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  • Books  (136)
  • Articles  (49,324)
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  • 1975-1979  (39,017)
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  • Books  (136)
  • Articles  (49,324)
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  • 1
    Electronic Resource
    Electronic Resource
    Editorial (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
    Details
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00738.x
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  • 2
    Electronic Resource
    Electronic Resource
    The Chance and Probability Concepts Project (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00739.x
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  • 3
    Electronic Resource
    Electronic Resource
    Old Problems in New Clothes (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00740.x
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  • 4
    Electronic Resource
    Electronic Resource
    Teaching Statistical Literacy (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00741.x
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  • 5
    Electronic Resource
    Electronic Resource
    On Calculating a Standard Deviation (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
    Details
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00743.x
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  • 6
    Electronic Resource
    Electronic Resource
    Learning from One's Mistakes (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00742.x
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  • 7
    Electronic Resource
    Electronic Resource
    The Stirling Recording Sheet for Experiments in Probability (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00744.x
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  • 8
    Electronic Resource
    Electronic Resource
    Seven, and wiser, Virgins (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
    Details
    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00745.x
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  • 9
    Electronic Resource
    Electronic Resource
    Letters (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00746.x
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  • 10
    Electronic Resource
    Electronic Resource
    Editorial (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00351.x
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  • 11
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    Book Reviews (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Book reviewed in this Article: Demystifying Social Statistics. J. Irvine, I. Miles J. Evans (eds.). Prciples of Statistical Techniques. By P. G. Moore.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00747.x
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  • 12
    Electronic Resource
    Electronic Resource
    Learning Statistic Through Project Work (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: What are the problems we can expect to meet when project work forms a significant part of a C.S.E. examination course in statistics? Mrs Dolan describes her experiences.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00352.x
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  • 13
    Electronic Resource
    Electronic Resource
    Applications of Probability Theory in Industry (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article is one of a series. Here we take a problem that has arisen in an industry and show how a simple application of probability theory helped in its solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00353.x
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  • 14
    Electronic Resource
    Electronic Resource
    Statistics Within Technician Courses (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Two of the newer bodies producing syllabuses for the 16 to 19 year age range are the Technician Education Council (TEC) and the Business Education Council (BEC). Trevor Easingwood, the chairman of the joint BEC/TEC committee for mathematics and statistics, describes the background to the statistics in the TEC courses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00354.x
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  • 15
    Electronic Resource
    Electronic Resource
    Animals in a Pond (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Bringing a pond into the classroom can enrich the teaching of statistics as well as biology and bring them together.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00355.x
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  • 16
    Electronic Resource
    Electronic Resource
    Statistics at County Hall (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: ‘But how is statistics used in practice?’ ask our pupils. Peter Reynolds outlines two applications that landed on his desk.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00356.x
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  • 17
    Electronic Resource
    Electronic Resource
    What is: the RSS? (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00357.x
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  • 18
    Electronic Resource
    Electronic Resource
    The First shall be Last (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Combining samples from different distributions is a hazardous process. Traditionally form orders in schools have been produced by combining the marks from different subjects. Bryan Wilson describes a teaching approach to sensitize student teachers to the dangers of doing this.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00358.x
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  • 19
    Electronic Resource
    Electronic Resource
    Have You Seen This? (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00360.x
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  • 20
    Electronic Resource
    Electronic Resource
    Faulty Questions (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00361.x
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  • 21
    Electronic Resource
    Electronic Resource
    Statistics at CEE (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: With large numbers of pupils staying on into the sixth form for one year there is a need for a suitable statistics course. Jim Hillyer describes one such course for which he is the chief examiner.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00359.x
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  • 22
    Electronic Resource
    Electronic Resource
    Book Reviews (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Books Reviewed in this Article: Statistics: A guide to the unknown. Edited by J. M. TANUR et al. Holden Day. Mathematical Carnival. By MARTIN GARDNER
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00362.x
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  • 23
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    News and Notes (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00363.x
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  • 24
    Electronic Resource
    Electronic Resource
    The First shall be Last-Answers (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00364.x
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  • 25
    Electronic Resource
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    Notes for Contributors (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 26
    Electronic Resource
    Electronic Resource
    Editorial (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 27
    Electronic Resource
    Electronic Resource
    Probability in a Primary School (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 28
    Electronic Resource
    Electronic Resource
    Do Bristlebacks Cluster? (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00729.x
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  • 29
    Electronic Resource
    Electronic Resource
    Blindfold Climbers (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9639.1979.tb00731.x
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  • 30
    Electronic Resource
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    Statistical Education 11 to 16 — The Schools Council Project (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 31
    Electronic Resource
    Electronic Resource
    Statistics in Sixth Form Economics (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 32
    Electronic Resource
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    What is: the ISI? (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 1 (1979), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 33
    Electronic Resource
    Electronic Resource
    John Arbuthnot (1979)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 34
    Electronic Resource
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    Book Reviews (1979)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Book reviewed in this Article: A Basic Course in Statistics. By G. M. Clarke and D. Cooke. How to use (and misuse) Statistics. By Gregory A. Kimble.
