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  • Artikel  (9.331)
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  • 1
    Digitale Medien
    Digitale Medien
    On biomass diversity in ecology (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 287-293 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We postulate that the biomass distribution function for an ecological population may be derived from the condition that the biomas diversity functional is maximal subject to an energetic constraint on the total biomass. This leads to a biomass distribution of the form $$p(m) = \bar m^{ - 1} \exp ( - m/\bar m)$$ , where $$\bar m$$ is the mean biomass per individual. The same condition yields a unique value for the biomass diversity functional. These predictions are tested against fishery data and found to be in good agreement. It is argued that the existence of a unique value for biomass diversity may provide a preliminary theoretical foundation for the observed upper limit to species diversity.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462362
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  • 2
    Digitale Medien
    Digitale Medien
    A model for hydranth regeneration inTubularia (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 311-321 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Pigment distribution presages hydranth regeneration in the marine hydroidTubularia. We suggest that such a distribution could result from a reaction-diffusion system. A model system based on a practical reaction scheme is studied and spatial structures found which closely resemble this pigment distribution. Finite-amplitude spatial structures in reaction-diffusion systems are considered. Whereas in one spatial dimension the final structures are normally very similar to the transient patterns which emerge from a linear analysis, it is shown that in more than one dimension this is not necessarily the case. The reasons for this are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459395
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  • 3
    Digitale Medien
    Digitale Medien
    On the fate of inhaled particles in the human: A comparison of experimental data with theoretical computations based on a symmetric and asymmetric lung (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 409-424 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An analytical model is used to described the behavior of inhaled particulate matter in the human respiratory tract. Three different geometries, symmetric and asymmetric, are utilized to simultate the tracheobronchial (TB) tree. The suitability of each geometry for representing the human is evaluated by comparing calculated aerosol deposition probabilities with experimental data from inhalation exposure tests. A symmetric, dichotomously branching pattern is found to be a reliable description of the TB tree for studies of factors affecting aerosol deposition in the human lung. Calculations with the theoretical model are in excellent agreement with measured aerosol deposition efficiencies. Furthermore, the model accurately predicts experimentally observed features of inhalation exposure data, such as effects of inter-subject lung morphology differences and relative efficiencies of specific deposition mechanisms, on aerosol deposition patterns in the TB tree.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459399
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  • 4
    Digitale Medien
    Digitale Medien
    Reply to letter by Jane Cronin (1982) (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 436-436 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459402
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  • 5
    Digitale Medien
    Digitale Medien
    Foreword (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 437-437 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459580
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  • 6
    Digitale Medien
    Digitale Medien
    Deductive biology—Some cautious steps (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 45-58 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract For certain environments, the Darwinian model allows unique prediction of a function that any surviving system adapted to such an environment has to perform. This is the case for those environments that determine a “survival functional” of position in space-time of known shape. Purely temporal survival functionals can be distinguished from spatial and mixed ones. In each case, there exists an optimum path in combined physical and (reduced) metabolic space. Dependent on the admissible error, approximate solutions of different complexity are sufficient. All solutions possess an afferent, a central, and an efferent part. Within this general frame, specific, “probably simplest”, solutions are proposed for adaptive chemotaxis, insect locomotion, lower vertebrates locomotion, higher vertebrates locomotion, chronobiological systems, and immune systems, respectively—or rather, for the underlying functionals.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463129
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  • 7
    Digitale Medien
    Digitale Medien
    The role of glucagon in the regulation of blood glucose: Model studies (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 59-77 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Mathematical models afford a procedure of unifying concepts and hypotheses by expressing quantitative relationships between observables. The model presented indicates the roles of both insulin and glucagon as regulators of blood glucose, albeit in different ranges of the blood glucose concentrations. Insulin secretion is induced during hyperglycemia, while glucagon secretion results during hypoglycemia. These are demonstrated by simulations of a mathematical model conformed to data from the oral glucose tolerance test and the insulin infusion test in normal control subjects and stable and unstable diabetic patients. The model studies suggest the parameters could prove of value in quantifying the diabetic condition by indicating the degree of instability.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463130
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  • 8
    Digitale Medien
    Digitale Medien
    A note on dynamics of population with history-dependent birth rate (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 123-131 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model for the dynamics of a single-species population whose birth rate depends on densities of previous generations is introduced. A difference equation formulation is proposed and the solutions classified for the various parameter values. Data from an experimental population of mice growing in limited space is cited and compared with the model predictions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463134
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  • 9
    Digitale Medien
    Digitale Medien
    Tension field theories for soft tissues (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 161-182 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract All soft tissues are modeled as either one-dimensionalstrings, two-dimensionalmembranes, or three-dimensionalsolids. Attention is restricted to tissues in which one of the principal stress components is large and positive in comparison with the other negligible components. Results indicate the following: (1) If a deformed string isconstrained to lie on a surface and is free of tangential pressure, the tension is carried by rays which are geodesics of the surface. If a string or membrane isfree to deform in space without normal pressure, the tension rays are straight lines. If a membrane deforms without tangential surface loads, the tension rays are always geodesics on the deformed surface. If a solid deforms without body forces, the tension rays are straight lines. (2) The stress in a string is a constant if the string is free of tangential pressure and has constant cross-sectional area. The stress in flat tension fields free of tangential surface loads decays inversely with distance along a tension ray from the edge of regression. The stress in a spherically symmetric tension field free of body forces decays inversely with the square of the distance from the center of the sphere. (3) Stress singularities can occur in soft tissues, such as at the corners of a closed rectangular hole in a flat membrane strip. (4) The tension rays in the torsion of soft annular membranes are more steeply inclined from the radial direction than the tension rays for hard metals equally displaced.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461433
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  • 10
    Digitale Medien
    Digitale Medien
    Invariant probabilities for systems in a random environment—With applications to the Brusselator (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 579-590 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper we are concerned with problems of the long-term behavior for nonlinear systems in random environment. The general model is assumed to be given by an ordinary differential equation with random parameters or random input. The disturbance process can be taken from a fairly general class of Markov processes having a bounded state space. In terms of the system’s dynamics we give sufficient conditions for the existence and uniqueness of invariant probabilities. Finally, we apply these results to the two-dimensional biochemical model which is known as the Brusselator.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459589
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  • 11
    Digitale Medien
    Digitale Medien
    Non-linear filtering with discontinuous observations and applications to life sciences (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 571-577 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In various applications one faces the problem of estimating a signal from discontinuous observations. For example, in biomedical applications the signal may be the ‘state’ of a given organ and one observes through an external counter the amount of radioactivity sequestered by the organ after injection of a radioactive tracer. Here the problem is studied in the context of nonlinear filtering when the signal can be modelled as either a random variable or a diffusion process, and the observations have a continuous and a purely discontinuous component; both components may be affected by the signal. When the signal is a random variable an explicitly computable solution is obtained; for the diffusion case the solution is given as a sequence of approximating filters that can be computed recursively.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459588
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  • 12
    Digitale Medien
    Digitale Medien
    Lateral diffusion and eigenvalue estimates (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 627-634 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Eigenvalue problems arise in various biological models. We outline a useful comparison method and a technique using Lyapunov functions that can be applied in many cases. An application to lateral diffusion is discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459594
