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  • Articles  (48,585)
  • Springer  (44,609)
  • Springer Nature  (3,976)
  • 1980-1984  (48,585)
  • 1982  (48,585)
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  • 1980-1984  (48,585)
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  • 1
    Electronic Resource
    Electronic Resource
    An equivalence result for integral equations with application to branching processes (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 1-15 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theorem is proved, concerning expected values of a multitype branching process in a varying environment. The consequence of the theorem is that the branching process can be treated (in the sense of expected values) as a dynamical system with control terms. This is of importance in situations where the process serves as an abstract model of the dynamics of malignant cells for use in chemotherapy. A simple example of this kind is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459415
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  • 2
    Electronic Resource
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    General solution for flow and stress phenomena in elastic vessles (Navier-Stokes) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 29-42 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method is developed for a full nonlinear evaluation of all velocities and stresses represented in the Navier-Stokes equations and in the general stress tensor. The information required is essentially that for solution of linearized forms. The solution is analytical except for the calculation of the axial velocity, which requires computer assistance to step through time and space. The treatment of the problem, although directed towards solutions involving fluid flow in elastic vessels, is also adaptable to solid deformations (strain vs rate of strain) where the general stress tensor applies. A special case for the distorting ellipse is presented as well as a limited, spatially analytic, solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459417
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  • 3
    Electronic Resource
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    Spatially localized interactive neural populations—II: Stability and dynamics of excitatory sets (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 43-56 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The stability characteristics and dynamical behavior of a system of mutually excitatory neurons in close spatial proximity are investigated with a mathematical model. The model predicts the existence of uniform, intermediate levels of activity other than those of no activity and maximal activity. The model also, yeilds a good explanation of data obtained from periglomerular neurons in the olfactory bulb of the cat.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459418
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  • 4
    Electronic Resource
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    Stochastic compartmental models with banching and immigrant particles (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 75-86 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A multicompartmental model in which particles enter the system from the environment and reproduce according to a Markov branching process has been considered. Explicit expressions have been obtained for the mean vector and the correlation structure for the numbers of particles in different compartments in different time points of the system. Growth rates of the mean vector and some special cases of the system are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459420
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  • 5
    Electronic Resource
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    Mode analysis of physiological oscillators intercoupled via pure time delays (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 57-74 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The study of bi-directionally coupled oscillators is relevant in biological modelling of such systems as gastro-intestinal electrical activity, cardiac pacemarkers, cardiovascular and respiratory interactions and circadian rhythms. Interconnecting pathways in biological systems often exhibit pure time-delay characteristics. In this paper the multiple-mode limit-cycle behaviour of such systems is analysed using the method of harmonic blance. It is shown that the coupling time delay radically affects the number, frequency and amplitudes of entrained limit-cycles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459419
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  • 6
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    Bifurcation, stability diagrams, and varying diffusion coefficients in reaction-diffusion equations (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 87-102 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The effect of keeping all the parameters constant, except the diffusion coefficients, in a pair of reaction-diffusion equations is studied. It is shown that the stability of the constant solution and the bifurcation points can be easily established by constructing a simple stability diagram. The possible qualitatively different diagrams are enumerated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459421
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  • 7
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    Random ecological systems with structure: Stability-complexity relationship (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 103-117 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We have numerically examined more than one million Large Complex Systems (LCS) of interacting variables (interpretable as interacting populations) governed by Generalized Lotka-Volterra Equations (GLV), with self-regulation term. The scope was to have some insight on the stability-complexity relationship. We considered systems of prey-predator type, and we gave appropriate rules for constructing the model systems, rules that specify the behaviour of model systems in order to put them near the biological reality. The results show, among other things, a strict correlation between the stability and the prey-predator ratio (which, in our model, uniquely determines the connectedness of the system).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459422
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  • 8
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    Remark on the article, “Applied catastrophe theory in the social and biological sciences” by M. A. B. Deakin (1980) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 149-150 
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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/BF02459425
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  • 9
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    Transient effects on the initial rate of oxygenation of red blood cells (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 119-134 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The rate-controlling process in the oxygenation of red blood cells is investigated using a Roughton-like model for oxygen diffusion and reaction with hemoglobin. The mathematical equations describing the model are solved using two independent techniques, numerical inversions of the Laplace transform of the equations and numerical solutions via an implicit-explicit finite difference form of the equations. The model is used to re-examine previous theoretical models that incorporate either a red cell membrane that is resistive to oxygen diffusion or an unstirred layer of water surrounding the cell. Although both models have been postulated to be equivalent, the results of the computer simulations demonstrate significant differences between the two models in the rate of oxygenation of the red cells, depending upon the values chosen for the diffusion coefficient for O2 in the membrane and the thickness of the water layer. The difference is apparently due to differences in the induction and transient periods of the water layer model relative to the membrane model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459423
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  • 10
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    Energy and biological evolution—II. The mathematical structure of equilibrium states (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 537-547 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We examine certain mathematical structures presented in Part I. The most important of these are the energy structures determined by the couple (ω×E, ψ) the space of causality defined by ψ-1(0) and the notion of collapsibility, i.e., the descent of a species from a higher to a lower equilibrium configuration as a result of energy loss.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459407
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  • 11
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    A stochstic model for a two-compartment reversible system (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 557-570 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper discusses a general stochastic model for a two-compartment reversible system with non-homogeneous Poisson inputs, arbitrary residence times at each of the compartments and time-dependent transition probabilities. The probability distributions of the number of particles in each compartment and in the system are obtained together with the number of particles which depart from the system. In addition, various covariance functions with a time lag are obtained. Some of the above obtained results are deduced for time-independent arrivals, exponential residence times and time-independent transition probabilities. Fluctuations of the particles present in the system are also analysed. Similar analysis is provided for the model into which some particles are initially introduced at the system. Some possible applications are discussed at the end.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459409
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  • 12
    Electronic Resource
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    Effects of dispersion on stability of multispecies prey-predator systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 571-578 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The general multispecies prey-predator system with Gompertz's antisymmetric interactions is nonlinearly stable in the absence of dispersion and continues to remain stable with dispersion under both homogeneous reservoir and zero flux boundary conditions in a region containing the equilibrium state. It is proved that a general multispecies food-web model without antisymmetric interactions is stable in the absence of dispersion and remains stable with dispersion in the above-mentioned region.
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    URL: http://dx.doi.org/10.1007/BF02459410
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  • 13
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    Repeatability of experiments (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 593-593 
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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/BF02459413
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  • 14
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    Graph theoretical criteria for stability and boundedness of predator-prey systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 579-585 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We introduce a graphical approach in the study of the qualitative behavior ofm species predator-prey systems. We prove that tree graphs imply global stability for Volterra models and local stability for general models; furthermore, we derive sufficient conditions so that loop graphs imply stability and boundedness of the solutions.
