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  • Springer  (88,702)
  • 1995-1999
  • 1980-1984
  • 1975-1979  (88,702)
  • 1925-1929
  • 1978  (44,825)
  • 1977  (43,877)
Collection
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  • 1995-1999
  • 1980-1984
  • 1975-1979  (88,702)
  • 1925-1929
Year
  • 1
    Electronic Resource
    Electronic Resource
    Deductive biology—Some cautious steps (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 45-58 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract For certain environments, the Darwinian model allows unique prediction of a function that any surviving system adapted to such an environment has to perform. This is the case for those environments that determine a “survival functional” of position in space-time of known shape. Purely temporal survival functionals can be distinguished from spatial and mixed ones. In each case, there exists an optimum path in combined physical and (reduced) metabolic space. Dependent on the admissible error, approximate solutions of different complexity are sufficient. All solutions possess an afferent, a central, and an efferent part. Within this general frame, specific, “probably simplest”, solutions are proposed for adaptive chemotaxis, insect locomotion, lower vertebrates locomotion, higher vertebrates locomotion, chronobiological systems, and immune systems, respectively—or rather, for the underlying functionals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463129
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  • 2
    Electronic Resource
    Electronic Resource
    The role of glucagon in the regulation of blood glucose: Model studies (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 59-77 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Mathematical models afford a procedure of unifying concepts and hypotheses by expressing quantitative relationships between observables. The model presented indicates the roles of both insulin and glucagon as regulators of blood glucose, albeit in different ranges of the blood glucose concentrations. Insulin secretion is induced during hyperglycemia, while glucagon secretion results during hypoglycemia. These are demonstrated by simulations of a mathematical model conformed to data from the oral glucose tolerance test and the insulin infusion test in normal control subjects and stable and unstable diabetic patients. The model studies suggest the parameters could prove of value in quantifying the diabetic condition by indicating the degree of instability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463130
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  • 3
    Electronic Resource
    Electronic Resource
    A note on dynamics of population with history-dependent birth rate (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 123-131 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model for the dynamics of a single-species population whose birth rate depends on densities of previous generations is introduced. A difference equation formulation is proposed and the solutions classified for the various parameter values. Data from an experimental population of mice growing in limited space is cited and compared with the model predictions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463134
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  • 4
    Electronic Resource
    Electronic Resource
    Tension field theories for soft tissues (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 161-182 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract All soft tissues are modeled as either one-dimensionalstrings, two-dimensionalmembranes, or three-dimensionalsolids. Attention is restricted to tissues in which one of the principal stress components is large and positive in comparison with the other negligible components. Results indicate the following: (1) If a deformed string isconstrained to lie on a surface and is free of tangential pressure, the tension is carried by rays which are geodesics of the surface. If a string or membrane isfree to deform in space without normal pressure, the tension rays are straight lines. If a membrane deforms without tangential surface loads, the tension rays are always geodesics on the deformed surface. If a solid deforms without body forces, the tension rays are straight lines. (2) The stress in a string is a constant if the string is free of tangential pressure and has constant cross-sectional area. The stress in flat tension fields free of tangential surface loads decays inversely with distance along a tension ray from the edge of regression. The stress in a spherically symmetric tension field free of body forces decays inversely with the square of the distance from the center of the sphere. (3) Stress singularities can occur in soft tissues, such as at the corners of a closed rectangular hole in a flat membrane strip. (4) The tension rays in the torsion of soft annular membranes are more steeply inclined from the radial direction than the tension rays for hard metals equally displaced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461433
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  • 5
    Electronic Resource
    Electronic Resource
    On the development of group insurance and collective saving in the Federal Republic of Germany and in Great Britain (1978)
    Springer
    The Geneva risk and insurance review 10 (1978), S. 50-66 
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    ISSN: 1554-9658
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02409807
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  • 6
    Electronic Resource
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    Social security versus private saving and insurance (1978)
    Springer
    The Geneva risk and insurance review 10 (1978), S. 44-49 
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    ISSN: 1554-9658
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Conclusion For all these reasons, the rediscovery of the equivalence theorem, first stated by David Ricardo in 1817, must be rejected as an adequate basis for policy, just as Ricardo had denied its applicability to the real world. Correspondingly, the concern with the adverse consequences of unfunded social insurance wealth for the supply of national saving, capital intensity, and living standards remains well founded. p ]If, as a practical matter, public pension and social security programs will never be funded actuarially in the United States and most other postindustrial countries, then government-supervised substitution of private for public retirement plans is the only way to achieve at least partial funding. If such substitution follows the British model of allowing employers to contract out of the earnings-related part of the state scheme if equivalent pensions are provided by the company plan, payroll taxes and social security wealth decline so as to reduce their adverse impact on capital formation.
