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  • Articles  (14,404)
  • Springer  (14,050)
  • Canadian Science Publishing
  • 2005-2009
  • 1980-1984  (14,404)
  • 1965-1969
  • 1925-1929
  • 1983  (14,404)
  • Medicine  (6,938)
  • Mathematics  (4,850)
  • Geosciences  (2,804)
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  • Articles  (14,404)
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  • 2005-2009
  • 1980-1984  (14,404)
  • 1965-1969
  • 1925-1929
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  • 1
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    Bulletin of mathematical biology 45 (1983), S. 287-293 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We postulate that the biomass distribution function for an ecological population may be derived from the condition that the biomas diversity functional is maximal subject to an energetic constraint on the total biomass. This leads to a biomass distribution of the form $$p(m) = \bar m^{ - 1} \exp ( - m/\bar m)$$ , where $$\bar m$$ is the mean biomass per individual. The same condition yields a unique value for the biomass diversity functional. These predictions are tested against fishery data and found to be in good agreement. It is argued that the existence of a unique value for biomass diversity may provide a preliminary theoretical foundation for the observed upper limit to species diversity.
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  • 2
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    Bulletin of mathematical biology 45 (1983), S. 311-321 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Pigment distribution presages hydranth regeneration in the marine hydroidTubularia. We suggest that such a distribution could result from a reaction-diffusion system. A model system based on a practical reaction scheme is studied and spatial structures found which closely resemble this pigment distribution. Finite-amplitude spatial structures in reaction-diffusion systems are considered. Whereas in one spatial dimension the final structures are normally very similar to the transient patterns which emerge from a linear analysis, it is shown that in more than one dimension this is not necessarily the case. The reasons for this are discussed.
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    Bulletin of mathematical biology 45 (1983), S. 409-424 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract An analytical model is used to described the behavior of inhaled particulate matter in the human respiratory tract. Three different geometries, symmetric and asymmetric, are utilized to simultate the tracheobronchial (TB) tree. The suitability of each geometry for representing the human is evaluated by comparing calculated aerosol deposition probabilities with experimental data from inhalation exposure tests. A symmetric, dichotomously branching pattern is found to be a reliable description of the TB tree for studies of factors affecting aerosol deposition in the human lung. Calculations with the theoretical model are in excellent agreement with measured aerosol deposition efficiencies. Furthermore, the model accurately predicts experimentally observed features of inhalation exposure data, such as effects of inter-subject lung morphology differences and relative efficiencies of specific deposition mechanisms, on aerosol deposition patterns in the TB tree.
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    Bulletin of mathematical biology 45 (1983), S. 436-436 
    ISSN: 1522-9602
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  • 5
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    Bulletin of mathematical biology 45 (1983), S. 437-437 
    ISSN: 1522-9602
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    Bulletin of mathematical biology 45 (1983), S. 579-590 
    ISSN: 1522-9602
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    Notes: Abstract In this paper we are concerned with problems of the long-term behavior for nonlinear systems in random environment. The general model is assumed to be given by an ordinary differential equation with random parameters or random input. The disturbance process can be taken from a fairly general class of Markov processes having a bounded state space. In terms of the system’s dynamics we give sufficient conditions for the existence and uniqueness of invariant probabilities. Finally, we apply these results to the two-dimensional biochemical model which is known as the Brusselator.
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    Bulletin of mathematical biology 45 (1983), S. 571-577 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract In various applications one faces the problem of estimating a signal from discontinuous observations. For example, in biomedical applications the signal may be the ‘state’ of a given organ and one observes through an external counter the amount of radioactivity sequestered by the organ after injection of a radioactive tracer. Here the problem is studied in the context of nonlinear filtering when the signal can be modelled as either a random variable or a diffusion process, and the observations have a continuous and a purely discontinuous component; both components may be affected by the signal. When the signal is a random variable an explicitly computable solution is obtained; for the diffusion case the solution is given as a sequence of approximating filters that can be computed recursively.
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  • 8
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    Bulletin of mathematical biology 45 (1983), S. 627-634 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Eigenvalue problems arise in various biological models. We outline a useful comparison method and a technique using Lyapunov functions that can be applied in many cases. An application to lateral diffusion is discussed.
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    Bulletin of mathematical biology 45 (1983), S. 605-616 
    ISSN: 1522-9602
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    Notes: Abstract This paper reviews, up to their recent developments, two types of models of the cell cycle: those considering the size controls over the cycle events and the transition probability models. The distribution of inter-mitotic time and the sister-sister and motherdaughter correlations implied by the two approaches are discussed in view of some relevant experimental data.
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    Bulletin of mathematical biology 45 (1983), S. 617-626 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract The development of a blood cell line originating from a pluripotent stem cell pool is modelled by a chain of multidimensional branching processes in which the sojourn times of the cells in certain resting states depend on the size of the following subpopulation. The stability of such a model is discussed qualitatively and some considerations concerning a possible malignant degeneration are presented. The behaviour of models for normal and malignant cell production are illustrated by stochastic stimulations. The model presented here describes the development of a certain line of blood cells (e.g. erythrocytes, monocytes or granulocytes) originating from the pluripotent stem cell up to the functional cell in the blood (for related models see, e.g., Rubinow and Lebowitz,J. math. Biol. 1, 87–225;Biophys. J. 16, 897–910).
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    Bulletin of mathematical biology 45 (1983), S. 635-641 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract This paper reviews some recent advances in single population stochastic differential equation growth models. They are a natural way to model population growth in a randomly varying environment. The question of which calculus, Itô or Stratonovich, is preferable is addressed. The two calculi coincide when the noise term is linear, if we take into account the differences in the interpretation of the parameters. This clarifies, among other things, the controversy on the theory of niche limiting similarity proposed by May and MacArthur. The effects of correlations in the environmental fluctuations and statistical methods for estimating parameters and for prediction based on a single population trajectory are mentioned. Applications to fisheries, wildlife management and particularly to environmental impact assessment are now becoming possible and are proposed in this paper.
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    Bulletin of mathematical biology 45 (1983), S. 643-658 
    ISSN: 1522-9602
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    Notes: Abstract A survey is given of the application of (functions of) continuous-time Markov chains in the statistical analysis of behavioural time series.
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    Bulletin of mathematical biology 45 (1983), S. 659-659 
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    Bulletin of mathematical biology 45 (1983), S. 661-664 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract This paper demonstrates that there is one and only one solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a spherical cell. Previous authors have calculated numerical results that differ substantially. Numerical computations using the multiple shooting method support the results of McElwain.
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    Bulletin of mathematical biology 45 (1983), S. 665-720 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract The mathematics of distance geometry constitutes the basis of a group of algorithms for revealing the structural consequences of diverse forms of information about a macromolecule's conformation. These algorithms are of proven utility in the analysis of experimental conformational data. This paper presents the basic theorems of distance geometry in Euclidean space and gives formal proofs of the correctness and, where possible, of the complexity of these algorithms. The implications of distance geometry for the energy minimization of macromolecules are also discussed.
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    Bulletin of mathematical biology 45 (1983), S. 721-737 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract A fully developed pulsatile flow in a circular rigid tube is analysed by a microcontinuum approach. Solutions for radial variation of axial velocity and cell rotational velocity across the tube are obtained using the momentum integral method. Simplified forms of the solutions are presented for the relevant physiological data. Marked deviations in the results are observed when compared to a Newtonian fluid model. It is interesting to see that there is sufficient reduction in the mass flow rate, phase lag and friction due to the micropolar character of the fluid.
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    Bulletin of mathematical biology 45 (1983), S. 749-758 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model of the transport of fluorescein across the blood-retina barrier in the transient state and the subsequent diffusion of fluorescein in the vitreous body is presented. The function of the barrier is lumped in a single parameter—the permeability. The sensitivity of this parameter due to changes in the other parameters of the model is given. This establishes the foundation for the quantitative assessment of the barrier function through vitreous fluorophotometry.
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    Bulletin of mathematical biology 45 (1983), S. 739-748 
    ISSN: 1522-9602
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    Notes: Abstract The objective of this preliminary study was to develop a new quantitative method of setting the initial insulin infusion patterns in treatment of diabetic patients. The method is based upon the mathematical estimation of the insulin profile required to maintain the glucose level within the normal range after glucose loading in diabetic patients. Using our previously developed equivalent circuit model of glucose kinetics and the reported data of an intravenous glucose tolerance test (IVGTT) in two groups of normal and diabetic patients, two important physiological parameters of the model (the peripheral tissue's insulin resistivity and the hepatic sensitivity to glucose level) were computed for two clinical groups. Then the insulin profile was obtained by computing the plasma insulin concentrations required to keep the total glucose utilization rate of the tissue and the liver in the diabetic group equal to that of the normal group. The simulation result indicated that the computed insulin profile produced a plasma glucose profile which was more closely matched to the normal group's glucose profile than with the case of emulating the normal group's insulin profile in the diabetic group.