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  • 13
    Digitale Medien
    Digitale Medien
    Recent views on the cell cycle structure (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 605-616 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper reviews, up to their recent developments, two types of models of the cell cycle: those considering the size controls over the cycle events and the transition probability models. The distribution of inter-mitotic time and the sister-sister and motherdaughter correlations implied by the two approaches are discussed in view of some relevant experimental data.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459592
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  • 14
    Digitale Medien
    Digitale Medien
    Controlled branching processes and their applications to normal and malignant haematopoiesis (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 617-626 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The development of a blood cell line originating from a pluripotent stem cell pool is modelled by a chain of multidimensional branching processes in which the sojourn times of the cells in certain resting states depend on the size of the following subpopulation. The stability of such a model is discussed qualitatively and some considerations concerning a possible malignant degeneration are presented. The behaviour of models for normal and malignant cell production are illustrated by stochastic stimulations. The model presented here describes the development of a certain line of blood cells (e.g. erythrocytes, monocytes or granulocytes) originating from the pluripotent stem cell up to the functional cell in the blood (for related models see, e.g., Rubinow and Lebowitz,J. math. Biol. 1, 87–225;Biophys. J. 16, 897–910).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459593
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  • 15
    Digitale Medien
    Digitale Medien
    Population growth in random environments (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 635-641 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper reviews some recent advances in single population stochastic differential equation growth models. They are a natural way to model population growth in a randomly varying environment. The question of which calculus, Itô or Stratonovich, is preferable is addressed. The two calculi coincide when the noise term is linear, if we take into account the differences in the interpretation of the parameters. This clarifies, among other things, the controversy on the theory of niche limiting similarity proposed by May and MacArthur. The effects of correlations in the environmental fluctuations and statistical methods for estimating parameters and for prediction based on a single population trajectory are mentioned. Applications to fisheries, wildlife management and particularly to environmental impact assessment are now becoming possible and are proposed in this paper.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459595
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  • 16
    Digitale Medien
    Digitale Medien
    Continuous-time Markov chains as models for animal behaviour (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 643-658 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A survey is given of the application of (functions of) continuous-time Markov chains in the statistical analysis of behavioural time series.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459596
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  • 17
    Digitale Medien
    Digitale Medien
    Tenth International Cell Cycle Conference (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 659-659 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459597
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  • 18
    Digitale Medien
    Digitale Medien
    On oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 661-664 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper demonstrates that there is one and only one solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a spherical cell. Previous authors have calculated numerical results that differ substantially. Numerical computations using the multiple shooting method support the results of McElwain.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460043
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  • 19
    Digitale Medien
    Digitale Medien
    The theory and practice of distance geometry (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 665-720 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The mathematics of distance geometry constitutes the basis of a group of algorithms for revealing the structural consequences of diverse forms of information about a macromolecule's conformation. These algorithms are of proven utility in the analysis of experimental conformational data. This paper presents the basic theorems of distance geometry in Euclidean space and gives formal proofs of the correctness and, where possible, of the complexity of these algorithms. The implications of distance geometry for the energy minimization of macromolecules are also discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460044
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  • 20
    Digitale Medien
    Digitale Medien
    Microcontinuum approach to the pulsatile flow in tubes with and without longitudinal vibration (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 721-737 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A fully developed pulsatile flow in a circular rigid tube is analysed by a microcontinuum approach. Solutions for radial variation of axial velocity and cell rotational velocity across the tube are obtained using the momentum integral method. Simplified forms of the solutions are presented for the relevant physiological data. Marked deviations in the results are observed when compared to a Newtonian fluid model. It is interesting to see that there is sufficient reduction in the mass flow rate, phase lag and friction due to the micropolar character of the fluid.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460045
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  • 21
    Digitale Medien
    Digitale Medien
    Transient transport across the blood-retina barrier (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 749-758 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model of the transport of fluorescein across the blood-retina barrier in the transient state and the subsequent diffusion of fluorescein in the vitreous body is presented. The function of the barrier is lumped in a single parameter—the permeability. The sensitivity of this parameter due to changes in the other parameters of the model is given. This establishes the foundation for the quantitative assessment of the barrier function through vitreous fluorophotometry.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460047
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  • 22
    Digitale Medien
    Digitale Medien
    Computed insulin profiles for normalization of glycemia in diabetic patients (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 739-748 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The objective of this preliminary study was to develop a new quantitative method of setting the initial insulin infusion patterns in treatment of diabetic patients. The method is based upon the mathematical estimation of the insulin profile required to maintain the glucose level within the normal range after glucose loading in diabetic patients. Using our previously developed equivalent circuit model of glucose kinetics and the reported data of an intravenous glucose tolerance test (IVGTT) in two groups of normal and diabetic patients, two important physiological parameters of the model (the peripheral tissue's insulin resistivity and the hepatic sensitivity to glucose level) were computed for two clinical groups. Then the insulin profile was obtained by computing the plasma insulin concentrations required to keep the total glucose utilization rate of the tissue and the liver in the diabetic group equal to that of the normal group. The simulation result indicated that the computed insulin profile produced a plasma glucose profile which was more closely matched to the normal group's glucose profile than with the case of emulating the normal group's insulin profile in the diabetic group.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460046
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  • 23
    Digitale Medien
    Digitale Medien
    Molecular mechanism of sodium conductance changes in nerve: The role of electron transfer and energy migration (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 759-780 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper shows that the Na conductance changes can be explained quantitatively, based on the following assumptions: (1) there exist in nerve membranes the electron transfer (ET) complexes and traps, (2) there is energy migration among them. The gating mechanism is explained in physical terms. Its mathematical expression differs from the Hodgkin-Huxley equations, but resembles the Hoyt formulation. In the present model, the physical parameters for the squid axon can be estimated from currently available experimental data. The density of the ET complexes is on the order of 105/μm2, and the density of the traps is 103/μm2. The magnitude of the energy transfer rate between ET complexes is about 106/sec at large depolarization and decreases with decreasing depolarizations, as does the Na inactivation rate. The energy gap between the two stable states of the transfer electron in the ET complex is estimated to be around 0.1 eV, which is approximately the same as that for the photosynthetic systems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460048
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  • 24
    Digitale Medien
    Digitale Medien
    The dynamics of symmetric nets (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 781-792 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The role of symmetry in simplifying the theory of complex neural systems is argued. When the structural symmetries of a network are expressed as an ismorphism group, implications emerge for the dynamics. Various qualitative possibilities concerning stability of uniform motion in homogeneous nets are discussed and an approach to neural hierarchies is outlined.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460049
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  • 25
    Digitale Medien
    Digitale Medien
    Conditions for global stability of two-species population models with discrete time delay (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 793-805 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract By constructing appropriate Liapunov functionals, asymptotic behaviour of the solutions of various delay differential systems describing prey-predator, competition and symbiosis models has been studied. It has been shown that equilibrium states of these models are globally stable, provided certain conditions in terms of instantaneous and delay interaction coefficients are satisfied.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460050
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  • 26
    Digitale Medien
    Digitale Medien