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  • 35
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    News and Notes (1979)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 36
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    Letters (1979)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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  • 37
    Electronic Resource
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    Modeling of biological tree structures (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 893-898 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Biological tree-like structures, such as mammalian tracheobronchial airways, are complicated branching systems. One problem in modeling such systems is the reassignment of the number of segments at a given generation in the model being constructed. A hypothesis is proposed which has successfully been used in modeling mammalian lung airways.
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  • 38
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    Diversity and diffusion in multidimensional niche space (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 129-138 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The results of an earlier effort to provide a geometrical analysis of Hutchinsonian niche space are extended. The concept of diversity of a species in niche space is introduced and the maximization of this diversity provides a rationale for a within-niche fitness distribution which is Gaussian. Niche expansion is seen as a consequence of diffusion in niche space, and an evolutionary version of the Volterra competition equations is proposed as a way to relate niche geometry with population dynamics. Applications to topics in community evolution, species packing and the statistical fitting of species abundance data are mentioned.
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  • 39
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    Stochastic compartmental modeling and parameter estimation with application to cancer treatment follow-up studies (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 203-215 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper we use marginal probabilities to derive expressions for the means, variances and covariances ofm-compartment systems. We also present an efficient algorithm for the estimation of the parameters of the system using time series data when measurements are available fromk of them compartments. An application of the analysis and parameter estimation procedure for a model representing the results of a cancer treatment follow-up study is given.
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  • 40
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    Self-organization in biological systems with multiple cellular contacts (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 193-201 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The self-organizing properties of an ensemble of interconnected units are studied by linear stability analyses. Small perturbations of a uniform steady-state may result in bifurcations to other solutions that exhibit spatial or temporal order. We show that increasing the number of connections that a unit makes with its neighbors changes the nature of these solutions and tends to destroy spatiotemporal patterns. If an unconnected system is orginally stable, the formation of multiple interconnections can never induce temporal periodicity but may, under certain circumstances, allow the emergence of stationary spatial patterns. We have verified the predictions of the linear stability analysis on a model system and comment on the implications of these results for multicellular ensembles.
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  • 41
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    Performance criteria for optimization of cardiac assistance (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 217-227 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A performance criterion and weighting factors for the optimal cardiac assistance are investigated by applying Tellegen's network theorem and tolerance analysis on animal experimental data for left ventricular (LV) bypass on the failing heart. Two major factors with respect to cardiac assistance (total power delivered to the peripheral circulatory system, and changes in temporal pattern of ventricular contraction) are represented by two performance criteria,J 1 andJ 2 whereJ 1 relates to the sum of LV and pump power, andJ 2 relates to the “peakedness” factor of LV power. The total performance index (J) is determined as the weighted sum ofJ 1 andJ 2;J=w 1J1+w2J2. The weighting factors,w 1 andw 2, are computed as inverses of the tolerance in the performance contours with respect to improvement of stroke work per minute from pre- to post-bypass condition.
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    URL: http://dx.doi.org/10.1007/BF02460880
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  • 42
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    Catastrophe theory: Selected papers 1972–1977 (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 253-255 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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  • 43
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    Volterra-Verhulst prey-predator systems with time dependent coefficients: Diffusion type approximation and periodic solutions (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 229-251 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract In treating the Volterra-Verhulst prey-predator system with time dependent coefficients, we ask how far this deterministic system represents or approximates the dynamics of the population evolving in a realistic environment which is stochastic in nature. We consider a stochastic system withsmall Gaussian noise type fluctuations. It is shown that the higher moments of the deviation of the deterministic system from the stochastic approach zero as the strength δ of the perturbation decays to zero. For any δ〉0 and allT〉0, ε〉0, the sample population paths that stay within ε distance from the deterministic path during [0,T] form a collection of positive probability. In comparing the stationary distributions of the two systems, we show that the weak limits of those of the stochastic system form a subset of those of the deterministic system. This is in analogy with a result of May connected with the stability of the two systems. Plant and rodent populations possess periodic parameters andexhibit periodic behaivor. We establish theoretically this periodicity under periodicity conditions on the coefficients and perturbing random forces. We also establish a central limit property for the prey-predator system.