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    Bulletin of mathematical biology 45 (1983), S. 759-780 
    ISSN: 1522-9602
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    Notes: Abstract This paper shows that the Na conductance changes can be explained quantitatively, based on the following assumptions: (1) there exist in nerve membranes the electron transfer (ET) complexes and traps, (2) there is energy migration among them. The gating mechanism is explained in physical terms. Its mathematical expression differs from the Hodgkin-Huxley equations, but resembles the Hoyt formulation. In the present model, the physical parameters for the squid axon can be estimated from currently available experimental data. The density of the ET complexes is on the order of 105/μm2, and the density of the traps is 103/μm2. The magnitude of the energy transfer rate between ET complexes is about 106/sec at large depolarization and decreases with decreasing depolarizations, as does the Na inactivation rate. The energy gap between the two stable states of the transfer electron in the ET complex is estimated to be around 0.1 eV, which is approximately the same as that for the photosynthetic systems.
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    Bulletin of mathematical biology 45 (1983), S. 781-792 
    ISSN: 1522-9602
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    Notes: Abstract The role of symmetry in simplifying the theory of complex neural systems is argued. When the structural symmetries of a network are expressed as an ismorphism group, implications emerge for the dynamics. Various qualitative possibilities concerning stability of uniform motion in homogeneous nets are discussed and an approach to neural hierarchies is outlined.
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    Bulletin of mathematical biology 45 (1983), S. 793-805 
    ISSN: 1522-9602
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    Notes: Abstract By constructing appropriate Liapunov functionals, asymptotic behaviour of the solutions of various delay differential systems describing prey-predator, competition and symbiosis models has been studied. It has been shown that equilibrium states of these models are globally stable, provided certain conditions in terms of instantaneous and delay interaction coefficients are satisfied.
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    Bulletin of mathematical biology 45 (1983), S. 807-826 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Sensitivity analyses have been used to examine the flow structure of two hypothetical ecosystem models. These analyses have results which relate to important aspects of ecosystem theory. Cycles are shown to increase the sensitivity of the network, while increased throughflow is shown to decrease the sensitivity. Such results indicate that several factors can be modified to decrease the sensitivity of ecosystems to environmental stress.
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    Bulletin of mathematical biology 45 (1983), S. 827-836 
    ISSN: 1522-9602
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    Notes: Abstract A continous, deterministic mathematical model is used to predict population distributions by age at any time, given the initial distribution and the variation of birth and death rates with age and time. Solutions are obtained on a computer using a semi-discretization algorithm in which time derivatives in the partial differential equations are replaced by finite-difference expressions. The resulting sets of ordinary differential equations are solved by a predictor-corrector method. Graphical results are shown for some examples.
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    Bulletin of mathematical biology 45 (1983), S. 849-855 
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    Notes: Abstract A new formula for the complexity of graphs is proposed and applied to the points lines and ‘connections’ of some chemically relevant graphs.
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    Bulletin of mathematical biology 45 (1983), S. 837-847 
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    Notes: Abstract This paper reports general and specialized results on analytical solutions to the governing phenomenological equations for chemotactic redistribution and population growth of motile bacteria. It is shown that the number of bacteria cells per unit volume,b, is proportional to a certain prescribed function ofs, the concentration of the critical substrate chemotactic agent, for steady-state solutions through an arbitrary spatial region with a boundary that is impermeable to bacteria cell transport. Moreover, it is demonstrated that the steady-state solution forb ands is unique for a prescribed total number of bacteria cells in the spatial region and a generic Robin boundary condition ons. The latter solution can be approximated to desired accuracy in terms of the Poisson-Green's function associated with the spatial region. Also, as shown by example, closed-form exact steady-state solutions are obtainable for certain consumption rate functions and geometrically symmetric spatial regions. A solutional procedure is formulated for the initialvalue problem in cases for which significant population growth is present and bacteria cell redistribution due to motility and chemotactic flow proceeds slowly relative to the diffusion of the chemoattractant substrate. Finally, a remarkably simple exact analytical solution is reported for a stradily propagating plane-wave which features motility, chemotactic motion and bacteria population growth regulated by substrate diffusion.
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    Bulletin of mathematical biology 45 (1983), S. 857-867 
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    Notes: Abstract This paper discusses the flow of blood in large artries under the influence of linear periodic acceleration. The governing equations and boundary conditions are established and analytical solutions for the velocity, fluid acceleration, bulk flow and shear stress are obtained. The results for these physical quantitites are computed for the case of an artery the size of a normal human aorta. It is found that the flow field variables are directly proportional to the external accelerating force. The behaviour of the velocity profile along the radial distance at different stages of times at fixed applied acceleration is also shown.
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    Bulletin of mathematical biology 45 (1983), S. 931-968 
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    Notes: Abstract The evolutionary selection circuits model of learning has been specified algorithmically. The basic structural components of the selection circuits model are enzymatic neurons, that is, neurons whose firing behavior is controlled by membrane-bound macromolecules called excitases. Learning involves changes in the excitase contents of neurons through a process of variation and selection. In this paper we report on the behavior of a basic version of the learning algorithm which has been developed through extensive interactive experiments with the model. This algorithm is effective in that it enables single neurons or networks of neurons to learn simple pattern classification tasks in a number of time steps which appears experimentally to be a linear function of problem size, as measured by the number of patterns of presynaptic input. The experimental behavior of the algorithm establishes that evolutionary mechanisms of learning are competent to serve as major mechanisms of neuronal adaptation. As an example, we show how the evolutionary learning algorithm can contribute to adaptive motor control processes in which the learning system develops the ability to reach a target in the presence of randomly imposed disturbances.
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    Bulletin of mathematical biology 45 (1983), S. 981-990 
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    Notes: Abstract In the present paper we discuss the behaviour of solutions of a dynamical system describing the growth of cells in a well-mixed continuous culture where the supply of the growth-limiting nutrient depends on the activity of an enzyme outside the cell membrane. It turns out that for positive dilution rates there exists an exponentially attractive two-dimensional simplex. Furthermore, the reversed system restricted to this simplex is quasimonotone. In every case all trajectories tend to an equilibrium state.
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    Bulletin of mathematical biology 45 (1983), S. 991-1004 
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    Notes: Abstract We present a Gause predator-prey model incorporating mutual interference among predators, a density-dependent predator death rate and a time lag due to gestation. It is well known that mutual interference is stabilizing, whereas time delays are destabilizing. We show that in combining the two, a long time-lag usually, but not always, destabilizes the system. We also show that increasing delays can cause a bifurcation into periodic solutions.
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    Bulletin of mathematical biology 45 (1983), S. 969-980 
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    Notes: Abstract The cycle structure of enzymatic neural networks may be characterized in terms of number of cycles exhibited, size of cycle state sets and cycle lengths. Simulation experiments show that the stability properties of these networks have some unusual features which are not exhibited by networks of two-state switching elements or by randomly constructed ecosystem models. The behavioral and structural stability of these systems decreases with their structural complexity, as measured by the number of components. The behavioral and structural stability of enzymatic neural networks also decreases with structural complexity, as measured by the number of excitase types, but only up to the middle level of excitases per neuron. This is the point of highest potential responsiveness of the system to environmental stimuli. Beyond this point the behavioral and structural stability increase. This is due to the fact that the number of possible states increases up to this point and decreases beyond it. The number of possible states, not the number of components, serves as the useful measure of complexity in these types of systems. The selection circuits learning algorithm has been used to evolve networks whose cycle structures have desired features.
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    Bulletin of mathematical biology 45 (1983), S. 1005-1011 
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    Notes: Abstract Similarity criteria of the functional design of the mammalian cardiovascular system are scant. For the analysis of mammalian cardiac energetics physiological parameters such as mean arterial blood pressure, stroke volume, heart rate, metabolic rate and heart and body weights are considered pertinent. Based on these parameters, a new similarity principle is established via allometric equations, dimensional analysis and Buckingham's pi-theorem. The principle states that the ratio of left ventricular external work to metabolic rate is inversely proportional to resting heart rates of mammals. The proportionality constant is dimensionless and is invariant of mammalian body weights.
