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  • Articles  (83,116)
  • Springer  (83,116)
  • 1980-1984  (43,709)
  • 1970-1974  (33,796)
  • 1930-1934  (5,611)
  • 1981  (43,709)
  • 1971  (33,796)
  • 1931  (5,611)
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  • 1980-1984  (43,709)
  • 1970-1974  (33,796)
  • 1930-1934  (5,611)
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  • 1
    Electronic Resource
    Electronic Resource
    Contributions to the theory of organismic sets, II: Aggressiveness and submissiveness (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 49-54 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the theory of organismic sets (Bull. Math. Biophysics,31, 159–198, 1969) we considered organisms as sets endowed with certain “activities,” the latter’s resulting in a set of “products.” Those products may be of a material nature, like a hormone secreted by a cell, or of a non-material nature, like a feeling or an attitude. In the present paper aggressiveness and submissiveness are considered as such non-material products of the activities of the brain cells. A general description of aggressiveness and submissiveness is given in terms of organismic sets. Cycles in “peck order” are thus naturally explained.
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    URL: http://dx.doi.org/10.1007/BF02476664
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  • 2
    Electronic Resource
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    Contribution to the theory of organismic sets, III (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 55-66 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In line with previous studies on organismic sets, the division of all organismic sets intogeneral autotrophic and heterotrophic is introduced. The first produce their food themselves from some external source of energy, which in general may be an energy of any kind. The others use other organismic sets as the source of their food and energy. On earth we know only one kind of generalgeneral autotrophic organismic sets, namely, the autotrophic plants which use solar radiation as their source of energy and for production of their own food. It is shown why autotrophic animals do not exist on earth except as microorganisms like, e.g.,Euglena. A rigorous proof of the previously derived theorem that in an organismic set of ordern〉1 no element can be completely specialized is given. It requires the introduction of new postulates. Finally, in considering the organic world as a whole, the notion of organismic sets ofmixed order is introduced.
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    URL: http://dx.doi.org/10.1007/BF02476665
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  • 3
    Electronic Resource
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    “A stochastic solution of the 3-body problem in chemical kinetics. The termolecular stochastic process I” (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 67-81 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It appears to be axiomatic that termolecular and higher order reactions occur relatively rarely. The basis for this judgment seems to lie in the supposition that successful 3-Body collisions of 3 interactive species of molecules cannot occur frequently enought to account for chemical or biochemical transformation. In order to provide a more complete mathematical framework than now exists for examining this hypothesis the probability of effective termolecular “δ-collisions” as a function of time is derived. This amounts to adding to the class of reactions for which stochastic models are now available the termolecular reaction. In common with the unimolecular and bimolecular cases this process is seen to satisfy the criterion of consistency-in-the-mean with respect to deterministic formulations. It is planned next to use the termolecular process and the lower order processes in computer-assistedin numero experimental studies aimed at comparing alternative mechanisms of reaction.
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    URL: http://dx.doi.org/10.1007/BF02476666
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  • 4
    Electronic Resource
    Electronic Resource
    Maximum likelihood estimation for stochastic first order reactions (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 83-96 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Small sample properties of the maximum likelihood estimator for the rate constant of a stochastic first order reaction are investigated. The approximate bias and variance of the maximum likelihood estimator are derived and tabulated. If observations of the system are made at timesiτ,i=1, 2, ...,N; τ〉0, the observational spacing τ which minimizes the approximate variance of the maximum likelihood estimator is found. The non-applicability of large sample theory to confidence interval derivation is demonstrated by examination of the relative likelihood. Bartlett’s method is employed to derive approximate confidence limits, and is illustrated by using simulated kinetic runs.
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    URL: http://dx.doi.org/10.1007/BF02476667
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  • 5
    Electronic Resource
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    Organismic supercategories and qualitative dynamics of systems (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 339-354 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The representation of biological systems by means of organismic supercategories, developed in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–71;32, 539–561), is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Băianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete result concerning dynamics of genetic system, development, fertilization, regeneration, analogies, and oncogenesis are derived.
