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  • Springer  (139,090)
  • American Physical Society  (15,840)
  • American Association for the Advancement of Science  (10,091)
  • 1980-1984  (53,177)
  • 1975-1979  (101,634)
  • 1950-1954  (10,210)
  • 1983  (53,177)
  • 1979  (50,397)
  • 1977  (51,237)
  • 1952  (10,210)
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  • 1980-1984  (53,177)
  • 1975-1979  (101,634)
  • 1950-1954  (10,210)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Modeling of biological tree structures (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 893-898 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Biological tree-like structures, such as mammalian tracheobronchial airways, are complicated branching systems. One problem in modeling such systems is the reassignment of the number of segments at a given generation in the model being constructed. A hypothesis is proposed which has successfully been used in modeling mammalian lung airways.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462385
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  • 2
    Electronic Resource
    Electronic Resource
    On biomass diversity in ecology (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 287-293 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We postulate that the biomass distribution function for an ecological population may be derived from the condition that the biomas diversity functional is maximal subject to an energetic constraint on the total biomass. This leads to a biomass distribution of the form $$p(m) = \bar m^{ - 1} \exp ( - m/\bar m)$$ , where $$\bar m$$ is the mean biomass per individual. The same condition yields a unique value for the biomass diversity functional. These predictions are tested against fishery data and found to be in good agreement. It is argued that the existence of a unique value for biomass diversity may provide a preliminary theoretical foundation for the observed upper limit to species diversity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462362
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  • 3
    Electronic Resource
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    A model for hydranth regeneration inTubularia (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 311-321 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Pigment distribution presages hydranth regeneration in the marine hydroidTubularia. We suggest that such a distribution could result from a reaction-diffusion system. A model system based on a practical reaction scheme is studied and spatial structures found which closely resemble this pigment distribution. Finite-amplitude spatial structures in reaction-diffusion systems are considered. Whereas in one spatial dimension the final structures are normally very similar to the transient patterns which emerge from a linear analysis, it is shown that in more than one dimension this is not necessarily the case. The reasons for this are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459395
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  • 4
    Electronic Resource
    Electronic Resource
    On the fate of inhaled particles in the human: A comparison of experimental data with theoretical computations based on a symmetric and asymmetric lung (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 409-424 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An analytical model is used to described the behavior of inhaled particulate matter in the human respiratory tract. Three different geometries, symmetric and asymmetric, are utilized to simultate the tracheobronchial (TB) tree. The suitability of each geometry for representing the human is evaluated by comparing calculated aerosol deposition probabilities with experimental data from inhalation exposure tests. A symmetric, dichotomously branching pattern is found to be a reliable description of the TB tree for studies of factors affecting aerosol deposition in the human lung. Calculations with the theoretical model are in excellent agreement with measured aerosol deposition efficiencies. Furthermore, the model accurately predicts experimentally observed features of inhalation exposure data, such as effects of inter-subject lung morphology differences and relative efficiencies of specific deposition mechanisms, on aerosol deposition patterns in the TB tree.
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    URL: http://dx.doi.org/10.1007/BF02459399
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  • 5
    Electronic Resource
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    Reply to letter by Jane Cronin (1982) (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 436-436 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459402
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  • 6
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    Foreword (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 437-437 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459580
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  • 7
    Electronic Resource
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    Invariant probabilities for systems in a random environment—With applications to the Brusselator (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 579-590 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper we are concerned with problems of the long-term behavior for nonlinear systems in random environment. The general model is assumed to be given by an ordinary differential equation with random parameters or random input. The disturbance process can be taken from a fairly general class of Markov processes having a bounded state space. In terms of the system’s dynamics we give sufficient conditions for the existence and uniqueness of invariant probabilities. Finally, we apply these results to the two-dimensional biochemical model which is known as the Brusselator.
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    URL: http://dx.doi.org/10.1007/BF02459589
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  • 8
    Electronic Resource
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    Non-linear filtering with discontinuous observations and applications to life sciences (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 571-577 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In various applications one faces the problem of estimating a signal from discontinuous observations. For example, in biomedical applications the signal may be the ‘state’ of a given organ and one observes through an external counter the amount of radioactivity sequestered by the organ after injection of a radioactive tracer. Here the problem is studied in the context of nonlinear filtering when the signal can be modelled as either a random variable or a diffusion process, and the observations have a continuous and a purely discontinuous component; both components may be affected by the signal. When the signal is a random variable an explicitly computable solution is obtained; for the diffusion case the solution is given as a sequence of approximating filters that can be computed recursively.
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    URL: http://dx.doi.org/10.1007/BF02459588
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  • 9
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    Lateral diffusion and eigenvalue estimates (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 627-634 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Eigenvalue problems arise in various biological models. We outline a useful comparison method and a technique using Lyapunov functions that can be applied in many cases. An application to lateral diffusion is discussed.
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    URL: http://dx.doi.org/10.1007/BF02459594
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  • 10
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    Recent views on the cell cycle structure (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 605-616 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper reviews, up to their recent developments, two types of models of the cell cycle: those considering the size controls over the cycle events and the transition probability models. The distribution of inter-mitotic time and the sister-sister and motherdaughter correlations implied by the two approaches are discussed in view of some relevant experimental data.
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    URL: http://dx.doi.org/10.1007/BF02459592
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  • 11
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    Controlled branching processes and their applications to normal and malignant haematopoiesis (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 617-626 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The development of a blood cell line originating from a pluripotent stem cell pool is modelled by a chain of multidimensional branching processes in which the sojourn times of the cells in certain resting states depend on the size of the following subpopulation. The stability of such a model is discussed qualitatively and some considerations concerning a possible malignant degeneration are presented. The behaviour of models for normal and malignant cell production are illustrated by stochastic stimulations. The model presented here describes the development of a certain line of blood cells (e.g. erythrocytes, monocytes or granulocytes) originating from the pluripotent stem cell up to the functional cell in the blood (for related models see, e.g., Rubinow and Lebowitz,J. math. Biol. 1, 87–225;Biophys. J. 16, 897–910).
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    URL: http://dx.doi.org/10.1007/BF02459593
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  • 12
    Electronic Resource
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    Population growth in random environments (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 635-641 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper reviews some recent advances in single population stochastic differential equation growth models. They are a natural way to model population growth in a randomly varying environment. The question of which calculus, Itô or Stratonovich, is preferable is addressed. The two calculi coincide when the noise term is linear, if we take into account the differences in the interpretation of the parameters. This clarifies, among other things, the controversy on the theory of niche limiting similarity proposed by May and MacArthur. The effects of correlations in the environmental fluctuations and statistical methods for estimating parameters and for prediction based on a single population trajectory are mentioned. Applications to fisheries, wildlife management and particularly to environmental impact assessment are now becoming possible and are proposed in this paper.
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    URL: http://dx.doi.org/10.1007/BF02459595
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  • 13
    Electronic Resource
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    Continuous-time Markov chains as models for animal behaviour (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 643-658 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A survey is given of the application of (functions of) continuous-time Markov chains in the statistical analysis of behavioural time series.
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    URL: http://dx.doi.org/10.1007/BF02459596
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  • 14
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    Tenth International Cell Cycle Conference (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 659-659 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02459597
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  • 15
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    On oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 661-664 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper demonstrates that there is one and only one solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a spherical cell. Previous authors have calculated numerical results that differ substantially. Numerical computations using the multiple shooting method support the results of McElwain.