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    Bulletin of mathematical biology 45 (1983), S. 1029-1045 
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    Notes: Abstract The mathematical theory of categories is used as a tool in the description of the structure and function of natural systems. The connections between the category of natural systems, with observables and dynamics, and the phenomenological calculus of response tensors, duality- and adjoint-invariance diagrams are established. The unified theory is applied to the analysis of hierarchies, pattern generation and the structure and dynamics of proteins.
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    Bulletin of mathematical biology 45 (1983), S. 1047-1072 
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    Notes: Abstract This is an investigation of natural systems from the standpoint of the mathematical theory of categories. It examines the relationships which exist between different descriptions through measurement of observables and dynamical interactions. We begin with a category theory of formal systems with observables, and then proceed to a category theory of dynamical systems. The two categories are then combined to represent natural systems. Topological considerations enter in the study of stability and bifurcation phenomena. Special emphasis is placed on natural systems which model biological processes. The categorical system theory developed is applied to the analysis of several biological problems and biological system theories.
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    Notes: Abstract Tetanic hyperpolarization for theXenopus node is simulated by means of iterative solutions of the Frankenhaeuser-Huxley excitation equations together with an active transport current density term which is dependent on sodium and potassium levels as well as the ADP/ATP ratio. All time-dependent variables at the end of one interspike interval are introduced as initial conditions for the next response, whereupon all time-dependent changes in voltage and permeability factors appear identical for the third and fourth responses of a sequence. Net change in internal sodium concentration is zero throughout the third and fourth intervals if sodium loading of the system is initially adjusted to a critical level. Extent of tetanic hyperpolarization is a function of the pump conductance.
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    Bulletin of mathematical biology 45 (1983), S. 1097-1097 
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    Bulletin of mathematical biology 45 (1983), S. 1073-1096 
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    Notes: Abstract The properties of nonlinear equations describing the solute and solvent transport across a simplified Patlak-Goldstein-Hoffman model (two membranes in series without unstirred layers) are investigated both analytically and numerically. The analysis shows that the principal coefficients measured in transport experiments in the presence of active transport are dependent on the experimental conditions. These ‘apparent’ system parameters are extensions of the corresponding parameters determined both in passive systems and in the linear Kedem-Katchalsky theory. Moreover, they are related to the local phenomenological coefficients of the single membranes of the array. Several relationships between measurable quantities and the local system parameters are indicated, allowing the planning of experiments aimed at the measurement of the latter. Data in the literature have been used to check the proposed volume flow equation.
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    Bulletin of mathematical biology 45 (1983), S. 139-142 
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    Notes: Abstract As an alternative to optimum-processor models in which sensors attempt to circumvent internal and external noise, a mechanism-independent argument is presented for Weber's law in vision and hearing. In vision, the argument is that categories of objects should be independent of the light intensity on these objects. In hearing, sound categorization should be independent of the distance from the sound source. An analogous desideratum for computer-based image segmentation is also presented.
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    Bulletin of mathematical biology 45 (1983), S. 193-207 
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    Notes: Abstract Rashevsky's treatment of general binary relations between sets of biological elements is extended using the novel mathematical concept of lattice-valued relation (l.v.r.). This yields a quantitative measure of the strength of the relations between components of a biological organism, and some illustrative examples are given. Specific l.v.r.'s are used to define (more precisely than in Rashevsky's preliminary theory of binary relations) the biologically important relationships amongst hormones, metabolism and energy exchange involved in metabolic reactions. The ‘strongest link’ between the set of hormones and the set of metabolic reactions is quantified using a special l.v.r., and other specific biological realisations of lattice-valued relations in abstract-relational biology are presented. L.v.r.'s may also be regarded as a form ofG-relation in relational biology, or as a particular case of generating diagrams. Further possible developments of this approach, using more complex tools of the newly developed mathematical theory of lattice-valued relations, such as function space l.v.r., group l.v.r., l.v.r. morphisms, l.v.r. homology andn-ary l.v.r.'s are suggested.
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    Bulletin of mathematical biology 45 (1983), S. 259-267 
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    Notes: Abstract The effects of the viscosity-concentration dependence and of the concentration profile on blood flow through a vessel with stenosis have been studied. The flow resistance and the wall shear stress have been found to be smaller than in the two-fluid model with constant viscosities.
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    Bulletin of mathematical biology 45 (1983), S. 507-519 
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    Notes: Abstract A survey is given of branching process type methods in cell kinetics. Some results are given that allow circadian rhythm and do not require complete independence between cells. Some more classical results on balanced exponential growth are given and some comments are made on flow microfluorometry.
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    Bulletin of mathematical biology 45 (1983), S. 439-442 
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    Bulletin of mathematical biology 45 (1983), S. 443-465 
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    Notes: Abstract The spike train activity of neurones is considered as a point process, and methods of analysing and interpreting recorded spike trains are considered. The generation of a continuous process (membrane noise) from interacting point processes is described.
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    Bulletin of mathematical biology 45 (1983), S. 521-554 
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    Notes: Abstract Stochastic models of population genetics are studied with special reference to the biological interest. Mathematical methods are described for treating some simple models and their modifications aimed at the problems of the molecular evolution. Unified theory for treating different quantities is extensively developed and applied to some typical problems of current interest in genetics. Mathematical methods for treating geographically structured populations are given. Approximation formulae and their accuracy are discussed. Some criteria are given for a structured population to behave almost like a panmictic population of the same total size. Some quantities are shown to be independent of the geographical structure and their dynamics are described.
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    Bulletin of mathematical biology 45 (1983), S. 11-20 
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    Notes: Abstract This paper is concerned with a generalization of the simple epidemic model in which the infective population is partitioned intom classes, each of specific infectiousness. Attention is restricted, however, to the case where all the meeting rates between two individuals are equal to each other. Both deterministic and stochastic versions are examined. In either case the development in time of the epidemic process is investigated by exploiting a connection with the standard simple epidemic model. Finally, it is shown that the technique used also applies to a similar model for the spread of information.
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    Bulletin of mathematical biology 45 (1983), S. 33-40 
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    Notes: Abstract For each rooted binary tree witht labeled terminal vertices (leaves) a natural number can be assigned uniquely. Unrooted trees witht labeled terminal vertices andt-2 unlabeled internal vertices of degree 3 can also be numbered uniquely using the same convention. Rooted trees in which the hights of the internal vertices are rank ordered are also considered. Applications to problems in taxonomy are discussed.
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    Bulletin of mathematical biology 45 (1983), S. 41-50 
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    Notes: Abstract Expressions and numerical values for hematocrit reduction are calculated as blood flows from a cylindrical feeding tube into a cylindrical capillary at a right-angle branch. Blood is considered to consist of two Newtonian fluids, plasma and red cell suspension, which have equal densities but different viscosities. The concentration profile of the red cells is concluded to depend on the size of the feeding tube. An estimate for the thickness of the plasma layer adjacent to the wall is obtained.
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    Bulletin of mathematical biology 45 (1983), S. 51-67 
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    Notes: Abstract Asimple model system of two self-reproducing objects is considered. A set of equations, similar to Eigen's equation, describing competition of these objects is derived and analyzed under the effect of an ‘ecological constraint’. The relation with other constraints used in the literature is discussed.
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    Bulletin of mathematical biology 45 (1983), S. 69-90 
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    Notes: Abstract A membrane with an arbitrary distribution of fixed charges inside and on its surfaces is considered. A procedure for calculating the local electrostatic potential at an arbitrary point of the system is described and its validity discussed. This procedure is based on the linearization of the 3-dimensional Poisson-Boltzmann equation around an exact 1-dimensional solution.
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    Bulletin of mathematical biology 45 (1983), S. 103-116 
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    Notes: Abstract In this, the first of a series of papers on stochastic and deterministic non-linear allometric growth models, a deterministic model is proposed which generalizes the widely applicable classical linear model of Huxley and Needham. There aren types of producers, each type depositing a product which accumulates monotonically in the environment. Producers interact via a mass action law satisfying an optimality condition. Coefficients may be interpreted as competition between the various producer types in the usual Volterra sense. An ideal coral reef is studied in which then species of coral polyps lay down aragonite calcium carbonate in building the reef framework. This deterministic model predicts that younger reefs are strongly unstable relative to initial species abundance, while older reefs grow in the classical sense of Huxley and Needham, asymptotically, as time goes to infinity.