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    URL: http://dx.doi.org/10.1007/BF02409806
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  • 7
    Electronic Resource
    Electronic Resource
    The expansion of social security in Italy (1978)
    Springer
    The Geneva risk and insurance review 10 (1978), S. 73-84 
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    ISSN: 1554-9658
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02409809
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  • 8
    Electronic Resource
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    Soziale sicherheit und staatsfinanzen (1978)
    Springer
    The Geneva risk and insurance review 10 (1978), S. 85-95 
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    ISSN: 1554-9658
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02409810
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  • 9
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    Problems of social under economic recession and inflation (1978)
    Springer
    The Geneva risk and insurance review 10 (1978), S. 96-98 
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    ISSN: 1554-9658
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02409811
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  • 10
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    La prévoyance dans l'economie italienne (1978)
    Springer
    The Geneva risk and insurance review 10 (1978), S. 67-72 
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    ISSN: 1554-9658
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary: Social Policy in the Italian Economy Favourable social and economic conditions constitute the essential framework for a stable development of savings. Saving in the form of insurance becomes advantageous for the individual, and private insurance can thus extend its activity, when social attitudes and the economic situation favour the propensity to save. If conditions change, the State can take over the coverage of risks through social insurance. By means of this institutions, an anti-cyclical policy can be pursued: the amount of social security contributions, for instance, can be increased during the expansion of the cycle and the amounts thus accumulated can be used to grant benefits during the recession period, when contributions can be fixed at a lower percentage of wages. Another type of policy can be pursued by government authorities: that of adjusting social security contributions to industrial profits, thereby directing the subsequent effects on economic growth. Inflation cab cause instability in decisional policies taken by private insurance companies. A solution to the unbalanced increase of costs can be found in index-linking. Life policies of this kind, for instance, cab be closely related to investments in houses, to be bought by the insured themselves in price-linked instalments. After a reference to present developments regarding risk instability and to possibilities of new forms of insurance, this paper considers the competition resulting from the opening of the EEC insurance markets as an opportunity for the Italian market to strengthen its structures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02409808
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  • 11
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    Observation and biological systems (1977)
    Springer
    Bulletin of mathematical biology 39 (1977), S. 663-678 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A number of apparently different lines of inquiry into fundamental biological processes point to the central role played by the notion of observation in the theory of biological systems. Not only do we use the results of our own observations to obtain the system descriptions which are the starting-points for an understanding of biological processes, but it is a basic postulate of physics that the interactions between biological systems themselves can be regarded as observations. On this basis, it is clear that we cannot properly understand biological interactions unless the observables we employ for system description are the same as those involved in the interactions we are describing. To do this requires a general theory of observables and system description, establishing the relationship between different modes of description. A sketch of such a theory is developed in the present paper, using only two postulates: (a) that all interactions are determined by the values of observables of a system evaluated on specific states, and (b) that real-valued observables suffice. As an application, a specific test is proposed whereby it can be determined whether the observables employed to describe interacting systems are sufficient to specify the observables involved in the interaction itself.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461776
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  • 12
    Electronic Resource
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    Cross-sectional shape of flexible tubes (1977)
    Springer
    Bulletin of mathematical biology 39 (1977), S. 679-691 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Differential equations are derived whose solution gives the cross-sectional shape of a flexible tube as a function of the transmural pressure. These equations are solved digitally to produce a series of closed curves, each curve representing the shape of a cross section for a particular set of conditions. These are then applied to the case of systemic arteries, pulmonary arteries, and large veins. The results predict that systemic arteries must always be circular, even when the internal and external pressures are equal. In veins, a small positive internal pressure causes them to become circular, regardless of their initial state, with negligible stretching. Further increases in internal pressure cause the area of the cross section to increase due only to stretching, the shape remaining essentially circular. With pulmonary arteries, known to be noncircular, changes in the cross-sectional area result from a combination of stretching and changes of shape.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461777
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  • 13
    Electronic Resource
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    Some techniques in building and validating stochastic models of human reproduction (1977)
    Springer
    Bulletin of mathematical biology 39 (1977), S. 693-704 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Stochastic models of human reproduction are beginning to play significant roles in the evaluation of family planning programs. A class of stochastic processes called absorbing, agedependent, semi-Markov processes frequently arises in the construction of such models. The paper begins with a discussion of some technicalities regarding absorbing, age-dependent, semi-Markov processes. Then, an algorithm due to Littman, which makes possible the computerization of this class of stochastic processes, is presented. Briefly, Littman’s algorithm provides an efficient method for numerically solving systems of renewal type integral equations, provided the system does not contain a large number of equations. After setting down a concrete model for a large clinical trial of intrauterine devices conducted in Taiwan, the paper concludes with a discussion of a method for validating the model based on the data collected in the clinical trial.
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    URL: http://dx.doi.org/10.1007/BF02461778
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  • 14
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    On peristaltic flow and its efficiency (1977)
    Springer
    Bulletin of mathematical biology 39 (1977), S. 743-743 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461781
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  • 15
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    Detection and analysis of recognition and selection in the immune response (1977)
    Springer
    Bulletin of mathematical biology 39 (1977), S. 705-719 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some theoretical requirements for the valid use of hemolytic plaque inhibition as a method for studying cellular selection and recognition in an immune response are reviewed. Aside from providing a rational basis for the use of this technique, the theory resolves a growing body of apparently conflicting results on the affinity regulation of IgM secreting cells and can also be used to deduce structural (in particular, morphological) features of the IgM molecule. The diverse predictions of the theory are examined in light of experimental results and find support in a wide data base. Additional specific experiments are proposed which can be used in conjunction with the theory to help clarify the relation between cellular proliferation and maturation.
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    URL: http://dx.doi.org/10.1007/BF02461779
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  • 16
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    A theory of cell swelling in high concentrations of KCl and other chloride salts (1977)
    Springer
    Bulletin of mathematical biology 39 (1977), S. 721-741 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theory of the cell volume is presented with emphasis on the swelling effect of high concentrations of KCl and other chloride salts. In this theory a particular cell volume represents a state of balance between the tendency of the cell water to build deeper layers of polarized water and the restraining forces exerted by the salt linkages and H-bonds. Taking into account also the different structure-breaking effects of different salts, theoretical curves can be constructed which describe the complex multiple peak-plateau of swelling curve observed in frog muscle in response to increasing concentrations of different chloride salts.
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    URL: http://dx.doi.org/10.1007/BF02461780
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  • 17
    Electronic Resource
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    Analysis of the transient behavior of kidney models (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 211-221 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Non-steady-state equations for kidney models are stated. General conservation relations for these equations are derived. Transient equations for the central core model of the renal medulla are developed. Solution of the equations by Laplace transform methods for time invariant volume flows is discussed. The general theory of solving models with time dependent flows by finite difference methods is developed.
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    URL: http://dx.doi.org/10.1007/BF02461436
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  • 18
    Electronic Resource
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    Ecosystem-like behavior of a random-interaction model I (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 513-524 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The behavior of large systems of randomly-interacting variables is examined using an intentionally simplified model. The stable positive solutions are found to exhibit to a significant degree some well-known properties of ecological systems. This resemblance (including for example the predominance of “predator-prey” interactions) is all the more striking in view of the lack of biological “data” at the input end. The findings suggest it advisable to distinguish two kinds of properties in ecosystems. One kind would depend on specifically biological mechanisms; the other would characterize a wide class of persistent systems, and arise from the need for a dynamic balance between positive and negative feedback.