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    URL: http://dx.doi.org/10.1007/BF02476778
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  • 6
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    Some realizations of (M, R)-systems and their interpretation (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 303-319 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some years ago (Rosen 1958a, b; 1959) we described a class of metaphorical, relational paradigms for cellular activity which we termed (M, R)-systems. A sizable amount of subsequent work, to be itemized below, has been devoted to an exploration of some of the properties of these systems. The main purpose of the present paper is to put this class of paradigms into a general system-theoretic perspective, with a particular view to appraising the relation between the type of system description embodied in the (M, R)-system and other kinds of physical and mathematical descriptions of cellular systems. Thus, the principal aim is to establish the relationships and connections between the global relational formalism embodied in the (M, R)-systems and the empirical descriptions which still represent the bulk of our biological knowledge.
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    URL: http://dx.doi.org/10.1007/BF02476776
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  • 7
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    Relational forces and structures produced by them (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 321-338 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract After giving a brief review of the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967;31, 159–198, 1969), in which the concept of relational forces, introduced earlier (Bull. Math. Biophysics,28, 283–308, 1966a) plays a fundamental role, the author discusses examples of possible different structures produced by relational forces. For biological organisms the different structures found theoretically are in general agreement with observation. For societies, which are also organismic sets as discussed in the above references, the structures can be described only in an abstract space, the nature of which is discussed. Different isomorphisms between anatomical structures, as described in ordinary Euclidean space, and the sociological structures described in an abstract space are noted, as should be expected from the theory of organismic sets.
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    URL: http://dx.doi.org/10.1007/BF02476777
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  • 8
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    Probabilistic and multiple regression modeling of the biologist’s decision processes and its implications for medical diagnosis (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 439-449 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Current psychological research into the inference (diagnostic) process is briefly reviewed, using as a vehicle an investigation of the prediction of the probability of success of hypothetical applicants to a graduate program in biology. Brunswik’s lens model and multiple regression analysis are used, as is a Bayesian approach. Four judges’ (biologists’) predictions are analyzed. Some general conclusions about inference, drawn from the current data in psychology, are presented.
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    URL: http://dx.doi.org/10.1007/BF02476785
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  • 9
    Electronic Resource
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    Anin numero study of glucose-insulin interaction (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 451-462 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model has been developed to simulate the glucose-insulin interaction following a glucose load such as occurs in an IVGTT. This model differs from earlier models in that the insulin response to glucose loading is a recurring all or none threshold response. The model has been simulated on a digital computer using the digital analog simulation language CSMP.
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    URL: http://dx.doi.org/10.1007/BF02476786
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  • 10
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    Wave propagation in bone media (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 463-479 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The composite nature of bone dictates the use of a model for bone which is transversely isotropic. We solve the associated sets of partial differential equations governing the dynamic elastic behavoor of a two-layered cylindrical-shaped bone. The solution is analyzed for long, short, and intermediate length waves. The special case of compact bone is treated for long and short wave lengths and a numerical example is worked out to determine the wave speeds (for short wave lengths) given a set of elastic constants, determined by ultrasonic methods, and the bone density, wave frequency, and radius.
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    URL: http://dx.doi.org/10.1007/BF02476787
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  • 11
    Electronic Resource
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    Fourth International Biophysics Congress (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 481-481 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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  • 12
    Electronic Resource
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    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.
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    URL: http://dx.doi.org/10.1007/BF02460935
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  • 13
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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.
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    URL: http://dx.doi.org/10.1007/BF02460938
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  • 14
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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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  • 15
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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.
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    URL: http://dx.doi.org/10.1007/BF02459439
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  • 16
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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.