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    Bulletin of mathematical biology 45 (1983), S. 151-153 
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    Notes: Abstract First-order spatial gradients are reliquished in the Schrödinger-Bloch equation for bacterial chemotaxis if and only if the flux coefficient-motility ratio equals 2, the precise value measured in recent experiments onEscherichia coli attracted by oxygen. Moreover, for δ/μ=2 the Schrödinger-Bloch function Ψ is simply equal to the number of bacteria cells per unit volume divided by the chemoattractant concentration.
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    Bulletin of mathematical biology 45 (1983), S. 169-192 
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    Notes: Abstract A mathematical formulation useful in characterizing the effects of light on the pupal eclosion rhythm of the fruit flyDrosophila pseudoobscura is presented. It is based upon the premise that the underlying pacemaker oscillator behaves in a manner analogous to a customized version of a phase-locked loop circuit. Theoretical analyses supplemented with numerical simulations reveal that this phase-locked loop approach yields a concise mathematical characterization which is quite comprehensive in its scope, yet surprisingly accurate in the detail with which it can be used to successfully predict observed experimental results.
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    Bulletin of mathematical biology 45 (1983), S. 155-168 
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    Notes: Abstract Pointwise upper and lower bounds for the solution of a class of nonlinear problems arising in the steady-state finite cable model of cell membranes are presented. Simple analytical bounding curves are obtained for an illustrative example in the theory of nerve membranes.
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    Bulletin of mathematical biology 45 (1983), S. 209-227 
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    Notes: Abstract Single-species reaction-diffusion models are analyzed to determine the effect of various diffusion mechanisms on species persistence or extinction.
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    Bulletin of mathematical biology 45 (1983), S. 401-408 
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    Notes: Abstract A restriction is imposed on the number of particles that can possibly move at any time from a compartment, so that any other particles present in the compartment must wait until such particles have moved out. The equations for such a system are formulated and the solution is given for a single compartment system; increased variability of the compartmental particle count is one effect of this restriction.
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    Bulletin of mathematical biology 45 (1983), S. 323-345 
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    Notes: Abstract Two classes of dose-effect models for cell killing (additive damage and independent effects) are developed under alternative hypotheses about the damage that leads to cell death. Generalized models, along with specific models for cell killing after exposure to a specific cytotoxicant, are used to make predictions about the effects of sequential or simultaneous exposure to different cytotoxicants. It is demonstrated that with the additive damage models developed one can adequately account for the combined effects of the cytotoxicants considered. Theoretical results are presented which suggest that after simultaneous exposure of cells to low total doses (〈0.1 Gy) of different ionizing radiations, use of the conventional relative biological effectiveness approach to predict cell killing risks is unnecessary; cell killing risks can adequately be determined by assuming the effects of the different radiations to be independent. Also, for simultaneous exposure of cells to total doses of different radiations much larger than 0.1 Gy, use of the conventional RBE approach to arrive at cell killing risk could lead to overestimation of the risk.
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    Bulletin of mathematical biology 45 (1983), S. 347-400 
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    Notes: Abstract A predator which is preying on a model-mimic system can choose either the single-trial strategy or a multi-trial strategy as its behavior in learning to prudently harvest such a prey system. In this learning behavior, an important and often-posed problem is to determine which among these two strategies is better suited for the predator and why one is preferable over the other. We present in this article, using Markov chain methods, an extensive analysis of these strategies (and also of eat-everything, strategy). We conclude that the multi-trial strategy is the one that the predator should adopt (but we will also describe the situations when the single-trial strategy seems to be better). Our conclusions are based on the comparisons of quantities such as the mean benefit to the predator, energy derived by a predator from the model-mimic system and (a newly introduced notion of) contagion in eating mimics and models (these quantities are computed for different strategies). The first two quantities are functions of the abundancep and noxiousnessb of models. The contagion is a function of onlyp; and, though independent ofb, it is also in support of multi-trial, strategy. We introduce, in the present context, a biological analog of the d'Alembert principle and also derive functions describing the influences of eating a specified type of prey at a given time on eating any type of prey at a later time. Various results of Estabrook-Jespersen (single-trial strategy) and Bobisud-Potratz (multi-trial strategy) are re-derived as special cases of our more general results. A central limit theorem under the eat-everything strategy is given.
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    Bulletin of mathematical biology 45 (1983), S. 431-435 
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    Bulletin of mathematical biology 45 (1983), S. 425-430 
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    Notes: Abstract We consider the one-dimension (one-compartment) exponential model using a diffusion process approach. In particular, we summarize the known results in the case where the stochastic component of the model is a Gaussian white noise process with mean zero and variance σ2. Finally, we briefly illustrate a number of cases where similar forms of model arise.
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    Bulletin of mathematical biology 45 (1983), S. 467-482 
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    Notes: Abstract The surfaces of many cells are viscous fluids; consequently, most membrane proteins are able to diffuse laterally, in a more or less random fashion, with diffusion coefficients typically of order 10−10 cm2/sec. If a molecule (ligand) in solution outside the cell and a protein molecule on the surface (receptor) each have two or more sites at which they can interact with one another, large, branched receptor-ligand networks can form on the cell surface by virtue of the chemical interactions that surface fluidity permits. Evidence from a variety of systems indicates that such receptor clustering plays a role in the sequence of events leading to cellular activity. This paper describes a number of mathematical problems that arise in the analysis of experiments in which clustering occurs. I begin by reviewing methods for finding the time evolution of the cluster size distribution function in terms of reaction rate constants. The methods solve an essentially infinite system of coupled nonlinear differential equations. Next, the rate constants are analyzed, the Brownian motion problems that arise in attempting to understand ligand recognition are described and relevant experimental systems are discussed. Finally the notion of ligand as a signal amplifier is introduced—an idea that emerges naturally from the requirement that receptors be clustered for a finite amount of time before a signal can be transmitted.
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    Bulletin of mathematical biology 45 (1983), S. 555-569 
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    Notes: Abstract The covariances among the populations of distinct compartments are studied for the multi-compartmental birthless death-migration-immigration process. The important role played by the transition matrix of the deterministic process is underlined. Several examples are discussed.
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    Bulletin of mathematical biology 45 (1983), S. 483-506 
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    Notes: Abstract Qualitative theory for multidimensional stochastic dynamical models $$\dot x = f(x, \xi )$$ is presented where the random influences ξ may be white or colored, i.e. a (possibly bounded) diffusion process. We concentrate on transience, stationary solutions and boundary behavior and discuss a set-up for reliable simulations. The method consists in associating a deterministic control system where the (approximate) controllability properties determine the qualitative behavior of the stochastic system. Applications to some biological systems indicate the usefulness of qualitative theory in life sciences.
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    Bulletin of mathematical biology 45 (1983), S. 599-603 
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    Notes: Abstract We study some linear stochastic differential equations in Hilbert spaces.
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    Bulletin of mathematical biology 45 (1983), S. 591-597 
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    Notes: Abstract In this article we show how linearity with respect to the output of a stochastic dynamic model can be exploited in order to simplify the computation of moments or conditional moments. The results are presented for two examples, one of which includes delays. This feature is often encountered in biological models.
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    Bulletin of mathematical biology 45 (1983), S. 873-874 
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    Bulletin of mathematical biology 45 (1983), S. 869-872 
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    Notes: Abstract In the derivation of the biomass distribution function for an ecological population critical use is made of an energetic constraint on the maximization of biomass diversity. The nature of this constraint is explored in detail using Kleiber's relation σ(m)=cm γ between animal metabolic rate σ(m) and body weightm in conjuction with the Prigogine-Wiame thermodynamic paradigm for specific entropy production in biological stationary states. These two inputs fix the energetic constraint on the maximization of biomass diversity to be the constancy of the mean metabolic rate of the ecosystem. The resulting biomass distribution function is tested against observational data.
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    Bulletin of mathematical biology 45 (1983), S. 875-875 
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    Bulletin of mathematical biology 45 (1983), S. 901-915 
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    Notes: Abstract A system of mixed integrodifferential and partial differential equations for an agestructured predator-prey system is studied here. The predator eats all ages of prey, but more of the very young and very old than of the intermediate ages. The existence of periodic solutions corresponding to stable coexistence is proved for a suitable range of parameters by bifurcation theory.
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    Bulletin of mathematical biology 45 (1983), S. 877-900 
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    Notes: Abstract In this paper, stability of two-prey, one-predator communities is investigated by Lyapunov's direct method and Hopf's bifurcation theory. Three patterns of three-species coexistence are possible. A globally stable non-negative equilibrium exists for the system even if two competing prey species without a predator cannot coexist. The stable equilibrium bifurcates to a periodic motion with a small amplitude when the predation rate increases. It is also shown that a chaotic motion emerges from the periodic motion when one of two prey has greater competitive abilities than the other. This predator-mediated coexistence can be realized by the intimate relationship between preferences of a predator and competitive abilities of two prey.