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    URL: http://dx.doi.org/10.1007/BF02459411
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  • 15
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    A reply to “repeatability of experiments” by R. B. Campbell (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 594-595 
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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/BF02459414
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  • 16
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    An epizootic model of an insect-fungal pathogen system (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 731-739 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A system of integro-differential equations is derived to describe epizootics of a fungal pathogen in an insect population. Because of piecewise continuous behavior under some parametric conditions, it is concluded that standard phase orbits can be misleading. Using a different analytic approach yields a simple system of finite difference equations. Both the continuous and discrete versions are compared to classical forms. The continuous version differs from a classical one in possessing a second derivative dependent on population density. The discrete version differs in maintaining positive, non-zero populations of both infectives and susceptibles in finite time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462280
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  • 17
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    On feedback control of gonadotropin secretion (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 741-748 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This note is an attempt to demonstrate that hypothalamic pulsatile GnRH secretion is not the result of a short-term, negative steroid hormone feedback. Clarification of this point is of importance for further modelling the control of gonads.
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    URL: http://dx.doi.org/10.1007/BF02462281
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  • 18
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    The development of largangians for biological models (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 749-760 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A modern theory of the calculus of variations is used to form necessary and sufficient conditions for the existence of a Lagrangian representation of a system of first-order ordinary differential equations. There exists a theorem to the effect that when a system of ordinary differential equations is variationally self-adjoint, the fulfillment of such conditions is guaranteed. In addition, self-adjointness, allows establishement of an algorithm by which a Lagrangian for the system may be explicitly constructed. Examples in mathematical biology are given to illustrate the use of the stated theorem.
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    URL: http://dx.doi.org/10.1007/BF02465178
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  • 19
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    An optimal control model of diabetes mellitus (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 793-808 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Engineering optimal control theory is applied to equations describing insulin and glucose interactions. The nature of the optimal controller is established. It is shown how the results can be utilized in a closed loop feedback control system.
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    URL: http://dx.doi.org/10.1007/BF02465181
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  • 20
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    Biological optimality: Comparison of generalized feasibility and optimality conditions for linear, error-minimizing systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 777-791 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An attempt is made to compare the conditions for the general error-optimality of linear systems developed by Kalman with the conditions for feasibility of linear models of neuromuscular and physiological control systems. Models of three actual physiological systems are tested for both the above criteria. Theoretical analysis presented here shows that there are no simple relationships between the two sets of conditions. Analysis carried out on the physiological systems models suggests the need for a general set of conditions for other optimality criteria, such as time and energy minimization, similar to Kalman's condition for error minimization.
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    URL: http://dx.doi.org/10.1007/BF02465180
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  • 21
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    The development of anoxia following occlusion (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 851-877 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Following arteriolar occlusion, tissue oxygen concentration decreases and anoxic tissue eventually develops. Although anoxia first appears in the region most distal to the capillary at the venous end, it eventually spreads throughout the entire region of supply. In this paper the changing oxygen concentration, from the time of occlusion until the tissue is entirely anoxic, is examined mathematically. The equations governing oxygen transport to tissue are solved by iterating a nonlinear integral equation. This solution is valid until anoxia first appears. After anoxia develops it is necessary to solve a moving boundary problem. This is done using the method of matched asymptotic expansions, and accurate solutions are obtained for a wide range of physiological conditions.
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    URL: http://dx.doi.org/10.1007/BF02465185
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  • 22
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    Announcements (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 899-900 
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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/BF02465188
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  • 23
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    Comparative performance of polynomial signal extraction (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 93-104 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A stochastic approximation problem for polynomic operators is formulated. The performance of polynomic operators of various degrees is compared. The effect of causality constraints is also examined.
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    URL: http://dx.doi.org/10.1007/BF01600036
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  • 24
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    Feedback system design: The single-variate case — Part I (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 137-169 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A recently developed algebraic approach to the feedback system design problem is reviewed via the derivation of the theory in the single-variate case. This allows the simple algebraic nature of the theory to be brought to the fore while simultaneously minimizing the complexities of the presentation. Rather than simply giving a single solution to the prescribed design problem we endeavor to give a complete parameterization of the set of compensators which meet specifications. Although this might at first seem to complicate our theory it, in fact, opens the way for a sequential approach to the design problem in which one parameterizes the subset of those compensators which meet the second specification...etc. Specific problems investigated include feedback system stabilization, the tracking and disturbance rejection problem, robust design, transfer function design, pole placement, simultaneous stabilization, and stable stabilization.
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    URL: http://dx.doi.org/10.1007/BF01600050
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  • 25
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    Editorial (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 267-268 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
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    URL: http://dx.doi.org/10.1007/BF01599010
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  • 26
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    Rational approximation via selective modal analysis (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 433-445 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We describe a recently developed framework for exploring the structure of linear time-invariant models of large systems, and for constructing interpretable or physically-based, reduced-order models that reproduce selected modes of the original systems to a desired accuracy. Application of this framework to constructing lumped approximations for interconnections of lumped and distributed systems is briefly explored.
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    URL: http://dx.doi.org/10.1007/BF01599022
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  • 27
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    Selection under random mutations in stochastic eigen model (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 17-28 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The concept of natural selection is examined, which is one of basic principles for the Darwinian interpretation of evolution. In this model selection is defined as a solution of the deterministic Eigen equation. Next, the random effect is introduced through the mutation term. However, the probability of finding the solution expressing the selection is shown to be smallest. The validity of the model and its applicability to polynucleotide replication are discussed.
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    URL: http://dx.doi.org/10.1007/BF02459416
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  • 28
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    Factors defining the rate of oxygen uptake by the red blood cell (1982)
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    Bulletin of mathematical biology 44 (1982), S. 135-147 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Using numerical methods, the initial rates of oxygen uptake by the red blood cell have been computed. The methods accommodate both a water layer and membrane which may act as diffusive impedance to gas influx. The differential solubilities of the gas in these two layers have also been incorporated in the methods. The presence of a 0.50–0.65 μm deoxygenated water layer has been calculated to simulate the experimental results by Roughton (1959). Experimental studies of CO and NO uptake by the red cell could also be simulated. Although a membrane-only model with given parameters can also account for the observed rates of oxygenation of the red cell (Weingardenet al., submitted for publication), the additional incorporation of differential solubilities of oxygen in the different layers of the RBC yields results that indicate a three layer model to be more plausible. Using a thin layer-red cell oxygenation system, the rates of oxygenation were determined for red cells surrounded by a 4.2 μm deoxygenated water layer. The rates were found to compare favorably to the results of the theoretical model.