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    URL: http://dx.doi.org/10.1007/BF02459446
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  • 17
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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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  • 18
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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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  • 19
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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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  • 20
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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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  • 21
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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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  • 22
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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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  • 23
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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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  • 24
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    The construction of homogeneous nets (1981)
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    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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  • 25
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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
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    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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  • 26
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    Limit cycles in periodically perturbed population systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 463-485 
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    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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  • 27
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    On a unified approach to pattern generation (1981)
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    Bulletin of mathematical biology 43 (1981), S. 513-516 
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  • 28
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    Stochastic models for an enzyme reaction in an open linear system (1971)
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    Bulletin of mathematical biology 33 (1971), S. 97-115 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract A stochastic model is developed for an enzyme reaction in an open linear system. The proposed model assumes that the open system maintains the concentration of substrate and inhibitor at constant levels and that the product molecules are removed from the system by a first order reaction. Stochastic models for several enzyme reactions occurring in this open system are shown to correspond to special cases of theGI/M/∞ queue. Takács’ (1958) results for this queueing system are used to obtain the stochastic properties of the enzyme systems. A specific model we studied assumed completely competitive inhibition in an open system. The stationary distribution for the number of product molecules in the system is obtained. The enzyme reaction which incorporated the “intermediate chain hypothesis” can also be investigated by the queueing theory approach. It is shown that for this open system, if the model which incorporated the intermediate chain hypothesis has the same deterministic properties as the Michaelis-Menten model, then the latter has greater stochastic variation than the former.
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  • 29
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    International Conference on Stochastic Point Processes (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 153-153 
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  • 30
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    An integral method for the analysis of blood flow (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 117-128 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract The existing methods to solve the problems of pulsatile flow in the cardiovascular system are based on either linear axisymmetric equations or non-linear one-dimensional equations. The solutions thus obtained give only a mediocre comparison with measurements. In this paper, a non-linear axisymmetric theory is proposed. The starting point of the present theory is a third degree polynomial representation of the velocity profile. Integral methods are then applied to obtain the governing equations. To ascertain the accuracy of the theory proposed above, the calculations for a simple case involving pulsatile flow in a long rigid tube were performed. The results are: (a) the average velocities compare very well with exact solutions and (b) the velocity profiles for a given frequency agree very well with exact solutions for flow in small tubes, but tend to differ as tube size is increased.
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  • 31
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    Methode d’objectivation d’organisations temporelles privilégiées d’activités neuronales unitaires (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 129-151 
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    Notes: Résumé Le but de ce travail est la mise en évidence d’éventuels “patterns” temporels privilégiés de potentiels d’action neuronaux masqués par la superposition d’une activité aléatoire. Dans la première partie, on propose un modèle susceptible de rendre compte de cette activité aléatoire. Dans la seconde, on expose une méthode d’extraction des patterns privilégiés, compatible avec les paramètres du modèle neuronal proposé. Son algorithme fait notamment intervenir l’estimation de la fonction d’expectation. Cette méthode peut, en fait, ment intervenir l’estimation de la fonction d’expectation. Cette méthode peut, en fait, être appliquée à l’étude de séries temporelles d’événements dans des domaines très divers.
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    International Symposium on Mathematical Biology (1971)
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    Bulletin of mathematical biology 33 (1971), S. 155-156 
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    Molecular set theory. III: The wide sense kinetics of molecular sets (1971)
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    Bulletin of mathematical biology 33 (1971), S. 355-372 
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    Notes: Abstract An effort is made to begin widening the scope of kinetics by merging the concepts and point of view of molecular set theory with the stochastic approach to kinetics, beginning with the simplest unimolecular molecular set transformation. In this spirit the new concept ofmolecular set variable is introduced as the basic unit of kinetics as opposed to simply the traditionalconcentration (or cardinality) unit, connoting that the composition as well as the size of a molecular set are significant dynamic features of a system. The changes in state (or “value”) of the molecular set variable are characterized by a Markovian stochastic process and the relationship between this process and the corresponding unimolecular process for the concentration variable introduced earlier is discussed. The possible role of molecular set theory in terms of the underlying biomathematical structure of relational biology is also considered.
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    Contribution a l’etude de la forme des plantes: discussion d’un modele de ramification (1971)
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    Bulletin of mathematical biology 33 (1971), S. 387-401 
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    Notes: Abstract The problem of the forms of plants and models of branching are discussed using experimental data on the mistletoe. The number of branches by division, the distribution of divisions with regard to the number of branches per division and to the level of division, the geometrical characters of branches according to the level of division and the host, the stability of model are studied. One gives an interpretation of the model of branching as a model of growth.