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    Bulletin of mathematical biology 45 (1983), S. 917-930 
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    Notes: Abstract A non-linear stability analysis using a multi-scale perturbation procedure is carried out on the practical Thomas reaction-diffusion mechanism which exhibits bifurcation to non-uniform states. The analytical results compare favourably with the numerical solutions. The sequential patterns generated by this model by variations in a parameter related to the reaction-diffusion domain indicate its capacity to represent certain key morphogenetic features required in a recent model by Kauffman for pattern formation in theDrosophila embryo.
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    Bulletin of mathematical biology 45 (1983), S. 1-9 
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    Notes: Abstract The urn model discussed in part is generalized so that the random depletion of balls from the urn in any cycle is not necessarily the same as the reinforcement in that cycle. This model is applied to an urn containing balls of three colors (white, red, black) for which the black balls always receive reinforcements, whereas there is only one cycle in which red balls are added. Experimental data are considered in which red balls correspond to radioactive iodine atoms, black balls to stable iodine atoms and white balls to empty space, all relating to the thyroid gland. Half-life periods for the radioactive iodine in relation to the time of uptake (ten years, fifteen years, etc.) are considered.
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    Bulletin of mathematical biology 45 (1983), S. 21-31 
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    Notes: Abstract Kinetic equations for the action of a reagent on a population which is increasing by Gompertzian growth are solved by a combination of analytical and numerical methods for both dilute distributions and cellular aggregates. For the aggregates an empirical function controlling extent of diffusion is used with external reagent concentration held constant, and the effective diminution of reagent activity caused by aggregation is related to the extent of penetration by diffusion. Diffusion from the centre is considered. Solutions with time-dependent reagent concentration are obtained for a distribution, and the effect of successive inputs of reagent studied.
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    Notes: Abstract Bilayer lipid membranes consist of an inner hydrocarbon tail region with the hydrophilic polar heads on either side. The order-disorder transition in the hydrocarbon tail reigon, from liquid crystalline (fluid) to gel state, is characterised in terms of a Landau-de Gennes description, in which the effect of an external electric field is incorporated through its description, in which the effect of an external electric field is incorporated through its interaction with the surface charges on the bilayer (placed as it is in an ionic medium) or with the polar heads. Biological implications of such a phase transition, for excitable membranes, resides in a model wherein ion channels (taken to be composed of protein bundles) are postulated to be surrounded by lipid molecules in the fluid phase when the membrane is in its resting state, while surface charges and/or the polar heads of the lipid molecules responding to an electric stimulus, if of adequate magnitude, induces a transition in the hydrocarbon tail region of the (boundary) lipid surrounding the ion channels from the liquid crystalline (fluid) to the crystalline (gel) phase which, in turn, through coupling with the relevant modes of the protein bundles, results in the opening of the ion channels, provinding thereby a mechanism for the desired response.
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    Bulletin of mathematical biology 45 (1983), S. 117-138 
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    Notes: Abstract Concepts of the uniqueness of the amino acid sequences of proteins were defined in a prior report (Saroff, H. A. and F. A. Kutyna. 1981. “The Uniqueness of Protein Sequences: A Monte Carlo Analysis.”Bull. math. Biol. 43, 619–639), which presented a detailed discussion ofi-uniqueness, i.e. the tendency of small peptides to be repeated within an amino acid sequence of a protein. We now report on the quantitative analysis ofo-uniqueness, which evaluates the tendency of small peptides to be repeated amongst different proteins, usually of a single species. A detailed analysis of theo-uniqueness of several proteins is presented to illustrate the method and the range of values encountered. Uniqueness data on sequences of human proteins in a data bank of sequences containing about 32,500 amino acids are made available in the form of a microfiche. Analysis of biologically active subsequences such as the angiotensins and the enkephalins suggest a tendency of the subsequences contributing to the property ofo-uniqueness to cluster in portions of the parent protein sequence which are biologically active. This property may provide a general method for predicting biologically active areas of proteins. Current data may already be adequate to permit useful predictions, and the rapidly accumulating and interrelated new data on nucleic acid and protein sequences will further enhance the power ofo-uniqueness analysis.
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    Bulletin of mathematical biology 45 (1983), S. 143-149 
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    Notes: Abstract In this note we examine Eigen's nonlinear rate equations for the relation of coupled biomacromolecules. We obtain an exact solution to the equations for constant overall population densities and constant rate parameters. We conclude that there is only one stationary solution where all molecular species coexist when they are coupled by mutation.
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    Bulletin of mathematical biology 45 (1983), S. 229-237 
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    Notes: Abstract Previously developed light absorption models have treated the effective quantity of light-absorbing material within the experimental environment as a constant, i.e. a parameter. These models are, however, probabilistic in nature and are properly applied and interpreted only in a statistical sense. Thus, it is clearly logical to regard the effective quantity of light-absorbing material to be a random variable. In this paper an asymptotic distribution is derived for this random quantity, and it is shown how this distribution may be incorporated into present models. These results may be applied to light absorption by plant and crop canopies as well as to liquid or solid media. Furthermore, previous models are based upon the assumption that light is parallel, or effectively so, as for solar light. Such models may be inadequate for an artificial (laboratory) environment which utilizes point source light. Present models for estimating light interception and radiation intensity are modified so as to accommodate a proximate point source of light. Numerical examples are included to illustrate the theory.
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    Bulletin of mathematical biology 45 (1983), S. 239-257 
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    Notes: Abstract This paper presents an exact analysis of a mutually coupled relay oscillator based on a method orignated by Tsypkin. Limit-cycle frequencies and phases can be determined exactly using this method, unlike other approximate methods based on describing functions and harmonic balance techniques. A new method of exact determination of limit-cycle stability is also shown to give excellent agreement with simulation studies. Different types of intercoupling are shown to give different stability conditions, and these are discussed in relation to gastrointestinal (GI) smooth muscle modelling. GI tract electrical activity has previously been modelled using bidirectionally coupled nonlinear oscillators, and the results of the present analysis of relay oscillators is compared with other studies using van der Pol dynamics.
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    Bulletin of mathematical biology 45 (1983), S. 269-285 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Information about the way of branching of dendritic arborizations may be obtained by comparing the frequency distributions of observed branching patterns with theoretical distributions based on well-defined growth models. Two models usually get much attention in geomorphological and (neuro)biological studies, viz. terminal growth and segmental growth. Formulae to construct the exact probability distributions for both growth models are presented. It is shown that ranking and lumping of the individual branching patterns enable the analysis of very large arborizations with relatively few data. The application of the Kolmogorov goodness-of-fit test for discrete distributions to the analysis is discussed.
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    Bulletin of mathematical biology 45 (1983), S. 295-309 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An autonomous system of two differential equations with an asymptotically stable steady state is considered. It is shown that there exists a class of time delays which preserves the stability of such a steady state. The charactristic return time (or decay rate) for the solutions to approach the steady state is estimated using the variational system for the perturbations.
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  • 79
    ISSN: 1436-6215
    Keywords: dietary cholesterol ; calves ; serum metabolites ; glucose tolerance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Zusammenfassung Mastkälber (ca. 9 Wochen alt; 3 Tiere pro Gruppe) wurden zweimal pro Tag während einer Periode von 7,5 Wochen mit einem Milchersatzmittel, das 60 % Magermilchpulver und 20 % Fett (Gewichtsprozente auf trockener Stoffbasis) enthielt, gefüttert. Beim Ersatz von 1 % Fett durch Cholesterin in der Diät stieg der Serumcholesteringehalt um 70 %. Sowohl bei den Kontrolltieren als auch bei den cholesteringefütterten Kälbern wurde kein Tagesrhythmus der Serumcholesterinkonzentration beobachtet. Die Serumtriglyceriden waren nach dem Füttern nicht deutlich erhöht, es wurde jedoch bei beiden Diätgruppen während des Tages eine ähnliche, gleichmäßige Erhöhung beobachtet. Cholesterin in der Diät verursachte nach dem Füttern um 8 Uhr eine Senkung der Harnstoffkonzentration im Serum und eine Erhöhung des Aminosäurestickstoffgehaltes. Dies wurde jedoch nach dem Füttern um 20 Uhr nicht beobachtet. Nahrungscholesterin erhöhte signifikant den postprandialen Glukosespiegel in den Mastkälbern. Es wird vorgebracht, daß Hypercholesterinämie eine verminderte Glukosetoleranz verursacht, möglicherweise auch beim Menschen.
