choice of effective axial dispersion, the solution closely approximates that for an axially symmetric representation, at least for Peclet numbers Pe〈1. Following earlier work a composite model of a uniform lung is formed by matching such a respiratory pathway (now having the more convenient one-dimensional form) onto a trumpet representation of the conducting airways. Enhanced mixing due to heart action, and isotropic volume changes of trumpet (in addition to the pathway) during breathing are additional factors included. Calculations are made of O2 concentrations during steady-state breathing and of the concentration of inert gas during single breath wash-out of a gas mixture containing it. Predicted alveolar levels in each case agree extremely well with published data, although no alveolar slope is obtained for the inert gas.
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    Effects of convective and dispersive interactions on the stability of two species (1981)
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    Bulletin of mathematical biology 43 (1981), S. 593-610 
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    Notes: Abstract The evolution and local stability of a system of two interacting species in a finite two-dimensional habitat is investigated by taking into account the effects of self- and cross-dispersion and convection of the species. In absence of cross-dispersion, an equilibrium state which is stable without dispersion is always stable with dispersion provided that the dispersion coefficients of the two species are equal. However, when the dispersion coefficients of the two species are different, the possibility of self-dispersive instability arises. It is also pointed out that the cross-dispersion of species may lead to stability or instability depending upon the nature and the magnitude of the cross-dispersive interactions in comparison to the self-dispersive interactions. The self-convective movement of species increases the stability of the equilibrium state and can stabilize an otherwise unstable equilibrium state. The effect of cross-convection (in absence of self-dispersion and self-convection) is to stabilize the equilibrium state in a prey-predator model with positive cross-dispersion coefficients for the prey species. Finally, it is shown that if the system is stable under homogeneous boundary conditions it remains so under non-homogeneous boundary conditions.
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    Role of the hypergeometric distribution in the transmission of excitation through sympathetic ganglia (1981)
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    Bulletin of mathematical biology 43 (1981), S. 611-618 
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    Notes: Abstract Various observations suggest that sympathetic ganglia act as local integrative centers redistributing preganglionic excitation (i.e. the information issued by the central nervous system) to the postganglionic fibers (and effector organs). In order to support this concept a simple mathematical model of the elementary integration process, treating the case of a single preganglionic compound action potential, has been developed. This quantitative description, based on a few elementary assumptions, shows a possible way of processing preganglionic excitation in the ganglion. It is shown that on a particular ganglion cell the probability distribution of the number of activated synapses obeys hypergeometric distribution and hence, the postganglionic compound action potential is built up of several compound action potentials occurring at different times. The former correspond to different groups of firing cells. The model discloses modes of structural and temporal pattern generation performed by the sympathetic ganglion.
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    The uniqueness of protein sequences: A Monte Carlo analysis (1981)
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    Bulletin of mathematical biology 43 (1981), S. 619-639 
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    Notes: Abstract Amino acid sequences have already been examined in some detail in order to relate them to structural aspects, homology and gene duplication. This report introduces the concept of internal uniqueness of tripeptides within protein sequences and uses the Monte Carlo method to study this property. Some idea of internal uniqueness may be obtained from such an analysis using only a single sequence if the probability of the random occurrence is about 0.001 or less. This method of analysis is similar to that used in quantitative evaluations of homology. When the probability of the random occurrence is larger than 0.001 a homologous group of sequences is required and the random probabilities may be compared with the real occurrences within the group. From such an examination insulin and cytochrome c are identified as protein sequences with high internal uniqueness. A comparison of data from internal uniqueness and gene duplication analyses shows that these two properties need not be related. Results of the analysis point to internal uniqueness as an additional parameter for inclusion in speculations on why twenty amino acids are coded in protein structure.
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    Tolerance nets (1981)
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    Bulletin of mathematical biology 43 (1981), S. 641-650 
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    Notes: Abstract The concept of a tolerance net formalises simultaneously spatial closeness and nearness of neuronal activity. A method of constructing tolerance group nets is presented, leading to a means of construction of all very homogenous tolerance nets as group quotients. The dihedral group of order eight is taken as an illustrative example.