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    A quantum model for controlled enzymic reactions (1971)
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    Bulletin of mathematical biology 33 (1971), S. 373-386 
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    Notes: Abstract A quantum model for the general enzymic reaction,E+S ⇌ ES → P, is presented, starting with the assumptions that any chemical substanceS, which may be a substrate for a particularE (S)-enzyme is a microphysical system and any enzymeE-molecule, capable of interacting with anS-substrate is a “measuring system” which will “measure” one or more of theS-observables. According to the above assumptions a stochastic model of the reaction is constructed and a computer simulation of the steady state performed. The results thus obtained predicted fluctuations in the enzymic reaction rate, function of the substrate “perturbation”. On an experimental basis it is demonstrated that the irradiation of an enzymic substrate with low energies results in the inducement of a dose-dependent oscillatory behavior in the corresponding enzymic reaction rate. In the reaction type, the oscillations thus induced in theE-activity by the corresponding substrates are out-of-phase, realizing a biochemical discriminating net. Likewise, in an $$S_1 \xleftarrow{{E_1 }}S\xrightarrow{{E_2 }}S_2$$ reaction type, the oscillations induced by the irradiatedS-substrate in the activities of the respective enzyme, realize a biochemical switching net.
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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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    Basic studies on metabolic steady state. Incompletely mixed systems (1971)
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    Bulletin of mathematical biology 33 (1971), S. 403-412 
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    Notes: Abstract This paper is the second of a pair dealing with some mathematical properties of metabolic steady state. An investigator wishing to compute the rate of appearance and/or disappearance of a metabolite in steady state within an intact biological system will usually appeal to a method involving radioactive tracers. It is shown that while the investigator’s choice of the mode of tracer administration (constant infusion or single injection) is largely arbitrary, the mathematical interpretation of the results may depend upon the presence or absence of gradients in certain of the variables of the system. The latter will be the case if the system is sampled at a point within the distribution space of the metabolite which is not a source point but is otherwise arbitrary. In order to deduce a formula which gives the required rate, he must have knowledge of the gradient of concentration of the traced substance, and sometimes of the gradient of specific activity.
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    Some mathematical aspects of the medical diagnostic process. I: a general mathematical model (1971)
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    Bulletin of mathematical biology 33 (1971), S. 413-424 
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    Notes: Abstract Making a medical diagnosis consists of correlating knownpatterns of disease with the various classes of clinical data elicited from the history, physical examination, and batteries of tests relative to the diagnostic dynamics symbolized by atree branching into the various possible diagnostic decisions. In this paper a relational mathematical model of the reasoning aspects of the conventional medical diagnostic process is suggested as a way of extracting a general, formal concept of medical diagnosis. Computer implementation of the model is discussed briefly.
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    Forecasting and chronic illness (1971)
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    Bulletin of mathematical biology 33 (1971), S. 425-437 
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    Notes: Abstract Biomedical data in the form of series of observations made on a single process at regular intervals constitute a discrete time series and are eligible for time series methods of analysis. The models yielded by this analysis provide the framework within which exponential smoothing methods may operate on the data to provide recurrent forecasts of future states of the process. Because the forecasts may be made on an individual basis and are sensitive to the past behavior of the individual process, the methods are presented as being potentially of great utility in the management of chronic and progressive illnesses. When incorporated into automated testing and diagnostic systems, the forecasting method will provide the capability of making prognoses for large numbers of individuals, quickly, routinely and reproducibly.