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    URL: http://dx.doi.org/10.1007/BF02459424
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  • 29
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    Book review (1982)
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    Bulletin of mathematical biology 44 (1982), S. 151-151 
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    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02459426
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  • 30
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    Role of the hypergeometric distribution in the transmission of excitation through sympathetic Ganglia (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 152-152 
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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/BF02459427
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  • 31
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    On a class of finite deformations of elastic soft tissues (1982)
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    Bulletin of mathematical biology 44 (1982), S. 175-192 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Due to the complicated physiological structure of soft biological tissues, stresses can only be measured after the specimen has been stretched to many times of its related length. Therefore, the classical constitutive equations of finite elasticity developed for vulcanized, rubbery materials and the linear theories developed for most engineering materials cannot be applied to soft tissues which are highly elastic in nature. In this article, utilizing a mechanical model developed by Demiray for soft tissues, a class of finite deformations of some tissues is studied and the results are compared with experiment and the existing literature. These problems are the simultaneous extension and twisting of a circular cylindrical bar, the bending of a rectangular block, and the pure shear of a rectangular prism. It is believed that solutions to these problems may find some applications in plastic surgery.
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    URL: http://dx.doi.org/10.1007/BF02463246
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  • 32
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    Effects of convective and dispersive migration on the linear stability of a two species system with mutualistic interactions and functional response (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 271-282 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper, effects of convective and dispersive migration on the linear stability of the equilibrium state of a two species system with mutualistic interactions and functional response have been investigated. In both finite and semi-infinite habitats, it has been shown that the otherwise stable equilibrium state without dispersal remains so with dispersal also, both under flux and reservior conditions. In the case of finite habitat, the degree of stability increases as dispersal coefficients of the two species increase. The effect of convective migration also is to stabilize the equilibrium state in this case.
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    URL: http://dx.doi.org/10.1007/BF02463251
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  • 33
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    Announcements (1982)
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    Bulletin of mathematical biology 44 (1982), S. 307-307 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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  • 34
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    A model of the spatial-temporal characteristics of the alpha rhythm (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 283-305 
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    Notes: Abstract A linear spatially distributed model of a chain of neurons and interneurons was investigated in relation to the generation of propagated alpha rhythmic activity. It was assumed that the elements of the chain were interconnected by means of recurrent collaterals and inhibitory fibres in such a way that the connectivity functions were assumed to be homogeneous and their strength was an exponentially decreasing function of distance. It was found that such a neuronal chain shows propagation properties for frequencies in the alpha band. The results obtained with the model are in agreement with the phase velocities encountered experimentally. In this way, it was possible to estimate the length of the neural fibres responsible for the phenomenon of propagated activity. The estimates obtained are in good agreement with recent quantitative neuroanatomical data on the circuitry of the neocortex.
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    A behavioral summary for completely random nets (1982)
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    Bulletin of mathematical biology 44 (1982), S. 309-320 
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    Notes: Abstract This paper characterizes the cycle structure of a completely random net. Variables such as number of cycles of a specified length, number of cycles, number of cyclic states and length of cycle are studied. A square array of indicator variables enables conveninent study of moment structure. Additionally, exact and asymptotic distributional results are presented.
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    Eigensolutions of nonlinear wave equations in one dimension (1982)
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    Bulletin of mathematical biology 44 (1982), S. 321-337 
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    Notes: Abstract A class of nonlinear equations describing the steady propagation of a disturbance on the infinite interval in one dimensional space are shown under certain conditions to admit solution with a unique velocity of propagation. The class of equations describe both initial and final homogeneous steady states which are asymptotically stable with respect to uniform perturbations, in contrast to the Fisher equation, which does not.
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    Comparison of models of insulin release (1982)
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    Bulletin of mathematical biology 44 (1982), S. 399-409 
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    Notes: Abstract A model for insulin secretion with a storage and a labile compartment, as well as a provisionary factor, is combined with a signal model in which the signal can be the difference between an excitation and an inhibition, or the difference in concentrations inside and outside some cell components. The model, using a single set of values for the parameters, accounts in a semiquantitative manner for all of the regularly appearing features of the insulin secretion from thein vitro perfused pancreas to a wide range of patterns of glucose and tolbutamide stimulation. Among the features which can be accounted for are: early and late secretion of insulin as a function of glucose in terms of a single parameter; the apparent depletion and recovery during a pulsed pattern of stimulation by tolbutamide; the hypersecretion following a short period of rest during a prolonged stimulation by glucose; the negative spike which occurs when the concentration of glucose, which has been maintained for a period of time, is suddenly reduced to a lower level; and the appropriate responses to slow and fast ramp functions of glucose concentration.
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    Example of a system which is computation universal but not effectively programmable (1982)
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    Bulletin of mathematical biology 44 (1982), S. 443-447 
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    Notes: Abstract The incorporation of a chaotic component in a computing system is incompatible with its being effectively programmable. The example presented shows that concepts of programming suitable for biological systems may differ from those which have grown out of our experience with present day digital computers.
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    Primary events in odour detection (1982)
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    Bulletin of mathematical biology 44 (1982), S. 411-423 
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    Notes: Abstract An analysis of the interaction between stimulus molecules and the olfactory receptor cell membrane is presented. The model is based upon a sequence of events, i.e. stimulus delivery at the olfactory epithelium, absorption of molecules in the mucus layer, diffusion of the molecules towards the receptor cells and molecule-receptor cell membrane interaction. The mathematical analysis considers the situation during electrophysiological experiments, where an odour puff is delivered at an exposed olfactory mucosa. Such a situation resembles sniffing of odour samples. The analysis is discussed in relation to experimental evidence.
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    Analytical model of hygroscopic particle behavior in human airways (1982)
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    Bulletin of mathematical biology 44 (1982), S. 425-442 
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    Notes: Abstract A model is developed to calculate the deposition of hygroscopic aerosols in the human tracheobronchial (TB) tree. The TB airflow pattern assumed is consistent with experimental observations and accounts for anatomical features such as the larynx and cartilaginous rings in large airways. Some original deposition efficiency formulae are presented for laminar and turbulent airstreams. Stepwise growth is simulated by changes in particle size and density at each TB generation. The dose distribution of NaCl aerosols is studied as a function of inhaled particle size and flow rate. Two NaCl growth rate curves are used which differ in the mode of aerosol-air mixing in the trachea. The initial rate of aerosol mixing in the human due to the laryngeal jet is shown to be an important factor affecting the deposition of hygroscopic aerosols. Total TB deposition of NaCl exceeds that for nonhygroscopic particles of the same inhaled aerodynamic size. Hygroscopic growth can also influence the regional TB distribution of dose when submicron NaCl particles grow rapidly enough to deposit by impaction and sedimentation.
