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  • 1
    Digitale Medien
    Digitale Medien
    Bimolecular systems: I. Linear systems of complexes (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 1-16 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A vast number of biologically important processes are based upon bimolecular systems. In these systems intermediate complexes are formed. Bimolecular systems in which no complex-complex interactions occur are called linear systems of complexes. A definition and some characteristic properties of these systems are given here. There may exist a contradiction of Onsager's principle of detailed balancing in these systems; however, no principal differences are found between the steady state behavior of an open system and that of a closed system. It is shown that the steady state behavior of a linear system of complexes of arbitrary complexity has some similarities with the steady state behavior of a simple bimolecular system, e.g., Michaelis-Menten enzymatic reaction. Multiplicity of action of the substances participating in biomolecular processes may produce some qualitative differences in the steady state behavior of the system.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476958
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  • 2
    Digitale Medien
    Digitale Medien
    DNA histograms of irradiated cells: The case of prophase-trapping (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 17-32 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A time-dependent DNA histogram is calculated for an irradiated population of cells under the limiting assumption that the cells cannot pass through prophase due to the effects of the radiation. The population is assumed to increase exponentially prior to irradiation, but after irradiation to neither gain nor lose cells. Chromosome-number dispersion is taken into account in the calculation. The qualitative behavior of the calculated and experimental histograms are in reasonable agreement. The quantitative agreement between the two is relatively good at short post-irradiation times but is poor at long post-irradiation times (say, greater than half the doubling time). This suggests that recovery phenomena cannot be neglected at long post-irradiation times.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476959
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  • 3
    Digitale Medien
    Digitale Medien
    A note on the mathematical biology of automobile driving (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 187-188 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is pointed out that the three different stimuli for a corrective turn, namely the distance from the edge of the lane, the rate of approach to the edge, and the angle between the direction of the car and the direction of the lane (Bull. Math. Biophysics,28, 645–654, 1966,29, 181–186, 1967) may act all three simultaneously. It is found that in that case the tracking curve of the car is stable below a critical speed and becomes unstable above it.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476971
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  • 4
    Digitale Medien
    Digitale Medien
    Mathematical biology of automobile driving (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 181-186 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Continuing a previous study (Bull. Math. Biophysics, 28, 645–654, 1966), the biophysical mechanism of a corrective turn is investigated for the case where the stimulus for the corrective turn is produced not only by the perception of the nearness of an edge of the lane, but also by the rate of approach of the car towards the edge. In that case it is found that the tracking curve of the car may consist of a series of damped sinusoids and safe driving would be possible at any speed if it were not for the endogenous fluctuation in the driver's central nervous system. If the effect of the rate of approach increases sufficiently rapidly as the distance to the edge of the lane decreases, then a stable undamped oscillating tracking curve is possible. The case is also studied where the driver makes a corrective turn in response to a direct perception of the angle between the direction of the lane and the longitudinal axis of the car.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476970
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  • 5
    Digitale Medien
    Digitale Medien
    Angles of branching and diameters of branches in the human bronchial tree (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 245-259 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The principle of minimal work requires that the conducting airways of the human lung should have a maximum radius for minimal resistance to gas flow. At the same time there is a requirement that the airways should have a minimal volume for economy of space. These two opposing requirements have been investigated mathematically, and a method for calculating the angle of branching which produces minimal volume has been derived. The relationship of the radii of the parent and daughter branches to produce minimal resistance has been similarly defined. By measurement of a bronchial cast from a human lung the extent to which the predicted optimum structure is realized in practice has been shown. The change in structure associated with change of function at the transition from conducting airway to diffusion zone has been demonstrated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476898
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  • 6
    Digitale Medien
    Digitale Medien
    Finite linnaean structures (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 191-206 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper considers a class of set-theoretical entities, calledn-rank Linnaean structures, which are intended as abstract models of the taxonomic classificatory systems of biology. In the first part, devoted to formalism, finite Linnaean structures are discussed in complete generality; but, in addition, eight distinct subclasses are noted and some of the properties of their elements are explored. In the second part, concerned with applications, it is shown that taxonomic systems may be recast in the form of finite Linnaean structures, and an effort is made to show that some undesirable features of earlier models are avoided without artificiality and without abandoning extensional mathematics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476893
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  • 7
    Digitale Medien
    Digitale Medien
    Abstract power structures (APS) and related bumping orders (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 207-216 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Generalizing an idea of M. Richardson (Fundamentals of Mathematics, New York: Macmillan Co., 1958), an APS on a given populationP is a non-empty collection of non-empty subsets ofP such that ifA is in the collection andA⊆B, thenB is in the collection. From a structure of this kind a partial ordering ofP, called therelated bumping order, is derived. The question is raised as to what kinds of partial orderings can be so obtained. For structures determined by voting weights of the members of the population, a complete characterization of all possible bumping orders is obtained.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476894
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  • 8
    Digitale Medien
    Digitale Medien
    Stability analysis of a mathematical neuron model (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 217-226 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The “second method” of Liapunov is used to perform a stability analysis of a mathematical model of the neuron. This analysis is based on the hypothesis that the firing of the neuron coincides with a temporary state of instability of the system, and that the initiation of all-or-none process depends on the magnitude of membrane depolarization and its first time derivative. It is found that the stability (and hence the possibility of a second firing) is restored approximately when the rate of membrane repolarization is at a maximum. This result predicts that the duration of the period of absolute refractoriness in neurons would be about 75 per cent of the spike duration, and thus shorter than the value usually obtained from experimental measurements.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476895
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  • 9
    Digitale Medien
    Digitale Medien
    A neural net model for masking phenomena (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 227-232 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Some aspects of masking phenomena are considered in terms of the simplest possible model of two-factor neural elements. The effect of a number of variables can be accounted for, but the introduction of an internuncial element results in a masking function which need not be symmetric about zero delay interval. As an illustration, the results for a special case are compared with available data. In general, such a model results in a masking function which depends on the intensity, area, and duration of the stimuli, as well as on the temporal and spatial separation between them.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476896
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  • 10
    Digitale Medien
    Digitale Medien
    The struggle for life: I. Two species (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 377-388 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The general equations are discussed describing two species in competition or in symbiosis or feeding one on the other.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476909
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  • 11
    Digitale Medien
    Digitale Medien
    A note on Rashevsky’s postulate of relational forces (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 403-404 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476912
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  • 12
    Digitale Medien
    Digitale Medien