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    A theoretical study of neural adaptation and transient responses due to inhibitory feedback (1979)
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    Bulletin of mathematical biology 41 (1979), S. 257-282 
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    Notes: Abstract Adaptation of repetitively firing sensory neurons and nerve models is correlated with specific inhibitory feedback phenomena—an electrogenic sodium pump, and post synaptic self inhibition. The quality of the adaptive responses depends on the excitation properties of the neuron in the interspike interval, or the description of these properties by the underlying impulse encoder model. THis model dependence is demonstrated by comparisons of the behavior of two classes of models; the “leaky integrator models” which assume a passive neural membrane, and the “variable-γ models”, for which the neural state of excitation varies according to first order differential equations. The complexity inherent in the variable-γ models is effectively boiled down to mathematically simple relationships which are derived from studies of the neural- and model frequency responses to small amplitude sinusoidal stimuli. It is argued, and supported with examples, that these relationships hold for impulse frequency transients resulting from more general stimulus conditions. Expressions are then derived which permit feedback parameters to be determined from impulse frequency data. In this connection, recent studies of neural dynamics are brought to bear to resolve ambiguities in data interpretation.
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    On the measurement of shape (1979)
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    Bulletin of mathematical biology 41 (1979), S. 283-304 
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    Notes: Abstract A setQ(n) of noncongruent connected shapes, constructed from a fixed numbern of congruent regular hexagons laid edge to edge, is defined. Various measures of shape are applied toQ(n) and the results are numerically analyzed in the special casesn≦9. The concept of spatial entropy is introduced which affords a measure of the “complexity” of shape. Possible biological applications include the analysis of ecological cover,stigmergy or the complex nest-building activities of social insects and morphogenesis. Essentially any comparative study of shape, regardless of the specific application, might be carried out along the lines suggested in the paper.
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    Mathematical approaches to optimization of cancer chemotherapy (1979)
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    Bulletin of mathematical biology 41 (1979), S. 305-324 
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    Notes: Abstract This paper uses optimal control theory in conjunction with a Gompertzian type model for cellular growth to determine the optimal method of administering cycle non-specific chemotherapy or more generally the optimal durations of treatment and rest periods during chemotherapy. The performance critera employed to determine the relative merits of the therapy include not only the destruction of malignant cells, but also the sparing of a critical normal tissue. Since these criteria are at odds with one another, the solutions are found which satisfy the Pareto optimality conditions.
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    Asymptotic solutions of differential equations with time delay in population dynamics (1979)
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    Bulletin of mathematical biology 41 (1979), S. 325-342 
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    Notes: Abstract Oscillations governed by generalized Volterra-Gause-Witt equations to include retardation effects in population dynamics are considered. Models containing either small or significant time delay are discussed. The Krylov-Bogoliubov-Mitropolskii perturbation method and its extension for differential equations with retarded argument is used.
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    Time development of probability distributions for interacting species (1979)
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    Bulletin of mathematical biology 41 (1979), S. 357-364 
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    Notes: Abstract A general solution to the dynamical equation for the probability distribution associated withn interacting species is obtained by employing the author's generic canonical expression for the rate functions. Interacting species models with limit-cycle dynamics and no stable equilibrium points feature probability distributions that are asymptotic for large values oft to Dirac δ-distributions concentrated on the limit-cycles, as illustrated here for an analytically solvable two-species model. For ann-species Volterra model, a stationary or temporally-averaged probability distribution should generally be much more complicated than the specialized Poisson form studied by Kerner and others.
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    Nernst-planck analog equations and stationary state membrane electric potentials (1979)
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    Bulletin of mathematical biology 41 (1979), S. 365-385 
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    Notes: Abstract A set of coupled nonlinear differential equations, determining the concentration profiles and electric potentials valid for isothermal transport of ions and molecules across a diffusion barrier are formulated, using a correction to the limiting expression for chemical potential gradients and the molecular expression for frictional force. These differential equations are similar to Nernst-Planck equations and reduce to these under appropriate approximations. Solutions of these equations valid under specified conditions are presented. Expressions for permeability, concentration profiles of many ion systems are included.
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    Global flow equations for membrane transport from local equations of motion—II. The case of a single nonelectrolyte solute plus water (1979)
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    Bulletin of mathematical biology 41 (1979), S. 629-640 
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    Notes: Abstract The global flow equations of nonequilibrium thermodynamics for a single nonelectrolyte solute and water passing through a membrane are obtained by solving the local equations of motion. The method follows that developed for the general,n-solute case in the previous paper (Mikulecky, 1978). It is easily seen in this simple case that the passage from local interactions, formulated as position dependent frictional interactions in the equations of motion, to ghe global result involves a loss of any simple way of identifying particulars about local information. Two particular cases are analyzed in further detail: the case of no interaction within the pore and the case of constant interaction for both solute and solvent across the pore. In the former case, Onsager reciprocity survives in the global result if a self-consistent definition of the partial viscosity coefficients is used, while in the latter case, reciprocity is lost. Since, in many biologically interesting cases, the presence of interaction of the type considered here is likely to occur, the reciprocity condition should not automatically be assumed to hold.