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    Remark on the letter by Zhitomirsky and Kagna (1980) (1982)
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    Bulletin of mathematical biology 44 (1982), S. 449-449 
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    Announcements (1982)
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    Bulletin of mathematical biology 44 (1982), S. 451-452 
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    Mathematical model for the study of fertility and viability in inbreeding populations (1982)
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    Bulletin of mathematical biology 44 (1982), S. 491-500 
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    Notes: Abstract Granted that a single or complex gene is responsible for inbreeding depression, theoretical expressions for fertility and viability are obtained in different diploid populations: brother-sister, half-brother-sister, cousins and double-cousins. The conclusions of the study of viability variations according to the coefficient of parentage are proved by the results of experiments and lead to a new view of genetic load.
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    Energy and biological evolution—I. The equilibrium states of biochemical processes (1982)
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    Bulletin of mathematical biology 44 (1982), S. 501-535 
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    Notes: Abstract The Thom gradient model of morphogenesis poses the followinga posteriori problem: “From the observed morphology of a given natural process (effect) determine the dynamics of the process (cause)”. In this paper we consider the classicala priori problem: “Given the cause (dynamics) determine the effect (resultant morphology)”. We find that in biochemical processes the mechanisms for energy activation, energy-matter interaction and energy dissipation determine the dynamics. Furthermore there exists basic energy mechanisms which drive the equilibrium states through the elementary catastrophes of Thom. A comparison with current theories shows that our models describe open ecological food chains and their dynamical systems generalize the equations of organisation posed by M. Eigen.
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    Energy and biological evolution—III. Theoretical ecology and macromolecular self-organization (1982)
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    Bulletin of mathematical biology 44 (1982), S. 549-555 
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    Notes: Abstract We show that the elementary models of biochemical evolutionary processes are the bases for the study of open ecological systems and macromolecular self-organisation. We deduce a biochemical analogue for the basic closed phytoplankton-zooplankton food chain. The perturbation of the Michaelis-Menten mechanism which determines the nutrient-dependent growth rate of the phytoplankton species leads to higher catastrophes for the nutrient equilibrium manifold. The umbilic models are generalizations of the equations of organization of Eigen.
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    Nonlinear generalizations of the Kedem-Katachalsky equations for ionic fluxes (1982)
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    Bulletin of mathematical biology 44 (1982), S. 761-775 
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    Notes: Abstract The transport equation of Kedem and Katchalsky for the flux of ions through a membrane is generalized to demonstrate explicitly the role of impermeant ions in determining its mathematical form. Whereas the Kedem-Katchalsky equation is linear in the salt concentrations in the bathing solutions, the more general equation is bilinear (and symmetric) in the ionic concentrations of the permeant species. The Kedem-Katchalsky flux equation is further generalized to include explicitly a term for ion-exchange in systems having more than a single permeant salt. This additional term is also bilinear (and antisymmetric) in the concentrations of the exchanging ionic species. Flux equations are derived for systems having (1) a single mono-monovalent salt, (2) two mono-monovalent salts and (3) an arbitrary number of salts with no restriction upon the valencies of the ionic components. Since it has no effect upon the form of concentration-dependent terms in the flux equations, coupling to volume flow is neglected.
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    Some applications of the concept of body forces for the myocardium (1982)
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    Bulletin of mathematical biology 44 (1982), S. 819-840 
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    Notes: Abstract A mathematical theory of the dynamics of the myocardium based on the concept of body forces is applied to account for two different experimental results. The first result consists of a relation between oxygen consumption and the kinetic energy of the myocardium. The second set of results provides a consistent interpretation of the relationship between different indices used to assess the ventricular performance.
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    On the stochastic theory of compartments: A semi-Markov approach for the analysis of theK-compartmental systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 809-817 
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    Notes: Abstract In this paper a semi-Markov process approach is developed to analyse stochastic compartmental systems using straightforward probabilistic arguments. Explicit expressions for several characteristics of thek-compartmental systems with a Poisson process input are derived and various models found in the literature arising from biological applications are generalised here using the semi-Markov process technique.
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    Analysis of a nonlinear diffusion problem With Michaelis-Menten kinetics by an integral equation method (1982)
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    Bulletin of mathematical biology 44 (1982), S. 841-849 
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    Notes: Abstract A mathematical model for oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics is analyzed by means of an intergral equation method. It is shown that an integral equation formulation can be used to obtain a numerical solution associated with this boundary and initial value problem. Through an illustrative numerical calculation we are able to obtain an accurate solution for both the steady and transient problems. Finally, a comparison is made with the numerical solution of McElwain and the variational solution of Anderson and Arthurs for the steady state and Lin's result concerning the unsteady state.
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    A note on exact solutions of two prey-predator equations (1982)
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    Bulletin of mathematical biology 44 (1982), S. 893-897 
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    Notes: Abstract Exact solutions are obtained and discussed for classes of Lotka-Volterra and Leslie-Gower systems governing the interaction of two species. The classes are defined by certain constraints which are imposed on the time-dependent parameters of the equations. A general result for such systems is that each species is characterised by two time-scales: one representing natural growth and the other, the interdependence of the species.
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    Diffusion along intercellular spaces: An analysis of a transient situation (1982)
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    Bulletin of mathematical biology 44 (1982), S. 879-891 
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    Notes: Abstract We present an analysis of the diffusion of a tracer in a model of a cell-intercellular space system. The problem reduces to the resolution of a system of a linear partial differential equation and of a linear integral differential equation. The mathematical results have been obtained in terms of their Laplace transforms, which have been inverted by a numerical procedure for some parameter values. The importance of considering gradients of concentrations in intercellular spaces instead of lumping them with the external mediums has been discussed together with the possibility of extending Ussing's relation to transient cases, in order to detect active transports. Some possible implementations of the model to take into account more general situations have been considered.
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    The asymptotic behavior of Hermite-Padé polynomials (1982)
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    Circuits, systems and signal processing 1 (1982), S. 305-309 
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    Notes: Abstract We present speculations on the asymptotic behavior of Hermite-Padé polynomials of type I constructed from a set of functions with common branch points. The proposed form is consistent with all known results and numerical work.
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    Nested-feedback-loops realization of 2-D systems (1982)
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    Circuits, systems and signal processing 1 (1982), S. 321-343 
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    Notes: Abstract Algorithms are derived for representation of double power series by branched continued fractions. Some properties of the branched continued fractions are given. Two new alternative structures for realization of a two-dimensional, zero memory nonlinear transfer characteristic are proposed. These structures permit the design of 2-D systems with relatively low sensitivity of the transfer function to coefficient errors. Generalized equivalence transformations of branched continued fractions are also presented. Illustrative examples are included.
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    Port properties of nonlinear reciprocal networks (1982)
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    Circuits, systems and signal processing 1 (1982), S. 77-92 
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    Notes: Abstract Time-invariantn-port networks are considered which are constructed from linear resistors and transformers, and nonlinear inductors and capacitors. A port property is sought which is analogous to the symmetry of the impedance matrix obtained in the linear case. Such a property is found using a stochastic characterization: with all resistors assumed to be at the one temperature and modelled to include the usual thermal noise, a fluctuating noise voltage will be observed at the ports of the networks. With some reasonable restrictions on the nature of the nonlinearities in the reactive elements, the vector of such noise voltages is shown to constitute what is known as a reversible stochastic process; in the linear case, reversibility holds if and only if the impedance matrix is symmetric.