    Notes: Summary Veal calves (aged about 9 weeks; three animals per group) were fed twice a day-liquid diets containing 60 % skim milk powder and 20 % crude fat (w/w) for 7.5 weeks. Addition of 1 % cholesterol to the diet, at the expense of fat, caused a 70 % increase in the level of serum cholesterol. Both in the control and cholesterol-fed calves, no diurnal rhythm in the concentration of cholesterol in the serum was observed. Serum triglycerides were not clearly elevated after feeding, but a steady increase during the day was observed, the increase being similar in both dietary groups. Cholesterol feeding seemed to induce lower postprandial levels of urea and higher levels of amino acid nitrogen, but this was only observed after feeding in the morning (8.00 a.m.), but not after feeding in the evening (8.00 p.m.). Dietary cholesterol significantly elevated postprandial glucose levels in veal calves. It is suggested that hypercholesterolemia effects an impaired glucose tolerance, possibly also in man.
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    European journal of nutrition 22 (1983), S. 78-84 
    ISSN: 1436-6215
    Keywords: ADP-ribose ; liver ; nuclei ; NAD ; protein-ADP ribosylation ; riboseprotein bonds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Zusammenfassung Aus der Rattenleber isolierte Zellkerne werden mit NAD⊕ inkubiert, dessen beide Ribosen mit jeweils3H oder14C markiert sind. Enzymatischer (Phosphodiesterase) und/oder chemischer (Hydroxylamin) Abbau markierter ADP-ribosylierter Proteine und Identifizierung der aus Zellkernrückständen freigesetzten Bruchstücke erweist, daß AMP nach Hydroxylaminolyse sowie iso-ADP-Ribose nach Phosphodiesterase und Hydroxylamin — bei Fehlen nachweisbarer Mengen an Ribose-5-phosphat — das Vorkommen zusätzlicher Bindungsformen zwischen Protein und Ribose in in vitro ADP-ribosylierten Zellkern-Proteinen verlangen: Neben C-1″ (Hayaishi u. a., Stocken u. a.) noch C-2′ und/oder C-3′ (Purin-nahe) und weiterhin C-2″ und/oder C-3″ (Pyrimidin-nahe), und dies nicht nur am Kettenende, sondern auch in der Mitte der Kette von Oligo-ADPR.
    Notes: Summary Nuclei isolated from rat liver were incubated with NAD⊕ whose two ribose moieties were respectively labeled with3H or14C. By enzymatic (phosphodiesterase) and/or chemical (hydroxylamine) attack on doubly labeled ADP-ribosylated nuclear proteins and identification of fragments released from nuclear residues, AMP was found after hydroxylaminolysis as well as iso-ADP-ribose after phosphodiesterase plus hydroxylamine, in the absence of detectable amounts of ribose-5-phosphate. This is taken to indicate the existence of additional ribose-protein binding sites in in vitro ADP-ribosylated nuclear proteins: Besides C-1″ (Hayaishi et al., Stocken et al.) C-2′ and/or C-3′ (purine-near) as well as C-2″ and/or C-3″ (pyrimidine-near), not only at the end but also within the chain of oligo-ADPR.
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  • 81
    ISSN: 1436-6215
    Keywords: 13C-Atemtest ; natürlicher Isotopengehalt von Nahrungsmitteln ; 13CO2-Gehalt der Atemluft ; parenterale Ernährung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary The long-term variation of the mean δ13C-value of breath-CO2 of Europeans (base value −26‰) was ±1‰ over a period of several months. However, the ingestion of products from corn, a C4-plant, caused remarkably higher shifts. In a fasted state and during rest a stability of the base value of ±0.3‰ could be attained for several hours. Longer fasting periods imply a shift of the CO2-δ-value due to the metabolism of body products. — By a change of the main energy source to corn products the δ13C-base line could be shifted to −18‰ within one day. After this shift even the metabolism of products from C3-plants could be investigated. The degradation curve and the integral degradation of fats were largely dependent on the method of application, and the base value largely interfered with the results. The period of maximum disintegration for a naturally and uniformly labelled fat was different from that of an artificially labelled trilinoleate. The results shall be used for the adjustment and the correction of the base line in13C-breath tests, especially with patients under parenteral nutrition.
    Notes: Zusammenfassung Der mittlere δ13C-Wert im CO2 der Atemluft von Europäern (Basiswert −26‰) zeigt eine Langzeitschwankung über mehrere Monate von ±1,0‰; der Verzehr von Produkten aus C4-Pflanzen (z. B. Mais) hat allerdings erheblich höhere Änderungen zur Folge. Im Nüchternzustand und in Ruhe wird während 6 h eine Stabilität des Basiswertes von ±0,3‰ erreicht; nach längeren Nüchternphasen kann aber der Abbau körpereigener Substanzen zu Verschiebungen führen. Durch Umstellung der Energieversorgung auf Maisprodukte ist es möglich, den Basiswert innerhalb eines Tages auf −18‰ zu heben; dann läßt sich auch der Abbau von Substanzen aus C3-Pflanzen verfolgen. Der Verlauf und die Rate des Abbaues von markierten Fetten sind stark von der Art der Applikation abhängig, und die Messung des Gesamtumsatzes wird durch den Untergrund stark beeinträchtigt. Der Zeitpunkt des maximalen Abbaues von uniform markiertem Fett (Sojaöl) unterschied sich von dem eines in der Carboxylgruppe markierten Trilinoleats. Die Resultate sind Grundlage zur Einstellung bzw. Korrektur von Basiswerten bei13C-Atemtests, besonders bei Patienten mit parenteraler Ernährung.
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    European journal of nutrition 22 (1983), S. 116-123 
    ISSN: 1436-6215
    Keywords: Zn deficiency ; 3′,5′-cyclo AMP content ; energy metabolism
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary Loss of appetite, strongly reduced feed intake, and stop in weight gain are characteristic signs of alimentary zinc deficiency. The present paper investigates some parameters of the energy metabolism of Zn-deficient rats in order to obtain information on possible disturbances. The blood of Zn-deficient rats showed an increased activity of adenosine triphosphatase (ATPase) in comparison to ad-libitum- and pair-fed control animals. Therefore the concentration of adenosine triphosphate (ATP) was reduced and the concentration of adenosine diphosphate (ADP) increased in deficient animals. As a consequence, the ratio ATP/ADP was strongly reduced in Zn-deficient rats compared with both control groups. The concentration of adenosine monophosphate (AMP) was reduced in the blood of Zn-deficient rats. The levels of c-AMP in serum and urine were markedly increased in Zn-deficient rats in comparison with both control groups. Key enzymes of energetic utilization of carbohydrates such as fructose-1,6-biphosphatase and glucose-6-phosphate dehydrogenase were reduced in their activities in livers and kidneys of Zn-deficient animals. The results show that alimentary Zn deficiency impairs some parameters of the energy metabolism. The problems of reduced feed intake in Zn deficiency still remain unsolved.
    Notes: Zusammenfassung Appetitlosigkeit, stark reduzierte Futteraufnahme und Wachstumsstopp sind charakteristische Zeichen eines alimentären Zn-Mangels. Um Hinweise zu erhalten, inwieweit hierbei Störungen im Energiestoffwechsel auftreten, wurden in der vorliegenden Arbeit bei Zn-Mangel-Ratten einige Parameter des Energiestoffwechsels untersucht. Im Blut der Zn-Mangel-Ratten zeigte sich gegenüber den Ad-libitum- als auch Pair-fed-Kontrolltieren eine erhöhte Aktivität der Adenosintriphosphatase (ATPase). Die Konzentration an Adenosintriphosphat (ATP) war deshalb bei den Mangeltieren reduziert und die Konzentration an Adenosindiphosphat (ADP) erhöht. Infolgedessen war das Verhältnis von ATP/ADP bei den Zn-Mangel-Ratten im Vergleich zu beiden Kontrollgruppen stark reduziert. Auch die Konzentration an Adenosinmonophosphat (AMP) war im Blut der Zn-Mangel-Ratten erniedrigt. Die Gehalte an 3′,5′-cyclo-AMP waren bei den Zn-Mangel-Ratten gegenüber beiden Kontrollgruppen in Serum und Urin stark erhöht. Schlüsselenzyme zur energetischen Verwertung der Kohlenhydrate, wie die Fructose-1,6-Diphosphatase und die Glucose-6-phosphat-Dehydrogenase, waren in ihrer Aktivität bei den Zn-Mangel-Tieren sowohl in der Leber als auch in der Niere reduziert. Die Ergebnisse zeigen, daß alimentärer Zn-Mangel einige Parameter des Energiestoffwechsels beeinträchtigt, wobei das Problem der reduzierten Futteraufnahme bei Zn-Mangel nach wie vor ungelöst bleibt.