    Flow analysis sensitivities for models of energy or material flow (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 807-826 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Sensitivity analyses have been used to examine the flow structure of two hypothetical ecosystem models. These analyses have results which relate to important aspects of ecosystem theory. Cycles are shown to increase the sensitivity of the network, while increased throughflow is shown to decrease the sensitivity. Such results indicate that several factors can be modified to decrease the sensitivity of ecosystems to environmental stress.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460051
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  • 27
    Digitale Medien
    Digitale Medien
    Population dynamics with age- and time-dependent birth and death rates (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 827-836 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A continous, deterministic mathematical model is used to predict population distributions by age at any time, given the initial distribution and the variation of birth and death rates with age and time. Solutions are obtained on a computer using a semi-discretization algorithm in which time derivatives in the partial differential equations are replaced by finite-difference expressions. The resulting sets of ordinary differential equations are solved by a predictor-corrector method. Graphical results are shown for some examples.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460052
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  • 28
    Digitale Medien
    Digitale Medien
    On the complexity of graphs and molecules (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 849-855 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A new formula for the complexity of graphs is proposed and applied to the points lines and ‘connections’ of some chemically relevant graphs.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460054
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  • 29
    Digitale Medien
    Digitale Medien
    Analytical solutions for distributions of chemotactic bacteria (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 837-847 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper reports general and specialized results on analytical solutions to the governing phenomenological equations for chemotactic redistribution and population growth of motile bacteria. It is shown that the number of bacteria cells per unit volume,b, is proportional to a certain prescribed function ofs, the concentration of the critical substrate chemotactic agent, for steady-state solutions through an arbitrary spatial region with a boundary that is impermeable to bacteria cell transport. Moreover, it is demonstrated that the steady-state solution forb ands is unique for a prescribed total number of bacteria cells in the spatial region and a generic Robin boundary condition ons. The latter solution can be approximated to desired accuracy in terms of the Poisson-Green's function associated with the spatial region. Also, as shown by example, closed-form exact steady-state solutions are obtainable for certain consumption rate functions and geometrically symmetric spatial regions. A solutional procedure is formulated for the initialvalue problem in cases for which significant population growth is present and bacteria cell redistribution due to motility and chemotactic flow proceeds slowly relative to the diffusion of the chemoattractant substrate. Finally, a remarkably simple exact analytical solution is reported for a stradily propagating plane-wave which features motility, chemotactic motion and bacteria population growth regulated by substrate diffusion.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460053
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  • 30
    Digitale Medien
    Digitale Medien
    Effects of periodic accelerations on blood flow in arteries (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 857-867 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper discusses the flow of blood in large artries under the influence of linear periodic acceleration. The governing equations and boundary conditions are established and analytical solutions for the velocity, fluid acceleration, bulk flow and shear stress are obtained. The results for these physical quantitites are computed for the case of an artery the size of a normal human aorta. It is found that the flow field variables are directly proportional to the external accelerating force. The behaviour of the velocity profile along the radial distance at different stages of times at fixed applied acceleration is also shown.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460055
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  • 31
    Digitale Medien
    Digitale Medien
    Computational modeling of evolutionary learning processes in the brain (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 931-968 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The evolutionary selection circuits model of learning has been specified algorithmically. The basic structural components of the selection circuits model are enzymatic neurons, that is, neurons whose firing behavior is controlled by membrane-bound macromolecules called excitases. Learning involves changes in the excitase contents of neurons through a process of variation and selection. In this paper we report on the behavior of a basic version of the learning algorithm which has been developed through extensive interactive experiments with the model. This algorithm is effective in that it enables single neurons or networks of neurons to learn simple pattern classification tasks in a number of time steps which appears experimentally to be a linear function of problem size, as measured by the number of patterns of presynaptic input. The experimental behavior of the algorithm establishes that evolutionary mechanisms of learning are competent to serve as major mechanisms of neuronal adaptation. As an example, we show how the evolutionary learning algorithm can contribute to adaptive motor control processes in which the learning system develops the ability to reach a target in the presence of randomly imposed disturbances.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458823
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  • 32
    Digitale Medien
    Digitale Medien
    Dynamics of a continuous culture with catalysis of the growth-limiting substrate by an enzyme of the cells (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 981-990 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In the present paper we discuss the behaviour of solutions of a dynamical system describing the growth of cells in a well-mixed continuous culture where the supply of the growth-limiting nutrient depends on the activity of an enzyme outside the cell membrane. It turns out that for positive dilution rates there exists an exponentially attractive two-dimensional simplex. Furthermore, the reversed system restricted to this simplex is quasimonotone. In every case all trajectories tend to an equilibrium state.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458825
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  • 33
    Digitale Medien
    Digitale Medien
    The trade-off between mutual interference and time lags in predator-prey systems (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 991-1004 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We present a Gause predator-prey model incorporating mutual interference among predators, a density-dependent predator death rate and a time lag due to gestation. It is well known that mutual interference is stabilizing, whereas time delays are destabilizing. We show that in combining the two, a long time-lag usually, but not always, destabilizes the system. We also show that increasing delays can cause a bifurcation into periodic solutions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458826
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  • 34
    Digitale Medien
    Digitale Medien
    Sequential behavior and stability properties of enzymatic neuron networks (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 969-980 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The cycle structure of enzymatic neural networks may be characterized in terms of number of cycles exhibited, size of cycle state sets and cycle lengths. Simulation experiments show that the stability properties of these networks have some unusual features which are not exhibited by networks of two-state switching elements or by randomly constructed ecosystem models. The behavioral and structural stability of these systems decreases with their structural complexity, as measured by the number of components. The behavioral and structural stability of enzymatic neural networks also decreases with structural complexity, as measured by the number of excitase types, but only up to the middle level of excitases per neuron. This is the point of highest potential responsiveness of the system to environmental stimuli. Beyond this point the behavioral and structural stability increase. This is due to the fact that the number of possible states increases up to this point and decreases beyond it. The number of possible states, not the number of components, serves as the useful measure of complexity in these types of systems. The selection circuits learning algorithm has been used to evolve networks whose cycle structures have desired features.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458824
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  • 35
    Digitale Medien
    Digitale Medien
    A new similarity principle for cardiac energetics (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 1005-1011 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Similarity criteria of the functional design of the mammalian cardiovascular system are scant. For the analysis of mammalian cardiac energetics physiological parameters such as mean arterial blood pressure, stroke volume, heart rate, metabolic rate and heart and body weights are considered pertinent. Based on these parameters, a new similarity principle is established via allometric equations, dimensional analysis and Buckingham's pi-theorem. The principle states that the ratio of left ventricular external work to metabolic rate is inversely proportional to resting heart rates of mammals. The proportionality constant is dimensionless and is invariant of mammalian body weights.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458827
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  • 36
    Digitale Medien
    Digitale Medien
    Categorical system theory and the phenomenological calculus (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 1029-1045 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The mathematical theory of categories is used as a tool in the description of the structure and function of natural systems. The connections between the category of natural systems, with observables and dynamics, and the phenomenological calculus of response tensors, duality- and adjoint-invariance diagrams are established. The unified theory is applied to the analysis of hierarchies, pattern generation and the structure and dynamics of proteins.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458829