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    Relation between diameter and flow in branches of the bronchial tree (1981)
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    Bulletin of mathematical biology 43 (1981), S. 681-691 
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    Notes: Abstract Two methods are described for calculating the value of the exponentx in the equation flow =k×diameter x , as pertaining to a branch of the bronchial tree. In the lungs from three humans, two dogs, one hamster, and one rat mean values ofx between 2.419 and 2.903 were found. They lie within the range of 2.333 to 3.0 predicted by the analysis of Uylings (Bull. Math. Biol. 39, 501–519, 1977).
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    Stochastic analysis of a nonlinear model for selection of biological macromolecules (1981)
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    Bulletin of mathematical biology 43 (1981), S. 665-680 
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    Notes: Abstract A stochastic analysis of a nonlinear selection model is presented. The model, based on Eigen and Schuster's theory of selection and evolution of biological macromolecules, considers the effects of fluctuations on the individual concentrations of macromolecules as well as the total population numbers in constrained systems. Our analysis shows that one of the models most often treated deterministically (referred to as constant organization in the literature) becomes unstable when fluctuations in the total population number are considered. An alternative model which apparently has built in self-regulating properties is analyzed and proves to be stable except for some special cases of degeneracy.
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    Compartmental models with multiple sources of stochastic variability: The one-compartment models with clustering (1981)
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    Bulletin of mathematical biology 43 (1981), S. 651-664 
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    Notes: Abstract Previous compartmental models have introduced variability either at the particle or at the replicate level. This paper integrates both types of variability through the concept of clustering. The paper develops two different, general clustered models, each with time-dependent hazard rates for the clusters and for the particles within the clusters, and each with random initial number and sizes of clusters. The coefficient of variation of the total number of particles,CV[X(t)], for either model is shown to be bounded below, under very broad conditions, by the coefficient of variation of the initial number of clusters,CV[c(0)]. This high relative variability of the clustered models makes them potentially very useful in kinetic modeling. In many applications, binding and clustering are common phenomena, and two applications of the models to such phenomena are breifly outlined.
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    Some trees are not interval graphs (1981)
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    Bulletin of mathematical biology 43 (1981), S. 717-717 
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    Annual Meeting of the Cell Kinetics Society (1981)
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    Bulletin of mathematical biology 43 (1981), S. 719-719 
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    Jagdbetriebliche Folgerungen aus dem Verhältnis zwischen der Größe der Jagdbezirke und dem Wohnraum einiger jagdbarer Tiere (1964)
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    European journal of wildlife research 10 (1964), S. 2-8 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary The Shooting Law in vigour within the Federal Republic is based upon the so-called districtsystem; there are 2 kinds of hunting territories, the hunting district of owners and the common hunting district. For each of these 2 kinds minimum sizes are required, 75 resp. 150 ha. The shooting district is the unit of management. It is investigated if the size of the management unit corresponds to the biological circumstances of the kinds of deer at the disposal of the shooting enterprise. Considering only the most important biological factor, the size of the yearly district — i. e. of the area which is inhabited by 1 piece of one kind of deer in the course of 1 year —, it has to be stated that this yearly district covers a multiple of the minimum size of a shooting district. This proportion - one should say disproportion - is recognized by some legal measures (for instance the possibility of rounding up the shooting district, shooting according to shooting plan); but these are insufficient. Especially considering the restriction of movement of free living animals because of the increase of human population, the intensification of agriculture and traffic, other measures (i. e. such of shooting management) ought to be taken.