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    European journal of nutrition 22 (1983), S. 169-184 
    ISSN: 1436-6215
    Keywords: Fetternährung ; Aminosäurekonzentrationen im Blut ; 3-Methylhistidinausscheidung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary Earlier studies in man could demonstrate that intravenous lipids decreased the concentration of amino acids in plasma (to 50%). In short- and long-term experiments in rat the effect of orally applied olive-oil on the concentration of amino acids in blood, on the excretion of 3-methylhistidin and of total nitrogen into urine was measured. Two control groups were used: rats with total restriction of food and rats which were fed ad libitum. 2 ml olive-oil given to rats within 12 hours decreased the concentration of alanine, valine, leucine, isoleucine. Whereas food restriction increased the excretion of 3-methylhistidin into urine and the blood concentration of leucine, isoleucine, valine, tyrosine, phenylalanine, threonine, and glutamine, the oil-fed rats showed no increase of amino acid levels in plasma and no increase of 3-methylhistidine excretion into urine. These experiments suggest that lipid application inhibits proteolysis in muscle, and thus diminishes the amino acid levels in blood.
    Notes: Zusammenfassung Der Einfloß von Fetternährung auf das Verhalten der Plasmaaminosäurekonzentrationen sollte bei Ratten geprüft werden. In vorausgegangenen Untersuchungen am Menschen war beobachtet worden, daß nach Lipidinfusionen die Konzentration der Aminosäuren im Plasma bis zu 50% vermindert war. In Kurz- und Langzeitversuchen wurde der Einfluß von Olivenöl auf die Konzentrationen der Aminosäuren im Plasma, auf die Ausscheidung von 3-Methylhistidin und von Gesamtstickstoff im Harn gemessen. Als Kontrollgruppen dienten hungernde Ratten und ad libitum ernährte Versuchstiere. In Kurzzeitversuchen konnte gezeigt werden, daß 2 ml Olivenöl über 12 Stunden einen kontinuierlichen Konzentrationsabfall von Alanin, Valin, Leucin, Isoleucin bewirkte. In mehrtägigen Versuchen stieg bei den Hungertieren die 3-Methylhistidin-Ausscheidung an, und im Blut werden die Konzentrationen von Leucin, Isoleucin, Valin, Tyrosin, Phenylalanin, Treonin, Glutamin erhöht. In den ölernährten Ratten blieb der Anstieg der Aminosäuren im Plasma aus. Da auch die 3-Methylhistidin-Ausscheidung während der Ölernährung unvermindert niedrig blieb, wird aus den Versuchen auf eine Hemmung der Proteolyse durch die Fetternährung geschlossen. Die Ursache der verminderten Aminosäurespiegel im Blut ist somit auf eine verminderte Bereitstellung von Aminosäuren in der Muskulatur zurückzuführen.
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    European journal of nutrition 22 (1983), S. 147-156 
    ISSN: 1436-6215
    Keywords: cholesterol ; β-carotene ; coronary heart disease ; fibre ; non-cardiovascular disease
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Zusammenfassung Um das mit Lipoprotein verbundene Risiko von koronarer Herzerkrankung zu vermindern, sind Ernährungsempfehlungen für Populationen mit Empfänglichkeit für Atherosklerose und seine Komplikationen dargelegt worden. Da solche Empfehlungen möglicherweise weitverbreitet anzuwenden sind, müssen diese gründlich untersucht werden, um sowohl Risiken als auch Vorteile zu bestimmen. Die vorliegende Arbeit bespricht epidemiologische, klinische und experimentelle Daten über Beziehungen zwischen diesen Nährstoffen und nichtkardiovaskulären Erkrankungen, mit Nachdruck auf Krebsmortalität. Veränderungen der Aufnahme von Fett (polyungesättigtes Fett mit eingeschlossen), Cholesterol, Kohlenhydraten, Natrium und β-Carotin werden diskutiert, und Beweise für eine Beziehung zwischen Serumcholesterol-Konzentration und Krebs werden geprüft. Es wird beschlossen, daß die jüngsten Ernährungsempfehlungen zur Verminderung von koronarer Herzerkrankung leidlich zuverlässig sind.
    Notes: Summary In order to reduce the lipoprotein-related risk of coronary heart disease, nutritional recommendations have been formulated for use by communities prone to atherosclerosis and its complications. As such recommendations are potentially of widespread application they require careful scrutiny to assess possible risks as well as benefits. Epidemiological, clinical and experimental data concerning relationships between these nutrients and non-cardiovascular diseases are reviewed with emphasis on cancer mortality. Changes in intake of fats, including polyunsaturated fat, of cholesterol, carbohydrate, fibre, sodium and β-carotene are discussed, and evidence of a relationship between serum cholesterol concentration and cancer is examined. These considerations offer reasonable reassurance as to the safety of recent dietary recommendations for the reduction of coronary heart disease.
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    European journal of nutrition 22 (1983), S. 213-218 
    ISSN: 1436-6215
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
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    European journal of nutrition 22 (1983), S. 205-212 
    ISSN: 1436-6215
    Keywords: Schwermetallwirkung ; Malatdehydrogenase ; Glutamatdehydrogenase ; Glycerinaldehyd-3-phosphatdehydrogenase ; Saccharomyces cerevisiae
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary The difference between cadmium, zinc, lead, and mercury in regard of their effects on the activity of the enzymes tested is very slight. Concentrations higher than 10−5 M reduce significantly the activity of the enzymes, and concentrations of approximately 10−3 M inhibit it completely. An increase of the activity cannot be detected. The addition of combinations of cadmium, zinc, and lead results in a summing up of the toxic effects, whereas the interaction between mercury and the other three heavy metals shows a cumulative effect, which is appointed nearly completely by the heavy metal more toxic. The findings suggest that under in-vitro conditions there exists a direct interaction between the heavy metals and the enzymes.
    Notes: Zusammenfassung Die vier Schwermetalle Cadmium, Zink, Blei und Quecksilber unterscheiden sich in ihrer Wirkung auf die Aktivität der untersuchten Enzyme nur sehr wenig. Konzentrationen über 10−5 M vermindern die Enzymaktivität signifikant, und Konzentrationen von etwa 10−3 M unterbinden sie völlig. Eine Steigerung der Enzymaktivität läßt sich nicht feststellen. Die Zugabe von Cadmium-, Zink- und Bleikombinationen führt zu einer Addition der toxischen Effekte, während bei der Interaktion zwischen Quecksilber und den anderen drei Schwermetallen die Gesamtwirkung fast ausschließlich durch das stärker hemmende Schwermetall allein bestimmt wird. Die erhaltenen Ergebnisse lassen vermuten, daß es unter Invitro-Bedingungen zu einer direkten Wechselwirkung zwischen den Schwermetallen und den Enzymen kommt.
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    European journal of nutrition 22 (1983), S. 219-233 
    ISSN: 1436-6215
    Keywords: Ostersche Hypothese ; Xanthinoxidase ; homogenisierte Kuhmilch ; Arteriosklerose
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary Oster has postulated that the enzyme xanthinoxidase in homogenized cow's milk is the cause of myocardial infarction and angina pectoris. This enzyme may be absorbed by ingestion, especially of the small particles of the fat globules, and then carried by lymph streams to the arterial vascular system, where it is deposited into the myocardium. Then it destroys the aldehydes liberated from the cell membrane-based plasmalogens. This results in the intimal damage to the cell membranes of the arterial intima and the myocardium and ultimately in the development of typical atherosclerotic lesions in the arteries. The presented review is a critical approach to this hypothesis. The following factors are discussed: the influence of conditions prevailing in the intestine and the stomach on the activity of the xanthinoxidase in milk, the possibility of this enzyme being absorbed in the intestine, the formation of antibodies against absorbed xanthinoxidase and the behaviour of xanthinoxidase administered intravenously. Compared with present knowledge, this theory gives little evidence only.