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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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    IV. Referate (1981)
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    European journal of wildlife research 27 (1981), S. 220-220 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Seroepidemiologische Untersuchungen zum Vorkommen von Leptospirosen bei Schalenwild in der Bundesrepublik Deutschland (1981)
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    European journal of wildlife research 27 (1981), S. 283-287 
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    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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    Rosenmißbildung bei einem Rehgehörn (1981)
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    European journal of wildlife research 27 (1981), S. 287-291 
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    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)
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    European journal of wildlife research 27 (1981), S. 293-294 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Chorioretinal temperature increases from solar observation (1971)
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    Bulletin of mathematical biology 33 (1971), S. 1-17 
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    Notes: Abstract Chorioretinal temperature increases produced by solar observations are computed digitally. The spectral characteristics of solar radiation and the spectral transmittances of the atmosphere, atmospheric water vapor and ocular media are considered. Image spread is employed in all calculations. The calculations are executed for a variety of observation angles, and the effects of pupil diameter, fixed filters and optical instruments are predicted. Temperature increases are also computed for solar eclipse observations by the appropriate superposition of unobscured solar disk solutions.
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    The kinetics of diffusion between a spherical cell and a surrounding medium with different diffusion properties (1971)
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    Bulletin of mathematical biology 33 (1971), S. 19-26 
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    Notes: Abstract The diffusion equation according to Fick’s law is solved for a spherical cell, surrounded by an infinite medium with different diffusion properties. The method of Laplace transform is used to obtain the formal solution, however, no inversion can be found for all times and an expansion suitable for small times is performed. The final expression found is expanded further to be more suited for the determination of the diffusion coefficient from an experimental curve. Application to a biological problem is dissussed.
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    A mathematical model for first degree block and the Wenckebach phenomenon (1971)
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    Bulletin of mathematical biology 33 (1971), S. 27-38 
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    Topics: Biology , Mathematics
    Notes: Abstract A simple mathematical model of first and second degree heart block is developed on the assumption that eachR wave, with its associated ventricular contraction, results in the release of a substance which raises the excitation threshold of the conducting tissue lying between theS-A andA-V nodes. The conduction pathway is represented by a chain of excitatory elements, the first member of which is acted upon by a regularly occurringP wave. The rate constant of the removal of this inhibitory substance, i.e., recovery rate, is the only constant necessary to be varied in order to pass from normal to first degree block to second degree. In this latter case one can predict the progressive increase inP-R interval until anR wave is missed, as occurs in the Wenckebach phenomenon. The model indicates that an increasedP wave frequency which would have little effect on theP-R inerval for a normal individual with rapid recovery, could produce a Wenckebach pattern in an individual with even a mild first degree block.
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    URL: http://dx.doi.org/10.1007/BF02476662
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    Temperature dependence of the Elovich equation derived from activated electron or ion transport across a biological interface, with an application to muscle spindle adaptation (1971)
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    Bulletin of mathematical biology 33 (1971), S. 39-47 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The temperature dependence of the Elovich equation, which is−dx/dt=m exp (nx) (wherex is concentration of substrate or ion,t is time, andm andn are coefficients dependent upon temperature), has been derived from the hypothesis of electron or ion conduction across an activation energy barrier at the surface of a biological particle or membrane, driven by a difference in redox or ion potentials. Using the additional hypothesis of reversible, temperature-dependent, inactivation of sites of reduction or complexing, the theory predicts that both coefficientsm andn have linear Arrhenius plots, in agreement with experimental data for gas adsorption on inorganic solid surfaces, and with two studies of muscle spindle adaptation.
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    Some recent results inn-person game theory (1971)
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    Mathematical programming 1 (1971), S. 58-67 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The discussion will center mainly on some work on two solution concepts: the core for gaines without side payments and the nucleolus for games with side payments (characteristic funtion games). The core has become an important equilibrium concept in mathematical economics. The nucleolus is related to the theory of bargaining sets.
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    Publications (1971)
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    Mathematical programming 1 (1971), S. 117-120 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01584078
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    The Mathematical Programming Society (1971)
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    Mathematical programming 1 (1971), S. 123-125 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01584080
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    Hybrid programs: Linear and least-distance (1971)
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    Mathematical programming 1 (1971), S. 153-167 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider a quadratic program equivalent to the general problem of minimizing a convex quadratic function of many variables subject to linear inequality constraints. In previous work [12], one of us presented an algorithm related to such problems, and classified them under “combinatorial equivalence”. The classification contained linear programs at one end (where the function has zero quadratic part) and least-distance programs at the other. A least-distance program is a problem of finding a point of a convex polyhedron which is at least distance from a given point; such programs have been studied by one of us [15, 17] and were shown to correspond to that case of the general problem where the function has positive definite quadratic part. We now extend the work on least-distance programs to those programs intermediate between linear and least-distance (called “essentially bisymmetric” in [12]), and show that such programs are really “hybrids”, with traits inherited from both parent programs: linear and leastdistance.