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    URL: http://dx.doi.org/10.1007/BF02460775
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  • 19
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    Mathematical analysis of cancer chemotherapy: The effects of chemotherapeutic agents on the cell cycle traverse (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 499-512 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract For the tumor model of Skipper and Zubrod, which has been analyzed previously for the theoretical FLM function and the effect of chemotherapy against tumors of known or assumed kinetic characteristics, the theoretical continuous labeling (CL) function is derived by considering an equivalent tumor (in terms of unlabeled cell populations) in which the density function of phase duration of cells inS-phasef 2(a 2)=δ(a 2−∞) and the loss functionL 2(t)=0. This mathematical concept of blocking is applied to the analysis of synchronization in tumor growth and blocking effects in cancer chemotherapy. These effects of chemical agents on the cell cycle progression are being incorporated into a previously written computer simulation program for cancer chemotherapy. Whereas, a program is written and used to simulate the CL functions for L1210 leukemia, and primary and metastatic Lewis lung carcinoma.
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    URL: http://dx.doi.org/10.1007/BF02460774
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  • 20
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    Global stability in a class of prey-predator models (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 525-533 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Global stability is established in a class of prey-predator models. This includes a prey-predator model in which the predator has Type 2 functional response and no intraspecific interactions. Two simple examples demonstrate that Kolmogoroff’s theorem does not apply to some members of this class of models.
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    URL: http://dx.doi.org/10.1007/BF02460776
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  • 21
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    A theoretical study of the temperature distribution in skeletal muscle undergoing rhythmic contractions (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 535-540 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The skeletal muscle is regarded as a periodically deformed plate. An equation of energy for the biological tissue in the system is used in the Lagrange variables. With the heat exchange through the above tissues to the exterior media and also with account of some relations between the physiological factors the approximate analytical solution for this equation is obtained and compared with the physiological data.
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    URL: http://dx.doi.org/10.1007/BF02460777
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  • 22
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    A comment on Bobisud's paper on evolution of cannibalism (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 541-545 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract One of Bobisud's (1976) models for the evolution, of cannibalism is discussed. His analysis is criticised for not being based on the principle of individual selection. Assuming the operation of that principle, we show by simulating his model that cannibals may establish themselves in a noncannibal population. This will happen both in cases where Bobisud concluded cannibalism to be optimal and in cases where he concluded cannibalism not to be optimal.
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    URL: http://dx.doi.org/10.1007/BF02460778
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  • 23
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    Prediction of light-induced transient thermal response of the retina (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 547-547 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02460779
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  • 24
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    Dynamical similarity and the theory of biological transformations (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 549-579 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The D'Arcy Thompson concept of biological transformations is developed in a form analogous to such physical concepts as the Law of Corresponding States in thermodynamics, and the Principles of Similitude found in engineering. We find that such concepts depend on a distinction between fundamental and derived quantities, in which the values assigned to the fundamental quantities set the natural scales for the derived ones. Among other things, we see that critical phenomena, such as phase transitions, arise as an immediate consequence of this distinction. In a biological context, we explore the implications of Thompson's hypothesis that closely related organisms are phenotypically similar, assuming that the organisms we see are the result of selection processes operating on phenotypes.
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    URL: http://dx.doi.org/10.1007/BF02460731
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  • 25
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    Distributed sensory coding applied to simulations of iconic storage and metacontrast (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 605-623 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract If information is coded in the combination of activities of many neurons operating in parallel, then information present in a network can be defined by the correlation of present network activity with the activity which had been elicited by a stimulus in the past; a high correlation indicates the presence of the previously encoded stimulus. Information is distributed in the network because coding is dependent upon the activities of all cells. A model based on Hartline-Ratliff lateral inhibition with a time delay shows that lateral inhibition can distribute information across a parallel network, reduce output noise, and also briefly store information. With no changes in model parameters, and the use of a correlation measure for recognition, the model can stimulate psychophysical results in eleven variations of the metacontrast masking paradigm.
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    URL: http://dx.doi.org/10.1007/BF02460733
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  • 26
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    Theoretical study of nasal deposition (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 581-604 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theory is derived to calculate the regional and total deposition of aerosol particles in the nasal passages during inhalation. The particle size studied range from 0.2 to 10.0 μm diameter. The deposition is calculated in five regions; (I) the region filled with nasal hair, (II) the nasal valve, (III) the expansion region, (IV) the turbinate region and (V) the posterior bend. Equations are derived to determine the deposition caused by direct impaction on the nasal hairs and bends of the passages. The calculations show the deposition due to direct impaction does not account for the amount or location of deposited particles measured in experiments. Secondary flows have been speculated to exist in the expansion region after the nasal valve and an equation is derived to estimate the deposition caused by the secondary flows. The calculated deposition, due to direct impaction and secondary flows, shows general agreement with the experiment as to the predicted amount and location of deposited particles.
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    URL: http://dx.doi.org/10.1007/BF02460732
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  • 27
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    What do mathematical models tell us about circadian clocks? (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 625-635 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper reviews a series of models for circadian clocks and discusses their conclusions and predictions. Attention is focused on Pittendrigh's empirical model, two mathematical models by the author and Winfree's work.
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    URL: http://dx.doi.org/10.1007/BF02460734
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  • 28
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    Electric field distribution, ionic selectivity and permeability in nerve (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 637-649 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract From a model of facilitated ionic transport across axonal membranes proposed by McIlroy (1975), the equipotentials and electric field distributions in the vicinity of a potassium conducting pore and of a sodium conducting pore are computed and presented as two-dimensional mappings. The model is then extended to include the effect of impurity ions in the conducting pores viz. of potassium ions in a sodium pore and of sodium ions in a potassium pore. The ionic selectivities and permeabilities of the transported species are discussed in relation to the extended model. Bounds are deduced for the ionic selectivity coefficients for both the sodium and potassium current-carrying systems in squid giant axons and the electric-field distributions in the vicinities of the pores are computed for the extended model and compared with the impurity-free fields first calculated. Finally the permeability coefficients defined in terms of the extended model are shown to reconcile the results of attempts to measure permeability by means of radioactive tracer techniques, with the classical description of the resting nerve.
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    URL: http://dx.doi.org/10.1007/BF02460735
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  • 29
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    Self-similar solution of a distributed model for transcapillary exchange and solute removal by the liver (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 661-669 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The partial differential equations describing transcapillary exchange and subsequent removal of solutis from an idealized liver sinusoid are amenable to solution by similarity analysis. The power and utility of this technique, which is not widely appreciated as a method for solving biological models, is illustrated here for a system whose Laplace transforms is difficult to invert.