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  • 37
    Digitale Medien
    Digitale Medien
    Categorical system theory (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 1047-1072 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This is an investigation of natural systems from the standpoint of the mathematical theory of categories. It examines the relationships which exist between different descriptions through measurement of observables and dynamical interactions. We begin with a category theory of formal systems with observables, and then proceed to a category theory of dynamical systems. The two categories are then combined to represent natural systems. Topological considerations enter in the study of stability and bifurcation phenomena. Special emphasis is placed on natural systems which model biological processes. The categorical system theory developed is applied to the analysis of several biological problems and biological system theories.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458830
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  • 38
    Digitale Medien
    Digitale Medien
    Simulated tetanic hyperpolarization by sodium loading of a neuronal system in which active transport is linked to the Frankenhaeuser-Huxley equations (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 1013-1028 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Tetanic hyperpolarization for theXenopus node is simulated by means of iterative solutions of the Frankenhaeuser-Huxley excitation equations together with an active transport current density term which is dependent on sodium and potassium levels as well as the ADP/ATP ratio. All time-dependent variables at the end of one interspike interval are introduced as initial conditions for the next response, whereupon all time-dependent changes in voltage and permeability factors appear identical for the third and fourth responses of a sequence. Net change in internal sodium concentration is zero throughout the third and fourth intervals if sodium loading of the system is initially adjusted to a critical level. Extent of tetanic hyperpolarization is a function of the pump conductance.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458828
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  • 39
    Digitale Medien
    Digitale Medien
    Announcement (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 1097-1097 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458832
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  • 40
    Digitale Medien
    Digitale Medien
    Further properties of the two-membrane model (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 1073-1096 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The properties of nonlinear equations describing the solute and solvent transport across a simplified Patlak-Goldstein-Hoffman model (two membranes in series without unstirred layers) are investigated both analytically and numerically. The analysis shows that the principal coefficients measured in transport experiments in the presence of active transport are dependent on the experimental conditions. These ‘apparent’ system parameters are extensions of the corresponding parameters determined both in passive systems and in the linear Kedem-Katchalsky theory. Moreover, they are related to the local phenomenological coefficients of the single membranes of the array. Several relationships between measurable quantities and the local system parameters are indicated, allowing the planning of experiments aimed at the measurement of the latter. Data in the literature have been used to check the proposed volume flow equation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458831
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  • 41
    Digitale Medien
    Digitale Medien
    Analysis of the transient behavior of kidney models (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 211-221 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Non-steady-state equations for kidney models are stated. General conservation relations for these equations are derived. Transient equations for the central core model of the renal medulla are developed. Solution of the equations by Laplace transform methods for time invariant volume flows is discussed. The general theory of solving models with time dependent flows by finite difference methods is developed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461436
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  • 42
    Digitale Medien
    Digitale Medien
    Ecosystem-like behavior of a random-interaction model I (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 513-524 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The behavior of large systems of randomly-interacting variables is examined using an intentionally simplified model. The stable positive solutions are found to exhibit to a significant degree some well-known properties of ecological systems. This resemblance (including for example the predominance of “predator-prey” interactions) is all the more striking in view of the lack of biological “data” at the input end. The findings suggest it advisable to distinguish two kinds of properties in ecosystems. One kind would depend on specifically biological mechanisms; the other would characterize a wide class of persistent systems, and arise from the need for a dynamic balance between positive and negative feedback.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460775
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  • 43
    Digitale Medien
    Digitale Medien
    Mathematical analysis of cancer chemotherapy: The effects of chemotherapeutic agents on the cell cycle traverse (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 499-512 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract For the tumor model of Skipper and Zubrod, which has been analyzed previously for the theoretical FLM function and the effect of chemotherapy against tumors of known or assumed kinetic characteristics, the theoretical continuous labeling (CL) function is derived by considering an equivalent tumor (in terms of unlabeled cell populations) in which the density function of phase duration of cells inS-phasef 2(a 2)=δ(a 2−∞) and the loss functionL 2(t)=0. This mathematical concept of blocking is applied to the analysis of synchronization in tumor growth and blocking effects in cancer chemotherapy. These effects of chemical agents on the cell cycle progression are being incorporated into a previously written computer simulation program for cancer chemotherapy. Whereas, a program is written and used to simulate the CL functions for L1210 leukemia, and primary and metastatic Lewis lung carcinoma.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460774
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  • 44
    Digitale Medien
    Digitale Medien
    Global stability in a class of prey-predator models (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 525-533 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Global stability is established in a class of prey-predator models. This includes a prey-predator model in which the predator has Type 2 functional response and no intraspecific interactions. Two simple examples demonstrate that Kolmogoroff’s theorem does not apply to some members of this class of models.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460776
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  • 45
    Digitale Medien
    Digitale Medien
    A theoretical study of the temperature distribution in skeletal muscle undergoing rhythmic contractions (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 535-540 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The skeletal muscle is regarded as a periodically deformed plate. An equation of energy for the biological tissue in the system is used in the Lagrange variables. With the heat exchange through the above tissues to the exterior media and also with account of some relations between the physiological factors the approximate analytical solution for this equation is obtained and compared with the physiological data.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460777
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  • 46
    Digitale Medien
    Digitale Medien
    A comment on Bobisud's paper on evolution of cannibalism (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 541-545 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract One of Bobisud's (1976) models for the evolution, of cannibalism is discussed. His analysis is criticised for not being based on the principle of individual selection. Assuming the operation of that principle, we show by simulating his model that cannibals may establish themselves in a noncannibal population. This will happen both in cases where Bobisud concluded cannibalism to be optimal and in cases where he concluded cannibalism not to be optimal.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460778
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  • 47
    Digitale Medien
    Digitale Medien
    Prediction of light-induced transient thermal response of the retina (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 547-547 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460779
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  • 48
    Digitale Medien
    Digitale Medien
    Dynamical similarity and the theory of biological transformations (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 549-579 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The D'Arcy Thompson concept of biological transformations is developed in a form analogous to such physical concepts as the Law of Corresponding States in thermodynamics, and the Principles of Similitude found in engineering. We find that such concepts depend on a distinction between fundamental and derived quantities, in which the values assigned to the fundamental quantities set the natural scales for the derived ones. Among other things, we see that critical phenomena, such as phase transitions, arise as an immediate consequence of this distinction. In a biological context, we explore the implications of Thompson's hypothesis that closely related organisms are phenotypically similar, assuming that the organisms we see are the result of selection processes operating on phenotypes.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460731
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  • 49
    Digitale Medien
    Digitale Medien
    Distributed sensory coding applied to simulations of iconic storage and metacontrast (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 605-623 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract If information is coded in the combination of activities of many neurons operating in parallel, then information present in a network can be defined by the correlation of present network activity with the activity which had been elicited by a stimulus in the past; a high correlation indicates the presence of the previously encoded stimulus. Information is distributed in the network because coding is dependent upon the activities of all cells. A model based on Hartline-Ratliff lateral inhibition with a time delay shows that lateral inhibition can distribute information across a parallel network, reduce output noise, and also briefly store information. With no changes in model parameters, and the use of a correlation measure for recognition, the model can stimulate psychophysical results in eleven variations of the metacontrast masking paradigm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460733