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    URL: http://dx.doi.org/10.1007/BF01584084
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    An “out-of-kilter” algorithm for solving minimum cost potential problems (1971)
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    Mathematical programming 1 (1971), S. 275-290 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An algorithm is given for solving the optimum potential problem, which is the dual of the classical “out-of-kilter” algorithm for flow problems. Moreover, a new proof of finiteness is provided, which holds even for non-rational data; it applies to all the algorithms of network theory which include a labeling process.
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    URL: http://dx.doi.org/10.1007/BF01584092
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    On the number of solutions to a class of complementarity problems (1981)
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    Mathematical programming 21 (1981), S. 190-203 
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    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)
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    Mathematical programming 21 (1981), S. 233-234 
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    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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    Direct theorems in semi-infinite convex programming (1981)
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    Mathematical programming 21 (1981), S. 301-318 
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    ISSN: 1436-4646
    Keywords: Semi-infinite Programs ; Open Helly-type Theorems ; Finite Subprograms ; Convex Programs ; Multi-criteria Programs ; Quasi-convex Programs ; Quasi-differentiable Programs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that a semi-infinite quasi-convex program with certain regularity conditions possesses finitely constrained subprograms with the same optimal value. This result is applied to various problems.
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    URL: http://dx.doi.org/10.1007/BF01584251
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    A statistical estimate of the structure of multi-extremal problems (1981)
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    Mathematical programming 21 (1981), S. 348-356 
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    ISSN: 1436-4646
    Keywords: Multi-extremal Optimization ; Multinomial Distribution ; Bayes Estimate ; Monte Carlo
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The solution of ak-extremal problem is defined as the set of pairs (x i * , θi),i = 1, ⋯ ,k, where x t * isi th local minimum andθ i is the volume of the set of attraction of this minimum. A Bayesian estimate ofk and (θ 1 , ⋯ , θ k ) is constructed.
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    Symposium on network flows (1981)
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    Mathematical programming 21 (1981), S. 120-120 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01584234
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    On solving a primal geometric program by partial dual optimization (1981)
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    Mathematical programming 21 (1981), S. 319-330 
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    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Geometric Programming ; Duality Theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The several published methods for mapping a dual solution estimate to a primal solution estimate in posynomial geometric programming provide no criteria for deciding how much deviation from primal feasibility, or discrepancy between the primal and dual objective function values, should be permitted before the primal solution estimate is accepted by the designer. This paper presents a new and simple dual-to-primal conversion method that uses the cost coefficients to provide a sound economic criterion for determining when to accept a primal solution estimate. The primal solution estimate generated is the exact solution to a modified primal obtained from the given primal by modifying the cost coefficients, with the exponent matrix left unchanged. The method is shown to have desirable properties when coupled with a convergent dual algorithm.
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    Minimum cost spanning tree games (1981)
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    Mathematical programming 21 (1981), S. 1-18 
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    ISSN: 1436-4646
    Keywords: Game Theory ; Cost Allocation ; Spanning Tree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the problem of cost allocation among users of a minimum cost spanning tree network. It is formulated as a cooperative game in characteristic function form, referred to as a minimum cost spanning tree (m.c.s.t.) game. We show that the core of a m.c.s.t. game is never empty. In fact, a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem. For m.c.s.t. games with efficient coalition structures we define and construct m.c.s.t. games on the components of the structure. We show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli, respectively, of the induced games on the components of the efficient coalition structure.
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    URL: http://dx.doi.org/10.1007/BF01584227
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    Institute on deterministic and stochastic scheduling (1981)
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    Mathematical programming 21 (1981), S. 119-119 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01584233
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