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    Qualitative analysis of a model generating long potential waves in Ba-treated nerve cells—I. Reduced systems (1979)
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    Bulletin of mathematical biology 41 (1979), S. 665-686 
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    Notes: Abstract This study is related to a model describing the behavior of barium-treatedAplysia neurons generating regular burst-plateau patterns. The model is represented by an autonomous dynamical system, defined inR 4 and depending on a small parameter. This paper is restricted to the qualitative study of three “reduced systems” deduced from the “complete system”. Part of the study is performed with the use of the qualitative theory of singular perturbations. The predicted behaviors are compared with experimental results.
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    Some results about nonlinear chemical systems represented by trees and cycles (1979)
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    Bulletin of mathematical biology 41 (1979), S. 641-664 
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    Notes: Abstract Using linear stability analysis, the qualitative stability properties of open nonlinear chemical systems, in which reactions of any order may occur, will be studied. Systems will be classified in three fundamental classes: trees, cycles and loops, according to their knot graphs. The study of the Jacobian matrix for the kinetic equations of the system shows that the symmetrizability by a particular procedure (calledD-symmetrizability) is a sufficient condition for stability. It has been proved that tree-graphs always satisfy the above condition. For the cycle-graphs, theD-symmetrizability condition leads to a cyclic relation between forward and reverse steady state flows. The stability may be assured, even if the cyclic relation is not satisfied, providing that the “symmetry breaking” be lower than an upper bound; further alternative criteria for stability of cycles have been derived. All these results are independent of the number of diffusive exchanges with the environment.
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    Analysis of the behaviour of Kauffman binary networks—I. State space description and the distribution of limit cycle lengths (1979)
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    Bulletin of mathematical biology 41 (1979), S. 687-705 
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    Notes: Abstract The basis of an analytical description of the behaviour of large random nets of binary elements of the type first investigated in detail by S. A. Kauffman is presented. It is shown that information about the network dynamics can be deduced from quite general considerations of the properties of the state transition graph and matrix. An expression for the matrix elements of the state transition matrix in terms of the Boolean function specification of the net is derived. Using these ideas the distribution of limit cycle lengthsl for a completely random net is calculated and shown to bex 1/l, a result which agrees well with experimental data.
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    Analysis of the behaviour of Kauffman binary networks—II. The state cycle fraction for networks of different connectivities (1979)
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    Bulletin of mathematical biology 41 (1979), S. 707-724 
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    Notes: Abstract The state-transition matrix description of Kauffman binary networks described in the previous paper is further developed to obtain an analytical expression for the fraction of states involved in limit cycles as a function of the network size and connectivity. The result obtained for totally connected networks agrees with that derived from quite different considerations by other workers. For low connectivity networks the results are in qualitative agreement with the experimental data of Kauffman but there is a quantitative discrepancy which remains to be resolved.
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    Persistence in food webs—I Lotka-Volterra food chains (1979)
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    Bulletin of mathematical biology 41 (1979), S. 877-891 
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    Notes: Abstract Persistence-extinction in simple food chains modelled by Lotka-Volterra dynamics is governed by a single parameter which depends upon the interspecific interaction coefficients, the intraspecific interaction coefficients, and the length of the food chain. In persistent systems with nonzero carrying capacity, two new features predominate. Trophic level influence factors relate persistence on different trophic levels and determine, in conjunction with the persistence parameter, the magnitude of persistence. Equilibrium component ordering, which results in persistent systems, mandates once again that systems need to be studied on the complete ecosystem level; static field measurements reflect species location in the food chain, the total length of the food chain and assume characteristics according to these factors.
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    Minimal oxygen consumption and optimal contractility of the heart: Theoretical approach to principle of physiological control of contractility (1979)
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    Bulletin of mathematical biology 41 (1979), S. 139-150 
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    Notes: Abstract Oxygen consumption of the left ventricle (MVO 2) was evaluated theoretically under the condition that the ventricle pumps a constant stroke volume against a constant arterial pressure, hence producing a constant external mechanical stroke work, with a widely varied contractility.MVO 2 was calculated by an empirical equation which had been inferred previously. Theoretical results indicated that the ventricle has a contractility at whichMVO 2 is minimal in spite of constant external work and therefore the mechanical efficiency as a pump is maximal. Such a contractility can be considered to be optimal from a standpoint of metabolic economy. The optimal contractility fell within the physiological range of contractility which had been observed experimentally. The result suggests a possibility that the contractility of a normal heart might be physiologically adapted to such an optimal level.