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    URL: http://dx.doi.org/10.1007/BF02460043
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  • 16
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    The theory and practice of distance geometry (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 665-720 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The mathematics of distance geometry constitutes the basis of a group of algorithms for revealing the structural consequences of diverse forms of information about a macromolecule's conformation. These algorithms are of proven utility in the analysis of experimental conformational data. This paper presents the basic theorems of distance geometry in Euclidean space and gives formal proofs of the correctness and, where possible, of the complexity of these algorithms. The implications of distance geometry for the energy minimization of macromolecules are also discussed.
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    URL: http://dx.doi.org/10.1007/BF02460044
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  • 17
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    Microcontinuum approach to the pulsatile flow in tubes with and without longitudinal vibration (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 721-737 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A fully developed pulsatile flow in a circular rigid tube is analysed by a microcontinuum approach. Solutions for radial variation of axial velocity and cell rotational velocity across the tube are obtained using the momentum integral method. Simplified forms of the solutions are presented for the relevant physiological data. Marked deviations in the results are observed when compared to a Newtonian fluid model. It is interesting to see that there is sufficient reduction in the mass flow rate, phase lag and friction due to the micropolar character of the fluid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460045
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  • 18
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    Transient transport across the blood-retina barrier (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 749-758 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model of the transport of fluorescein across the blood-retina barrier in the transient state and the subsequent diffusion of fluorescein in the vitreous body is presented. The function of the barrier is lumped in a single parameter—the permeability. The sensitivity of this parameter due to changes in the other parameters of the model is given. This establishes the foundation for the quantitative assessment of the barrier function through vitreous fluorophotometry.
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    URL: http://dx.doi.org/10.1007/BF02460047
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  • 19
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    Computed insulin profiles for normalization of glycemia in diabetic patients (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 739-748 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The objective of this preliminary study was to develop a new quantitative method of setting the initial insulin infusion patterns in treatment of diabetic patients. The method is based upon the mathematical estimation of the insulin profile required to maintain the glucose level within the normal range after glucose loading in diabetic patients. Using our previously developed equivalent circuit model of glucose kinetics and the reported data of an intravenous glucose tolerance test (IVGTT) in two groups of normal and diabetic patients, two important physiological parameters of the model (the peripheral tissue's insulin resistivity and the hepatic sensitivity to glucose level) were computed for two clinical groups. Then the insulin profile was obtained by computing the plasma insulin concentrations required to keep the total glucose utilization rate of the tissue and the liver in the diabetic group equal to that of the normal group. The simulation result indicated that the computed insulin profile produced a plasma glucose profile which was more closely matched to the normal group's glucose profile than with the case of emulating the normal group's insulin profile in the diabetic group.
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    URL: http://dx.doi.org/10.1007/BF02460046
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  • 20
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    Molecular mechanism of sodium conductance changes in nerve: The role of electron transfer and energy migration (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 759-780 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper shows that the Na conductance changes can be explained quantitatively, based on the following assumptions: (1) there exist in nerve membranes the electron transfer (ET) complexes and traps, (2) there is energy migration among them. The gating mechanism is explained in physical terms. Its mathematical expression differs from the Hodgkin-Huxley equations, but resembles the Hoyt formulation. In the present model, the physical parameters for the squid axon can be estimated from currently available experimental data. The density of the ET complexes is on the order of 105/μm2, and the density of the traps is 103/μm2. The magnitude of the energy transfer rate between ET complexes is about 106/sec at large depolarization and decreases with decreasing depolarizations, as does the Na inactivation rate. The energy gap between the two stable states of the transfer electron in the ET complex is estimated to be around 0.1 eV, which is approximately the same as that for the photosynthetic systems.
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    URL: http://dx.doi.org/10.1007/BF02460048
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  • 21
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    The dynamics of symmetric nets (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 781-792 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The role of symmetry in simplifying the theory of complex neural systems is argued. When the structural symmetries of a network are expressed as an ismorphism group, implications emerge for the dynamics. Various qualitative possibilities concerning stability of uniform motion in homogeneous nets are discussed and an approach to neural hierarchies is outlined.
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    URL: http://dx.doi.org/10.1007/BF02460049
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  • 22
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    Conditions for global stability of two-species population models with discrete time delay (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 793-805 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By constructing appropriate Liapunov functionals, asymptotic behaviour of the solutions of various delay differential systems describing prey-predator, competition and symbiosis models has been studied. It has been shown that equilibrium states of these models are globally stable, provided certain conditions in terms of instantaneous and delay interaction coefficients are satisfied.
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    URL: http://dx.doi.org/10.1007/BF02460050
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  • 23
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    Flow analysis sensitivities for models of energy or material flow (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 807-826 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Sensitivity analyses have been used to examine the flow structure of two hypothetical ecosystem models. These analyses have results which relate to important aspects of ecosystem theory. Cycles are shown to increase the sensitivity of the network, while increased throughflow is shown to decrease the sensitivity. Such results indicate that several factors can be modified to decrease the sensitivity of ecosystems to environmental stress.
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    URL: http://dx.doi.org/10.1007/BF02460051
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  • 24
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    Population dynamics with age- and time-dependent birth and death rates (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 827-836 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A continous, deterministic mathematical model is used to predict population distributions by age at any time, given the initial distribution and the variation of birth and death rates with age and time. Solutions are obtained on a computer using a semi-discretization algorithm in which time derivatives in the partial differential equations are replaced by finite-difference expressions. The resulting sets of ordinary differential equations are solved by a predictor-corrector method. Graphical results are shown for some examples.
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    URL: http://dx.doi.org/10.1007/BF02460052
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  • 25
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    On the complexity of graphs and molecules (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 849-855 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new formula for the complexity of graphs is proposed and applied to the points lines and ‘connections’ of some chemically relevant graphs.
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    URL: http://dx.doi.org/10.1007/BF02460054
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  • 26
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    Analytical solutions for distributions of chemotactic bacteria (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 837-847 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper reports general and specialized results on analytical solutions to the governing phenomenological equations for chemotactic redistribution and population growth of motile bacteria. It is shown that the number of bacteria cells per unit volume,b, is proportional to a certain prescribed function ofs, the concentration of the critical substrate chemotactic agent, for steady-state solutions through an arbitrary spatial region with a boundary that is impermeable to bacteria cell transport. Moreover, it is demonstrated that the steady-state solution forb ands is unique for a prescribed total number of bacteria cells in the spatial region and a generic Robin boundary condition ons. The latter solution can be approximated to desired accuracy in terms of the Poisson-Green's function associated with the spatial region. Also, as shown by example, closed-form exact steady-state solutions are obtainable for certain consumption rate functions and geometrically symmetric spatial regions. A solutional procedure is formulated for the initialvalue problem in cases for which significant population growth is present and bacteria cell redistribution due to motility and chemotactic flow proceeds slowly relative to the diffusion of the chemoattractant substrate. Finally, a remarkably simple exact analytical solution is reported for a stradily propagating plane-wave which features motility, chemotactic motion and bacteria population growth regulated by substrate diffusion.
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    URL: http://dx.doi.org/10.1007/BF02460053
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  • 27
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    Effects of periodic accelerations on blood flow in arteries (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 857-867 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper discusses the flow of blood in large artries under the influence of linear periodic acceleration. The governing equations and boundary conditions are established and analytical solutions for the velocity, fluid acceleration, bulk flow and shear stress are obtained. The results for these physical quantitites are computed for the case of an artery the size of a normal human aorta. It is found that the flow field variables are directly proportional to the external accelerating force. The behaviour of the velocity profile along the radial distance at different stages of times at fixed applied acceleration is also shown.