    Notes: Zusammenfassung Der amerikanische Arzt Oster hat das Enzym Xanthinoxidase in der homogenisierten Kuhmilch beschuldigt, für das Entstehen der Arteriosklerose und von koronaren Herzkrankheiten verantwortlich zu sein. Dieses Enzym soll durch den Verzehr der zerkleinerten Fettkügelchen im Magen-Darm-Kanal absorbiert und über die Lymphe zum Herzen transportiert werden, wo es abgelagert werde. Dort zerstöre es die aus den Plasmalogenen stammenden Aldehyde. Dadurch würde die Zellmembran geschädigt, und es würden sich schlußendlich typische arteriosklerotische Läsionen in den Arterien entwickeln. In diesem Übersichtsartikel wird zu dieser Hypothese kritisch Stellung genommen. Es werden dabei diskutiert: der Einfluß der Verhältnisse im Magen und Darm auf die Xanthinoxidase-Aktivität der Milch, die Möglichkeit einer Absorption dieses Enzyms im Darm, die Antikörperbildung gegenüber absorbierter Xanthinoxidase und das Verhalten von intravenös verabreichtem Enzym. Aufgrund der heutigen Kenntnisse ist die Beweiskraft dieser Hypothese als gering anzusehen.
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  • 88
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    OR spectrum 5 (1983), S. 1-13 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Das Ellipsoidverfahren ist das erste bekannte Verfahren, das lineare und konvexe Optimierungsprobleme im Sinne der Komplexitätstheorie effizient löst. Mithilfe eines einfachen Rechnermodells führen wir kurz einige zum Verständnis notwendige Begriffe der Komplexitätstheorie ein und geben anschließend einen Überblick über die algorithmischen Vorläufer, die zur Entwicklung des Ellipsoidverfahrens geführt haben. Wir beschreiben die grundlegende geometrische Idee sowie eine Basisversion des Verfahrens, für die wir den Nachweis führen, daß sie lineare Programme im komplexitätstheoretischen Sinne effizient löst. Wir diskutieren einige Modifikationen der Basisversion und skizzieren die algorithmische Äquivalenz von Optimierung und Separation, die auf der Ellipsoidmethode beruht. Anhand eines Beispiels erläutern wir, wie diese Äquivalenz zu einem einheitlichen Modell effizienter Methoden geführt hat, das es erlaubte, weitere, effizient lösbare Probleme zu entdecken.
    Notes: Summary The ellipsoid method is the first known algorithm which in the sense of computational complexity solves linear and convex programming problems efficiently. Based on a simple computational model we introduce some notions from complexity theory and survey the historical antecessors which led to the development of the ellipsoid method. We discribe the fundamental geometric idea as well as a basic version of the algorithm and prove that this basic version gives an efficient algorithm for linear programming problems. We discuss some modifications of the basic method and outline the algorithmic equivalence of optimization and separation which is a consequence of the ellipsoid algorithm. By means of an example we show how this equivalence has led to a unifying framework for efficient algorithms which allowed to discover further efficiently solvable problems.
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    OR spectrum 5 (1983), S. 25-32 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Wir betrachten ein Parallelsystem ausn identischen fehleranfälligen Komponenten. Ausgefallene Komponenten werden in einem Reparaturkanal repariert. Unter der Annahme, daß die Lebensdauern exponentialverteilt sind und die Reparaturdauern eine Verteilung vom Phasentyp besitzen, zeigen wir: Die Verteilung der Beschäftigungsperiode im Reparaturkanal, der Anzahl der während der Beschäftigungsperiode reparierten Komponenten und der stationären Ausfallzeit des Systems sind ebenfalls vom Phasentyp. Wir geben eine auch algorithmisch brauchbare Analyse des stationären Verhaltens Modells und berichten über einige numerische Ergebnisse.
    Notes: Summary We consider a parallel system consisting ofn identical components subject to failures. Failed components are repaired by a single repairman. Under the assumptions that the failure times are exponential and the repair times are of phase type, it is shown that the busy period of the repairman, the density of the number of components repaired during a busy period and the stationary down time of the system are also of phase type. Some numerical examples and an algorithmically tractable steady state analysis of the model are presented.
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    OR spectrum 5 (1983), S. 59-59 
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    Topics: Mathematics , Economics
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    OR spectrum 5 (1983), S. 33-43 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In diesem Beitrag werden zwei grundsätzlich verschiedene Vorgehensweisen zur Bestimmung optimaler Losgrößen für mehrstufige, mehrperiodige Produktionssysteme mit Fließbandstruktur untersucht. Bei der ersten Lösungsmethodik werden zunächst Losgrößen für die erste Produktionsstufe ermittelt, die dann bei der Bestimmung der Losgröße für die nächste Stufe berücksichtigt werden. Bei der zweiten Vorgehensweise werden zuerst die Losgrößen füralle Produktionsstufen der ersten Periode berechnet, dann die Losgrößen füralle Produktionsstufen der zweiten Periode etc. Diese zweite Vorgehensweise besitzt den Vorteil, daß bei ihr die Kosten- und Produktionsstruktur des Systems gleichzeitig berücksichtigt werden. Der Vergleich erfolgt mit Hilfe einer großen Zahl von Simulationsexperimenten.
    Notes: Summary This paper focuses on heuristic procedures for multi-stage assembly systems. Level-by-Level and Period-by-Period approaches are compared based on a large set of simulation experiments. The Period-by-Period approach we propose is of practical importance because the method considers the cost structure and the product structure of the system simultaneously.
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  • 93
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    Topics: Mathematics , Economics
    Description / Table of Contents: Summary Various methods of estimating the road distances between cities are known by literature. In application to the Federal Republic of Germany, they all do not satisfy the user. Therefore a new model is suggested in this paper. Compared with the traditional method, which inflates the straight-line distance between two cities by a constant factor, the new approach gives much better mileage estimates.
    Notes: Zusammenfassung Für das Schätzen von realen Straßenentfernungen sind in der Literatur verschiedene Verfahren vorgestellt worden, die aber — bezogen auf die Bundesrepublik Deutschland — keine befriedigenden Ergebnisse zeigen. Im vorliegenden Beitrag wird daher zur Entfernungsschätzung das Konzept der gebietspaarspezifischen Umwegfaktoren entwickelt. Das neue Verfahren ist unmittelbar anwendbar und bringt gegenüber dem gebräuchlichen Arbeiten mit einem konstanten Umwegfaktor um 25% bzw. 40% genauere Schätzungen der realen Entfernungen.
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    OR spectrum 5 (1983), S. 87-90 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird ein Algorithmus zur Ermittlung nächstbester Wege in zyklenfreien Netzen dargestellt. Das Verfahren beginnt mit der Bestimmung eines kürzesten Baumes, der auf eine Kandidatenliste gesetzt wird. Mit jedem Schritt wird ein Baum von der Kandidatenliste entfernt, dessen zugehöriger Weg zwischen Netzanfang und -ende minimal ist. Anschließend werden jeweils benachbarte Bäume des soeben entfernten Baumes erzeugt und derart in die Liste aufgenommen, daß Wiederholungen ausgeschlossen sind. Diese Vorgehensweise wiederholt sich, bis alle gewünschten Wege ermittelt sind. Auch die Komplexität des Verfahrens wird untersucht.
    Notes: Summary In this paper an algorithm for ranking paths in acyclic networks is presented. The algorithm is initialized with the determination of the shortest tree, which is placed in a candidateList. At each step the tree for which is minimal the distance of the path between two specified nodes is removed fromList. Some adjacent trees of the removed one are generated and placed inList in such a way that repetitions are avoided. This method is repeated until the desired paths have been determined. The computational complexity of the algorithm is studied too.
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    OR spectrum 5 (1983), S. 104-104 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
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    OR spectrum 5 (1983), S. 105-118 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary In this paper maintenance models are surveyed. Stochastic models are emphasized which involve maintenance actions as preventive renewals, inspections and supply with standby and repair units. The focus is on work describing the optimal policy for a given cost structure.
    Notes: Zusammenfassung Dieser Artikel gibt einen Überblick über Instandhaltungsmodelle. Es werden überwiegend stochastische Modelle betrachtet, die den Einsatz von Instandhaltungsaktionen wie vorbeugende Erneuerungen, Inspektionen und Bereitstellung von Ersatzelementen und Reparatureinheiten beschreiben. Der Schwerpunkt liegt auf Arbeiten, welche die optimale Strategie bei gegebener Kostenstruktur angeben.
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    OR spectrum 5 (1983), S. 123-123 
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    Topics: Mathematics , Economics
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  • 98
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    OR spectrum 5 (1983), S. 129-148 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
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    OR spectrum 5 (1983), S. 174-174 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
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    OR spectrum 5 (1983), S. 193-193 
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
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