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    Nonlinear diffusion in biological systems (1979)
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    Bulletin of mathematical biology 41 (1979), S. 151-162 
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    Notes: Abstract Diffusion problem with variabale diffusion coefficient in a spherical biological system is investigated. Also included in this study is the biological reaction of the Michaelis-Menten type. The problem formulated consists of a highly nonlinear differential equation which, however, can be efficiently solved by the orthogonal collocation method on a digital computer. The effects of the dimensionless governing parameters on the transient and steady state concentration responses are parametrically examined for the diffusion system with and without biological reaction.
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    Electric potential in three-dimensional electrically syncytial tissues (1979)
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    Bulletin of mathematical biology 41 (1979), S. 163-181 
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    Notes: Abstract The problem of calculating the potential induced in an electrical syncytium by a point source of current is studied. The interiors of the many interconnected cells are treated as one continuum with resistivity ρ i . The interdigitated extracellular space is treated as a second continuum of resistivity ρ e , occupying the same overall volume, coupled to the first via the resistanceR m and capacitanceC m of the cell membranes. The intra- and extracellular potentials are then solutions to a pair of coupled partial differential equations. The equations are uncoupled, yielding a cable equation for the transmembrane potential and a Poisson equation for a second auxiliary potential. For an unbounded syncytium the potential for a step function source is obtained in terms of error functions. For a spherical syncytium of radiusa, bounded by a membrane with surface resistanceR a, and capacitanceC a, expansions are obtained in spherical harmonics and spherical Bessel functions. For ɛ=ρ ia/R a and β=ρ i /ρ e small, an asymptotic expansion of the potential is developed. The results are compared to earlier results for a spherical cell as well as to microelectrode measurements of the lens of the eye.
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    Electric potential in cylindrical syncytia and muscle fibers (1979)
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    Bulletin of mathematical biology 41 (1979), S. 183-192 
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    Notes: Abstract The model developed in an earlier paper using two coupled partial differential equations for calculating the intracellular and extracellular electric potentials in a syncytium is applied here to cylindrical geometry. Eigenfunction expansions are obtained for the potentials resulting from an intracellular point source of current. The required orthogonality relations for the two sets of coupled radial eigenfunctions are derived. The model is applied to the structure composed of the interior and the transverse tubules of a muscle fiber. Asymtotic expansions for ζ and β→0 are obtained, where ζ is the product of the effective intracellular resistivity, the fiber radius and the outer surface membrane admittance per unit area, and β is the ratio of the effective intracellular resistivity to that of the tubular lumen. Earlier results from the distributed circuit model of a muscle fiber are recovered when ζ and β are small, and for a nerve axon when β=0.
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    Analysis of potassium conductance in squid giant axons (1979)
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    Bulletin of mathematical biology 41 (1979), S. 343-356 
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    Notes: Abstract Assuming a model of facilitated ionic transport across axonal membranes proposed by McIlroy (1975) and extended by McIlroy and Hahn (1978), it is shown that if the selectivity coefficient, πK, of the potassium conducting system ≃59 the permeabilityP Ks, of the periaxonal barrier of the squid giant axon for K+ ions≃(1.2±0.44)×10−4 cm sec−1 and the thickness of the periaxonal space ≃477±168 Å. Using a value (10−4 cm sec−1) ofP Ks in the foregoing range the experimental curves for the steady state membrane ionic conductance versus measured membrane potential difference (p.d.), ϕ, of Gilbert and Ehrenstein (1969) are corrected for the effect of accumulation of K+ in the periaxonal space. This correction is most marked for the axon immersed in a natural ionic environment, whose conductance curve is shifted ≃70mV along the voltage axis in the hyperpolarization direction. By assuming that the physico-chemical connection between a depolarization of the axonal membrane and the consequent membrane conductance changes is a Wien dissociative effect of the membrane's electric field on a weak electrolyte situated in the axolemma, the position of the peaks of the corrected conductance versus ϕ curves can be identified with zero membrane electric field and hence with zero p.d.across the axolemma. A set of values for the double-layer p.d.s at the axonal membrane interfaces with the external electrolytes in the vicinity of the K+ conducting pores can therefore be deduced for the various external electrolytes employed by Gilbert and Ehrenstein. A model of these double-layer p.d.s in which the membrane interfaces are assumed to possess fixed monovalent negatively charged sites, at least in the neighbourhood of the K+ conducting pores, is constructed. It is shown that, using the previously deduced values for the doublelayer p.d.s, such a model has a consistent, physically realistic solution for the distance between the fixed charged sites and for the dissociation constants of these sites in their interaction with the ions of the extramembrane electrolytes.