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    URL: http://dx.doi.org/10.1007/BF02460055
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  • 28
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    Computational modeling of evolutionary learning processes in the brain (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 931-968 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The evolutionary selection circuits model of learning has been specified algorithmically. The basic structural components of the selection circuits model are enzymatic neurons, that is, neurons whose firing behavior is controlled by membrane-bound macromolecules called excitases. Learning involves changes in the excitase contents of neurons through a process of variation and selection. In this paper we report on the behavior of a basic version of the learning algorithm which has been developed through extensive interactive experiments with the model. This algorithm is effective in that it enables single neurons or networks of neurons to learn simple pattern classification tasks in a number of time steps which appears experimentally to be a linear function of problem size, as measured by the number of patterns of presynaptic input. The experimental behavior of the algorithm establishes that evolutionary mechanisms of learning are competent to serve as major mechanisms of neuronal adaptation. As an example, we show how the evolutionary learning algorithm can contribute to adaptive motor control processes in which the learning system develops the ability to reach a target in the presence of randomly imposed disturbances.
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    URL: http://dx.doi.org/10.1007/BF02458823
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  • 29
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    Dynamics of a continuous culture with catalysis of the growth-limiting substrate by an enzyme of the cells (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 981-990 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the present paper we discuss the behaviour of solutions of a dynamical system describing the growth of cells in a well-mixed continuous culture where the supply of the growth-limiting nutrient depends on the activity of an enzyme outside the cell membrane. It turns out that for positive dilution rates there exists an exponentially attractive two-dimensional simplex. Furthermore, the reversed system restricted to this simplex is quasimonotone. In every case all trajectories tend to an equilibrium state.
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    URL: http://dx.doi.org/10.1007/BF02458825
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  • 30
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    The trade-off between mutual interference and time lags in predator-prey systems (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 991-1004 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present a Gause predator-prey model incorporating mutual interference among predators, a density-dependent predator death rate and a time lag due to gestation. It is well known that mutual interference is stabilizing, whereas time delays are destabilizing. We show that in combining the two, a long time-lag usually, but not always, destabilizes the system. We also show that increasing delays can cause a bifurcation into periodic solutions.
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    URL: http://dx.doi.org/10.1007/BF02458826
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  • 31
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    Sequential behavior and stability properties of enzymatic neuron networks (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 969-980 
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    Notes: Abstract The cycle structure of enzymatic neural networks may be characterized in terms of number of cycles exhibited, size of cycle state sets and cycle lengths. Simulation experiments show that the stability properties of these networks have some unusual features which are not exhibited by networks of two-state switching elements or by randomly constructed ecosystem models. The behavioral and structural stability of these systems decreases with their structural complexity, as measured by the number of components. The behavioral and structural stability of enzymatic neural networks also decreases with structural complexity, as measured by the number of excitase types, but only up to the middle level of excitases per neuron. This is the point of highest potential responsiveness of the system to environmental stimuli. Beyond this point the behavioral and structural stability increase. This is due to the fact that the number of possible states increases up to this point and decreases beyond it. The number of possible states, not the number of components, serves as the useful measure of complexity in these types of systems. The selection circuits learning algorithm has been used to evolve networks whose cycle structures have desired features.
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    A new similarity principle for cardiac energetics (1983)
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    Bulletin of mathematical biology 45 (1983), S. 1005-1011 
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    Notes: Abstract Similarity criteria of the functional design of the mammalian cardiovascular system are scant. For the analysis of mammalian cardiac energetics physiological parameters such as mean arterial blood pressure, stroke volume, heart rate, metabolic rate and heart and body weights are considered pertinent. Based on these parameters, a new similarity principle is established via allometric equations, dimensional analysis and Buckingham's pi-theorem. The principle states that the ratio of left ventricular external work to metabolic rate is inversely proportional to resting heart rates of mammals. The proportionality constant is dimensionless and is invariant of mammalian body weights.
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    Categorical system theory and the phenomenological calculus (1983)
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    Bulletin of mathematical biology 45 (1983), S. 1029-1045 
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    Notes: Abstract The mathematical theory of categories is used as a tool in the description of the structure and function of natural systems. The connections between the category of natural systems, with observables and dynamics, and the phenomenological calculus of response tensors, duality- and adjoint-invariance diagrams are established. The unified theory is applied to the analysis of hierarchies, pattern generation and the structure and dynamics of proteins.
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    Categorical system theory (1983)
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    Bulletin of mathematical biology 45 (1983), S. 1047-1072 
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    Notes: Abstract This is an investigation of natural systems from the standpoint of the mathematical theory of categories. It examines the relationships which exist between different descriptions through measurement of observables and dynamical interactions. We begin with a category theory of formal systems with observables, and then proceed to a category theory of dynamical systems. The two categories are then combined to represent natural systems. Topological considerations enter in the study of stability and bifurcation phenomena. Special emphasis is placed on natural systems which model biological processes. The categorical system theory developed is applied to the analysis of several biological problems and biological system theories.
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    Simulated tetanic hyperpolarization by sodium loading of a neuronal system in which active transport is linked to the Frankenhaeuser-Huxley equations (1983)
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    Bulletin of mathematical biology 45 (1983), S. 1013-1028 
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    Notes: Abstract Tetanic hyperpolarization for theXenopus node is simulated by means of iterative solutions of the Frankenhaeuser-Huxley excitation equations together with an active transport current density term which is dependent on sodium and potassium levels as well as the ADP/ATP ratio. All time-dependent variables at the end of one interspike interval are introduced as initial conditions for the next response, whereupon all time-dependent changes in voltage and permeability factors appear identical for the third and fourth responses of a sequence. Net change in internal sodium concentration is zero throughout the third and fourth intervals if sodium loading of the system is initially adjusted to a critical level. Extent of tetanic hyperpolarization is a function of the pump conductance.
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    Announcement (1983)
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    Bulletin of mathematical biology 45 (1983), S. 1097-1097 
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    Further properties of the two-membrane model (1983)
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    Bulletin of mathematical biology 45 (1983), S. 1073-1096 
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    Notes: Abstract The properties of nonlinear equations describing the solute and solvent transport across a simplified Patlak-Goldstein-Hoffman model (two membranes in series without unstirred layers) are investigated both analytically and numerically. The analysis shows that the principal coefficients measured in transport experiments in the presence of active transport are dependent on the experimental conditions. These ‘apparent’ system parameters are extensions of the corresponding parameters determined both in passive systems and in the linear Kedem-Katchalsky theory. Moreover, they are related to the local phenomenological coefficients of the single membranes of the array. Several relationships between measurable quantities and the local system parameters are indicated, allowing the planning of experiments aimed at the measurement of the latter. Data in the literature have been used to check the proposed volume flow equation.
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    The risk-sharing problem (1979)
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    The Geneva risk and insurance review 11 (1979), S. 5-13 
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    Topics: Economics
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    Observation and biological systems (1977)
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    Bulletin of mathematical biology 39 (1977), S. 663-678 
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    Notes: Abstract A number of apparently different lines of inquiry into fundamental biological processes point to the central role played by the notion of observation in the theory of biological systems. Not only do we use the results of our own observations to obtain the system descriptions which are the starting-points for an understanding of biological processes, but it is a basic postulate of physics that the interactions between biological systems themselves can be regarded as observations. On this basis, it is clear that we cannot properly understand biological interactions unless the observables we employ for system description are the same as those involved in the interactions we are describing. To do this requires a general theory of observables and system description, establishing the relationship between different modes of description. A sketch of such a theory is developed in the present paper, using only two postulates: (a) that all interactions are determined by the values of observables of a system evaluated on specific states, and (b) that real-valued observables suffice. As an application, a specific test is proposed whereby it can be determined whether the observables employed to describe interacting systems are sufficient to specify the observables involved in the interaction itself.