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    Continuation algorithms for the eigenvalue problems (1982)
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    Circuits, systems and signal processing 1 (1982), S. 123-134 
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    Notes: Abstract Three algorithms for the solution of the eigenvalue problem for a continuously parameterized family of sparse matrices are presented; a continuousLU (orLR) algorithm, a continuousQR algorithm, and a continuous Hessenberg algorithm. Each of the three algorithms may be implemented recursively and the sparsity of the given matrices is preserved throughout the numerical process.
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    Stability analysis of complex dynamical systems (1982)
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    Circuits, systems and signal processing 1 (1982), S. 171-202 
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    Notes: Abstract We present two new algorithms to estimate the domain of attraction of the equilibriumx=0 of a nonlinear systemx=f(x). One of these algorithms utilizes quadratic Lyapunov functions while the second algorithm makes use of norm Lyapunov functions. Both of these procedures yield estimates for the domain of attraction which are comparable to those obtained by existing methods; however, the present algorithms appear to be significantly more efficient than existing algorithms. We also show how sometimes the applicability of the above results can be extended to high order systems by invoking the comparison principle. In doing so, we establish some results for the comparison principle which are of interest in their own right. Specifically, we relate the domain of attraction of a low order comparison system to the domain of attraction of a higher order system and we give an interpretation of the comparison principle in terms of stability preserving maps. In order to demonstrate the applicability of the present results, and in order to compare the present results with existing results, several specific examples are presented.
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    A block matrix representation of permutation networks (1982)
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    Circuits, systems and signal processing 1 (1982), S. 251-266 
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    Notes: Abstract This work provides a mathematical framework for topologically-independent analysis of permutation networks. First, a structure-dependent representation is provided using matrices whose entries are switching expressions. Then, a transformation is presented which maps these matrices into structure-independent representations which are matrices whose entries are 0/1 matrices. Algebraic tools for manipulating the second type of matrices are also provided. Notions such as permutations realizable by a network, the rearrangeability property, and series and parallel connections of networks are defined and discussed with regard to the proposed representations.
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    Toeplitz equations and Kronecker's algorithm (1982)
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    Circuits, systems and signal processing 1 (1982), S. 289-304 
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    Notes: Abstract A reliable algorithm, similar to the modifed Kronecker algorithm, is provided for the solution of the Polish polynomial approximation problem. Implicit in this solution is an efficient and reliable method for the algebraic solution of Toeplitz equations.
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    Stieltjes series and soliton interaction (1982)
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    Circuits, systems and signal processing 1 (1982), S. 311-320 
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    Notes: Abstract TheKdV andMkdV multisoliton solutions are found to be generated by rational Stieltjes functions of the non-linearity parameter, each pole of which can be associated with a soliton. The well-known asymptotic emergence of the separate solitons follows at once from the motion of the poles. Successive (n-1/n) Padé approximants to theN-soliton series are considered to show how the solitons are reconstructed from an increasing number of perturbation terms (n ≤N). Their asymptotic behaviour is particularly striking: as time increases the behaviour of then th approximation becomes that of an actualn-soliton solution, constituted by then leading solitons. Furthermore, it turns out that each such Padé approximation satisfies a conservation law: the mass of the approximated solution, equal to that of then solitons included, is conserved.
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    A remark on the numerics of rational approximation and the rate of convergence of equally spaced interpolation of ¦x ¦ (1982)
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    Circuits, systems and signal processing 1 (1982), S. 367-377 
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    Notes: Abstract In this note we review the technique for rational Chebyshev approximation as given by the generalization of the Remes algorithm and point out its connection to the generalized eigenvalue problem for symmetric Hankel matrices. By a classical example and some recent work it can be shown that interpolation with rational functions (even) on equidistant knots may lead to results that are superior to Chebyshev approximation by means of polynomials for comparable numerical work.
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    Optimal Hankel-norm approximation of continuous-time linear systems (1982)
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    Circuits, systems and signal processing 1 (1982), S. 407-431 
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    Notes: Abstract A problem on optimal approximation of continuous-time linear systems is studied. The performance measure (error) is chosen to be the spectral norm of the difference between the Hankel operators associated with the original system and the approximant. It is shown that the Hankel operators associated with continuous-time systems and the Hankel matrices associated with discrete-time systems are related by an interesting correspondence property via bilinear transforms. This fact is then used to derive the continuous-time results (theory and algorithms) from the established discrete-time ones. Some simple examples are presented.
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    Scattering theory and matrix orthogonal polynomials on the real line (1982)
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    Circuits, systems and signal processing 1 (1982), S. 471-495 
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    Notes: Abstract The techniques of scattering and inverse scattering theory are used to investigate the properties of matrix orthogonal polynomials. The discrete matrix analog of the Jost function is introduced and its properties investigated. The matrix distribution function with respect to which the polynomials are orthonormal is constructed. The discrete matrix analog of the Marchenko equation is derived and used to obtain further results on the matrix Jost function and the distribution function.
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    An efficient large systems analysis method using system dynamic behavior (1982)
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    Circuits, systems and signal processing 1 (1982), S. 57-76 
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    Notes: Abstract This paper presents our unified approach to the solution of large system analysis problems. The macromodular behavioral technique combines multiple-logic function macromodeling, functional latency and nested macromodel. We take advantage of the dynamic behavior and the repetitive modular structure of a system to improve the computational efficiency during system analysis. Several Bipolar and MOSFET electronic networks are used to demonstrate the merits of the macromodular behavioral method for large system analysis.
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    Design of FIR digital filters using tapped cascaded FIR Subfilters (1982)
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    Circuits, systems and signal processing 1 (1982), S. 43-56 
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    Notes: Abstract This paper considers the design of an FIR digital filter by interconnecting a number of identical FIR subfilters with the aid of a few additional multipliers and adders. The overall structure is in the form of a tapped cascaded FIR subfilters. A composite method to determine the tapping coefficients along with the coefficients of the subfilter to approximate overall frequency response characteristic is proposed. Several numerical examples illustrating the proposed method are included.
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    A general theory of broadband matching of an active load (1982)
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    Circuits, systems and signal processing 1 (1982), S. 105-122 
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    Notes: Abstract Given a passive frequency-dependent source impedance and an active or passive load and a preassigned transducer power-gain characteristic, necessary and sufficient conditions are given for the existence of a lossless reciprocal equalizer which, when operating between the given source and the given load, yields the desired transducer power-gain characteristic. The significance of the present approach is that the realization of the equalizer involves only driving-point synthesis by the Darlington theory.