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    URL: http://dx.doi.org/10.1007/BF02460737
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    Steady-state distribution of bacteria chemotactic toward oxygen (1978)
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    Bulletin of mathematical biology 40 (1978), S. 671-674 
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    Notes: Abstract The phenomenological theory for the chemotaxis and consumption of oxygen by motile aerobic bacteria is shown to yield a remarkably simple one-dimensional steady-state solution for a congregation of bacteria close to the surface of an oxygen-depleted aqueous medium.
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    On the identification by filtering techniques of a biologicaln-compartment model in which the transport rate parameters are assumed to be stochastic processes (1978)
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    Bulletin of mathematical biology 40 (1978), S. 651-660 
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    Notes: Abstract In this paper biological compartmental models are considered which take into account the intrinsic randomness of the transport rate parameters and their possible variability in time. An identification procedure is presented for the estimation of the stochastic processes representing the transport rate parameters of a compartmental model from a noisy input-output experiment. The problem is formulated in terms of nonlinear filtering. A simple model is discussed for the case in which the transport rate parameters are independent of each other. The possibility of testing possible important features of the behavior of the transport rate parameters is also evidenced.
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    Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations (1978)
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    Bulletin of mathematical biology 40 (1978), S. 853-863 
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    Notes: Abstract For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂ci/∂t=Di∇2ci+Qi(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c 1(x,t),...,c n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.
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    Mathematical models in biological discovery. Lecture notes in biomathematics (1978)
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    Bulletin of mathematical biology 40 (1978), S. 873-875 
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    On the geometry of space-and time-equivalent catastrophes (1978)
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    Bulletin of mathematical biology 40 (1978), S. 1-25 
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    Notes: Abstract The geometrical nature of the Elementary catastrophes (Thom, 1969) is reviewed. Histories of the movement of catastrophe manifolds and bifurcation sets are presented for some of the space-equivalent unfoldings described by Wassermann (1975). These unfoldings provide descriptions of the variation with time of the stability of stationary states of associated potential energy functions. Identification of these stationary energy states with stationary states of a system therefore provides a description of its behavior with time. Qualitative descriptions of this type are particularly useful when the complexity of a system prevents a detailed quantitative description. Histories of bifurcation set movements suggest different types of system behavior at different space-like coordinates. This type of theory may be a useful model for the processes leading to differentiation of cells and to emergence of adult forms of a biological organism.
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    Prediction of limit cycles in mathematical models of biological oscillations (1978)
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    Bulletin of mathematical biology 40 (1978), S. 27-44 
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    Notes: Abstract Three conjectures are given which predict the existence of unique stable limit cycle oscillations in a class of piecewise linear (PL) differential equations. The equations are appropriate to model biological or other complex systems in which there are switchlike interactions between the elements of the network. Methods are presented which can be used to develop mathematical models which are conjectured to display stable limit cycle oscillations, from qualitative experimental information about relative phases of activity in the dynamical systems. Several illustrative numerical examples are given, and one experimental example from neurobiology is discussed.
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    Least energy regulation of the arterial system (1978)
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    Bulletin of mathematical biology 40 (1978), S. 79-93 
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    Notes: Abstract The formulation and results of the Kalman State Regulator Problem are applied to a mathematical model of the arterial system of a dog to obtain an optimal control for blood pressure. The criterion for optimality is minimum energy per cycle.
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    Pressure-flow relationships in a model for the arterial system (1978)
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    Bulletin of mathematical biology 40 (1978), S. 95-105 
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    Notes: Abstract A mathematical model is developed in state variable form suitable for the study of the control of blood pressure and flow in the mammalian cardiovascular system. The applicability of the model to steady state, both mean and pulsatile, and transient phenomena is demonstrated by the agreement of the results with experimental data. This model was developed to study the neural and renal-endocrine-electrolyte control of cardiovascular functions.
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    Conditions for periodic solutions of volterra differential systems (1978)
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    Bulletin of mathematical biology 40 (1978), S. 133-160 
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    Notes: Abstract As a contribution to the discussion of oscillatory models for interacting species it is shown that two-species Volterra models can never have limit cycles, and a complete enumeration is given of conditions which the parameters of these models must satisfy in order that a part of the phase space be filled with a family of closed curves; sketches of phase portraits are also given. These results complement and correct older results by Bautin and by Coppel on quadratic differential systems. The paper opens with a brief discussion of some more practical aspects of the ecological application of oscillatory models.
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    The kinetics of diffused substances in some biological systems (1978)
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    Bulletin of mathematical biology 40 (1978), S. 107-121 
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    Notes: Abstract The purpose of this paper is to present a method for the determination of a solution for a coupled system of first order initial boundary-value problems arising from some biological systems. The physical problem is to determine the suspended and the superficial molecular concentrations of a traced substance passing through an organ containing a tangle of vessels, such as the kidney-ureter system. The approach to the problem is by successive approximation which leads to a recursion formula for the determination of the solution as well as error estimates for the approximations. The recursion formula involves only direct integration which indicates a promising possibility in obtaining numerical results by using a computer. In addition to the determination of a solution, some qualitative analysis of the solution is given. This includes the existence of a unique solution, the continuous dependency of the solution on the data, and the stability problem of a steady-state solution.
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    State, security and insurance (1978)
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    The Geneva risk and insurance review 10 (1978), S. 3-43 
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    Topics: Economics
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    Heat transfer in perfused biological tissue—II. The “macroscopic” temperature distribution in tissue (1978)
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    Bulletin of mathematical biology 40 (1978), S. 183-199 
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    Notes: Abstract In Part I, the general solution of the heat transport equation was given for a medium of constant thermal properties, containing a general convection fieldv(r,t). Starting from this general solution, an average or “macroscopic” temperature distribution is calculated in this paper, since in most physiological problems only an average or “macroscopic” temperature is accessible to the measurement. It is shown that the averaged temperature distribution is influenced alone by the order of the local symmetries of the convection field. These local symmetries can be deduced from anatomical data on the vascular architecture. In order to perform the averaging process, a detailed discussion, and an estimate of the correlation between the microscopic temperature variation and the convection field is carried out. Hereby, great emphasis is put on the experimental consequences of these results. As an illustrative example, the calculation of the macroscopic temperature distribution in a medium traversed by parallel capillaries is outlined.