    Organismic sets and biological epimorphism (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 389-393 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is shown that the principle of biological epimorphism (Rashevsky,Mathematical Principles in Biology and Their Applications, Springfield, Ill.: Charles Thomas, 1960) is contained in the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967) if an additional postulate not directly connected to mappings is made.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476910
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  • 13
    Digitale Medien
    Digitale Medien
    Out-of-print volumes and back issues of the Bulletin of Mathematical Biophysics (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 407-407 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476914
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  • 14
    Digitale Medien
    Digitale Medien
    Model of urethra under uniform circumferential tension (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 409-409 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476915
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  • 15
    Digitale Medien
    Digitale Medien
    Multibreath tracer species dynamics in the lung (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 1-19 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460935
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  • 16
    Digitale Medien
    Digitale Medien
    Global stability of population models (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 47-58 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460938
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  • 17
    Digitale Medien
    Digitale Medien
    The logistic equation with a diffusionally coupled delay (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 125-140 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Layapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopf's bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459438
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  • 18
    Digitale Medien
    Digitale Medien
    Uncertainty in physiology and physics (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 141-149 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It was hypothesized in an earlier work that sensory perception can occur only when the perceiving system is uncertain about the nature of the event being perceived. In the absence of any uncertainty, perception will not take place. The response of the sensory afferent neuron (impulse transmission rate) was calculated using Shannon's measure of uncertainty or entropy. It will now be shown that when the event being perceived is the position and momentum of a particle, Shannon's measure of uncertainty leads to the Heisenberg Uncertainty relationship.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459439
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  • 19
    Digitale Medien
    Digitale Medien
    Bimolecular systems: II. Nonlinear systems of complexes (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 605-613 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper deals with bimolecular systems in which also complex-complex interactions occur. Because of the complexity of the problem, an approximation in a form of coupled linear systems of complexes (Bull. Math. Biophysics,29, 1–16, 1967) is considered. Two types of couplings, serial and parallel, are studied. In the serial coupling the nonlinear system of complexes has the same behavior as its subsystems. An entity, initial sensitivity, has interesting properties: in serial coupling it is at most equal to the product and in parallel coupling, at most equal to the sum of partial initial sensitivities.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476597
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  • 20
    Digitale Medien
    Digitale Medien
    Bimolecular systems: III. Catalytic systems (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 615-623 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Amplification effect in the catalytic bimolecular systems is a consequence of the kinetic characteristic of the catalyst. Two types of the coefficient of amplification are defined. The applicability of these definitions is given by the type of the bimolecular system. In a simple example it is shown that the concept of amplification is meaningful in these systems. Furthermore, two rules, analogous to those for a coupling of amplifiers, are derived for the two basic modes of coupling of catalytic systems. Thus, in biological systems the catalytic reactions may be regarded as biologically effective amplifiers.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476598
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  • 21
    Digitale Medien
    Digitale Medien
    A theory of cell hydration governed by adsorption of water on cell proteins rather than by osmotic pressure (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 583-596 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is postulated that cell hydration is governed by adsorption of water on cell proteins in accord with the Bradley adsorption isotherm, and that the action of a solute in the surrounding solution is to lower the vapor pressure of the solution so that cell water adsorption is decreased by moving down the Bradley isotherm. From these concepts, it is derived that cell volume (V) should be related to solute concentration (x) by the equationV=−E log10 x+F whereE andF are constants which are independent of type of solute. For a non-adsorbed solute this agrees well with experimental data. For solutes which are adsorbed by cell proteins, a correction in the above equation may be necessary at higher solute concentrations, which is shown to be compatible with various experimental data. The types of experiments which are generally used to support the osmotic pressure theory of cell hydration agree equally well with the adsorption theory. The virtue of the adsorption theory is that, unlike the osmotic pressure theory of cell swelling, it is compatible with permeability of the cell membrane to solutes, which has been experimentally observed for various solutes.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476595
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  • 22
    Digitale Medien
    Digitale Medien
    Consensusn-trees (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 239-244 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is not unusual for several classifications to be given for the same collection of objects. We present a method, called majority rule, which can be used to define a consensus of these classifications. We also discuss some mathematical properties of this consensus tree.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459446
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  • 23
    Digitale Medien
    Digitale Medien
    Morphogen pattern formation and development in growth (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 259-270 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The dependence of the spatial concentration profiles of morphogens on a characteristic dimension is obtained by continuation techniques for Gierer and Meinhardt's activator-inhibitor model of morphogenesis. The study of the behaviour of the system during growth, where the linear and exponential increase of the characteristic dimension is considered, revealed that more complex patterns of morphogen spatial concentrations appear regularly in a reproducible way.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462200
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  • 24
    Digitale Medien
    Digitale Medien
    Simulation experiments with a model for cellular growth (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 271-278 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Computer models have been used by various authors to simulate both the growth of normal cellular tissue and the development of cancerous cells within normal tissue. As these models were the result of considerable idealization, the purpose of the present paper is to propose a model in which the degree of simplification is relaxed: the features of simultaneous growth, and cell growth whose rate depends on the free absorbing periphery of the cell are introduced. Simulation experiments have been conducted using the model, and the results are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462201
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  • 25
    Digitale Medien
    Digitale Medien
    Complementary extremum principles for a nonlinear model of heat conduction in the human head (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 341-346 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for a nonlinear model of heat conduction in the human head. Accurate variational solutions are obtained in illustrative calculations. The effect of nonlinearity is seen to be significant from a comparison with the linearized model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462204
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  • 26
    Digitale Medien
    Digitale Medien
    On Zeeman's equations for the nerve impulse (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 279-325 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462202
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  • 27
    Digitale Medien
    Digitale Medien
    Considerations of quasi-stationarity in electrophysiological systems (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 657-664 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Conditions under which a time varying electromagnetic field problem (such as arises in electrophysiology, electrocardiography, etc.) can be reduced to the conventional quasistatic problem are summarized. These conditions are discussed for typical physiological parameters.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476917
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  • 28
    Digitale Medien
    Digitale Medien