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    Cross-sectional shape of flexible tubes (1977)
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    Bulletin of mathematical biology 39 (1977), S. 679-691 
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    Notes: Abstract Differential equations are derived whose solution gives the cross-sectional shape of a flexible tube as a function of the transmural pressure. These equations are solved digitally to produce a series of closed curves, each curve representing the shape of a cross section for a particular set of conditions. These are then applied to the case of systemic arteries, pulmonary arteries, and large veins. The results predict that systemic arteries must always be circular, even when the internal and external pressures are equal. In veins, a small positive internal pressure causes them to become circular, regardless of their initial state, with negligible stretching. Further increases in internal pressure cause the area of the cross section to increase due only to stretching, the shape remaining essentially circular. With pulmonary arteries, known to be noncircular, changes in the cross-sectional area result from a combination of stretching and changes of shape.
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    Some techniques in building and validating stochastic models of human reproduction (1977)
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    Bulletin of mathematical biology 39 (1977), S. 693-704 
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    Notes: Abstract Stochastic models of human reproduction are beginning to play significant roles in the evaluation of family planning programs. A class of stochastic processes called absorbing, agedependent, semi-Markov processes frequently arises in the construction of such models. The paper begins with a discussion of some technicalities regarding absorbing, age-dependent, semi-Markov processes. Then, an algorithm due to Littman, which makes possible the computerization of this class of stochastic processes, is presented. Briefly, Littman’s algorithm provides an efficient method for numerically solving systems of renewal type integral equations, provided the system does not contain a large number of equations. After setting down a concrete model for a large clinical trial of intrauterine devices conducted in Taiwan, the paper concludes with a discussion of a method for validating the model based on the data collected in the clinical trial.
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    On peristaltic flow and its efficiency (1977)
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    Bulletin of mathematical biology 39 (1977), S. 743-743 
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    Detection and analysis of recognition and selection in the immune response (1977)
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    Bulletin of mathematical biology 39 (1977), S. 705-719 
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    Notes: Abstract Some theoretical requirements for the valid use of hemolytic plaque inhibition as a method for studying cellular selection and recognition in an immune response are reviewed. Aside from providing a rational basis for the use of this technique, the theory resolves a growing body of apparently conflicting results on the affinity regulation of IgM secreting cells and can also be used to deduce structural (in particular, morphological) features of the IgM molecule. The diverse predictions of the theory are examined in light of experimental results and find support in a wide data base. Additional specific experiments are proposed which can be used in conjunction with the theory to help clarify the relation between cellular proliferation and maturation.
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    A theory of cell swelling in high concentrations of KCl and other chloride salts (1977)
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    Bulletin of mathematical biology 39 (1977), S. 721-741 
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    Notes: Abstract A theory of the cell volume is presented with emphasis on the swelling effect of high concentrations of KCl and other chloride salts. In this theory a particular cell volume represents a state of balance between the tendency of the cell water to build deeper layers of polarized water and the restraining forces exerted by the salt linkages and H-bonds. Taking into account also the different structure-breaking effects of different salts, theoretical curves can be constructed which describe the complex multiple peak-plateau of swelling curve observed in frog muscle in response to increasing concentrations of different chloride salts.
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    Diversity and diffusion in multidimensional niche space (1979)
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    Bulletin of mathematical biology 41 (1979), S. 129-138 
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    Notes: Abstract The results of an earlier effort to provide a geometrical analysis of Hutchinsonian niche space are extended. The concept of diversity of a species in niche space is introduced and the maximization of this diversity provides a rationale for a within-niche fitness distribution which is Gaussian. Niche expansion is seen as a consequence of diffusion in niche space, and an evolutionary version of the Volterra competition equations is proposed as a way to relate niche geometry with population dynamics. Applications to topics in community evolution, species packing and the statistical fitting of species abundance data are mentioned.
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    Stochastic compartmental modeling and parameter estimation with application to cancer treatment follow-up studies (1979)
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    Bulletin of mathematical biology 41 (1979), S. 203-215 
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    Notes: Abstract In this paper we use marginal probabilities to derive expressions for the means, variances and covariances ofm-compartment systems. We also present an efficient algorithm for the estimation of the parameters of the system using time series data when measurements are available fromk of them compartments. An application of the analysis and parameter estimation procedure for a model representing the results of a cancer treatment follow-up study is given.
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    Self-organization in biological systems with multiple cellular contacts (1979)
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    Bulletin of mathematical biology 41 (1979), S. 193-201 
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    Notes: Abstract The self-organizing properties of an ensemble of interconnected units are studied by linear stability analyses. Small perturbations of a uniform steady-state may result in bifurcations to other solutions that exhibit spatial or temporal order. We show that increasing the number of connections that a unit makes with its neighbors changes the nature of these solutions and tends to destroy spatiotemporal patterns. If an unconnected system is orginally stable, the formation of multiple interconnections can never induce temporal periodicity but may, under certain circumstances, allow the emergence of stationary spatial patterns. We have verified the predictions of the linear stability analysis on a model system and comment on the implications of these results for multicellular ensembles.
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    Performance criteria for optimization of cardiac assistance (1979)
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    Bulletin of mathematical biology 41 (1979), S. 217-227 
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    Notes: Abstract A performance criterion and weighting factors for the optimal cardiac assistance are investigated by applying Tellegen's network theorem and tolerance analysis on animal experimental data for left ventricular (LV) bypass on the failing heart. Two major factors with respect to cardiac assistance (total power delivered to the peripheral circulatory system, and changes in temporal pattern of ventricular contraction) are represented by two performance criteria,J 1 andJ 2 whereJ 1 relates to the sum of LV and pump power, andJ 2 relates to the “peakedness” factor of LV power. The total performance index (J) is determined as the weighted sum ofJ 1 andJ 2;J=w 1J1+w2J2. The weighting factors,w 1 andw 2, are computed as inverses of the tolerance in the performance contours with respect to improvement of stroke work per minute from pre- to post-bypass condition.
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    Catastrophe theory: Selected papers 1972–1977 (1979)
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    Bulletin of mathematical biology 41 (1979), S. 253-255 
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    Volterra-Verhulst prey-predator systems with time dependent coefficients: Diffusion type approximation and periodic solutions (1979)
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    Bulletin of mathematical biology 41 (1979), S. 229-251 
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    Notes: Abstract In treating the Volterra-Verhulst prey-predator system with time dependent coefficients, we ask how far this deterministic system represents or approximates the dynamics of the population evolving in a realistic environment which is stochastic in nature. We consider a stochastic system withsmall Gaussian noise type fluctuations. It is shown that the higher moments of the deviation of the deterministic system from the stochastic approach zero as the strength δ of the perturbation decays to zero. For any δ〉0 and allT〉0, ε〉0, the sample population paths that stay within ε distance from the deterministic path during [0,T] form a collection of positive probability. In comparing the stationary distributions of the two systems, we show that the weak limits of those of the stochastic system form a subset of those of the deterministic system. This is in analogy with a result of May connected with the stability of the two systems. Plant and rodent populations possess periodic parameters andexhibit periodic behaivor. We establish theoretically this periodicity under periodicity conditions on the coefficients and perturbing random forces. We also establish a central limit property for the prey-predator system.