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    A note on dipole sources in conducting biological tissues (1978)
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    Bulletin of mathematical biology 40 (1978), S. 201-209 
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    Notes: Abstract The study of current flow fields in biologicaltissue requires finding the potential field from dipole sources such that the normal gradient vanishes at the exterior surface. A convenient way to determine the dipole field is by taking the gradient of the potential field set up by a point source. However, the point source problem is ill-posed when the normal gradient is required to vanish at the outer surface. In the paper the nature of this problem is discussed and several methods for overcoming the difficulty are presented.
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    A hydrodynamic model of aqueous flow in the posterior chamber of the eye (1978)
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    Bulletin of mathematical biology 40 (1978), S. 223-235 
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    Notes: Abstract An analysis of the hydrodynamics of aqueous flow in the posterior chamber of the anterior segment of the eye is presented. The viscid, incompressible description of fluid dynamics in a spherical geometry is utilized to reduce the problem to a biharmonic-type equation using a “Stokes Stream Function”. Analogous to Poiseuille flow in a cylindrical pipe, velocity profiles are deduced and an Ohms Law relationship between pressure and flow is derived in terms of the geometry of the assumed model. This result is then incorporated into a synthesized electric circuit analog of flow between ciliary artery and episcleral vein. Applications to open angle and pupilary block glaucoma are discussed.
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    On the nerve impulse equation: The dynamic responses of nerve impulse (1978)
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    Bulletin of mathematical biology 40 (1978), S. 247-255 
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    Notes: Abstract With the assumption of dipole interaction with the membrane matrix, the dipole barrier under an applied field shows a minimum in its time transient. Kinetic equations governing the migration of ions are presented. Na+ activation, Na+ inactivation and K+ delay are all part of the same mechanism in this model with no other separate assumptions needed. Voltage Clamp equation and action potential equation are presented.
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    Metabolic model and dosimetric data for copper (1978)
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    Bulletin of mathematical biology 40 (1978), S. 265-269 
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    Notes: Abstract A metabolic model for copper is derived and presented in the context of the International Commission on Radiological Protection (ICRP) dosimetry models for the lungs and gastrointestinal tract.
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    Analytical conditions for the conservative form of the ecological equations (1978)
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    Bulletin of mathematical biology 40 (1978), S. 257-264 
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    Notes: Abstract The analytical conditions by which a Volterra's general system describingn interacting species can be put in the “conservative” form have been examined. The cases forn=2, 3, 4 have been analyzed in detail and a general condition for any value ofn is deduced. The analytical and biological constraints following by this approach are compared to the conclusions drawn by Leigh on the ground of purely biological considerations.
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    On the stochastic theory of compartments: III. General time-dependent reversible systems (1978)
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    Bulletin of mathematical biology 40 (1978), S. 237-246 
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    Notes: Abstract General formulation of stochastic single- and multi-compartment reversible systems with time-dependent transitions is made. The correspondence between the stochastic mean and the deterministic value is established in case of time-dependence and it is shown how the consequence of this can be utilized to compute the distribution and the moments of each individual compartment of the system. A two-compartment reversible system previously proposed by Cardenas and Matis (1975a) is analyzed on the basis of the theory.
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    Mathematical models of metabolic regulation, symposia biologica hungarica (1978)
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    Bulletin of mathematical biology 40 (1978), S. 271-272 
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    Optimal control of pests in the presence of predators (1978)
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    Bulletin of mathematical biology 40 (1978), S. 319-333 
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    Notes: Abstract Optimal control theory is applied to the problem of controlling pests by biological and chemical means simultaneously. The net birth rate of the pests is controlled chemically while at the same time predators are allowed to operate. Several numerical examples are included.
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    Transient behaviour of the single loop solute cycling model of the renal medulla (1978)
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    Bulletin of mathematical biology 40 (1978), S. 273-300 
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    Notes: Abstract Transient solutions are developed for the buildup of a concentration gradient in the single loop solute cycling model of the renal medulla. The “pump” from ascending limb to descending limb is considered in both unsaturated and completely saturated modes of operation. Both analytic solutions and semianalytic solutions obtained from inverting Laplace transforms are considered. The classic representation of concentration buildup by the multiplication process is compared with calculated profiles. The “single effect” is found to vary both in time and space.
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    The Krylov-Bogoliubov-Mitropolskii method applied to models of population dynamics (1978)
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    Bulletin of mathematical biology 40 (1978), S. 335-345 
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    Notes: Abstract In this study the possibility of applying the asymptotic method of Krylov-Bogoliubov-Mitropolskii to problems of population dynamics is shown. Especially a general Volterra-Gause-Witt type model for prey-predator interaction is investigated. A discussion on the results obtained is given for the general model and for a particular case as well.
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    A dynamical field theory for dissipative systems: The hierarchical structure of field thermodynamics (1978)
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    Bulletin of mathematical biology 40 (1978), S. 301-318 
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    Notes: Abstract The analytical exploration of hierarchical structures is a central problem in modern biology. In many ways, the most basic tenet of any theory of any biological system is that its behavior lies within the laws of thermodynamics. Thus an investigation into the hierarchical structure of field thermodynamics is in effect an investigation into the underlying structures common to all biological systems. In field thermodynamics, the dynamics is prescribed at the hierarchical level of description concerned with the motions of classes of the various molecular species flowing in the system. Of crucial importance are scale factors which convert potentials into potential energies per mole of the various molecular species. On the other hand, the overall behavior of the system is presented at a higher hierarchical level of description in terms of systemic properties such as charge density or entropy density. Three questions are investigated: (1) how is the transition from the specific to the systemic level of description effected, (2) given the scale factors at the specific level how does one find those at the systemic level, and (3) what relationship can one, find between the scale factors at the two levels of description? Answering these questions necessitates an examination of the nature of the forces at the two levels of the hierarchy of descriptions.
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    Reconstitution of the transition matrix from experimental data (1978)
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    Bulletin of mathematical biology 40 (1978), S. 369-376 
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    Notes: Abstract The identification of a linear compartment model, which may describe a chemical or biological process, is a difficult task, since the available data is generally limited. In this paper we propose a method for determining the state transition matrix by minimizing a given quadratic criterion. To solve the resulting matrix equation, an assumption has to be made which constitutes a necessary condition for the identifiability of the model. Moreover when this assumption is satisfied, it is shown that the knowledge of one line or one column of the transition matrix is sufficient to define it completely.