    Abstract: Résumé La loi cynegétique coutumier de la République Féderale d'Allemagne est basé sur le système des districts. Elle connait deux formes de terrains de chasse: districts de chasse particuliers et districts de chasse communs. L'étendue pour chaque forme est fixé à un minimum de 75 ou 150 has. Chaque district de chasse est une unité d'exploitation. La question est posée si l'étendue d'une unite d'exploitation est approprié aux données biologiques de gibier vivant sur cette domaine. Regardant une des plus importantes données biologiques, l'étendue du district annuel, c'est à dire l'aréal donc a besoin une seule bête d'une espèce pendant une année de chasse, on constate alors que le district annuel est largement au dessus de l'étendue minimum d'un district de chasse. On tache de rendre compte à cette proportion - mieux vaut dire disproportion - par quelques mésures législatives (p. e. possibilité d'arrondir les districts de chasse, abattement suivant un plan conçu) toutes ces mésures restent cependant inefficace. Quand on regarde le rétrécissement pour bêtes fauves de circuler librement, rétrécissement dû à l'augmentation de la population humaine, l'intensité de la culture des terres et densité de la circulation sur routes, il fallait envisager encore d'autres mésures, c'est à dire ceux pour l'exploitation des chasses.
    Notes: Zusammenfassung Das in der Bundesrepublik Deutschland geltende Jagdgesetz fußt auf dem sogenannten Reviersystem; es kennt zwei Arten von Jagdbezirken, den Eigenjagdbezirk und den Gemeinschaftlichen Jagdbezirk. Für jede dieser zwei Arten bestehen Mindestgrößen, 75 bzw. 150 ha. Der Jagdbezirk ist die Betriebseinheit. Es wird untersucht, ob die Größe der Betriebseinheit den biologischen Gegebenheiten der dem Jagdbetrieb zur Verfügung stehenden Wildarten angemessen ist. Wenn man dabei als eine der wichtigsten biologischen Gegebenheiten die Größe des Jahresbezirkes - also des Areals, das ein Stück einer Wildart im Laufe eines Jagdjahres einnimmt -herausgreift, so stellt man fest, daß dieser Jahresbezirk ein Vielfaches der Mindestgröße eines Jagdbezirkes beträgt. Diesem Verhältnis - besser gesagt Mißverhältnis - wird wohl durch einige gesetzliche Maßnahmen (z. B. Möglichkeit zur Abrundung der Jagdbezirke, Bejagung nach Abschußplan) Rechnung getragen; diese sind jedoch unzureichend. Insbesondere mit Rücksicht auf die Einengung der Bewegungsfreiheit der freilebenden Tiere infolge der Zunahme der Bevölkerung, der Intensivierung der Landeskultur und des Verkehrs, sollten noch andere Maßnahmen (nämlich solche des Jagdbetriebes) Platz greifen.
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    IV. Referate (1964)
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    European journal of wildlife research 10 (1964), S. 38-40 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Der Marderhund (Nyctereutes procyonoides Gray) in Rumänien (1964)
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    European journal of wildlife research 10 (1964), S. 51-54 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary The raccoon-dog (Nyctereutes procyonoides Gray) has been signalized for the first time in Roumania in 1951 in a locality in the South of Roumania, near Bucharest. Lately this dog has been identified in several localities in the North and North-East of the country in Moldavia. Recently, the raccoon-dog gains, more and more, ground, especially in the Danube delta, where the largest number has been observed. In Roumania, the penetration of the raccoon-dog was accomplished by migration-way, by the specimens colonised in U.R.S.S. (Ukraina and the Moldavian Republic).
    Abstract: Résumé Le chien raton (Nyctereutes procyonoides Gray) a été signalé pour la première fois en Roumanie en 1951, dans une localité dans le sud de la Roumanie, près de Bucarest. Plus tard il a été identifié dans plusieurs localités dans le nord el le nord-est du pays — en Moldavie. Dernièrement, le chien raton gagne, de plus en plus, du terrain, spécialement dans le delta du Danube, où il a été observé le plus grand nombre de spécimens. En Roumanie, la pénétration du chien raton s'est faite par voie de migration, des exemplair s colonisés en U.R.S.S. (l'Ukrain et la République Moldave).
    Notes: Zusammenfassung Der Marderhund wurde in Rumänien zum ersten Male im Jahre 1951 beobachtet, und zwar im Süden des Landes, in der Umgebung von Bukarest. Später wurde er an mehreren Stellen im Norden und Nordosten des Landes, in der Moldova, festgestellt. In letzter Zeit besetzt der Marderhund immer mehr Gebiete im Donaudelta, wo die größte Zahl beobachtet wurde. Das Eindrigen des Marderhundes nach Rumänien erfolgte durch Zuwanderung aus den in der UdSSR geschaffenen Ansiedlungen (Ukraine und der Moldauischen Republik).