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    A theoretical study of neural adaptation and transient responses due to inhibitory feedback (1979)
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    Bulletin of mathematical biology 41 (1979), S. 257-282 
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    Notes: Abstract Adaptation of repetitively firing sensory neurons and nerve models is correlated with specific inhibitory feedback phenomena—an electrogenic sodium pump, and post synaptic self inhibition. The quality of the adaptive responses depends on the excitation properties of the neuron in the interspike interval, or the description of these properties by the underlying impulse encoder model. THis model dependence is demonstrated by comparisons of the behavior of two classes of models; the “leaky integrator models” which assume a passive neural membrane, and the “variable-γ models”, for which the neural state of excitation varies according to first order differential equations. The complexity inherent in the variable-γ models is effectively boiled down to mathematically simple relationships which are derived from studies of the neural- and model frequency responses to small amplitude sinusoidal stimuli. It is argued, and supported with examples, that these relationships hold for impulse frequency transients resulting from more general stimulus conditions. Expressions are then derived which permit feedback parameters to be determined from impulse frequency data. In this connection, recent studies of neural dynamics are brought to bear to resolve ambiguities in data interpretation.
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    On the measurement of shape (1979)
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    Bulletin of mathematical biology 41 (1979), S. 283-304 
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    Notes: Abstract A setQ(n) of noncongruent connected shapes, constructed from a fixed numbern of congruent regular hexagons laid edge to edge, is defined. Various measures of shape are applied toQ(n) and the results are numerically analyzed in the special casesn≦9. The concept of spatial entropy is introduced which affords a measure of the “complexity” of shape. Possible biological applications include the analysis of ecological cover,stigmergy or the complex nest-building activities of social insects and morphogenesis. Essentially any comparative study of shape, regardless of the specific application, might be carried out along the lines suggested in the paper.
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    Mathematical approaches to optimization of cancer chemotherapy (1979)
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    Bulletin of mathematical biology 41 (1979), S. 305-324 
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    Notes: Abstract This paper uses optimal control theory in conjunction with a Gompertzian type model for cellular growth to determine the optimal method of administering cycle non-specific chemotherapy or more generally the optimal durations of treatment and rest periods during chemotherapy. The performance critera employed to determine the relative merits of the therapy include not only the destruction of malignant cells, but also the sparing of a critical normal tissue. Since these criteria are at odds with one another, the solutions are found which satisfy the Pareto optimality conditions.
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    Asymptotic solutions of differential equations with time delay in population dynamics (1979)
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    Bulletin of mathematical biology 41 (1979), S. 325-342 
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    Notes: Abstract Oscillations governed by generalized Volterra-Gause-Witt equations to include retardation effects in population dynamics are considered. Models containing either small or significant time delay are discussed. The Krylov-Bogoliubov-Mitropolskii perturbation method and its extension for differential equations with retarded argument is used.
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    Time development of probability distributions for interacting species (1979)
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    Bulletin of mathematical biology 41 (1979), S. 357-364 
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    Notes: Abstract A general solution to the dynamical equation for the probability distribution associated withn interacting species is obtained by employing the author's generic canonical expression for the rate functions. Interacting species models with limit-cycle dynamics and no stable equilibrium points feature probability distributions that are asymptotic for large values oft to Dirac δ-distributions concentrated on the limit-cycles, as illustrated here for an analytically solvable two-species model. For ann-species Volterra model, a stationary or temporally-averaged probability distribution should generally be much more complicated than the specialized Poisson form studied by Kerner and others.
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    Nernst-planck analog equations and stationary state membrane electric potentials (1979)
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    Bulletin of mathematical biology 41 (1979), S. 365-385 
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    Notes: Abstract A set of coupled nonlinear differential equations, determining the concentration profiles and electric potentials valid for isothermal transport of ions and molecules across a diffusion barrier are formulated, using a correction to the limiting expression for chemical potential gradients and the molecular expression for frictional force. These differential equations are similar to Nernst-Planck equations and reduce to these under appropriate approximations. Solutions of these equations valid under specified conditions are presented. Expressions for permeability, concentration profiles of many ion systems are included.
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    Global flow equations for membrane transport from local equations of motion—II. The case of a single nonelectrolyte solute plus water (1979)
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    Bulletin of mathematical biology 41 (1979), S. 629-640 
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    Notes: Abstract The global flow equations of nonequilibrium thermodynamics for a single nonelectrolyte solute and water passing through a membrane are obtained by solving the local equations of motion. The method follows that developed for the general,n-solute case in the previous paper (Mikulecky, 1978). It is easily seen in this simple case that the passage from local interactions, formulated as position dependent frictional interactions in the equations of motion, to ghe global result involves a loss of any simple way of identifying particulars about local information. Two particular cases are analyzed in further detail: the case of no interaction within the pore and the case of constant interaction for both solute and solvent across the pore. In the former case, Onsager reciprocity survives in the global result if a self-consistent definition of the partial viscosity coefficients is used, while in the latter case, reciprocity is lost. Since, in many biologically interesting cases, the presence of interaction of the type considered here is likely to occur, the reciprocity condition should not automatically be assumed to hold.
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    Qualitative analysis of a model generating long potential waves in Ba-treated nerve cells—I. Reduced systems (1979)
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    Bulletin of mathematical biology 41 (1979), S. 665-686 
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    Notes: Abstract This study is related to a model describing the behavior of barium-treatedAplysia neurons generating regular burst-plateau patterns. The model is represented by an autonomous dynamical system, defined inR 4 and depending on a small parameter. This paper is restricted to the qualitative study of three “reduced systems” deduced from the “complete system”. Part of the study is performed with the use of the qualitative theory of singular perturbations. The predicted behaviors are compared with experimental results.
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    Some results about nonlinear chemical systems represented by trees and cycles (1979)
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    Bulletin of mathematical biology 41 (1979), S. 641-664 
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    Notes: Abstract Using linear stability analysis, the qualitative stability properties of open nonlinear chemical systems, in which reactions of any order may occur, will be studied. Systems will be classified in three fundamental classes: trees, cycles and loops, according to their knot graphs. The study of the Jacobian matrix for the kinetic equations of the system shows that the symmetrizability by a particular procedure (calledD-symmetrizability) is a sufficient condition for stability. It has been proved that tree-graphs always satisfy the above condition. For the cycle-graphs, theD-symmetrizability condition leads to a cyclic relation between forward and reverse steady state flows. The stability may be assured, even if the cyclic relation is not satisfied, providing that the “symmetry breaking” be lower than an upper bound; further alternative criteria for stability of cycles have been derived. All these results are independent of the number of diffusive exchanges with the environment.
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    Analysis of the behaviour of Kauffman binary networks—I. State space description and the distribution of limit cycle lengths (1979)
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    Bulletin of mathematical biology 41 (1979), S. 687-705 
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    Notes: Abstract The basis of an analytical description of the behaviour of large random nets of binary elements of the type first investigated in detail by S. A. Kauffman is presented. It is shown that information about the network dynamics can be deduced from quite general considerations of the properties of the state transition graph and matrix. An expression for the matrix elements of the state transition matrix in terms of the Boolean function specification of the net is derived. Using these ideas the distribution of limit cycle lengthsl for a completely random net is calculated and shown to bex 1/l, a result which agrees well with experimental data.
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    Analysis of the behaviour of Kauffman binary networks—II. The state cycle fraction for networks of different connectivities (1979)
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    Bulletin of mathematical biology 41 (1979), S. 707-724 
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    Notes: Abstract The state-transition matrix description of Kauffman binary networks described in the previous paper is further developed to obtain an analytical expression for the fraction of states involved in limit cycles as a function of the network size and connectivity. The result obtained for totally connected networks agrees with that derived from quite different considerations by other workers. For low connectivity networks the results are in qualitative agreement with the experimental data of Kauffman but there is a quantitative discrepancy which remains to be resolved.