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    Editorial (1982)
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    Circuits, systems and signal processing 1 (1982), S. 135-135 
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    Semistate design theory (1982)
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    Circuits, systems and signal processing 1 (1982), S. 203-216 
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    Notes: Abstract Using semistate theory forward and reverse binary hysteresis operators are defined from which design equations result for relevant circuits. Through variation of the design parameters swept hysteresis is introduced and experimental results presented on it.
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    Minimum round-off noise realization of block-state recursive digital filters (1982)
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    Circuits, systems and signal processing 1 (1982), S. 217-231 
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    Notes: Abstract The development of a block-state structure with minimum round-off noise subject to ℓ2-norm dynamic range constraint is outlined. The pertinent equations for scaling and for round-off noise analysis of block-state structures implemented using fixed-point arithmetic are first derived. Next, a lower bound and the global minimum of the output noise due to the round-off of the block-state-variables are derived. A method of deriving the minimum round-off noise block state-structure is outlined. A numerical example is included. With regard to computational complexity and overall noise performance, the block-state realization of recursive digital filters is shown to be superior.
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    Solvability and error bounds for nonlinear circuits containing operational amplifiers (1982)
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    Circuits, systems and signal processing 1 (1982), S. 233-249 
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    Notes: Abstract Although an operational amplifier is a nonlinear device, the existing methods of analysis of circuits with operational amplifiers view it as a linear element which possibly has an infinite gain. As a result, it is not clear to what extent the results thus obtained hold. In this paper we construct a general model of a (nonlinear) circuit containing operational amplifiers. Viewing such a network as an interconnection of a multiport withn operational amplifiers, we give conditions for solvability (i.e., for the existence of an input-output operator), and establish estimates for the error incurred by replacing such a system by an idealized system whose operational amplifiers have infinite gain. In this way we determine ranges for variables within which the traditional linear analysis gives results that fulfill given accuracy requirements.
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    Generalisations of Padé approximants (1982)
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    Circuits, systems and signal processing 1 (1982), S. 279-287 
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    Notes: Abstract A brief account is given of a number of generalisations of Padé approximants defined and studied over the past twenty years. These generalisations include multi-point approximants, approximants based upon differential equations, multivalued approximants, multivariate approximants, and approximants defined from series of orthogonal functions. The general class of Hermite-Padé approximants is discussed, and various applications are noted.
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    Moment problems and low rank Toeplitz approximations (1982)
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    Circuits, systems and signal processing 1 (1982), S. 345-366 
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    Notes: Abstract Recent signal processing research suggests that a theory of moments for finite Toeplitz matrices and forms would help in understanding and solving certain model approximation problems. Such a theory is developed in this paper and it is shown how these moment parameterizations can make approximating by low rank Toeplitz matrices tractable. In the case of Toeplitz forms, this moment representation gives a simple solution to the extendibility problem for finite sections of a Toeplitz form.
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    Estimation of structure by minimum description length (1982)
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    Circuits, systems and signal processing 1 (1982), S. 395-406 
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    Notes: Abstract A theorem is proved which demonstrates that an earlier derived minimum description length estimation criterion is capable of distinguishing between structures in linear models for vector processes. A fairly simple algorithm is described for the estimation of the best model, including its structure and the number of its parameters.
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    Singular value analysis of deformable systems (1982)
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    Circuits, systems and signal processing 1 (1982), S. 447-470 
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    Notes: Abstract Singular value analysis, balancing, and approximation of a class of deformable systems are investigated. The deformable systems considered herein include several important cases of flexible aerospace vehicles and are characterized by countably infinitely many poles and zeros on the imaginary axis. The analysis relies completely on the so-called asymptotic singular value decompositon of the Hankel operator associated with the impulse response of the system. A parametric study of a six-dimensional single-input single-output case is performed.
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    Common source epidemics I: A stochastic model (1982)
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    Bulletin of mathematical biology 44 (1982), S. 259-269 
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    Notes: Abstract A discrete time stochastic model is formulated for the spread of a disease which is transmitted to an uninfected but susceptible individual through an environmental source and not through contact (either direct or indirect) with infected individuals. The model incorporates both exposure and infection components. The exposure component includes consideration of the introduction of an infectious agent into the environment and the subsequent diffusion of the agent. It also includes time and location patterns for visits by individuals in the target population to the affected environment. The infection component incorporates physiological responses of exposed individuals to the infectious agent. The goal of the model is to provide a method for developing a predicted epidemic curve. Comments are given on an application of the model to the study of an outbreak of toxoplasmosis in Atlanta, Georgia, in 1977.
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    Reply to letter by Jane Cronin (1982) (1982)
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    Bulletin of mathematical biology 44 (1982), S. 450-450 
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    A kinetics model of abrin binding in a virus transformed lymphocyte cell culture (1982)
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    Bulletin of mathematical biology 44 (1982), S. 453-476 
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    Notes: Abstract The second order nonlinear differential equation $$\ddot x + \left( {\alpha _0 x + \alpha _1 } \right)\dot x + \alpha _2 x + \left( {x + \alpha _3 } \right) = 0$$ arises from a kinetics model of abrin binding in an Epstein-Barr virus-transformed lymphocyte culture. Some results on the dynamical behavior of this equation are given. These results are then discussed in relation to the known kinetics behavior of abrin in an EBV-lymphocyte cell culture.
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    Determination of dependence of binding parameters on receptor occupancy (1982)
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    Bulletin of mathematical biology 44 (1982), S. 477-489 
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    Notes: Abstract Measurements of the binding of ligand to receptors that are macromolecules, either free or components of biomembranes, often show deviation from what is expected of a simple reaction described by an association and a dissociation rate constant. A more versatile model and more discriminating experiments are required for a satisfactory explanation. This paper is based on a general model of the binding reaction in which the rate constants and equilibrium constant are dependent upon occupancy of receptors. The analysis of the model leads to three kinds of experiments: (1) equilibrium measurements which permit quantitative determination of a dissociation equilibrium parameter as a function of receptor occupancy; (2) measurements prior to equilibrium which yield the same information; and (3) measurements prior to equilibrium which reveal quantitatively the dependence of both association and dissociation rate parameters separately, on occupancy.
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    Solitary waves and macromolecular systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 705-713 
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    Notes: Abstract Macromolecules and their aggregates (such as protein bundles in biomembranes) possess polar modes which, when excited, tend to deform the system and call into play elastic restoring forces. A model of such systems, characterised typically by electric polarisation modes stabilised on the one hand by quartic self-interactions and on the other through coupling to the elastic deformations, admits the possibility of localised excitations (solitary waves) propagating with subsonic velocities, possessing the features of relative stability and efficient transport characteristics (associated with the collective nature of the phenomena), and at the same time provides a mechanism of control and variability which could be of considerable interest in biology.