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    Vergleich einiger amerikanischer Wildschadenverhütungsmittel mit deutschen Präparaten (1964)
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    European journal of wildlife research 10 (1964), S. 62-68 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary Seven wildlife repellents made in USA were tested in a series of preliminary experiments. In these preliminary tests succes was required for admittance to the decisive field test, which is a part of the official recognition procedure of german wildlife repellents. The repulsivity, observed for fenced animals (red-, fallow- and roe-deer, mufflon and rabbits) was compared with nine german official recognized repellents. The results of phytotolerancy using the pelargonium-test and those relating to the technical properties are shortly explained.
    Abstract: Résumé Sept répulsifs de fabrication américaine et utilisés contre les dégâts causés par le gibier ont été soumis à une série d'essais préliminaires. Ce test préliminaire doit avoir été subi avec succès pour que, dans la procédure de reconnaissance officielle des répulsifs pour le gibier mis sur le marché en Allemagne fédérale, ceux-ci soient admis à subir un test décisif sur le terrain. L'action répulsive, observée chez des animaux en enclos (cerfs, daims, chervreuils, mouflons et lapins), a été comparée à celle de neuf produits allemands officiellement reconnus. Les résultats de phytotolérance d'après le test au Pelargonium et ceux relatifs aux propriétés techniques sont brièvement exposés.
    Notes: Zusammenfassung Sieben amerikanische Präparate zur Abwehr von Wildschäden wurden nach der Methode, die bei der Vorprüfung deutscher Wildschadenverhütungsmittel im Rahmen des amtlichen Anerkennungsverfahrens eingeführt ist, getestet. Die im Gehege ermittelte Abwehrwirkung gegen Rotwild, Damwild, Rehwild, Muffelwild und Kaninchen wird mit den Ergebnissen für neun deutsche Präparate verglichen. Weiterhin werden Ergebnisse zur Pflanzenverträglichkeit nach dem Test mit der Pelargonie und einige Ergebnisse der technischen Prüfung vorgelegt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01964656
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    Von Steinadler (Aquila chrysaëtos) in Tirol (1964)
    Springer
    European journal of wildlife research 10 (1964), S. 54-61 
    Details
    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary After the population of golden eagles in Tyrol had been much reduced by shooting at least 20 head in the years 1958/59, it was demanded that further shooting must be subject to exact scientific investigation concerning density of population ecc. During the following years 13 eyries were controlled and the young eagles were ringed. Offhand tests in the course of these investigations informed us also of the young eagles' diet. Finally the act of putting the rings on is described and the first results of distant findings (South of France) are treated. The possibilities of shooting golden eagle are considered and it is recommended to prefer the clearing of eyries in certain cases.
    Abstract: Résumé L'état en grand-aigles dans le pays Tyrol fut pendant les années 1958/1959 fortement réduit par l'abattement d'au moins 20 exemplaires. La demande fut alors posée que des recherches scientifiques exacte sur l'état etc. devraient précéder futures abattements. Pendant les années suivantes on tenait donc sous contrôle 13 aires d'aigles couverts de jeunes pousses et garnissait les aiglons d'un anneau. Recherches sur épreuves au hasard donnaient des éclaircissements sur la nourriture des jeunes. On parle enfin du garnissage avec anneau et des premiers resultats sur trouvailles éloignés (venant du Midi de la France). Pour conclure on se répand sur les possibilités d'une chasse aux grand-aigles mais croit plus efficase une vidange de l'aire.
    Notes: Zusammenfassung Nachdem im Jahre 1958/59 in Tirol der Bestand an Steinadlern durch Abschuß von mindestens 20 Exemplaren stark reduziert worden war, wurde gefordert, daß weiteren Abschüssen genaue wissenschaftliche Untersuchungen über Bestand u. dgl. vorausgehen müssen. In den folgenden Jahren wurden 13 beflogene Horste kontrolliert und die Jungadler beringt. Stichprobenartige Untersuchungen gaben dabei auch über die Ernährung der Jungen Aufschluß. Schließlich wird über die Beringung, berichtet, erste Ergebnisse von Fernfunden (aus Südfrankreich) werden behandelt. Abschließend wird auf die Möglichkeit der Bejagung des Steinadlers eingegangen und eher eine fallweise Aushorstung für günstig angesehen.