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  • 50
    Digitale Medien
    Digitale Medien
    Theoretical study of nasal deposition (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 581-604 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A theory is derived to calculate the regional and total deposition of aerosol particles in the nasal passages during inhalation. The particle size studied range from 0.2 to 10.0 μm diameter. The deposition is calculated in five regions; (I) the region filled with nasal hair, (II) the nasal valve, (III) the expansion region, (IV) the turbinate region and (V) the posterior bend. Equations are derived to determine the deposition caused by direct impaction on the nasal hairs and bends of the passages. The calculations show the deposition due to direct impaction does not account for the amount or location of deposited particles measured in experiments. Secondary flows have been speculated to exist in the expansion region after the nasal valve and an equation is derived to estimate the deposition caused by the secondary flows. The calculated deposition, due to direct impaction and secondary flows, shows general agreement with the experiment as to the predicted amount and location of deposited particles.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460732
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  • 51
    Digitale Medien
    Digitale Medien
    What do mathematical models tell us about circadian clocks? (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 625-635 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The paper reviews a series of models for circadian clocks and discusses their conclusions and predictions. Attention is focused on Pittendrigh's empirical model, two mathematical models by the author and Winfree's work.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460734
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  • 52
    Digitale Medien
    Digitale Medien
    Electric field distribution, ionic selectivity and permeability in nerve (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 637-649 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract From a model of facilitated ionic transport across axonal membranes proposed by McIlroy (1975), the equipotentials and electric field distributions in the vicinity of a potassium conducting pore and of a sodium conducting pore are computed and presented as two-dimensional mappings. The model is then extended to include the effect of impurity ions in the conducting pores viz. of potassium ions in a sodium pore and of sodium ions in a potassium pore. The ionic selectivities and permeabilities of the transported species are discussed in relation to the extended model. Bounds are deduced for the ionic selectivity coefficients for both the sodium and potassium current-carrying systems in squid giant axons and the electric-field distributions in the vicinities of the pores are computed for the extended model and compared with the impurity-free fields first calculated. Finally the permeability coefficients defined in terms of the extended model are shown to reconcile the results of attempts to measure permeability by means of radioactive tracer techniques, with the classical description of the resting nerve.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460735
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  • 53
    Digitale Medien
    Digitale Medien
    Self-similar solution of a distributed model for transcapillary exchange and solute removal by the liver (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 661-669 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The partial differential equations describing transcapillary exchange and subsequent removal of solutis from an idealized liver sinusoid are amenable to solution by similarity analysis. The power and utility of this technique, which is not widely appreciated as a method for solving biological models, is illustrated here for a system whose Laplace transforms is difficult to invert.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460737
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  • 54
    Digitale Medien
    Digitale Medien
    Steady-state distribution of bacteria chemotactic toward oxygen (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 671-674 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The phenomenological theory for the chemotaxis and consumption of oxygen by motile aerobic bacteria is shown to yield a remarkably simple one-dimensional steady-state solution for a congregation of bacteria close to the surface of an oxygen-depleted aqueous medium.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460738
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  • 55
    Digitale Medien
    Digitale Medien
    On the identification by filtering techniques of a biologicaln-compartment model in which the transport rate parameters are assumed to be stochastic processes (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 651-660 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper biological compartmental models are considered which take into account the intrinsic randomness of the transport rate parameters and their possible variability in time. An identification procedure is presented for the estimation of the stochastic processes representing the transport rate parameters of a compartmental model from a noisy input-output experiment. The problem is formulated in terms of nonlinear filtering. A simple model is discussed for the case in which the transport rate parameters are independent of each other. The possibility of testing possible important features of the behavior of the transport rate parameters is also evidenced.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460736
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  • 56
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    Digitale Medien
    Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 853-863 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂ci/∂t=Di∇2ci+Qi(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c 1(x,t),...,c n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460611
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  • 57
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    Digitale Medien
    Mathematical models in biological discovery. Lecture notes in biomathematics (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 873-875 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460613
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  • 58
    Digitale Medien
    Digitale Medien
    Weber's law and perceptual categories: Another teleological view (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 139-142 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract As an alternative to optimum-processor models in which sensors attempt to circumvent internal and external noise, a mechanism-independent argument is presented for Weber's law in vision and hearing. In vision, the argument is that categories of objects should be independent of the light intensity on these objects. In hearing, sound categorization should be independent of the distance from the sound source. An analogous desideratum for computer-based image segmentation is also presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459392
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  • 59
    Digitale Medien
    Digitale Medien
    Lattices and lattice-valued relations in biology (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 193-207 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Rashevsky's treatment of general binary relations between sets of biological elements is extended using the novel mathematical concept of lattice-valued relation (l.v.r.). This yields a quantitative measure of the strength of the relations between components of a biological organism, and some illustrative examples are given. Specific l.v.r.'s are used to define (more precisely than in Rashevsky's preliminary theory of binary relations) the biologically important relationships amongst hormones, metabolism and energy exchange involved in metabolic reactions. The ‘strongest link’ between the set of hormones and the set of metabolic reactions is quantified using a special l.v.r., and other specific biological realisations of lattice-valued relations in abstract-relational biology are presented. L.v.r.'s may also be regarded as a form ofG-relation in relational biology, or as a particular case of generating diagrams. Further possible developments of this approach, using more complex tools of the newly developed mathematical theory of lattice-valued relations, such as function space l.v.r., group l.v.r., l.v.r. morphisms, l.v.r. homology andn-ary l.v.r.'s are suggested.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462356
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  • 60
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    Digitale Medien
    On the effect of the concentration profile of red cells on blood flow in the artery with stenosis (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 259-267 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The effects of the viscosity-concentration dependence and of the concentration profile on blood flow through a vessel with stenosis have been studied. The flow resistance and the wall shear stress have been found to be smaller than in the two-fluid model with constant viscosities.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462360
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  • 61
    Digitale Medien
    Digitale Medien
    On the geometry of space-and time-equivalent catastrophes (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 1-25 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The geometrical nature of the Elementary catastrophes (Thom, 1969) is reviewed. Histories of the movement of catastrophe manifolds and bifurcation sets are presented for some of the space-equivalent unfoldings described by Wassermann (1975). These unfoldings provide descriptions of the variation with time of the stability of stationary states of associated potential energy functions. Identification of these stationary energy states with stationary states of a system therefore provides a description of its behavior with time. Qualitative descriptions of this type are particularly useful when the complexity of a system prevents a detailed quantitative description. Histories of bifurcation set movements suggest different types of system behavior at different space-like coordinates. This type of theory may be a useful model for the processes leading to differentiation of cells and to emergence of adult forms of a biological organism.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463127
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  • 62
    Digitale Medien
    Digitale Medien