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    Persistence in food webs—I Lotka-Volterra food chains (1979)
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    Bulletin of mathematical biology 41 (1979), S. 877-891 
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    Notes: Abstract Persistence-extinction in simple food chains modelled by Lotka-Volterra dynamics is governed by a single parameter which depends upon the interspecific interaction coefficients, the intraspecific interaction coefficients, and the length of the food chain. In persistent systems with nonzero carrying capacity, two new features predominate. Trophic level influence factors relate persistence on different trophic levels and determine, in conjunction with the persistence parameter, the magnitude of persistence. Equilibrium component ordering, which results in persistent systems, mandates once again that systems need to be studied on the complete ecosystem level; static field measurements reflect species location in the food chain, the total length of the food chain and assume characteristics according to these factors.
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    Weber's law and perceptual categories: Another teleological view (1983)
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    Bulletin of mathematical biology 45 (1983), S. 139-142 
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    Notes: Abstract As an alternative to optimum-processor models in which sensors attempt to circumvent internal and external noise, a mechanism-independent argument is presented for Weber's law in vision and hearing. In vision, the argument is that categories of objects should be independent of the light intensity on these objects. In hearing, sound categorization should be independent of the distance from the sound source. An analogous desideratum for computer-based image segmentation is also presented.
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    Lattices and lattice-valued relations in biology (1983)
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    Bulletin of mathematical biology 45 (1983), S. 193-207 
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    Notes: Abstract Rashevsky's treatment of general binary relations between sets of biological elements is extended using the novel mathematical concept of lattice-valued relation (l.v.r.). This yields a quantitative measure of the strength of the relations between components of a biological organism, and some illustrative examples are given. Specific l.v.r.'s are used to define (more precisely than in Rashevsky's preliminary theory of binary relations) the biologically important relationships amongst hormones, metabolism and energy exchange involved in metabolic reactions. The ‘strongest link’ between the set of hormones and the set of metabolic reactions is quantified using a special l.v.r., and other specific biological realisations of lattice-valued relations in abstract-relational biology are presented. L.v.r.'s may also be regarded as a form ofG-relation in relational biology, or as a particular case of generating diagrams. Further possible developments of this approach, using more complex tools of the newly developed mathematical theory of lattice-valued relations, such as function space l.v.r., group l.v.r., l.v.r. morphisms, l.v.r. homology andn-ary l.v.r.'s are suggested.
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    On the effect of the concentration profile of red cells on blood flow in the artery with stenosis (1983)
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    Bulletin of mathematical biology 45 (1983), S. 259-267 
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    Notes: Abstract The effects of the viscosity-concentration dependence and of the concentration profile on blood flow through a vessel with stenosis have been studied. The flow resistance and the wall shear stress have been found to be smaller than in the two-fluid model with constant viscosities.
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    Stochastic models for cell kinetics (1983)
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    Bulletin of mathematical biology 45 (1983), S. 507-519 
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    Notes: Abstract A survey is given of branching process type methods in cell kinetics. Some results are given that allow circadian rhythm and do not require complete independence between cells. Some more classical results on balanced exponential growth are given and some comments are made on flow microfluorometry.
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    Introduction (1983)
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    Bulletin of mathematical biology 45 (1983), S. 439-442 
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    Stochastic processes in neurophysiology: Transformation from point to continuous processes (1983)
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    Bulletin of mathematical biology 45 (1983), S. 443-465 
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    Notes: Abstract The spike train activity of neurones is considered as a point process, and methods of analysing and interpreting recorded spike trains are considered. The generation of a continuous process (membrane noise) from interacting point processes is described.
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    Stochastic theory of population genetics (1983)
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    Bulletin of mathematical biology 45 (1983), S. 521-554 
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    Notes: Abstract Stochastic models of population genetics are studied with special reference to the biological interest. Mathematical methods are described for treating some simple models and their modifications aimed at the problems of the molecular evolution. Unified theory for treating different quantities is extensively developed and applied to some typical problems of current interest in genetics. Mathematical methods for treating geographically structured populations are given. Approximation formulae and their accuracy are discussed. Some criteria are given for a structured population to behave almost like a panmictic population of the same total size. Some quantities are shown to be independent of the geographical structure and their dynamics are described.
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    Linear feedback system design (1983)
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    Circuits, systems and signal processing 2 (1983), S. 35-44 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Via fractional representation methods, this paper tries to clarify the role of various conditions used in the feedback system design and stability with respect to the well-posedness of the system, the existence of a solution for stability and design, and the parameterization of the set of complete solutions. The design criterion for stable feedback system design can be used for filters design, as shown in Section 5. Systems to be considered in this paper include the linear time-varying case and results can easily be extended to the case where systems do not have the same number of inputs and outputs.
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    On the existence of self-excited oscillations in systems with discontinuous elements (1983)
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    Circuits, systems and signal processing 2 (1983), S. 57-76 
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    Notes: Abstract Conditions are established which ensure the existence (or non-existence) of limit cycles in feedback systems containing discontinuous elements or elements with hysteresis. The results are applied to a specific example.
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    Consistent initial conditions for singular nonlinear systems (1983)
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    Circuits, systems and signal processing 2 (1983), S. 45-55 
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    Notes: Conclusion A necessary condition for consistent initial conditions for singular nonlinear systems has been discussed. It is shown that for linear systems or systems of index less than three these conditions are equivlaent to previously reported results. However, for nonlinear systems of index greater than two these new conditions correct those previously reported. One consequence is that Euler's method may fail to estimate solutions for some semi-state equations. R. W. Newcomb's provision of an earlier version of [14] and subsequent correspondence is gratefully acknowledged.
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    Scattering and admittance matrices of SAW transducers (1983)
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    Circuits, systems and signal processing 2 (1983), S. 161-177 
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    Notes: Abstract Thep-plane scattering and admittance matrices of SAW transducers consisting ofn equal sections modeled through the hybrid equivalent circuit are explicitly calculated. The results are specialized to the in-line and crossed-field models, and the technique is developed for unequal section transducers.
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    On the properties of linear spectral transformations for 2-dimensional digital filters (1983)
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    Circuits, systems and signal processing 2 (1983), S. 203-211 
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    Notes: Abstract A set of eight linear spectral transformations which can be used in the design of two-dimensional digital filters is studied from a group-theoretic point of view. Several properties of the transformations, some of them known and some of them new, are deduced and are then applied in the implementation of 2-D digital filters. It is shown that trade-offs exist which can be used to reduce either the amount of memory required for the programming or the amount of data manipulation.
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    A new negative resistance oscillator model (1983)
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    Circuits, systems and signal processing 2 (1983), S. 213-238 
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    Notes: Abstract A physically justifiable mathematical model is proposed for a class of current-controlled, negative resistance oscillators having terminal characteristics which are poorly represented by the van der Pol, Scott, and Ceschia-Zecchin equations. Such resonators are typified by the monolithic emitter-coupled astable multivibrator (ECAM). A unique, three-parameter equation, based on the inverse hyperbolic tangent, is matched to the ECAM voltage-current curve. Using the method of Kryloff and Bogoliuboff, the transient and steady-state behavior of the ECAM is derived for oscillation with single-mode and double-mode LCR networks under quasi-linear conditions. An expression for the time of amplitude build-up and decay is derived. A phase plane is constructed for the double-mode case, yielding a system apparently free of simultaneous modes. The validity of the model is experimentally verified for quartz-controlled ECAM devices. The analysis results are extendable ton resonant modes and may be generalized to voltage-controlled devices.
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    High-resolution spectral analysis using multiple-interval adaptive prediction (1983)
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    Circuits, systems and signal processing 2 (1983), S. 421-443 
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    Notes: Abstract The problem of adaptively detecting two sinusoids corrupted by noise is considered, with emphasis on resolution properties. The approach is to form a spectral estimate from the coefficients of a Δ-step-ahead adaptive predictor. A theoretical analysis reveals that attention to the choice of the prediction horizon Δ gives a distinct improvement in the spectral estimate and in the resolution of the signals. The theoretical results are illustrated with numerical examples. Comparisons with previously suggested techniques are also made.