    The dead space in a compartmental lung model (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 711-718 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A compartmental lung model with any number of synchronously filling and emptying functional chambers and a common dead space or conducting region is considered. It is shown that the model gives rise to an output, in an open circuit washout determination, which is a weighted sum of exponentials. From estimates of these weights and exponential components, estimates of the model parameters can be recovered. Relations giving the unique correspondence between the output parameters and the model parameters are derived and the existence and uniqueness of solutions established.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476922
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  • 29
    Digitale Medien
    Digitale Medien
    A charge transfer process in the visual pigments (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 677-690 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A physical model that incorporates all the experimental information on the formation of the visual pigment rhodopsin is presented. The visual pigments consist of a chromophore bound to an appropriate protein. Thus rhodopsin (λm 505 mμ) is formed by a Schiff’s base linkage C19H27CH=NH+-opsin (λm 440 mμ) between 11-cis retinal (λm 380 mμ) and the protein opsin (λm 280 mμ). It is found that there exists a red shift in the spectrum of rhodopsin from the Schiff’s base. The model brings an explanation for this red shift. It is shown that such a shift may be due to a charge transfer process (R. S. Mulliken,J. Am. Chem. Soc.,74, 811–824, 1952) between an electron at the double bond of carbons C11−C12 and an atomic orbital of the sulphur present in cysteine. This provides an explanation of the presence of SH-groups in the protein after the absorption of light. A one-electron approximation is used and the dipole momentμ NV ; hence, the oscillator strengthf of the transitionNV is estimated and compared with the experimentally determined extinction coefficient ∈m by mixing 3.5×10−3 M of 11-cis retinal with 8.3×10−5 M of cysteine at pH ranges 6 through 8. Reasonable agreement is found. Solvent, concentration and temperature dependence are shown also.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476919
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  • 30
    Digitale Medien
    Digitale Medien
    Asymptotic analysis of the Michaelis-Menten reaction equations (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 375-388 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The irreversible Michaelis-Menten reaction is studied by the use of the method of multiple scales. Three stages of the reaction are identified, one of which is studied in detail. The results are compared with those of two earlier analyses.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459428
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  • 31
    Digitale Medien
    Digitale Medien
    Pulse evolution on coupled nerve fibres (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 389-400 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A numerical study of the coupled nerve fibre problem is given which verifies and extends the perturbation theory of Luzader. Pulses on adjacent fibres can couple together with two possible stable pulse separations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459429
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  • 32
    Digitale Medien
    Digitale Medien
    Field-induced forces at dielectric interfaces as a possible mechanism of RF hearing effects (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 401-413 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A possible mechanism for effects of microwave radiation on the auditory system is the generation of field-induced forces at interfaces that divide materials of dissimilar electrical properties. A general expression for these “Maxwell stresses” is derived and then used to calculate the approximate magnitude of field-induced force within the organ of Corti during microwave exposure. Comparison of the results with data on the force needed to excite cochlear hair cells indicates auditory responses could be evoked by this mechanism at power densities near the threshold of rf hearing sensations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459430
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  • 33
    Digitale Medien
    Digitale Medien
    The construction of homogeneous nets (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 415-426 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A definition of homogeneity for neural networks is given which permits their construction as group quotients. The significance of this for neural dynamics is discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459431
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  • 34
    Digitale Medien
    Digitale Medien
    Contractile analysis and kinetic energy of the myocardium (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 447-461 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The left ventricle is represented as a cylinder contracting both radially and longitudinally. A simple method is indicated to derive an expression for the rate of change of the kinetic energy of this three-dimensional model, which quantity can be used as an index for the study of the contractile behaviour of the myocardium. An application to the study of muscle mechanics is also indicated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459433
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  • 35
    Digitale Medien
    Digitale Medien
    Limit cycles in periodically perturbed population systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 463-485 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459434
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  • 36
    Digitale Medien
    Digitale Medien
    On a unified approach to pattern generation (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 513-516 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459437
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  • 37
    Digitale Medien
    Digitale Medien
    Optimal models for social change (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 841-862 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract By assigning coordinates to the environmental function space comprising all physical and mental stimuli, mathematical interpretations can be based on such terms as adaptability, and reactivity which relate to individuals interacting with their environment within a society. These psychometric concepts are incorporated into a framework of functional analysis, which permits the optimization of social change by maximizing the satisfaction integral through the use of variational or dynamic programming methods in conjunction with some optimal social policy. The approach provides a mathematical connection between psychology and sociology, and further demonstrates that existing forms of government are simulated by differential equations belonging to the same general class. The synthesis of new classes of functional equations describing social progress is visualized as a legitimate objective for abstract mathematical sociology.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476932
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  • 38
    Digitale Medien
    Digitale Medien
    A suggestion for a new approach to the mathematical theory of imitative behavior (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 863-877 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The theory of imitative behavior as developed hitherto by the author was based on the assumption that each individual has a natural preference for one of the two mutually exclusive behaviors. The endogenous fluctuations in the central nervous system then result in the individual’s exhibiting the two behaviors alternately with a relative frequency determined by the natural preference. Imitation shifts the natural preference towards one or the other of the two mutually exclusive behaviors. In the present approach it is suggested that the relative frequency of the two mutually exclusive behaviors exhibited alternately is determined by maximizing the “satisfaction function” of the individual, that is by hedonistic factors rather than by purely random fluctuations. Corresponding equations are developed. It is shown that in certain cases, even when the imitation effect is absent, a sort of “pseudoimitation” may occur. Another situation leads, in the case of two individuals only, to a complete “division of labor” between them, with respect to the two behaviors. Each one exhibits only one behavior. After that imitation is introduced explicitly by assuming that imitation by one individual or another increases the satisfaction function of the imitating individual. Results thus obtained show similarities to the results of the old theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476933
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  • 39
    Digitale Medien
    Digitale Medien
    An equivalence result for integral equations with application to branching processes (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 1-15 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A theorem is proved, concerning expected values of a multitype branching process in a varying environment. The consequence of the theorem is that the branching process can be treated (in the sense of expected values) as a dynamical system with control terms. This is of importance in situations where the process serves as an abstract model of the dynamics of malignant cells for use in chemotherapy. A simple example of this kind is given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459415
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  • 40
    Digitale Medien
    Digitale Medien