    Stochastic models for cell kinetics (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 507-519 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A survey is given of branching process type methods in cell kinetics. Some results are given that allow circadian rhythm and do not require complete independence between cells. Some more classical results on balanced exponential growth are given and some comments are made on flow microfluorometry.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459585
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  • 63
    Digitale Medien
    Digitale Medien
    Introduction (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 439-442 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459581
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  • 64
    Digitale Medien
    Digitale Medien
    Stochastic processes in neurophysiology: Transformation from point to continuous processes (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 443-465 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The spike train activity of neurones is considered as a point process, and methods of analysing and interpreting recorded spike trains are considered. The generation of a continuous process (membrane noise) from interacting point processes is described.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459582
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  • 65
    Digitale Medien
    Digitale Medien
    Stochastic theory of population genetics (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 521-554 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Stochastic models of population genetics are studied with special reference to the biological interest. Mathematical methods are described for treating some simple models and their modifications aimed at the problems of the molecular evolution. Unified theory for treating different quantities is extensively developed and applied to some typical problems of current interest in genetics. Mathematical methods for treating geographically structured populations are given. Approximation formulae and their accuracy are discussed. Some criteria are given for a structured population to behave almost like a panmictic population of the same total size. Some quantities are shown to be independent of the geographical structure and their dynamics are described.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459586
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  • 66
    Digitale Medien
    Digitale Medien
    Prediction of limit cycles in mathematical models of biological oscillations (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 27-44 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Three conjectures are given which predict the existence of unique stable limit cycle oscillations in a class of piecewise linear (PL) differential equations. The equations are appropriate to model biological or other complex systems in which there are switchlike interactions between the elements of the network. Methods are presented which can be used to develop mathematical models which are conjectured to display stable limit cycle oscillations, from qualitative experimental information about relative phases of activity in the dynamical systems. Several illustrative numerical examples are given, and one experimental example from neurobiology is discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463128
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  • 67
    Digitale Medien
    Digitale Medien
    Least energy regulation of the arterial system (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 79-93 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The formulation and results of the Kalman State Regulator Problem are applied to a mathematical model of the arterial system of a dog to obtain an optimal control for blood pressure. The criterion for optimality is minimum energy per cycle.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463131
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  • 68
    Digitale Medien
    Digitale Medien
    Pressure-flow relationships in a model for the arterial system (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 95-105 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model is developed in state variable form suitable for the study of the control of blood pressure and flow in the mammalian cardiovascular system. The applicability of the model to steady state, both mean and pulsatile, and transient phenomena is demonstrated by the agreement of the results with experimental data. This model was developed to study the neural and renal-endocrine-electrolyte control of cardiovascular functions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463132
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  • 69
    Digitale Medien
    Digitale Medien
    Conditions for periodic solutions of volterra differential systems (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 133-160 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract As a contribution to the discussion of oscillatory models for interacting species it is shown that two-species Volterra models can never have limit cycles, and a complete enumeration is given of conditions which the parameters of these models must satisfy in order that a part of the phase space be filled with a family of closed curves; sketches of phase portraits are also given. These results complement and correct older results by Bautin and by Coppel on quadratic differential systems. The paper opens with a brief discussion of some more practical aspects of the ecological application of oscillatory models.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461432
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  • 70
    Digitale Medien
    Digitale Medien
    The kinetics of diffused substances in some biological systems (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 107-121 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The purpose of this paper is to present a method for the determination of a solution for a coupled system of first order initial boundary-value problems arising from some biological systems. The physical problem is to determine the suspended and the superficial molecular concentrations of a traced substance passing through an organ containing a tangle of vessels, such as the kidney-ureter system. The approach to the problem is by successive approximation which leads to a recursion formula for the determination of the solution as well as error estimates for the approximations. The recursion formula involves only direct integration which indicates a promising possibility in obtaining numerical results by using a computer. In addition to the determination of a solution, some qualitative analysis of the solution is given. This includes the existence of a unique solution, the continuous dependency of the solution on the data, and the stability problem of a steady-state solution.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463133
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  • 71
    Digitale Medien
    Digitale Medien
    Heat transfer in perfused biological tissue—II. The “macroscopic” temperature distribution in tissue (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 183-199 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In Part I, the general solution of the heat transport equation was given for a medium of constant thermal properties, containing a general convection fieldv(r,t). Starting from this general solution, an average or “macroscopic” temperature distribution is calculated in this paper, since in most physiological problems only an average or “macroscopic” temperature is accessible to the measurement. It is shown that the averaged temperature distribution is influenced alone by the order of the local symmetries of the convection field. These local symmetries can be deduced from anatomical data on the vascular architecture. In order to perform the averaging process, a detailed discussion, and an estimate of the correlation between the microscopic temperature variation and the convection field is carried out. Hereby, great emphasis is put on the experimental consequences of these results. As an illustrative example, the calculation of the macroscopic temperature distribution in a medium traversed by parallel capillaries is outlined.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461434
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  • 72
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    Digitale Medien
    A note on dipole sources in conducting biological tissues (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 201-209 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The study of current flow fields in biologicaltissue requires finding the potential field from dipole sources such that the normal gradient vanishes at the exterior surface. A convenient way to determine the dipole field is by taking the gradient of the potential field set up by a point source. However, the point source problem is ill-posed when the normal gradient is required to vanish at the outer surface. In the paper the nature of this problem is discussed and several methods for overcoming the difficulty are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461435
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  • 73
    Digitale Medien
    Digitale Medien
    A hydrodynamic model of aqueous flow in the posterior chamber of the eye (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 223-235 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An analysis of the hydrodynamics of aqueous flow in the posterior chamber of the anterior segment of the eye is presented. The viscid, incompressible description of fluid dynamics in a spherical geometry is utilized to reduce the problem to a biharmonic-type equation using a “Stokes Stream Function”. Analogous to Poiseuille flow in a cylindrical pipe, velocity profiles are deduced and an Ohms Law relationship between pressure and flow is derived in terms of the geometry of the assumed model. This result is then incorporated into a synthesized electric circuit analog of flow between ciliary artery and episcleral vein. Applications to open angle and pupilary block glaucoma are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461437
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  • 74
    Digitale Medien
    Digitale Medien
    On the nerve impulse equation: The dynamic responses of nerve impulse (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 247-255 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract With the assumption of dipole interaction with the membrane matrix, the dipole barrier under an applied field shows a minimum in its time transient. Kinetic equations governing the migration of ions are presented. Na+ activation, Na+ inactivation and K+ delay are all part of the same mechanism in this model with no other separate assumptions needed. Voltage Clamp equation and action potential equation are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461439
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  • 75
    Digitale Medien
    Digitale Medien
    Metabolic model and dosimetric data for copper (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 265-269 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A metabolic model for copper is derived and presented in the context of the International Commission on Radiological Protection (ICRP) dosimetry models for the lungs and gastrointestinal tract.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461441