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    Analytical solution to isometric mechanogram of hill’s model of striated muscle (1978)
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    Bulletin of mathematical biology 40 (1978), S. 359-368 
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    Notes: Abstract The two-element muscle model considered consists of a contractile element defined by a hyperbolic force-velocity relation connected in series with an “exponential spring”. Differential equations for the isometrically developed force during a tetanic contraction and the corresponding contractile element shortening velocity are derived and their stability is investigated. Analytical solutions to both equations are obtained. Two numerical examples are given, the second chosen to illustrate pressure-induced hypertrophy of a cardiac muscle.
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    Lag time in microbe growth as an age-dependent branching process with two phase types (1978)
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    Bulletin of mathematical biology 40 (1978), S. 347-358 
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    Notes: Abstract We study a two-type, age-dependent branching process in which the branching probabilities of one of the types may vary with time. Specifically this modification of the Bellman-Harris process starts with a Type I particle which may either die or change to a Type II particle depending upon a time varying probability. A Type II particle may either die or reproduce with fixed probabilities but may not return to a particle of Type I. In this way the process models the lag phenomenon observed in microbe growth subsequent to transfer to a new culture medium while the organism is adapting to its new environment. We show that if the mean reproduction rate of Type II particles exceeds 1, then the population size grows exponentially. Further the extinction probability for this process is related to that of the Bellman-Harris process. Finally the governing equations are solved for several choices of the growth parameters and the solutions are graphically displayed showing that a wide variety of behavior can be modeled by this process.
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    Linear age-dependent population growth with harvesting (1978)
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    Bulletin of mathematical biology 40 (1978), S. 377-385 
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    Notes: Abstract This paper studies the effect of harvesting a fraction of a population where the population growth is modelled by a linear age-dependent model, the Von Foerster equation. Two harvesting strategies are considered: the first is where a fraction of the population greater than agec is removed, and the second is where a fraction of the population of age greater thanc but less thanc+n is removed. In the case where the death rate and fertility rate are time independent, the effect of harvesting on the stable age distribution is examined.
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    A comment on the Richardson-Miekisz field theory of thermodynamics (1978)
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    Bulletin of mathematical biology 40 (1978), S. 425-426 
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    Multiple speciation, competitive exclusion, evolutionary pattern, and the grand ensemble in volterra eco-dynamics (1978)
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    Bulletin of mathematical biology 40 (1978), S. 387-410 
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    Notes: Abstract The general means are set forth by which, in a highly speciated Volterra eco-system, the bifurcation of a species into two in a competitive-exclusion configuration, provides a description of odd as well as even systems. The the Gibbs ensemble theory earlier developed is extended to grand ensembles in which the number of ecotypical species in genera-like clusters is allowed to be variable. The probability law for the sizes of clusters is deduced, and shown very closely to imply independent Poisson statistics for the cluster sizes, in answer to a fundamental issue of bioevolution. The role of the eco-analogs of Gibbs’ chemical potentials is brought forth, with a suggestion of how to describe cluster-to-cluster eco-genetic flows, and therewith a definite relationship between the degrees of speciation of genetically linked clusters on the one hand, and amplitudes of population fluctuations of member species within the clusters on the other hand.
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    The stochastic theory of compartments—a mammillary system (1978)
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    Bulletin of mathematical biology 40 (1978), S. 427-427 
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    Ionic concentration profiles and charge distribution for the domain of a polarized spherical cell (1978)
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    Bulletin of mathematical biology 40 (1978), S. 411-424 
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    Notes: Abstract Solutions of the Poisson-Boltzmann equation yield potential profiles and equilibrium distributions of ions on either side of a spherical shell membrane across which there exists a separation of ionic charges. For the special case in which the membrane is permeable to only one ion the total charge separation is analyzed in terms of the potential difference given by the Nernst equation. Potential profiles and ionic charge distributions are also given for situations involving a uniform distribution of fixed charges within the membrane.
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    An elementary approach to catastrophe theory (1978)
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    Bulletin of mathematical biology 40 (1978), S. 429-450 
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    Notes: Abstract The recently proved classification theorem of René Thom has led to the development of the new science of Catastrophe Theory. This theory has been widely held to be particularly relevant in biological applications. The present paper presents a simplified proof of Thom’s Theorem and assesses its importance in biology.
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    Mechanical behaviour of ventricular aneurysms (1978)
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    Bulletin of mathematical biology 40 (1978), S. 451-464 
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    Notes: Abstract A mathematical model describes the mechanical behaviour of ventricular aneurysms assuming a spherical geometry for the left ventricle. Employing pressure-volume data obtained from normal dog hearts 1–2 hours after infarction, conditions are obtained on infarct thickness and angle of damage for ventricular rupture to occur. The results indicate that rupture is more likely to occur in the early period following infarction and that the dominant factor is the per cent thickness of the infarct.
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    A stochastic approach to predator-prey models (1978)
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    Bulletin of mathematical biology 40 (1978), S. 483-498 
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    Notes: Abstract A deterministic investigation of a linear differential equation system which describes predator vs prey behavior as a function of equilibrium densities and reproductive rates is given. A more realistic structure of this model in a stochastic framework is presented. The reproductive rates and initial population sizes are considered to be random variables and their probabilistic behavior characterized by various joint probability distributions. The deterministic behaviors of the prey and predator species as functions of time are compared with the mean behaviors in the stochastic model.
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    Effects of external pressures on the pressure-volume relation of the left ventricle (1978)
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    Bulletin of mathematical biology 40 (1978), S. 465-482 
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    Notes: Abstract The effects of ventricular geometry, muscle mass, muscle elasticity and external pressures on the pressure-volume and muscle stiffness-stress relations have been quantitated on the basis of a theoretical model. Data taken from patients before and after interventions with nitroprusside and angiotensin were applied to the model in order to explain the possible causes for the marked shifts in the pressure-volume relations. The results indicate that (a) ventricular geometry does not markedly alter the pressure-volume and stiffness-stress relations unless there is a drastic change from a spherical shape to an ellipsoidal shape orvice versa, (b) increases in muscle mass and muscle elasticity of the order of 30% result in significant alterations in the P-V relations but are not the cause for the parallel shifts unless accompanied by substantial external pressures, (c) the parallel shifts in the pressure-volume relations can be accounted for entirely by the presence of external pressures without changes in muscle mass or muscle elasticity. Thus manipulation of right ventricular pressures or pericardial pressures by drug interventions may be useful in the treatment of left heart disease and the presence of such pressures must be considered in the analysis of ventricular function curves.