    General solution for flow and stress phenomena in elastic vessles (Navier-Stokes) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 29-42 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A method is developed for a full nonlinear evaluation of all velocities and stresses represented in the Navier-Stokes equations and in the general stress tensor. The information required is essentially that for solution of linearized forms. The solution is analytical except for the calculation of the axial velocity, which requires computer assistance to step through time and space. The treatment of the problem, although directed towards solutions involving fluid flow in elastic vessels, is also adaptable to solid deformations (strain vs rate of strain) where the general stress tensor applies. A special case for the distorting ellipse is presented as well as a limited, spatially analytic, solution.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459417
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  • 41
    Digitale Medien
    Digitale Medien
    Spatially localized interactive neural populations—II: Stability and dynamics of excitatory sets (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 43-56 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The stability characteristics and dynamical behavior of a system of mutually excitatory neurons in close spatial proximity are investigated with a mathematical model. The model predicts the existence of uniform, intermediate levels of activity other than those of no activity and maximal activity. The model also, yeilds a good explanation of data obtained from periglomerular neurons in the olfactory bulb of the cat.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459418
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  • 42
    Digitale Medien
    Digitale Medien
    Stochastic compartmental models with banching and immigrant particles (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 75-86 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A multicompartmental model in which particles enter the system from the environment and reproduce according to a Markov branching process has been considered. Explicit expressions have been obtained for the mean vector and the correlation structure for the numbers of particles in different compartments in different time points of the system. Growth rates of the mean vector and some special cases of the system are also discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459420
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  • 43
    Digitale Medien
    Digitale Medien
    Mode analysis of physiological oscillators intercoupled via pure time delays (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 57-74 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The study of bi-directionally coupled oscillators is relevant in biological modelling of such systems as gastro-intestinal electrical activity, cardiac pacemarkers, cardiovascular and respiratory interactions and circadian rhythms. Interconnecting pathways in biological systems often exhibit pure time-delay characteristics. In this paper the multiple-mode limit-cycle behaviour of such systems is analysed using the method of harmonic blance. It is shown that the coupling time delay radically affects the number, frequency and amplitudes of entrained limit-cycles.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459419
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  • 44
    Digitale Medien
    Digitale Medien
    Bifurcation, stability diagrams, and varying diffusion coefficients in reaction-diffusion equations (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 87-102 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The effect of keeping all the parameters constant, except the diffusion coefficients, in a pair of reaction-diffusion equations is studied. It is shown that the stability of the constant solution and the bifurcation points can be easily established by constructing a simple stability diagram. The possible qualitatively different diagrams are enumerated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459421
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  • 45
    Digitale Medien
    Digitale Medien
    Random ecological systems with structure: Stability-complexity relationship (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 103-117 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We have numerically examined more than one million Large Complex Systems (LCS) of interacting variables (interpretable as interacting populations) governed by Generalized Lotka-Volterra Equations (GLV), with self-regulation term. The scope was to have some insight on the stability-complexity relationship. We considered systems of prey-predator type, and we gave appropriate rules for constructing the model systems, rules that specify the behaviour of model systems in order to put them near the biological reality. The results show, among other things, a strict correlation between the stability and the prey-predator ratio (which, in our model, uniquely determines the connectedness of the system).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459422
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  • 46
    Digitale Medien
    Digitale Medien
    Remark on the article, “Applied catastrophe theory in the social and biological sciences” by M. A. B. Deakin (1980) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 149-150 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459425
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  • 47
    Digitale Medien
    Digitale Medien
    Transient effects on the initial rate of oxygenation of red blood cells (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 119-134 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The rate-controlling process in the oxygenation of red blood cells is investigated using a Roughton-like model for oxygen diffusion and reaction with hemoglobin. The mathematical equations describing the model are solved using two independent techniques, numerical inversions of the Laplace transform of the equations and numerical solutions via an implicit-explicit finite difference form of the equations. The model is used to re-examine previous theoretical models that incorporate either a red cell membrane that is resistive to oxygen diffusion or an unstirred layer of water surrounding the cell. Although both models have been postulated to be equivalent, the results of the computer simulations demonstrate significant differences between the two models in the rate of oxygenation of the red cells, depending upon the values chosen for the diffusion coefficient for O2 in the membrane and the thickness of the water layer. The difference is apparently due to differences in the induction and transient periods of the water layer model relative to the membrane model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459423
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  • 48
    Digitale Medien
    Digitale Medien
    Energy and biological evolution—II. The mathematical structure of equilibrium states (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 537-547 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We examine certain mathematical structures presented in Part I. The most important of these are the energy structures determined by the couple (ω×E, ψ) the space of causality defined by ψ-1(0) and the notion of collapsibility, i.e., the descent of a species from a higher to a lower equilibrium configuration as a result of energy loss.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459407
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  • 49
    Digitale Medien
    Digitale Medien
    A stochstic model for a two-compartment reversible system (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 557-570 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper discusses a general stochastic model for a two-compartment reversible system with non-homogeneous Poisson inputs, arbitrary residence times at each of the compartments and time-dependent transition probabilities. The probability distributions of the number of particles in each compartment and in the system are obtained together with the number of particles which depart from the system. In addition, various covariance functions with a time lag are obtained. Some of the above obtained results are deduced for time-independent arrivals, exponential residence times and time-independent transition probabilities. Fluctuations of the particles present in the system are also analysed. Similar analysis is provided for the model into which some particles are initially introduced at the system. Some possible applications are discussed at the end.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459409
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  • 50
    Digitale Medien
    Digitale Medien
    Effects of dispersion on stability of multispecies prey-predator systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 571-578 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The general multispecies prey-predator system with Gompertz's antisymmetric interactions is nonlinearly stable in the absence of dispersion and continues to remain stable with dispersion under both homogeneous reservoir and zero flux boundary conditions in a region containing the equilibrium state. It is proved that a general multispecies food-web model without antisymmetric interactions is stable in the absence of dispersion and remains stable with dispersion in the above-mentioned region.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459410
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  • 51
    Digitale Medien
    Digitale Medien
    Repeatability of experiments (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 593-593 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459413
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  • 52
    Digitale Medien
    Digitale Medien
    Graph theoretical criteria for stability and boundedness of predator-prey systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 579-585 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We introduce a graphical approach in the study of the qualitative behavior ofm species predator-prey systems. We prove that tree graphs imply global stability for Volterra models and local stability for general models; furthermore, we derive sufficient conditions so that loop graphs imply stability and boundedness of the solutions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459411
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  • 53
    Digitale Medien
    Digitale Medien