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    Mutation-absorption model of the enzyme (1979)
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    Bulletin of mathematical biology 41 (1979), S. 387-405 
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    Notes: Abstract Gradual changes in function of proteins in response to single changes in primary structure are often observed to occur and are a necessary condition for evolution by variation and natural selection at the protein level. A probabilistic (entropy theory_ analysis of the effect of changes in primary structure on three-dimensional shape and function shows that such gradualism is based on the presence of a control system in the molecule involving a definite general form of structure-function degeneracy. The assumptions of the analysis are that primary structure determines tertiary structure (or a thermal distribution of tertiary configurations and allosteric forms), tertiary structure determines function (characterized by rate and other parameters), and that certain features of tertiary structure may be specialized for particular functions. The main conclusion is that embodied in the molecule is a subsystem which serves as a buffer, absorbing mutation or other forms of genetic variation and expressing these as graceful variations in features of the shape critical for function. This buffer system may be realized by numerical redundancy of amino acids or other mechanisms which increase the redundancy of weak interactions responsible for folding, utilization of amino acids having a greater number of analogs with redundant features, or local and global structural formats which allow for more effective utilization of redundancy. The mutation-absorption model has implications for the interpretation of structure-function relations in biology, the topology of the adaptive landscape, the interpretation of isoenzymes and allozymes, the relationship between selection and neutralism in evolution, and the relation between the complexity of and energy required by biological systems and the effectiveness of evolutionary optimization.
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    Some comments on activation and inhibition (1979)
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    Bulletin of mathematical biology 41 (1979), S. 427-445 
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    Notes: Abstract A system of rate equations gives rise to a corresponding pattern of activation and inhibition between the state variables. We consider the converse question: to what extent does the specification of a pattern of activation and inhibition between interacting quantities determine the rate equations? Among other things, it is shown that in order to determine a closed set of rate equations, a set of integrability conditions among the interactions must be satisfied; hence there is a sense in which an activation-inhibition pattern is more general than systems of rate equations. Questions of the structural interactions, are briefly discussed. A comparison is made between the properties of such activation-inhibition patterns and those of neural networks, or more general modular automata.
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    Global flow equations for membrane transport from local equations of motion: 1. The general case for (n−1) nonelectrolyte solutes plus water (1979)
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    Bulletin of mathematical biology 41 (1979), S. 447-447 
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    A teleological explanation of Weber's law and the motor unit size law (1979)
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    Bulletin of mathematical biology 41 (1979), S. 407-425 
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    Notes: Abstract It is shown that the Weber-Fechner law. which relates the response of a sensory biosystem to the intensity of the input stimulus, can be derived from a teleological principle of minimum transentropy (maximal noise reduction) provided the relative mean fluctuation (coefficient of variation) of the input intensity can be assumed to be (approximately) constant for all feasible mean input intensities. A law is then deduced from experimental results which quantifies the relationship existing between the relative amount of activated muscle mass and the “size” (which term is clearly defined) of a newly recruited motor unit. This law is found to be formally equivalent to the Weber-Fechner law when applied to motor unit recruitment. It is then shown that, in general, the ratio of the force increment upon recruitment, to the present force output does not obey Weber's law. Finally, it is proved that the “motor unit size law” as derived in this paper implies a fixed sequential order in the recruitment of motor units and that it may be viewed as the realization, by the mammalian neuromuscular system, of a general principle of maximum grading sensitivity.
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    Stability and selection in self-reproducing macromolecular systems (1979)
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    Bulletin of mathematical biology 41 (1979), S. 449-460 
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    Notes: Abstract In this paper we develop stability criteria applicable to Eigen's model for the selection and evolution of biological macromolecules. We show that it is possible to characterize the time evolution of the macromolecular system by Lyapounov-like functionals. The Lyapounov method is used to discuss the general stability of the system and the metastable nature of the selected states are discussed.
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    Chemical patterns in circular morphogenetic fields (1979)
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    Bulletin of mathematical biology 41 (1979), S. 461-468 
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    Notes: Abstract A model of morphogenetic pattern formation recently proposed by Frenchet al. (1976) is investigated in relation to the properties of reaction-diffusion systems operating on two-dimensional circular medium. One of the basic requirements of this model is the existence of a circular morphogenetic gradient exhibiting no discontinuity. We explain how bifur-cation theory may account for the generation of such a spatial pattern through reaction-diffusion processes. For this, we study the emergence of multiple-order bifurcations.