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    Simulation of an automobile portfolio (1979)
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    The Geneva risk and insurance review 11 (1979), S. 40-46 
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    Topics: Economics
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    A mathematical model of insurance business and how it may be used (1979)
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    The Geneva risk and insurance review 11 (1979), S. 34-39 
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    Topics: Economics
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    The characteristics approach and its application to financial liabilities, financial assets and portfolio choice (1979)
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    The Geneva risk and insurance review 11 (1979), S. 52-62 
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    Introduction (1979)
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    The Geneva risk and insurance review 12 (1979), S. 3-4 
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    Topics: Economics
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    Human capital and risk-bearing (1979)
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    The Geneva risk and insurance review 12 (1979), S. 5-22 
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    Minimal oxygen consumption and optimal contractility of the heart: Theoretical approach to principle of physiological control of contractility (1979)
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    Bulletin of mathematical biology 41 (1979), S. 139-150 
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    Notes: Abstract Oxygen consumption of the left ventricle (MVO 2) was evaluated theoretically under the condition that the ventricle pumps a constant stroke volume against a constant arterial pressure, hence producing a constant external mechanical stroke work, with a widely varied contractility.MVO 2 was calculated by an empirical equation which had been inferred previously. Theoretical results indicated that the ventricle has a contractility at whichMVO 2 is minimal in spite of constant external work and therefore the mechanical efficiency as a pump is maximal. Such a contractility can be considered to be optimal from a standpoint of metabolic economy. The optimal contractility fell within the physiological range of contractility which had been observed experimentally. The result suggests a possibility that the contractility of a normal heart might be physiologically adapted to such an optimal level.
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    Nonlinear diffusion in biological systems (1979)
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    Bulletin of mathematical biology 41 (1979), S. 151-162 
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    Notes: Abstract Diffusion problem with variabale diffusion coefficient in a spherical biological system is investigated. Also included in this study is the biological reaction of the Michaelis-Menten type. The problem formulated consists of a highly nonlinear differential equation which, however, can be efficiently solved by the orthogonal collocation method on a digital computer. The effects of the dimensionless governing parameters on the transient and steady state concentration responses are parametrically examined for the diffusion system with and without biological reaction.
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    Electric potential in three-dimensional electrically syncytial tissues (1979)
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    Bulletin of mathematical biology 41 (1979), S. 163-181 
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    Notes: Abstract The problem of calculating the potential induced in an electrical syncytium by a point source of current is studied. The interiors of the many interconnected cells are treated as one continuum with resistivity ρ i . The interdigitated extracellular space is treated as a second continuum of resistivity ρ e , occupying the same overall volume, coupled to the first via the resistanceR m and capacitanceC m of the cell membranes. The intra- and extracellular potentials are then solutions to a pair of coupled partial differential equations. The equations are uncoupled, yielding a cable equation for the transmembrane potential and a Poisson equation for a second auxiliary potential. For an unbounded syncytium the potential for a step function source is obtained in terms of error functions. For a spherical syncytium of radiusa, bounded by a membrane with surface resistanceR a, and capacitanceC a, expansions are obtained in spherical harmonics and spherical Bessel functions. For ɛ=ρ ia/R a and β=ρ i /ρ e small, an asymptotic expansion of the potential is developed. The results are compared to earlier results for a spherical cell as well as to microelectrode measurements of the lens of the eye.
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    Electric potential in cylindrical syncytia and muscle fibers (1979)
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    Bulletin of mathematical biology 41 (1979), S. 183-192 
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    Notes: Abstract The model developed in an earlier paper using two coupled partial differential equations for calculating the intracellular and extracellular electric potentials in a syncytium is applied here to cylindrical geometry. Eigenfunction expansions are obtained for the potentials resulting from an intracellular point source of current. The required orthogonality relations for the two sets of coupled radial eigenfunctions are derived. The model is applied to the structure composed of the interior and the transverse tubules of a muscle fiber. Asymtotic expansions for ζ and β→0 are obtained, where ζ is the product of the effective intracellular resistivity, the fiber radius and the outer surface membrane admittance per unit area, and β is the ratio of the effective intracellular resistivity to that of the tubular lumen. Earlier results from the distributed circuit model of a muscle fiber are recovered when ζ and β are small, and for a nerve axon when β=0.
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    Analysis of potassium conductance in squid giant axons (1979)
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    Bulletin of mathematical biology 41 (1979), S. 343-356 
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    Notes: Abstract Assuming a model of facilitated ionic transport across axonal membranes proposed by McIlroy (1975) and extended by McIlroy and Hahn (1978), it is shown that if the selectivity coefficient, πK, of the potassium conducting system ≃59 the permeabilityP Ks, of the periaxonal barrier of the squid giant axon for K+ ions≃(1.2±0.44)×10−4 cm sec−1 and the thickness of the periaxonal space ≃477±168 Å. Using a value (10−4 cm sec−1) ofP Ks in the foregoing range the experimental curves for the steady state membrane ionic conductance versus measured membrane potential difference (p.d.), ϕ, of Gilbert and Ehrenstein (1969) are corrected for the effect of accumulation of K+ in the periaxonal space. This correction is most marked for the axon immersed in a natural ionic environment, whose conductance curve is shifted ≃70mV along the voltage axis in the hyperpolarization direction. By assuming that the physico-chemical connection between a depolarization of the axonal membrane and the consequent membrane conductance changes is a Wien dissociative effect of the membrane's electric field on a weak electrolyte situated in the axolemma, the position of the peaks of the corrected conductance versus ϕ curves can be identified with zero membrane electric field and hence with zero p.d.across the axolemma. A set of values for the double-layer p.d.s at the axonal membrane interfaces with the external electrolytes in the vicinity of the K+ conducting pores can therefore be deduced for the various external electrolytes employed by Gilbert and Ehrenstein. A model of these double-layer p.d.s in which the membrane interfaces are assumed to possess fixed monovalent negatively charged sites, at least in the neighbourhood of the K+ conducting pores, is constructed. It is shown that, using the previously deduced values for the doublelayer p.d.s, such a model has a consistent, physically realistic solution for the distance between the fixed charged sites and for the dissociation constants of these sites in their interaction with the ions of the extramembrane electrolytes.
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    Mutation-absorption model of the enzyme (1979)
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    Bulletin of mathematical biology 41 (1979), S. 387-405 
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    Notes: Abstract Gradual changes in function of proteins in response to single changes in primary structure are often observed to occur and are a necessary condition for evolution by variation and natural selection at the protein level. A probabilistic (entropy theory_ analysis of the effect of changes in primary structure on three-dimensional shape and function shows that such gradualism is based on the presence of a control system in the molecule involving a definite general form of structure-function degeneracy. The assumptions of the analysis are that primary structure determines tertiary structure (or a thermal distribution of tertiary configurations and allosteric forms), tertiary structure determines function (characterized by rate and other parameters), and that certain features of tertiary structure may be specialized for particular functions. The main conclusion is that embodied in the molecule is a subsystem which serves as a buffer, absorbing mutation or other forms of genetic variation and expressing these as graceful variations in features of the shape critical for function. This buffer system may be realized by numerical redundancy of amino acids or other mechanisms which increase the redundancy of weak interactions responsible for folding, utilization of amino acids having a greater number of analogs with redundant features, or local and global structural formats which allow for more effective utilization of redundancy. The mutation-absorption model has implications for the interpretation of structure-function relations in biology, the topology of the adaptive landscape, the interpretation of isoenzymes and allozymes, the relationship between selection and neutralism in evolution, and the relation between the complexity of and energy required by biological systems and the effectiveness of evolutionary optimization.