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    Specific roles of the different boolean mappings in random networks (1982)
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    Bulletin of mathematical biology 44 (1982), S. 715-730 
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    Notes: Abstract Random Boolean networks have striking properties of self-organization. In this paper we propose an algorithm based on the different roles of Boolean mappings and on the connection structure to analyze the organization of the network. For a few cases— transfer mappings, AND/OR, equivalence/XOR—rigorous results are obtained about the dynamics of homogeneous networks. Conclusions are then drawn concerning the non-homogeneous networks.
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    Editorial (1982)
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    Circuits, systems and signal processing 1 (1982), S. 1-2 
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    System identification techniques for adaptive signal processing (1982)
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    Circuits, systems and signal processing 1 (1982), S. 3-41 
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    Notes: Abstract Many problems in adaptive filtering can be approached from the point of view of system identification. The close interconnection between these two disciplines is explored in some detail. This approach makes it possible to apply recursive parameter estimation algorithms to adaptive signal processing. Several examples are discussed including: adaptive line enhancement, generalized adaptive noise cancelling, adaptive deconvolution and adaptive TDOA estimation. It is shown how the recursive maximum likelihood algorithm can be used for both FIR and IIR filtering, and some preliminary results are presented. Several alternative algorithms are briefly discussed.
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    Special issue on rational approximations for systems (1982)
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    Circuits, systems and signal processing 1 (1982), S. 269-278 
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    Notes: Conclusions To conclude our discussion we can only confess to our shortcomings as organizers and editors. We have been incomplete, we have been biased, and, worst of all, we have not been able to produce the most essential connections in any firm way. Perhaps our major achievement — if we may say so — has been to point the way to many possible new results and to new research. The field discussed here seemed at first very conventional. May we have convinced the reader that it is not. That the major problems have not been solved. That here lies an open field for system engineers, numerical analysts, and mathematicians.
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    Contractive intertwining dilations and norm approximation techniques (1982)
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    Circuits, systems and signal processing 1 (1982), S. 379-394 
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    Notes: Abstract Recent results in labelling all contractive intertwining dilations and in studying connections between labellings are presented. These facts are used to describe the general solution of the Carathéodory-Fejér extrapolation problem. This turns out to be useful for some numerical problems such as: computation of the norm of an analytic Toeplitz matrix, an algorithm for detecting reflection coefficients in seismic exploration, and a model for controlling the errors in Wiener prediction.
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    A variational calculus approach to the suspension flow problem using the minimal force hypothesis (1982)
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    Bulletin of mathematical biology 44 (1982), S. 153-174 
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    Notes: Abstract Analytic expressions for the velocity profile and distribution of neutrally buoyant particles in laminar flow were obtained as functions of the radial distance. A modified Einstein viscosity model and the hypothesis that the total force on all the particles flowing in the tube is a minimum were used. The methods of the variational calculus were used in the mathematical development. A velocity profile differing only slightly from the parabolic form of that for Hagan-Poiseuille flow was obtained. For particle distribution the equations developed predict a maximum concentration along the center-line for some flows and a maximum concentration in a ring some distance from the center line in other flows. Both of these concentration profiles have been observed experimentally. Quantitative predictions from the equations derived must await further experimental work to permit calculation of the parameters included in the equations.
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    Electromagnetic mediated pharmacokinetics in a three-layer diffusional system (1982)
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    Bulletin of mathematical biology 44 (1982), S. 215-229 
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    Notes: Abstract The effect of an applied electromagnetic field on drug diffusion in a one dimensional, three-layer drug-receptor model has been analyzed and expressed in terms of a normalized turnover rate parameter. The analysis reveals that an imposed harmonic time-varying electromagnetic field may enhance or retard the drug turnover rate depending on the diffusional pattern, the equivalent Michaelis constant, the maximum drug turnover rate of the intrinsic drug-receptor system, as well as the power density and frequency of the applied electromagnetic field. It is estimated that the power density in the order of magnitude of 1μW/cm2 at 100 MHz frequency range may be required to induce significant rate effects.
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    Large signal, low frequency characteristics of the systemic arterial system (1982)
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    Bulletin of mathematical biology 44 (1982), S. 193-213 
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    Notes: Abstract A 4-parameter model to represent the relationship between slowly changing arterial inflow and the resulting pressure change was proposed. In order to determine values for the parameters and test the model in a wide range of pressure and flow, two experimental procedures were used. Firstly, slow oscillations in aortic pressure (period, 4 sec) were produced by means of an external pump connected to the aorta, and secondly, cardiac arrest was induced for about 2–3 sec by stimulating the right vagus. It was shown mathematically that the pressure and pump displacement information obtained in these experiments could be related to the model parameters. Values for the model parameters were obtained in 6 anesthetized dogs using a least squares adjustment procedure. Using aX 2-test, it was concluded that the model represented the arterial system for each animal well.
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    An asymmetrical kinetic model for veratridine interactions with sodium channels in molluscan neurons (1982)
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    Bulletin of mathematical biology 44 (1982), S. 231-258 
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    Notes: Abstract Veratridine alkaloid induces bi-stability or saw-tooth-shaped long potential waves in molluscan neurons. Voltage clamp experiments reveal the production of a slow sodium current whose changes are described by an asymmetric kinetic diagram relating the states of the sodium channels. Methods of the qualitative theory of differential equations were used to determine the condition necessary for such a model to have either an oscillatory solution or a bi-stable behavior. The kinetic diagram was modified to account for the frequency dependence of the slow sodium current production upon repeated short depolarizations. The modified kinetic diagram suggests that open and inactivated sodium channels are turned into channels with slow kinetic parameters; the transition from open channels would be fast, irreversible and restricted to part of the open channels, whereas that from inactivated channels would be slow and fully reversible upon repolarization.
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    Dissipative structures associated to certain reaction-diffusion equations in mathematical ecology (1982)
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    Bulletin of mathematical biology 44 (1982), S. 339-348 
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    Notes: Abstract Sufficient conditions are determined for the existence of stable spatially heterogeneous solutions of the Lotka-Volterra many species equations extended to include spatial diffusion. Some properties of such solutions are obtained. A general definition is proposed for the concept of a dissipative structure associated with a given reaction-diffusion equation. Finally, an approximate solution is presented for two interacting species in one spatial dimension, although the question of stability for this example is left open.
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    Common source epidemics II: Toxoplasmosis in Atlanta (1982)
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    Bulletin of mathematical biology 44 (1982), S. 377-398 
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    Notes: Abstract A discrete time stochastic model formulated for the study of common source epidemics (Shonkwiler and Thompson, 1982) is implemented to study an outbreak of toxoplasmosis in Atlanta, Georgia, in 1977. A computer simulation program is described and conclusions are drawn on the basis of the simulations. Also, the detailed empirical data are organized to illuminate the roles of visitation and location patterns, and the variation in the empirical epidemic curve with different reporting schemes.