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    Bistability in fluctuating environments. Implications in tumor immunology (1979)
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    Bulletin of mathematical biology 41 (1979), S. 469-490 
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    Notes: Abstract We analyze under different environmental conditions the occurrence of bistability, i.e. of two simultaneously stables steady states, in a biological model system which describes the immunological interactions of neoplastic-target cells and cytotoxic-effector cells. As a result of environmental fluctuations such complex biological systems may undergo drastic modifications of their steady state properties. In particular, when the variance of fluctuations increases around a well defined mean value, transition phenomena appear which are absent in the usual bifurcation diagrams. The properties of the non-fluctuating systems can no longer be considered as a first approximation of the properties of the real system. Interestingly, in the case of the model, these transitions correspond to a rejection of tumor cells.
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    Some results on light penetration of an absorbing medium (1979)
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    Bulletin of mathematical biology 41 (1979), S. 517-523 
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    Notes: Abstract Two results on light penetration of an absorbing medium are presented in this paper: (1) It is shown, using the general light penetration law of Mannet al. (1977), that a random distribution of absorbing bodies (cells, leaves, etc.) is most efficient at intercepting direct beam (parallel) light. (2) A transmission coefficient is added to the general law in a manner similar to Monteith's (1965). This leads to the partitioning of the radiation regime beneath an absorbing medium into unintercepted, once intercepted, twice intercepted, etc., components. We are thus enabled to calculate the mean radiation intensity beneath the absorbing medium.
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    Compartmental models with multiple sources of stochastic variability: The one-compartment, time invariant hazard rate case (1979)
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    Bulletin of mathematical biology 41 (1979), S. 491-515 
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    Notes: Abstract Previous stochastic compartmental models have introduced the primary source of stochasticity through either a probabilistic transfer mechanism or a random rate coefficient. This paper combines these primary sources into a unified stochastic compartmental model. Twelve different stochastic models are produced by combining various sources of stochasticity and the mean value and the covariance for each of the twelve models is derived. The covariance of each model has a different form whereby the individual sources of stochasticity are identificable from data. The various stochastic models are illustrated for certain specified distributions of the rate coefficient and of the initial count. Several properties of the models are derived and discussed. Among these is the fact that the expected count of a model with a random rate coefficient will always exceed the expected count of a model with a fixed coefficient evaluated at the mean rate. A general modeling strategy for the onecompartment, time invariant hazard rate is also proposed.
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    Coexistence of photosynthetic microorganisms with growth rates depending on the spectral quality of light (1979)
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    Bulletin of mathematical biology 41 (1979), S. 525-542 
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    Notes: Abstract A new equation for the growth rate of photosynthetic microorganisms is derived. It is based on a series formulation of the mechanism of photosynthesis and it has the form of a functional of the spectral qualities of light. Using this functional to model their growth it is shown that populations of photosynthetic microorganisms can coexist in the same homogeneous environment even though they compete for the available light.
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    Stochastic prey-predator relationships: A random evolution approach (1979)
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    Bulletin of mathematical biology 41 (1979), S. 543-554 
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    Notes: Abstract The formalism and results of the theory of random evolutions are used to establish and investigate a model for two randomly interacting populations. The asymptotic stability of the expected solution is studied and contrasted to that of the associated deterministic system.
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    On a mathematical model describing the aggregation of amoebae (1979)
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    Bulletin of mathematical biology 41 (1979), S. 555-571 
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    Notes: Abstract In this paper an extension of a mathematical model of Keller and Segel (1970) describing the aggregation of amoebae is presented. In their paper (Keller and Segel, 1970) they showed that the onset of the aggregation could be viewed as a spatial instability. Their instability condition involved diffusion constants of the cyclic AMP and of the amoebae as well as a constant describing the chemotactic behavior of the amoebae. In our case we consider a temporal instability that depends only on the kinetics of cyclic AMP production, degradation and transport through the cell wall. Our model then explains the oscillatory behavior of the cyclic AMP in well-stirred suspensions of amoebae. In addition we discuss existence and non-existence of nonuniform steady states of the nonlinear parabolic system involved.
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    Markov branching processes with varying growth rates (1979)
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    Bulletin of mathematical biology 41 (1979), S. 607-610 
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    Notes: Abstract A branching processZ(t) which behaves as Markov branching processesZ 1(t) andZ 2(t) during the free and dead times of a counter process is considered. Expression forE[Z(t)] is given.