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  • 76
    Digitale Medien
    Digitale Medien
    Analytical conditions for the conservative form of the ecological equations (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 257-264 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The analytical conditions by which a Volterra's general system describingn interacting species can be put in the “conservative” form have been examined. The cases forn=2, 3, 4 have been analyzed in detail and a general condition for any value ofn is deduced. The analytical and biological constraints following by this approach are compared to the conclusions drawn by Leigh on the ground of purely biological considerations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461440
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  • 77
    Digitale Medien
    Digitale Medien
    On the stochastic theory of compartments: III. General time-dependent reversible systems (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 237-246 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract General formulation of stochastic single- and multi-compartment reversible systems with time-dependent transitions is made. The correspondence between the stochastic mean and the deterministic value is established in case of time-dependence and it is shown how the consequence of this can be utilized to compute the distribution and the moments of each individual compartment of the system. A two-compartment reversible system previously proposed by Cardenas and Matis (1975a) is analyzed on the basis of the theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461438
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  • 78
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    Digitale Medien
    Mathematical models of metabolic regulation, symposia biologica hungarica (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 271-272 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461442
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  • 79
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    Digitale Medien
    Optimal control of pests in the presence of predators (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 319-333 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Optimal control theory is applied to the problem of controlling pests by biological and chemical means simultaneously. The net birth rate of the pests is controlled chemically while at the same time predators are allowed to operate. Several numerical examples are included.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461604
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  • 80
    Digitale Medien
    Digitale Medien
    Transient behaviour of the single loop solute cycling model of the renal medulla (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 273-300 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Transient solutions are developed for the buildup of a concentration gradient in the single loop solute cycling model of the renal medulla. The “pump” from ascending limb to descending limb is considered in both unsaturated and completely saturated modes of operation. Both analytic solutions and semianalytic solutions obtained from inverting Laplace transforms are considered. The classic representation of concentration buildup by the multiplication process is compared with calculated profiles. The “single effect” is found to vary both in time and space.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461602
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  • 81
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    Digitale Medien
    The Krylov-Bogoliubov-Mitropolskii method applied to models of population dynamics (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 335-345 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this study the possibility of applying the asymptotic method of Krylov-Bogoliubov-Mitropolskii to problems of population dynamics is shown. Especially a general Volterra-Gause-Witt type model for prey-predator interaction is investigated. A discussion on the results obtained is given for the general model and for a particular case as well.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461605
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  • 82
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    Digitale Medien
    A dynamical field theory for dissipative systems: The hierarchical structure of field thermodynamics (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 301-318 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The analytical exploration of hierarchical structures is a central problem in modern biology. In many ways, the most basic tenet of any theory of any biological system is that its behavior lies within the laws of thermodynamics. Thus an investigation into the hierarchical structure of field thermodynamics is in effect an investigation into the underlying structures common to all biological systems. In field thermodynamics, the dynamics is prescribed at the hierarchical level of description concerned with the motions of classes of the various molecular species flowing in the system. Of crucial importance are scale factors which convert potentials into potential energies per mole of the various molecular species. On the other hand, the overall behavior of the system is presented at a higher hierarchical level of description in terms of systemic properties such as charge density or entropy density. Three questions are investigated: (1) how is the transition from the specific to the systemic level of description effected, (2) given the scale factors at the specific level how does one find those at the systemic level, and (3) what relationship can one, find between the scale factors at the two levels of description? Answering these questions necessitates an examination of the nature of the forces at the two levels of the hierarchy of descriptions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461603
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  • 83
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    Digitale Medien
    Reconstitution of the transition matrix from experimental data (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 369-376 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The identification of a linear compartment model, which may describe a chemical or biological process, is a difficult task, since the available data is generally limited. In this paper we propose a method for determining the state transition matrix by minimizing a given quadratic criterion. To solve the resulting matrix equation, an assumption has to be made which constitutes a necessary condition for the identifiability of the model. Moreover when this assumption is satisfied, it is shown that the knowledge of one line or one column of the transition matrix is sufficient to define it completely.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461608
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  • 84
    Digitale Medien
    Digitale Medien
    Analytical solution to isometric mechanogram of hill’s model of striated muscle (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 359-368 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The two-element muscle model considered consists of a contractile element defined by a hyperbolic force-velocity relation connected in series with an “exponential spring”. Differential equations for the isometrically developed force during a tetanic contraction and the corresponding contractile element shortening velocity are derived and their stability is investigated. Analytical solutions to both equations are obtained. Two numerical examples are given, the second chosen to illustrate pressure-induced hypertrophy of a cardiac muscle.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461607
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  • 85
    Digitale Medien
    Digitale Medien
    Lag time in microbe growth as an age-dependent branching process with two phase types (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 347-358 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We study a two-type, age-dependent branching process in which the branching probabilities of one of the types may vary with time. Specifically this modification of the Bellman-Harris process starts with a Type I particle which may either die or change to a Type II particle depending upon a time varying probability. A Type II particle may either die or reproduce with fixed probabilities but may not return to a particle of Type I. In this way the process models the lag phenomenon observed in microbe growth subsequent to transfer to a new culture medium while the organism is adapting to its new environment. We show that if the mean reproduction rate of Type II particles exceeds 1, then the population size grows exponentially. Further the extinction probability for this process is related to that of the Bellman-Harris process. Finally the governing equations are solved for several choices of the growth parameters and the solutions are graphically displayed showing that a wide variety of behavior can be modeled by this process.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461606
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  • 86
    Digitale Medien
    Digitale Medien
    Linear age-dependent population growth with harvesting (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 377-385 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper studies the effect of harvesting a fraction of a population where the population growth is modelled by a linear age-dependent model, the Von Foerster equation. Two harvesting strategies are considered: the first is where a fraction of the population greater than agec is removed, and the second is where a fraction of the population of age greater thanc but less thanc+n is removed. In the case where the death rate and fertility rate are time independent, the effect of harvesting on the stable age distribution is examined.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461609
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  • 87
    Digitale Medien
    Digitale Medien
    A comment on the Richardson-Miekisz field theory of thermodynamics (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 425-426 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461612
    Standort Signatur Erwartet Verfügbarkeit
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  • 88
    Digitale Medien
    Digitale Medien
    Multiple speciation, competitive exclusion, evolutionary pattern, and the grand ensemble in volterra eco-dynamics (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 387-410 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The general means are set forth by which, in a highly speciated Volterra eco-system, the bifurcation of a species into two in a competitive-exclusion configuration, provides a description of odd as well as even systems. The the Gibbs ensemble theory earlier developed is extended to grand ensembles in which the number of ecotypical species in genera-like clusters is allowed to be variable. The probability law for the sizes of clusters is deduced, and shown very closely to imply independent Poisson statistics for the cluster sizes, in answer to a fundamental issue of bioevolution. The role of the eco-analogs of Gibbs’ chemical potentials is brought forth, with a suggestion of how to describe cluster-to-cluster eco-genetic flows, and therewith a definite relationship between the degrees of speciation of genetically linked clusters on the one hand, and amplitudes of population fluctuations of member species within the clusters on the other hand.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461610