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    Film models for multicomponent mass transfer: Diffusion in physiological gas mixtures (1982)
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    Bulletin of mathematical biology 44 (1982), S. 361-376 
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    Notes: Abstract The exact solution of the Maxwell-Stefan equations for steady state diffusion in a stagnant film due to Krishna and Standart (1976) is compared to the approximate solutions of Toor (1964) and Stewart and Prober (1964) for osmotic diffusion of oxygen in the three physiological gas mixtures He−N2−O2, He−SF6−O2, N2−SF6−O2. It is found that the predicted fluxes of He, N2 and SF6 are usually in excellent agreement but that the two methods could predict differing directions of transfer of oxygen. Concentration profiles obtained from the linearized equations may be significantly different from the profiles calculated from an exact solution of the film model.
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    A generalization of the optimal models of arterial branching (1982)
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    Bulletin of mathematical biology 44 (1982), S. 349-360 
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    Notes: Abstract Optimal models of arterial branching angles are usually based on the assumption that the equation relating flow and radius is given byf=kr 3, as proposed by Murray in 1926. An exception is the model of Uylings (1977), in which he allowed the exponent ofr to vary from 2.33 to 3.0. Theoretical considerations coupled with empirical evidence suggest that the cubic flow equation may not be appropriate to describe the branching pattern of the arterial tree. The optimal models are modified to accommodate a more general flow equationf=kr x . Models that minimize a geometric feature such as surface or volume are sensitive to variations inx in a different way from those which minimize flow-related parameters, such as power loss due to friction and shear stress.
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    Distribution of survival times in the Fix and Neyman model (1982)
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    Bulletin of mathematical biology 44 (1982), S. 587-591 
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    Notes: Abstract In this paper we consider a general illness-death stochastic model in which the transition intensities all vary proportionally to a time function ϕ(t). We extend Chiang's earlier work to include processes which are both reversible and have parameters which are time varying, and obtain survival time distributions and the expectation and variance of survival times.
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    Local geometry of arterial branching (1982)
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    Bulletin of mathematical biology 44 (1982), S. 597-607 
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    Notes: Abstract A model of the geometrical structure of arterial bifurcations is proposed in the context of optimality of the bifurcation as a fluid conducting system. Optimality is considered both globally, in terms of the cardiovascular system as a whole, and locally, in terms of the orderliness of the flow in the bifurcation region. It is shown that a bifurcation can be optimal both globally and locally. Typical examples of such bifurcations are given.
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    Simulation of chemical oscillations in membranes (1982)
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    Bulletin of mathematical biology 44 (1982), S. 637-645 
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    Notes: Abstract A computer simulation model has been developed to follow chemical oscillations in a membrane for immobilized enzyme systems. It is a discrete particle type model which follows the spatial and temporal fluctuations of the concentrations in a reaction involving two substrates. The parameters can be readily varied to allow dissipative structures to result from the sustained nonlinear reaction kinetics and to determine which parameters cause damping of the oscillations. The nature of the diffusion mechanism allows extension to more than one dimension.
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    Peak drug levels in linear pharmacokinetic systems—III. Multimodal impulse responses in multicompartment systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 609-635 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper deals with the unimodality of the ‘impulse response’ in compartmental systems, where the ‘impulse response’ in any given compartment is the time course of the amount of diffusing substance in that compartment after an initial instantaneous injection of the substance into that or some other compartment. It is shown that in certain compartmental structures, with injection in certain compartments, the impulse response is always unimodal or monotonic in all compartments, regardless of the numerical values of the various transfer rate coefficients. Structures with this property are here named ‘UM structures’, and they include the familiar mammillary and catenary structures. In this paper, the set of all UM structures is described. Structures which are not UM (NUM structures) are identified by showing that, by removal of certain connections and compartments according to certain rules, they can be reduced to small structures which can be shown to be NUM by numerical computation. Computations on two systems with bimodal impulse responses show that with constant infusions of a fixed amount of substance the peak level may increase paradoxically with decrease in the infusion rate over a certain range. This effect is extremely small, however.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462271
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    Representations of (M, R)-systems by categories of automata (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 661-668 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Arbib in a paper entitled ‘Categories of (M, R)-Systems' represents both simple (M, R)-systems and those with varying genome as subcategories of the category of automata. An alternative characterisation of general (M, R)-systems as automata is proposed and two theorems on (M, R)-automata are proved. The two categories of automata, namely Arbib in a paper entilled ‘Categories of (M,R)-Systems’ represents both simple (M, R)-systems with variable genetic structure, are compared.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462274
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  • 97
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    An eight-parameter model of human mortality—The single decrement case (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 647-659 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Developed in this paper is an eight-parameter model of human mortality. A step-wise nonlinear least-squares procedure for estimating the parameters from abridged life tables is also described and implemented. Used for purposes of illustration were nine period life tables, ranging from 1900 to 1977, for the United States white male population. The agreement between the observed and calculated survival functions in the nine life tables was very good. Apart from its phenomenological interest, the model provides an effective means for calculating interpolations and extrapolations of abridged life tables, which are useful making population projections and in computer graphics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462273
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  • 98
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    Equilibrium electropotentials in electrolyte systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 669-687 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The determinationof electric potentials in finite regions of symmetrical electrolyte in one-dimensional equilibrium situations requires the solution of the one-dimensional Poisson-Boltzmann equation in which the dependent variable is linearly related to the electric potential and contains unknown parameters. These require evaluation as part of the solution to a given boundary value problem. The general solution of the equation is presented. This involves elliptic functions and integrals and is sectionally isomorphic with respect to an integration parameter. The application to problems posed in terms of both initial values and two-point boundary values is discussed. The solution is used to determine the potential and concentration distributions between two flat-faced charged particles immersed in an electrolyte liquid and having interacting double layers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462275
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  • 99
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    Some thoughts on quantum non-demolition measurements in biological systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 689-696 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A brief review of measurement theory in quantum mechanical and biological systems is made, the concept of quantum nondemolition experiments is discussed and a possible resolution to a previous discussion on the existence of nonrepeatable experiments is presented.
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    URL: http://dx.doi.org/10.1007/BF02462276
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  • 100
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    Evolution of a predator-prey Volterra-Lotka ecosystem with saturation effect (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 697-704 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper has studied the evolution of a predator-prey Volterra-Lotka ecosystem with saturation effect for the general case where both predator and prey evolve. We have interesting results under the evolutional condition, as follows: (1) the predator population and the ratio of predator to prey populations increase; (2) the parameters of the prey drift in the direction of increasing multiplication rate and saturation level, while the parameters of the predator drift in the direction of decreasing death rate.
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    URL: http://dx.doi.org/10.1007/BF02462277
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