    A reply to “repeatability of experiments” by R. B. Campbell (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 594-595 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459414
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  • 54
    Digitale Medien
    Digitale Medien
    An epizootic model of an insect-fungal pathogen system (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 731-739 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A system of integro-differential equations is derived to describe epizootics of a fungal pathogen in an insect population. Because of piecewise continuous behavior under some parametric conditions, it is concluded that standard phase orbits can be misleading. Using a different analytic approach yields a simple system of finite difference equations. Both the continuous and discrete versions are compared to classical forms. The continuous version differs from a classical one in possessing a second derivative dependent on population density. The discrete version differs in maintaining positive, non-zero populations of both infectives and susceptibles in finite time.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462280
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  • 55
    Digitale Medien
    Digitale Medien
    On feedback control of gonadotropin secretion (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 741-748 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This note is an attempt to demonstrate that hypothalamic pulsatile GnRH secretion is not the result of a short-term, negative steroid hormone feedback. Clarification of this point is of importance for further modelling the control of gonads.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462281
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  • 56
    Digitale Medien
    Digitale Medien
    The development of largangians for biological models (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 749-760 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A modern theory of the calculus of variations is used to form necessary and sufficient conditions for the existence of a Lagrangian representation of a system of first-order ordinary differential equations. There exists a theorem to the effect that when a system of ordinary differential equations is variationally self-adjoint, the fulfillment of such conditions is guaranteed. In addition, self-adjointness, allows establishement of an algorithm by which a Lagrangian for the system may be explicitly constructed. Examples in mathematical biology are given to illustrate the use of the stated theorem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465178
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  • 57
    Digitale Medien
    Digitale Medien
    An optimal control model of diabetes mellitus (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 793-808 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Engineering optimal control theory is applied to equations describing insulin and glucose interactions. The nature of the optimal controller is established. It is shown how the results can be utilized in a closed loop feedback control system.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465181
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  • 58
    Digitale Medien
    Digitale Medien
    Biological optimality: Comparison of generalized feasibility and optimality conditions for linear, error-minimizing systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 777-791 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An attempt is made to compare the conditions for the general error-optimality of linear systems developed by Kalman with the conditions for feasibility of linear models of neuromuscular and physiological control systems. Models of three actual physiological systems are tested for both the above criteria. Theoretical analysis presented here shows that there are no simple relationships between the two sets of conditions. Analysis carried out on the physiological systems models suggests the need for a general set of conditions for other optimality criteria, such as time and energy minimization, similar to Kalman's condition for error minimization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465180
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  • 59
    Digitale Medien
    Digitale Medien
    The development of anoxia following occlusion (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 851-877 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Following arteriolar occlusion, tissue oxygen concentration decreases and anoxic tissue eventually develops. Although anoxia first appears in the region most distal to the capillary at the venous end, it eventually spreads throughout the entire region of supply. In this paper the changing oxygen concentration, from the time of occlusion until the tissue is entirely anoxic, is examined mathematically. The equations governing oxygen transport to tissue are solved by iterating a nonlinear integral equation. This solution is valid until anoxia first appears. After anoxia develops it is necessary to solve a moving boundary problem. This is done using the method of matched asymptotic expansions, and accurate solutions are obtained for a wide range of physiological conditions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465185
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  • 60
    Digitale Medien
    Digitale Medien
    Announcements (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 899-900 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465188
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  • 61
    Digitale Medien
    Digitale Medien
    Comparative performance of polynomial signal extraction (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 93-104 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract A stochastic approximation problem for polynomic operators is formulated. The performance of polynomic operators of various degrees is compared. The effect of causality constraints is also examined.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600036
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  • 62
    Digitale Medien
    Digitale Medien
    Feedback system design: The single-variate case — Part I (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 137-169 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract A recently developed algebraic approach to the feedback system design problem is reviewed via the derivation of the theory in the single-variate case. This allows the simple algebraic nature of the theory to be brought to the fore while simultaneously minimizing the complexities of the presentation. Rather than simply giving a single solution to the prescribed design problem we endeavor to give a complete parameterization of the set of compensators which meet specifications. Although this might at first seem to complicate our theory it, in fact, opens the way for a sequential approach to the design problem in which one parameterizes the subset of those compensators which meet the second specification...etc. Specific problems investigated include feedback system stabilization, the tracking and disturbance rejection problem, robust design, transfer function design, pole placement, simultaneous stabilization, and stable stabilization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600050
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  • 63
    Digitale Medien
    Digitale Medien
    Editorial (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 267-268 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599010
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  • 64
    Digitale Medien
    Digitale Medien
    Rational approximation via selective modal analysis (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 433-445 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract We describe a recently developed framework for exploring the structure of linear time-invariant models of large systems, and for constructing interpretable or physically-based, reduced-order models that reproduce selected modes of the original systems to a desired accuracy. Application of this framework to constructing lumped approximations for interconnections of lumped and distributed systems is briefly explored.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599022
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  • 65
    Digitale Medien
    Digitale Medien
    A model for neuron firing with exponential decay of potential resulting in diffusion equations for probability density (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 233-243 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A neuron is assumed to receive synaptic input of both excitatory and inhibitory natures from a large number of neighboring neurons; it is also assumed that a large number of such impulses are required to raise the neuron’s transmembrane potential to its threshold potential, at which it “fires” or “spikes”. The model is similar to one of Gerstein and Mandelbrot, except that in the absence of input an exponential decay of potential toward a resting level is introduced. Computational methods of determining the spike timeinterval distribution are discussed, along with the inverse problem of estimating the parameters of the system from observed spike time-interval data.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476897
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  • 66
    Digitale Medien
    Digitale Medien
    Pulse velocities in an orthotropic elastic tube (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 311-318 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Moens-Korteweg relations are developed for the velocity of wave propagation through an orthotropic elastic tube based on the three dimensional equations of elasticity. Numerical examples are presented for the femoral artery of a dog and several other orthotropic materials. These results are compared with those obtained from the equations of motion for an orthotropic elastic medium.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476902
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  • 67
    Digitale Medien
    Digitale Medien