    Standort Signatur Erwartet Verfügbarkeit
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  • 89
    Digitale Medien
    Digitale Medien
    The stochastic theory of compartments—a mammillary system (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 427-427 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461613
    Standort Signatur Erwartet Verfügbarkeit
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  • 90
    Digitale Medien
    Digitale Medien
    Ionic concentration profiles and charge distribution for the domain of a polarized spherical cell (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 411-424 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Solutions of the Poisson-Boltzmann equation yield potential profiles and equilibrium distributions of ions on either side of a spherical shell membrane across which there exists a separation of ionic charges. For the special case in which the membrane is permeable to only one ion the total charge separation is analyzed in terms of the potential difference given by the Nernst equation. Potential profiles and ionic charge distributions are also given for situations involving a uniform distribution of fixed charges within the membrane.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461611
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  • 91
    Digitale Medien
    Digitale Medien
    An elementary approach to catastrophe theory (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 429-450 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The recently proved classification theorem of René Thom has led to the development of the new science of Catastrophe Theory. This theory has been widely held to be particularly relevant in biological applications. The present paper presents a simplified proof of Thom’s Theorem and assesses its importance in biology.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460770
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  • 92
    Digitale Medien
    Digitale Medien
    Mechanical behaviour of ventricular aneurysms (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 451-464 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model describes the mechanical behaviour of ventricular aneurysms assuming a spherical geometry for the left ventricle. Employing pressure-volume data obtained from normal dog hearts 1–2 hours after infarction, conditions are obtained on infarct thickness and angle of damage for ventricular rupture to occur. The results indicate that rupture is more likely to occur in the early period following infarction and that the dominant factor is the per cent thickness of the infarct.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460771
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  • 93
    Digitale Medien
    Digitale Medien
    A stochastic approach to predator-prey models (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 483-498 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A deterministic investigation of a linear differential equation system which describes predator vs prey behavior as a function of equilibrium densities and reproductive rates is given. A more realistic structure of this model in a stochastic framework is presented. The reproductive rates and initial population sizes are considered to be random variables and their probabilistic behavior characterized by various joint probability distributions. The deterministic behaviors of the prey and predator species as functions of time are compared with the mean behaviors in the stochastic model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460773
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  • 94
    Digitale Medien
    Digitale Medien
    Effects of external pressures on the pressure-volume relation of the left ventricle (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 465-482 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The effects of ventricular geometry, muscle mass, muscle elasticity and external pressures on the pressure-volume and muscle stiffness-stress relations have been quantitated on the basis of a theoretical model. Data taken from patients before and after interventions with nitroprusside and angiotensin were applied to the model in order to explain the possible causes for the marked shifts in the pressure-volume relations. The results indicate that (a) ventricular geometry does not markedly alter the pressure-volume and stiffness-stress relations unless there is a drastic change from a spherical shape to an ellipsoidal shape orvice versa, (b) increases in muscle mass and muscle elasticity of the order of 30% result in significant alterations in the P-V relations but are not the cause for the parallel shifts unless accompanied by substantial external pressures, (c) the parallel shifts in the pressure-volume relations can be accounted for entirely by the presence of external pressures without changes in muscle mass or muscle elasticity. Thus manipulation of right ventricular pressures or pericardial pressures by drug interventions may be useful in the treatment of left heart disease and the presence of such pressures must be considered in the analysis of ventricular function curves.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460772
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  • 95
    Digitale Medien
    Digitale Medien
    Qualitative similarities between the behavior of coupled oscillators and circadian rhythms (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 675-692 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper summarizes in a nonmathematical way the major properties of coupled oscillators which relate to circadian rhythms. For certain values of the coupling strength it is far easier to maintain synchrony than to achieve it among the various interacting units. This property not only simulates the free run period lability but also the effects of critical pulses.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460599
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  • 96
    Digitale Medien
    Digitale Medien
    The effects of asymptomatic attacks on the spread of infectious disease: A deterministic model (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 707-718 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A deterministic model for a multi-agent disease epidemic with asymptomatic attacks is proposed and investigated. The limitations inherent in the assumptions of the model are discussed in connection with specific agents of disease. The mathematical treatment of the model is separated into analyses of the equilibrium situation and the transient behavior of the disease outbreak. Explicit formulas are derived for the number of susceptibles in the population as well as for the numbers of each type of infective—those with and without symptoms. These theoretical results are followed by a discussion of the practical considerations which must be taken into account to obtain useful information from the model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460601
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  • 97
    Digitale Medien
    Digitale Medien
    On a model and the kinetics of photo-enhanced enzyme reactions (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 719-726 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The recently observed enhancement, by laser irradiation, of the specific activity of the enzyme chymotrypsin (which hydrolyses Benzoyl-L-tyrosine-ethyl ester) at low enzyme concentration is considered. The enhancement of the reaction rate is attributed to a coherently excited state of the enzyme molecule (activated through Raman scattering of the laser light) following a prediction due to Fröhlich. The model is described, the kinetics of the process is framed and the observed enzyme-concentration dependence of the specific activity is reproduced. Predictions of the model are delineated to urge verification of the main contentions through further experimentation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460602
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  • 98
    Digitale Medien
    Digitale Medien
    A two-component theory of aerosol deposition in lung airways (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 693-706 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The deposition of aerosol particles in the human lung airways is due to two distinct mechanisms. One is by direct deposition resulting from diffusion, sedimentation and impaction as the aerosol moves in and out of the lung. The other is an indirect mechanism by which particles are transported mechanically from the tidal air to the residential air and eventually captured by the airways due to intrinsic particle motion. This last mechanism is not well understood at present. Using a trumpet airway model constructed from Weibel's data, a two-component theory is developed. In this theory, the particle concentrations in the airways and the alveoli at a given airway depth are considered to be quantitatively different. This difference in concentrations will cause a net mixing between the tidal and residential aerosol as the aerosol is breathed in and out. A distribution parameter is then introduced to account for the distribution of ventilation. The effect of intrinsic particle motion on the aerosol mixing is also included. From this theory, total and regional deposition in the lung at the steady mouth breathing without pause is calculated for several different respiratory cycles. The results agree reasonably well with the experimental data.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460600
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  • 99
    Digitale Medien
    Digitale Medien
    On the kinetics of enzyme reactions (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 727-734 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The Abel type differential equation governing the kinetics of the enzyme reactions is derived. Approximate solutions of this equation corresponding to the transient phase of the reaction, before a steady state is reached, are considered. It is shown that in several cases it is possible to obtain explicit, approximate solutions to the transient phase.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460603
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  • 100
    Digitale Medien
    Digitale Medien
    Complementary variational principles for the steady-state finite cable model of nerve membranes (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 735-742 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Maximum and minimum principles for the steady-state finite cable model of nerve membranes are derived from the canonical theory of complementary variational principles. An accurate variational solution is obtained in an illustrative calculation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460604
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