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    Qualitative similarities between the behavior of coupled oscillators and circadian rhythms (1978)
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    Bulletin of mathematical biology 40 (1978), S. 675-692 
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    Notes: Abstract This paper summarizes in a nonmathematical way the major properties of coupled oscillators which relate to circadian rhythms. For certain values of the coupling strength it is far easier to maintain synchrony than to achieve it among the various interacting units. This property not only simulates the free run period lability but also the effects of critical pulses.
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    The effects of asymptomatic attacks on the spread of infectious disease: A deterministic model (1978)
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    Bulletin of mathematical biology 40 (1978), S. 707-718 
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    Notes: Abstract A deterministic model for a multi-agent disease epidemic with asymptomatic attacks is proposed and investigated. The limitations inherent in the assumptions of the model are discussed in connection with specific agents of disease. The mathematical treatment of the model is separated into analyses of the equilibrium situation and the transient behavior of the disease outbreak. Explicit formulas are derived for the number of susceptibles in the population as well as for the numbers of each type of infective—those with and without symptoms. These theoretical results are followed by a discussion of the practical considerations which must be taken into account to obtain useful information from the model.
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    On a model and the kinetics of photo-enhanced enzyme reactions (1978)
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    Bulletin of mathematical biology 40 (1978), S. 719-726 
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    Notes: Abstract The recently observed enhancement, by laser irradiation, of the specific activity of the enzyme chymotrypsin (which hydrolyses Benzoyl-L-tyrosine-ethyl ester) at low enzyme concentration is considered. The enhancement of the reaction rate is attributed to a coherently excited state of the enzyme molecule (activated through Raman scattering of the laser light) following a prediction due to Fröhlich. The model is described, the kinetics of the process is framed and the observed enzyme-concentration dependence of the specific activity is reproduced. Predictions of the model are delineated to urge verification of the main contentions through further experimentation.
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    A two-component theory of aerosol deposition in lung airways (1978)
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    Bulletin of mathematical biology 40 (1978), S. 693-706 
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    Notes: Abstract The deposition of aerosol particles in the human lung airways is due to two distinct mechanisms. One is by direct deposition resulting from diffusion, sedimentation and impaction as the aerosol moves in and out of the lung. The other is an indirect mechanism by which particles are transported mechanically from the tidal air to the residential air and eventually captured by the airways due to intrinsic particle motion. This last mechanism is not well understood at present. Using a trumpet airway model constructed from Weibel's data, a two-component theory is developed. In this theory, the particle concentrations in the airways and the alveoli at a given airway depth are considered to be quantitatively different. This difference in concentrations will cause a net mixing between the tidal and residential aerosol as the aerosol is breathed in and out. A distribution parameter is then introduced to account for the distribution of ventilation. The effect of intrinsic particle motion on the aerosol mixing is also included. From this theory, total and regional deposition in the lung at the steady mouth breathing without pause is calculated for several different respiratory cycles. The results agree reasonably well with the experimental data.
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    On the kinetics of enzyme reactions (1978)
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    Bulletin of mathematical biology 40 (1978), S. 727-734 
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    Notes: Abstract The Abel type differential equation governing the kinetics of the enzyme reactions is derived. Approximate solutions of this equation corresponding to the transient phase of the reaction, before a steady state is reached, are considered. It is shown that in several cases it is possible to obtain explicit, approximate solutions to the transient phase.
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    Complementary variational principles for the steady-state finite cable model of nerve membranes (1978)
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    Bulletin of mathematical biology 40 (1978), S. 735-742 
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    Notes: Abstract Maximum and minimum principles for the steady-state finite cable model of nerve membranes are derived from the canonical theory of complementary variational principles. An accurate variational solution is obtained in an illustrative calculation.
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    Dynamical systems under constant organization I. Topological analysis of a family of non-linear differential equations —A model for catalytic hypercycles (1978)
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    Bulletin of mathematical biology 40 (1978), S. 743-769 
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    Notes: Abstract The paper presents a qualitative analysis of the following systems ofn differential equations: $$\dot x_i = x_i x_j - x_i \sum\nolimits_r^n { = 1} x_r x_s {\mathbf{ }}(j = i - 1 + n\delta _{i1} {\mathbf{ }}and{\mathbf{ }}s = r - 1 + n\delta _{r1} )$$ , which show cyclic symmetry. These dynamical systems are of particular interest in the theory of selforganization and biological evolution as well as for application to other fields.
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    Turing's theory in morphogenesis (1978)
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    Bulletin of mathematical biology 40 (1978), S. 771-789 
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    Notes: Abstract Bifurcation theoretical and numerical analyses of one of Turing's models are performed. It is shown that at the first instability point of the homogeneous state the bifurcating branches aresubcritical, and thus emerge as unstable solutions. This, together with the presence of concentration-independent sink terms is responsible for the solutions becoming negative ast→∞. It is pointed out that this deficiency is an accident related to the choice of the model, and that the general idea of symmetry-breaking is perfectly compatible with the generation of regular morphogenetic patterns.
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    On phase locking of pulse encoders (1978)
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    Bulletin of mathematical biology 40 (1978), S. 807-821 
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    Notes: Abstract Several models have been proposed to underststand the patterns of nerve impulses produced by periodic stimuli. This paper shows that for a very large class of such models there exists a pattern of phases that repeats periodically after a finite number of pulses; the actual pulses produced by the model depend on its initial condition, but in all cases they either follow such a pattern or approach it asymptotically.
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    Global flow equations for membrane transport from local equations of motion: I. The general case for (n−1) nonelectrolyte solutes plus water (1978)
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    Bulletin of mathematical biology 40 (1978), S. 791-805 
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    Notes: Abstract The global force-flow equations of nonequilibrium thermodynamics are obtained by solving the local equations of motion for a system ofn-components (n−1 solutes plus water) passing through a membrane. When viscous forces and position dependent membranepermeating species frictional interactions are considered, it becomes more difficult to obtain the result because even the stationary state problem becomes one of solving a second order linear ordinary differential equation for the barycentric velocity in a space divided inton+1 regions. Using the continuity of the boundary velocities and their gradients as well as the usual boundary conditions for the hydrodynamic problem, a set of 2n+1 linear equations in the intergration constants can be obtained and a closed form solution is possible. The resultant global description of the system does not obey Onsager reciprocity. What is more, the interpretation of global phenomenological coefficients in terms of local interactions in any simple way is next to impossible. This makes the hope of a molecular level interpretation of phenomenological membrane transport coefficients very slim. The relevance of this finding to the validity of reductionist approaches to biological transport is discussed.