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    Zu “Folgen des Winters 1962/63” (1964)
    Springer
    European journal of wildlife research 10 (1964), S. 69-70 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01964657
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    Abwurf des Bastgehörns (1964)
    Springer
    European journal of wildlife research 10 (1964), S. 70-71 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01964658
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    Doppelkopfbildung beim Rothirsch (1964)
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    European journal of wildlife research 10 (1964), S. 71-72 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01964659
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    Laufverletzung bei einem Rehbock (1964)
    Springer
    European journal of wildlife research 10 (1964), S. 72-74 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01964660
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    Ehrenpromotion Dr. Lindner (1964)
    Springer
    European journal of wildlife research 10 (1964), S. 74-77 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01964661
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    Professor Dr. Gösta Notini (1964)
    Springer
    European journal of wildlife research 10 (1964), S. 77-78 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Eugen Fischer 90 Jahre (1964)
    Springer
    European journal of wildlife research 10 (1964), S. 78-78 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    URL: http://dx.doi.org/10.1007/BF01964663
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    Referate (1964)
    Springer
    European journal of wildlife research 10 (1964), S. 78-88 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01964664
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    IV. Referate (1981)
    Springer
    European journal of wildlife research 27 (1981), S. 220-220 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243718
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  • 96
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    Seroepidemiologische Untersuchungen zum Vorkommen von Leptospirosen bei Schalenwild in der Bundesrepublik Deutschland (1981)
    Springer
    European journal of wildlife research 27 (1981), S. 283-287 
    Details
    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary 399 serum samples collected from native cloven-hoofed game were investigated by means of agglutinating-lysis reaction for antibodies against leptospirosis. Antibodies were found in 1,8 % of 169 sera from roe deer(Capreolus capreolus), in 2,1 % of 96 sera from red deer(Cervus elaphus) and in 18,6 % of sera from wild boars(Sus scrofa) in a serum dilution of 1:400 and higher. In 5,7 % of sera from 35 fallow deer(Dama dama) were only found suspicious titers (1:200). In 29 sera of mouflon(Ovis musimon) antibodies against leptospirosis were not detected. The most reactions were found againstL. icterohaemorrhagiae (31,7 %),L. ballum (17,1 %) andL. grippotyphosa (12,2 %). The significance of the serological findings is discussed.
    Abstract: Résumé 399 échantillons de sérum de 5 espèces d'Ongulés-gibier indigènes ont été analysés au moyen de la réaction d'agglutination quant à la présence d'anticorps contre les Leptospires. Dans 1,8 % des sérums de 169 chevreuils(Capreolus capreolus), dans 2,1 % des sérums de 96 cerfs(Cervus elaphus) et dans 18,6 % des sérums de 70 sangliers(Sus scrofa) le titrage s'avéra positif (1:400 et plus). 5,7 % des échantillons de sérum de 35 daims(Dama dama) révélèrent des teneurs suspectes (1:200), tandis que dans 29 échantillons de sérums de mouflons(Ovis musimon), aucun anticorps contre les leptospires n'a été décelé. Le plus souvent, les sérums réagissaient auxL. icterohaemorrhagiae (31,7 %),L. ballum (17,1 %) etL. grippotyphosa (12,2 %). La portée des constatations sérologiques fait l'objet d'une discussion.