    An investigation of basic assumption in enzyme kinetics using results of the geometric theory of differential equations (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 335-341 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Up to the present time, the following property of the product component in the reversible one substrate-one intermediate-one product enzymic mechanism has been taken only as anassumption, viz., during the course of the reaction, the time-rate of change of product concentration is never negative and the product concentration never exceeds its equilibrium value. Applying the methods of the geometric theory of ordinary differential equations it is shown that this result follows as a direct deduction from the differential equations governing the mechanism together with the initial conditions. Further, the nature of the equilibrium point as a stable node is established.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476904
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  • 68
    Digitale Medien
    Digitale Medien
    Analysis of tracer experiments: VIII. Integro-differential equation treatment of partly accessible, partly injectable multicompartment systems (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 319-333 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An integro-differential equation treatment of multi-compartment systems is developed which permits formal analysis of the incomplete data which is available from partly accessible, partly injectable systems. New transport functions are defined which can be obtained directly from the experimental data. These functions serve to characterize the communication and topology between different accessible compartments and also the reentrant contributions from inaccessible sites. The method gives solutions consistent with those of the differential equation approach when the system is uniformly contiguous and accessible, more complete solutions than those of the integral equation approach when all measured compartments are injectable, and in addition provides complete or partial solutions for certain otherwise analytically intractable systems. Detailed numerical illustrations of the method are given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476903
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  • 69
    Digitale Medien
    Digitale Medien
    General two factor models (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 405-405 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476913
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  • 70
    Digitale Medien
    Digitale Medien
    Mathematical theory of the possible role of intercellular fluid and of vascularization on physiological periodicities (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 395-401 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In continuation of previous work (Rashevsky,Some Medical Aspects of Mathematical Biology, Springfield, Ill.: Charles C. Thomas, 1964, Chap. 23 and Appendix 14), the study of the effects of the physical parameters of the cells of endocrine glands on the onset of sustained periodical oscillations in the interaction between the anterior pituitary and the thyroid hormones is generalized to include the possible effect of the intercellular fluid and of the degree of vascularization. Some conclusions of the previous study remain valid although some modifications must be made. A decreased relative volume of the intercellular fluid and an increased vascularization favor the conditions for sustained oscillations. The permeability of the cells and the permeability of the capillaries appear explicitly in the expressions which show the conditions for sustained periodicities.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476911
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  • 71
    Digitale Medien
    Digitale Medien
    Limits on the computing power of biological systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 59-67 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The theory of computational complexity and certain explicitly-stated hypotheses imply limitations on the information processing power of biological systems. Parallelism, special purpose organization, and analog mechanisms may provide speedup critical for life processes, but have little power in the face of exponential growth. We show that “polynomially simulatable” biological systems cannot exhibit dynamic behavior which produces the solution of an intractable problem. The argument implies that parallelism does not allow biological systems to defeat the exponential explosion, but rather is important because it allows polynomial time algorithms to be used more efficiently.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460939
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  • 72
    Digitale Medien
    Digitale Medien
    Equilibrium conditions in polysomic inheritance for a panmictic population (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 437-449 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A general model of a large 2m-ploid breeding population, withr loci ands h alleles at the h th locus is considered. It is assumed that the population is bisexual, non-overlapping and breeds by random mating. The genotypic structure of the population is presented as a bilinear form in the gametic output vectors where the genotype distribution is in the matrix form. Using the concept of the segregation distribution, the genotype proportions in the (n+1)st generation are given. An equilibrium condition for random chromosome segregation is obtained in terms of gene frequencies.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476583
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  • 73
    Digitale Medien
    Digitale Medien
    A topological study of the base sequences of MS2 and ϕX174 genoma (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 81-88 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A correlation matrix analysis is applied to the base sequence of MS2 and ϕX174 in comparison with sets of simulated sequences with different degrees of constaint Significant differences between a codified sequence, and a statistical one in terms of the “correlation matrix” for sets of different length cannot be found. This result is analysed in terms of nucleotide sequences with different levels of informational content.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460941
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  • 74
    Digitale Medien
    Digitale Medien
    Volume of the conducting airways calculated from morphometric parameters (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 101-109 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A method of calculating the volume of a tree distal to a cut at the origin of a branch, using branching, diameter and length ratios, has been developed. The method was applied to bronchial tree casts from human, dog, sheep, hamster, and rat lungs. It was found that the exponenta in the equation weight=k×diameter a is approximately equal to 3.0 in sheep lung casts, as found by Hooper (1977), but it is greater than 3.0 in casts from the other four species.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460943
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  • 75
    Digitale Medien
    Digitale Medien
    Variability in a single compartment system: A note on S. R. Bernard's model (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 111-116 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this note we examine a continuous time version of a compartmental model introduced in a discrete time setting by S. R. Bernard. The model allows for more than one particle to leave the system at any time. This introduces additional randomness into the system, over the pure death system and this is reflected in the variance function.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460944
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  • 76
    Digitale Medien
    Digitale Medien
    The diffusion transit time; A simple derivation (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 89-99 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The mean first passage time for free diffusion can be derived directly by solving a simple analogue steady state problem. In this problem the diffusion starting region is considered as a time independent source of diffusing particles and the diffusion target assumes the behaviour of a perfectly absorbing sink. It is shown here that the transit time between the source and the sink, which in this particular problem is equal to the ratio between the holdup of the system and the total flux, is identical to the Brownian movement concept of the mean first passage time for free diffusion. This established identity considerably facilitates the derivation and investigation of the timing of diffusion in complicated structures such as those commonly found in living organisms.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460942
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  • 77
    Digitale Medien
    Digitale Medien
    Nonlinear oscillations in biology (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 121-123 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460946
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  • 78
    Digitale Medien
    Digitale Medien
    A comment on Lin's paper on nonlinear diffusion in biological systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 117-120 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460945
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  • 79
    Digitale Medien
    Digitale Medien
    The blood flow of the brain (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 541-548 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The rigidity of the skull and the inertial characteristics and incompressibility of its contents cause the elastic cerebral arteries and veins to act over brief periods of time like rigid tubes of relatively small diameter. Poiseuille's law is applicable to their behavior. The use of this law, in combination with the fact that, during brief intervals, the total volume of the cerebral arteries and veins remains constant, permits derivation of a mathematical expression for the average arterial flow in terms of an average arterial radius. The differentiated equation has five positive roots which represent maxima and minima of the average flow in terms of the average arterial radius. The theoretical results have physiological implications and potential clinical usefulness, which are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476591