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    Some comments on activation and inhibition (1979)
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    Bulletin of mathematical biology 41 (1979), S. 427-445 
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    Notes: Abstract A system of rate equations gives rise to a corresponding pattern of activation and inhibition between the state variables. We consider the converse question: to what extent does the specification of a pattern of activation and inhibition between interacting quantities determine the rate equations? Among other things, it is shown that in order to determine a closed set of rate equations, a set of integrability conditions among the interactions must be satisfied; hence there is a sense in which an activation-inhibition pattern is more general than systems of rate equations. Questions of the structural interactions, are briefly discussed. A comparison is made between the properties of such activation-inhibition patterns and those of neural networks, or more general modular automata.
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    Global flow equations for membrane transport from local equations of motion: 1. The general case for (n−1) nonelectrolyte solutes plus water (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 447-447 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460822
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    A teleological explanation of Weber's law and the motor unit size law (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 407-425 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that the Weber-Fechner law. which relates the response of a sensory biosystem to the intensity of the input stimulus, can be derived from a teleological principle of minimum transentropy (maximal noise reduction) provided the relative mean fluctuation (coefficient of variation) of the input intensity can be assumed to be (approximately) constant for all feasible mean input intensities. A law is then deduced from experimental results which quantifies the relationship existing between the relative amount of activated muscle mass and the “size” (which term is clearly defined) of a newly recruited motor unit. This law is found to be formally equivalent to the Weber-Fechner law when applied to motor unit recruitment. It is then shown that, in general, the ratio of the force increment upon recruitment, to the present force output does not obey Weber's law. Finally, it is proved that the “motor unit size law” as derived in this paper implies a fixed sequential order in the recruitment of motor units and that it may be viewed as the realization, by the mammalian neuromuscular system, of a general principle of maximum grading sensitivity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460820
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    Stability and selection in self-reproducing macromolecular systems (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 449-460 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper we develop stability criteria applicable to Eigen's model for the selection and evolution of biological macromolecules. We show that it is possible to characterize the time evolution of the macromolecular system by Lyapounov-like functionals. The Lyapounov method is used to discuss the general stability of the system and the metastable nature of the selected states are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458323
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    Chemical patterns in circular morphogenetic fields (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 461-468 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model of morphogenetic pattern formation recently proposed by Frenchet al. (1976) is investigated in relation to the properties of reaction-diffusion systems operating on two-dimensional circular medium. One of the basic requirements of this model is the existence of a circular morphogenetic gradient exhibiting no discontinuity. We explain how bifur-cation theory may account for the generation of such a spatial pattern through reaction-diffusion processes. For this, we study the emergence of multiple-order bifurcations.
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    URL: http://dx.doi.org/10.1007/BF02458324
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    Bistability in fluctuating environments. Implications in tumor immunology (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 469-490 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We analyze under different environmental conditions the occurrence of bistability, i.e. of two simultaneously stables steady states, in a biological model system which describes the immunological interactions of neoplastic-target cells and cytotoxic-effector cells. As a result of environmental fluctuations such complex biological systems may undergo drastic modifications of their steady state properties. In particular, when the variance of fluctuations increases around a well defined mean value, transition phenomena appear which are absent in the usual bifurcation diagrams. The properties of the non-fluctuating systems can no longer be considered as a first approximation of the properties of the real system. Interestingly, in the case of the model, these transitions correspond to a rejection of tumor cells.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458325
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    Some results on light penetration of an absorbing medium (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 517-523 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two results on light penetration of an absorbing medium are presented in this paper: (1) It is shown, using the general light penetration law of Mannet al. (1977), that a random distribution of absorbing bodies (cells, leaves, etc.) is most efficient at intercepting direct beam (parallel) light. (2) A transmission coefficient is added to the general law in a manner similar to Monteith's (1965). This leads to the partitioning of the radiation regime beneath an absorbing medium into unintercepted, once intercepted, twice intercepted, etc., components. We are thus enabled to calculate the mean radiation intensity beneath the absorbing medium.
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    URL: http://dx.doi.org/10.1007/BF02458327
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    Compartmental models with multiple sources of stochastic variability: The one-compartment, time invariant hazard rate case (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 491-515 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Previous stochastic compartmental models have introduced the primary source of stochasticity through either a probabilistic transfer mechanism or a random rate coefficient. This paper combines these primary sources into a unified stochastic compartmental model. Twelve different stochastic models are produced by combining various sources of stochasticity and the mean value and the covariance for each of the twelve models is derived. The covariance of each model has a different form whereby the individual sources of stochasticity are identificable from data. The various stochastic models are illustrated for certain specified distributions of the rate coefficient and of the initial count. Several properties of the models are derived and discussed. Among these is the fact that the expected count of a model with a random rate coefficient will always exceed the expected count of a model with a fixed coefficient evaluated at the mean rate. A general modeling strategy for the onecompartment, time invariant hazard rate is also proposed.
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    URL: http://dx.doi.org/10.1007/BF02458326
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    Coexistence of photosynthetic microorganisms with growth rates depending on the spectral quality of light (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 525-542 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new equation for the growth rate of photosynthetic microorganisms is derived. It is based on a series formulation of the mechanism of photosynthesis and it has the form of a functional of the spectral qualities of light. Using this functional to model their growth it is shown that populations of photosynthetic microorganisms can coexist in the same homogeneous environment even though they compete for the available light.
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    URL: http://dx.doi.org/10.1007/BF02458328
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    Stochastic prey-predator relationships: A random evolution approach (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 543-554 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The formalism and results of the theory of random evolutions are used to establish and investigate a model for two randomly interacting populations. The asymptotic stability of the expected solution is studied and contrasted to that of the associated deterministic system.
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    URL: http://dx.doi.org/10.1007/BF02458329
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    On a mathematical model describing the aggregation of amoebae (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 555-571 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper an extension of a mathematical model of Keller and Segel (1970) describing the aggregation of amoebae is presented. In their paper (Keller and Segel, 1970) they showed that the onset of the aggregation could be viewed as a spatial instability. Their instability condition involved diffusion constants of the cyclic AMP and of the amoebae as well as a constant describing the chemotactic behavior of the amoebae. In our case we consider a temporal instability that depends only on the kinetics of cyclic AMP production, degradation and transport through the cell wall. Our model then explains the oscillatory behavior of the cyclic AMP in well-stirred suspensions of amoebae. In addition we discuss existence and non-existence of nonuniform steady states of the nonlinear parabolic system involved.
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    URL: http://dx.doi.org/10.1007/BF02458330
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    Markov branching processes with varying growth rates (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 607-610 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A branching processZ(t) which behaves as Markov branching processesZ 1(t) andZ 2(t) during the free and dead times of a counter process is considered. Expression forE[Z(t)] is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458333
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    The method of harmonic balance applied to coupled asymmetrical van der Pol oscillators for intestinal modelling (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 573-589 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The spontaneous electrical rhythms recorded from the gastro-intestinal tract of humans and animals have been successfully modelled by an array of interconnected van der Pol oscillators. To account for asymmetry in the recorded waveforms (with particular reference to the human small intestine) an additional term in the van der Pol dynamics has been included. It is shown that the method of harmonic balance can be used to give analytical results for this asymmetrical condition. The non-linear algebraic equations are solved by hill-climbing to give values of d.c., fundamental and second harmonic amplitudes together with the entrained frequency. The results correlate well with actual measurements made on an analogue simulation by three different methods for waveshape factors of 0.1 and 1.0
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    URL: http://dx.doi.org/10.1007/BF02458331
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