    Notes: Zusammenfassung 399 Serumproben von 5 einheimischen Schalenwildarten wurden mittels Agglutination-Lysis-Reaktion auf das Vorhandensein von Antikörpern gegen Leptospiren untersucht. In 1,8 % der Seren von 169 Stück Rehwild(Capreolus capreolus), in 2,1 % der Seren von 96 Stück Rotwild(Cervus elaphus) und in 18,6 % der Seren von 70 Stück Schwarzwild(Sus scrofa) wurden positive Titer (1:400 und höher) gefunden. 5,7 % der Serumproben von 35 Stück Damwild(Dama dama) wiesen verdächtige Titer (1:200) auf, während in 29 Serumproben von Muffelwild(Ovis musimon) keine Antikörper gegen Leptospiren nachgewiesen wurden. Am häufigsten reagierten die Seren gegenL. icterohaemorrhagiae (31,7 %),L. ballum (17,1 %) undL. grippotyphosa (12,2 %). Die Bedeutung der serologischen Befunde wird diskutiert.
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    URL: http://dx.doi.org/10.1007/BF02243678
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    Rosenmißbildung bei einem Rehgehörn (1981)
    Springer
    European journal of wildlife research 27 (1981), S. 287-291 
    Details
    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary The suspicion of a formation of a double rose in a roe head from the Minden-Lübbecke District in Nordrhein-Westfalen is taken as the occasion to discuss the phenomenom of double rose formation as described in the literature. The bulkiness and disorganised growth of the rose is seen as the chief characteristic of the head from the Minden-Lübbecke District. The cause of the malformation similar to a double rose is taken to be a disturbance of the hormones which affected the rose formation and then later faded away, so that the head was able to mature and be frayed largely in the normal way.
    Abstract: Résumé La présomption d'avoir à faire à une formation de meules superposées chez un bois de Chevreuil originaire du district de Minden-Lübbecke en Rhénanie-Westphalie est à l'origine d'une recherche bibliographique sur le phénomène. La caractéristique principale du bois du district de Minden-Lübbecke est la masse et le développement désordonné de ses meules. On admet que la cause de cette formation de meules superposées réside dans un déséquilibre hormonal passager ayant provoqué la malformation des meule, sans empêcher pour autant la maturation ultérieure du bois de telle sorte qu'il a pu être frayé normalement.
    Notes: Zusammenfassung Der Verdacht einer Doppelrosenbildung bei einem aus dem Kreis Minden-Lübbecke in Nordrhein-Westfalen stammenden Rehgehörn wird zum Anlaß genommen, das Phänomen der Doppelrosenbildung nach der Literatur abzuhandeln. Für das Gehörn aus dem Kreis Minden-Lübbecke wird als Hauptcharakteristikum die Massigkeit, das unorganisierte Wachstum der Rose gesehen. Als Ursache für die doppelrosenähnliche Mißbildung wird eine hormonelle Störung angenommen, die sich auf die Rosenbildung auswirkte, später abklang, so daß das Gehörn ausreifen und weitgehend normal gefegt werden konnte.
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    Dr. Heribert Kalchreuter Leiter des Fachgebietes „Wild- und Jagdökologie“ in der Bundesforschungsanstalt für Naturschutz und Landschaftsökologie (1981)
    Springer
    European journal of wildlife research 27 (1981), S. 293-294 
    Details
    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243681
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  • 99
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    On the number of solutions to a class of complementarity problems (1981)
    Springer
    Mathematical programming 21 (1981), S. 190-203 
    Details
    ISSN: 1436-4646
    Keywords: Complementarity Problem ; Cones ; Topological Degree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we consider the problem of establishing the number of solutions to the complementarity problem. For the case when the Jacobian of the mapping has all principal minors negative, and satisfies a condition at infinity, we prove that the problem has either 0, 1, 2 or 3 solutions. We also show that when the Jacobian has all principal minors positive, and satisfies a condition at infinity, the problem has a unique solution.
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    URL: http://dx.doi.org/10.1007/BF01584240
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    Finding simplicial subdivisions of polytopes (1981)
    Springer
    Mathematical programming 21 (1981), S. 233-234 
    Details
    ISSN: 1436-4646
    Keywords: Polytope ; Subdivision ; Simplex ; Volume ; Centroid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Subdivisions of polytopes are described which place any chosen vertex in a (near-) minimal number of simplices. Ancillary procedures to find volumes and centroids of polytopes are indicated.
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    URL: http://dx.doi.org/10.1007/BF01584244
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