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  • 80
    Digitale Medien
    Digitale Medien
    Erythrocyte distribution in arterial blood flow: I. Basic equations and anisotropic effects (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 549-563 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Equations are derived for the flow of an anisotropic fluid in a tube. It is argued that these provide a model for arterial blood flow. Particular attention is paid to the effect of radial differences in hematocrit. Sequels to this paper (Bull. Math. Biophysics,29, 565–574; forthcoming, 1967) will respectively demonstrate possible wall-directed forces on the erythrocyte and enlarge on the physiological consequence of hematocrit variations. The present article develops the basic equations and explores the possible role of anisotropic effects in blood flow.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476592
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  • 81
    Digitale Medien
    Digitale Medien
    A re-evaluation of X-ray diffraction patterns of DNA (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 575-581 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Concentric circular lines are present on X-ray diffraction patterns of DNA. They cannot be accounted for by the double helix model. It is suggested that they may indicate the presence of double helical side chains.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476594
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  • 82
    Digitale Medien
    Digitale Medien
    On the stochastic theory of compartments: The leaving process of the two-compartment systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 201-211 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper three stochastic models are developed for a class of two-compartment systems to analyse the randomness of the leaving process of the particles in the system. Results in closed form for the distribution of the leaving process of the particles in the system are given both for general and exponential sojourn time distributions and also in association with forward recurrence time distributions with and without Poisson input.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459443
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  • 83
    Digitale Medien
    Digitale Medien
    Models on prebiotic polymer competition: A deterministic approach (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 213-232 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Two simple models are proposed and analysed, in which it is shown that the formation of a new polymer, resulting from an “error” in the template action mechanism of production of an old polymer, may compromise the stability of the initial system under specific conditions, in the context of prebiotic evolution. Autocatalysis is shown to be a “selective advantage”, enabling the “mutant” to dominate in concentration and even replace the initial polymer. The addition of a third molecule playing the role of a catalyst causes hysteresis effects.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459444
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  • 84
    Digitale Medien
    Digitale Medien
    Extinction probabilities in microbial predation: A birth and death approach (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 165-181 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The problem of extinction of the prey population in a microbial predator-prey interaction in a chemostat has been examined. Usual deterministic lumped parameter models were used for the dynamics of the chemostat for large numbers of the two populations; the generalized birth and death stochastic process was employed for the description of the random variations at small prey numbers. Extinction probabilities of the prey population were calculated for different holding times and chemostat volumes, and their dependence upon the growth parameters of the two populations was studied. It was found that extinction was possible when the Monod model was used for the specific growth rate of the predators as a function of the prey number density. On the other hand, the decrease of the feeding activity of the predators at low prey densities predicted by the multiple saturation model acts as a regulatory factor that prevents extinction of the prey. In view of the fact that extinction of the prey has never been observed in the laboratory, the latter model seems more appropriate to describe the dynamics of microbial predation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459441
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  • 85
    Digitale Medien
    Digitale Medien
    Prediction of the effect of the choroidal circulation on the retinal temperature during illumination (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 233-238 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract During exposures of the eye to light, the choroidal circulation may have a regulatory influence on the retinal temperature. This is investigated using a mathematical model and a finite-difference technique. It is predicted that the choroidal blood flow a small effect on retinal temperature, which may be important.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459445
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  • 86
    Digitale Medien
    Digitale Medien
    Spatially localized interactive neural populations—I. A mathematical model (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 427-446 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A probabilistic model of a spatially localized, mutually exitatory (inhibitory) population of neurons is formulated to help explain average evoked potential and post-stimulus time histogram measurements. The model is based on the stochastic activity of single neurons within interactive masses of neurons which exhibit co-operative behavior. Macrostate variables corresponding to the above measurements are related through the model to features of neural operation at the individual and ensemble level. Steady-state solution are obtained and their physiological implications are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459432
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  • 87
    Digitale Medien
    Digitale Medien
    A one-compartment model with stochastic parameter (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 503-512 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We consider a one-compartment system with stochastic transfer rate characterized either by Gaussian or by two-level jump process and study the time evolution of the (statistical) moments of the (random) amount of the substance present in the system. The effect of the coloured as well as of the white noise is investigated and it is found that the presence of stochasticity in the transfer rate parameter increases the relaxation time of the system. Finally, we obtain the conditions for the stability of the system in the moment sense.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459436
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  • 88
    Digitale Medien
    Digitale Medien
    A dose-response model for estimating lifetime tumor risks when cell killing occurs (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 487-501 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model is described in which damage to a single intracellular locus can lead to a tumorigenic transformation. Assuming a large number of independent intracellular loci to be at risk and assuming that damage to a locus sufficient to cause a tumorigenic transformation occurs with probability greater than zero for all doses greater than zero, leads to the use of the Weibull distribution to characterize the probability of a nonspontaneous tumorigenic cellular transformation occurring after exposure to a given dose of carcinogen. The excess lifetime tumor incidence (i.e., the proportion of tumor bearers) above the spontaneous incidence is used as an estimate of the non-spontaneous incidence and is characterized by a tumor incidence function that represents the probability of occurrence of one or more non-spontaneous tumorigenic cellular transformations amongN(D) independent surviving cells per individual, after exposure to a doseD of carcinogen. The tumor incidence function is fitted to published data for the excess tumor incidence after exposure of animals or humans to ionizing radiation and after exposure of animals to chemical carcinogens.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459435
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  • 89
    Digitale Medien
    Digitale Medien
    A model for circadian clocks (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 781-791 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An extension of an earlier model simulating the effects of light on the drosophila eclosion rhythm is presented. The effects of variable light intensity are described. This allows not only the simulation of certain experiments not covered by the earlier model, but also it permits an extension of the model to other organisms. By changing only its sensitivity to light the model simulates the phase response curves of certain mammals as well as Aschoff’srule.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476928
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  • 90
    Digitale Medien
    Digitale Medien
    A note on the derivation of the stevens power law (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 827-829 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Previous derivations of the Stevens Power Law relating loudness to intensity assume, in addition to level invariance, that the relation must be analytic or at least differentiable. This last condition is replaced here by the weaker one of requiring only continuity.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476930