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    A mathematical model of transmural transport of oxygen to the retina (1978)
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    Bulletin of mathematical biology 40 (1978), S. 823-837 
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    Notes: Abstract A mathematical model of transmural transport of oxygen to a metabolizing retina is presented based on the equations of fluid dynamics. The equations of oxygen transfer are derived and then solved subject to the condition that the capillaries begin to transport oxygen at an initial time. The resulting transient analysis gives us insight into how diffusive and filtrative processes lead to the oxygen distributions both inside and outside capillaries. On the other hand, the steady state solution allows us to predict the cutoff intraocular pressure above which no oxygen is transferred to retinal tissue. It also gives quantitative relationships which allow us to postulate how intracapillary hypertension counterbalances elevated intraocular pressures and how low pressure glaucoma may arise from ineffective diffusive and filtrative processes of oxygen transport.
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    Interactions among biological systems: An analysis of asymptotic stability (1978)
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    Bulletin of mathematical biology 40 (1978), S. 839-851 
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    Notes: Abstract An analysis of the interactions among asymptotically stable dynamical systems is formulated by making use of the dynamical system theory. Some results coming from previous mathematical analyses have been slightly modified to take into account some typical biological constraints as the boundedness properties of the solutions. In particular it has been shown that when the “coupling” among the subsystems is “loose” enough (in a sense that has to be made mathematically precise) the asymptotic behaviour of a complex system is the same of that of its individual components. The mathematical theory has been used to analyze two systems of biological significance: the coupling among chemical reactions and the stability properties of a 4-dimensional system describing the kinetics of a chemical transmitter.
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    Steady state bifurcation analysis of reaction-diffusion equations-A critique (1978)
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    Bulletin of mathematical biology 40 (1978), S. 865-872 
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    Notes: Abstract This note supplies missing details and corrects some mathematical errors in the recent significant paper by Auchmuty and Nicolis (1975).
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    Preface (1977)
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    The Geneva risk and insurance review 4 (1977), S. 3-3 
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    2. Risk and insurance economics (1977)
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    The Geneva risk and insurance review 4 (1977), S. 16-40 
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    1. Aims, methods, and limits of the present study (1977)
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    The Geneva risk and insurance review 4 (1977), S. 5-15 
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    3. Course outlines and suggested bibliographies (1977)
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    The Geneva risk and insurance review 4 (1977), S. 41-55 
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    4. Catalogue of teaching in risk and insurance economics (1977)
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    The Geneva risk and insurance review 4 (1977), S. 56-57 
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    5. Professional training in insurance (1977)
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    The Geneva risk and insurance review 4 (1977), S. 58-63 
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    Bibliography (1977)
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    The Geneva risk and insurance review 4 (1977), S. 64-64 
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    Introduction (1977)
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    The Geneva risk and insurance review 5 (1977), S. 3-8 
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    L'approche empirique de la demande d'assurance-vie (1977)
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    The Geneva risk and insurance review 5 (1977), S. 22-34 
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    Ansätze einer Betriebswirtschaftlichen theorie des versicherungsunternehmens (1977)
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    The Geneva risk and insurance review 5 (1977), S. 9-21 
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    Notes: Zusammenfassung Insgesamt liegen für eine güterliche Theorie des Wirtschaftens im Versicherungsunternehmen bereits heute viele Ansätze vor, insbesondere soweit es den Risikoausgleichsprozeß betrifft. Dagegen stecken die produktionstheoretischen Ansätze für die übrigen Input-Output-Beziehungen noch in den Kinderschuhen. Dies entpricht dem allgemein zu beobachtenden Rückstand in der betriebswirtschaftlichen Erforschung von Dienstleistungsunternehmen.
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    La demande d'assurance non-vie: L'état actuel de la théorie (1977)
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    The Geneva risk and insurance review 5 (1977), S. 35-42 
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    Optimal life insurance (1977)
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    The Geneva risk and insurance review 6 (1977), S. 3-16 
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    International insurance transactions and the balance of payments (1977)
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    The Geneva risk and insurance review 6 (1977), S. 17-35 
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    Economics, vulnerability and the diminishing returns of technology (1977)
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    The Geneva risk and insurance review 6 (1977), S. 36-52 
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    Insurance in the national accounts: A case-study of France (1977)
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    The Geneva risk and insurance review 6 (1977), S. 76-89 
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    New dimensions of risk: Consequences for management (1978)
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    The Geneva risk and insurance review 7 (1978), S. 3-15 
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    Business cycles and insurance (1977)
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    Notes: Concluding remarks In order to learn from the relations between business cycle and single branches of insurance, we should not only analyse the kind of their cyclical dependences but also regard the quantitative effects. But already, the submitted investigation allows the conclusion, that the oscillations of the claims not always are random but to a large degree cyclical. p ]Whether it will be possible to use leading business indicators for the forecast of premium income can not yet be proofed for sure. Nevertheless, the present, study suggests the assumption that further investigations in this direction may lead to success.
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    Trends of risk and security problems for states and emerging strategies for coping with those trends (1978)
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    The Geneva risk and insurance review 7 (1978), S. 16-25 
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    The investments of insurance companies: Difficulties new and old (1978)
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    The Geneva risk and insurance review 7 (1978), S. 26-34 
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    Industrial management flexibility in times of economic change (1978)
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    The Geneva risk and insurance review 7 (1978), S. 35-41 
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    Foreword (1978)
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    The Geneva risk and insurance review 8 (1978), S. 3-3 
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    Security as a service (1978)
    Springer
    The Geneva risk and insurance review 7 (1978), S. 42-55 
    Details
    ISSN: 1554-9658
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02153551
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    Paper (German National Licenses)
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  • 100
    Electronic Resource
    Electronic Resource
    Risk allocation and information: Some recent theoretical developments (1978)
    Springer
    The Geneva risk and insurance review 8 (1978), S. 5-19 
    Details
    ISSN: 1554-9658
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02153620
    Location Call Number Expected Availability
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    Paper (German National Licenses)
    Fulltext
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