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  • 91
    Digitale Medien
    Digitale Medien
    A stochastic model for then-compartment irreversible system (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 549-561 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper deals with a stochasticn-compartment irreversible system with a non-homogeneous Poisson input and arbitrary residence time for each of the compartments. Results relating to the number of particles present in each of the compartments as well as the total number of particles present in the system at any time are derived. Further, explicit expressions for the auto covariance function for each compartment and the cross-covariance function between any two compartments with a given time lag are obtained. As a particular case, then-compartment irreversible system is analyzed with homogeneous Poisson input and exponential residence time distribution for each of the compartments. The possible applications of the model are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462312
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  • 92
    Digitale Medien
    Digitale Medien
    Pulsatile blood flow in a rigid pulmonary alveolar sheet with porous walls (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 563-577 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462313
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  • 93
    Digitale Medien
    Digitale Medien
    Dynamic structure theory: A structural approach to social and biological systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 579-591 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The relationships that define the structure of a given ecosystem, social system, or even a physiological function can only exist if certain parameters are confined to a certain range of values. As the values change and exceed this given range the relationships are forced to change, and so produce a new pattern of relationships. The concept of a dynamic structure captures this potential for structural change in relation to a set of parameters. The precise definition of structure and allowable transformation constitutes the definition of a category. The total range of parameters associated with all the relevant structures provides a parameter space which is assumed to be a manifold. Maps with extra structure from the manifold to the category define dynamic structures. The domain of differential dynamic systems is the manifold, and a flow or movement across the manifold is associated with a series of structural transformations in the category. In some cases a structure outruns its parameter range, to be faced with an obstruction—an absence of possible transformations. Ways of studying such “obstructions” are considered along with the related problem of extending a dynamic structure beyond a previously given set of parameters. The cost or resistance of transformations is also studied. The concepts of dynamic structures are illustrated by the structural change of food webs and they are used in a necessarily qualitative fashion to study dominance structures of social orders and finally to speculate on the qualitative nature of evolutionary change of functional aspects of organisms.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462314
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  • 94
    Digitale Medien
    Digitale Medien
    Peak drug levels in linear pharmacokinetic systems—II. Conditions for a paradoxical injection rate effect with rectangular input (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 705-715 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The preceding paper (Thorn, 1981) has shown that in a linear pharmacokinetic system with a multimodal impulse response the peak drug level may sometimes be smaller with slower rates of injection. This paper presents two theorems on this paradoxical injection rate effect where the injection is a constant infusion of finite duration. The first theorem establishes a graphical method for determining whether a given impulse response will give a paradoxical injection rate effect; and the second establishes that the maximum paradoxical increase in peak drug level is by a factor of two. It is further shown that in order to approach this maximum paradoxical increase the impulse response must contain two isolated, sharp, narrow pulses of approximately equal area. Some examples of bimodal arterial dye-dilution curves from the literature are discussed as impulse responses; and there is also a discussion of the behavior of drug level maxima and minima at different injection rates.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458419
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  • 95
    Digitale Medien
    Digitale Medien
    Peak drug levels in linear pharmacokinetic systems—I. Effect of rate of injection (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 693-703 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper presents three theorems on the peak drug levels that result from injection into a linear pharmacokinetic system. As a preliminary, the “rate of injection” is defined in terms of time expansion or time contraction of the injection function (input). The first theorem then states that the peak drug level will not be greater when the rate of injection is slow than when it is fast, if the impulse response is unimodal. The second theorem sets limits for the time of the maximum drug level, in relation to the time of the maximum of the (unimodal) impulse response and the duration of the input. The third theorem defines conditions which assure a definitely lower peak drug level if the rate of injection is slower. A graphical method is suggested for determining the times and magnitudes of the peak drug levels that result from constant infusions of a fixed dose at different rates. An example is provided to show that if the impulse response is multimodal then the peak drug level may sometimes increase with a decrease in the injection rate.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458418
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  • 96
    Digitale Medien
    Digitale Medien
    Selection under random mutations in stochastic eigen model (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 17-28 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The concept of natural selection is examined, which is one of basic principles for the Darwinian interpretation of evolution. In this model selection is defined as a solution of the deterministic Eigen equation. Next, the random effect is introduced through the mutation term. However, the probability of finding the solution expressing the selection is shown to be smallest. The validity of the model and its applicability to polynucleotide replication are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459416
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  • 97
    Digitale Medien
    Digitale Medien
    Factors defining the rate of oxygen uptake by the red blood cell (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 135-147 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Using numerical methods, the initial rates of oxygen uptake by the red blood cell have been computed. The methods accommodate both a water layer and membrane which may act as diffusive impedance to gas influx. The differential solubilities of the gas in these two layers have also been incorporated in the methods. The presence of a 0.50–0.65 μm deoxygenated water layer has been calculated to simulate the experimental results by Roughton (1959). Experimental studies of CO and NO uptake by the red cell could also be simulated. Although a membrane-only model with given parameters can also account for the observed rates of oxygenation of the red cell (Weingardenet al., submitted for publication), the additional incorporation of differential solubilities of oxygen in the different layers of the RBC yields results that indicate a three layer model to be more plausible. Using a thin layer-red cell oxygenation system, the rates of oxygenation were determined for red cells surrounded by a 4.2 μm deoxygenated water layer. The rates were found to compare favorably to the results of the theoretical model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459424
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  • 98
    Digitale Medien
    Digitale Medien
    Book review (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 151-151 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459426
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  • 99
    Digitale Medien
    Digitale Medien
    Role of the hypergeometric distribution in the transmission of excitation through sympathetic Ganglia (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 152-152 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459427
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  • 100
    Digitale Medien
    Digitale Medien
    On a class of finite deformations of elastic soft tissues (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 175-192 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Due to the complicated physiological structure of soft biological tissues, stresses can only be measured after the specimen has been stretched to many times of its related length. Therefore, the classical constitutive equations of finite elasticity developed for vulcanized, rubbery materials and the linear theories developed for most engineering materials cannot be applied to soft tissues which are highly elastic in nature. In this article, utilizing a mechanical model developed by Demiray for soft tissues, a class of finite deformations of some tissues is studied and the results are compared with experiment and the existing literature. These problems are the simultaneous extension and twisting of a circular cylindrical bar, the bending of a rectangular block, and the pure shear of a rectangular prism. It is believed that solutions to these problems may find some applications in plastic surgery.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463246
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