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    The method of harmonic balance applied to coupled asymmetrical van der Pol oscillators for intestinal modelling (1979)
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    Bulletin of mathematical biology 41 (1979), S. 573-589 
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    Notes: Abstract The spontaneous electrical rhythms recorded from the gastro-intestinal tract of humans and animals have been successfully modelled by an array of interconnected van der Pol oscillators. To account for asymmetry in the recorded waveforms (with particular reference to the human small intestine) an additional term in the van der Pol dynamics has been included. It is shown that the method of harmonic balance can be used to give analytical results for this asymmetrical condition. The non-linear algebraic equations are solved by hill-climbing to give values of d.c., fundamental and second harmonic amplitudes together with the entrained frequency. The results correlate well with actual measurements made on an analogue simulation by three different methods for waveshape factors of 0.1 and 1.0
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    A mathematical study of non-equimolar ternary gas diffusion (1979)
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    Bulletin of mathematical biology 41 (1979), S. 591-606 
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    Notes: Abstract In view of the increasing evidence that multicomponent diffusion effects could be significant in biological gas exchange systems, a non-equimolar film model of multicomponent diffusion was derived. “Osmotic” ternary diffusion was studied for the gas systems He−N2−O2, He−SF6−O2, and N2−SF6−O2. Diffusional fluxes and concentration profiles were calculated under both the “square-root” and the “product” flux conditions. Results were also compared with those obtained using the equimolar flux condition. It was found that the greater the difference of the diffusibilities between the two active components in a system, the greater the osmotic fluxes, and also the more alinear the concentration profiles. These results support the suggestion that the “product” condition applies to molecular diffusion in free space, the “square-root” condition to molecular diffusion in pores, and the equimolar flux condition to closed diffusion systems.
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    On stochastic compartmental modeling (1979)
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    Bulletin of mathematical biology 41 (1979), S. 611-613 
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    Notes: Abstract This communication contains a proof of the fact that the coefficient of variation of the contents of a compartment of a stochastic compartmental model with deterministic rate parameters is small for large populations. We can therefore conclude that the use of stochastic compartmental models is not of great consequence in the case of systems involving large populations when only the randomness of the transfer mechanism is considered.
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    Catastrophe theory and its applications (Surveys and reference works in mathematics2) (1979)
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    Bulletin of mathematical biology 41 (1979), S. 615-616 
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    Existence of a limiting pattern for a system of nonlinear equations describing interpopulation competition (1979)
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    Bulletin of mathematical biology 41 (1979), S. 617-628 
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    Notes: Abstract A system of arbitrarily many nonlinear ordinary differential equations which can be interpreted as describing competition between populations is studied here. It is found that limits exist for the system given specified constraints on the “signal function” which describes input-output relations at the level of single populations. Existence of limits is shown by means of a function which records which variable in the system is growing fastest at a given time i.e. who is winning the competition. Generalizations are discussed to sigmoid signal functions which appear in models of pattern discrimination by neuron populations.
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    On the distribution of the general irreversiblen-compartmental model having time-dependent transition probabilities (1979)
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    Bulletin of mathematical biology 41 (1979), S. 737-749 
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    Notes: Abstract The cumulant generating function and first two moments are derived for the stochastic distribution of units in a general irreversiblen-compartment model with time-dependent transition probabilities. In this model, a unit in the first compartment can transfer to any one of the remainingn−1 compartments and a unit in the second compartment can transfer to any of the remainingn−2 compartments and so on. In addition, a unit can enter or leave the system through any compartment. The work is related to previous research and a numerical example is given.
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    On the study of two interacting populations one of which acts independently of the other (1979)
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    Bulletin of mathematical biology 41 (1979), S. 725-735 
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    Notes: Abstract Many ecological and biological systems can be studied in terms of a bivariate stochastic branching process, {X 1 (t), X 2 (t)}, each of whose components (or populations) varies in magnitude according to the laws of a generalized birth-death process. Of particular interest is such a model in which the birth and death rates of the first population,X 1, are constant while those of the second population,X 2, exhibit a functional dependence upon the magnitude of the first. It is shown, first, that the existence of the stochastic mean of a birth death process implies the existence of all higher moments. The values of all the factorial moments of such a process are then determined. The moments of the dependent population of the bivariate process are given in terms of its expectation and the joint probability density function of the process is determined. It is possible, therefore, to use Bayesian techniques to infer conclusions about the independent population, given information about the variation of the dependent one.
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    On feasible random ecosystems (1979)
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    Bulletin of mathematical biology 41 (1979), S. 751-755 
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    Notes: Abstract Only a fraction of the total number of equilibrium solutions of the differential system which describes the populations of species in an ecosystem are feasible: that is only a fraction of the solutions give non-negative values for all the populations. The feasible equilibrium solutions of a generalized logistic equation are considered for the limiting cases of strongly and weakly interacting species. It is found that only about one third of all the possible species are generally expected to be present (i.e. to have non-zero populations) at any given equilibrium solution.
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    Book reviews (1979)
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    Bulletin of mathematical biology 41 (1979), S. 757-759 
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    Selection in systems of self-reproducing macromolecules under the constraint of controlled energy fluxes (1979)
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    Bulletin of mathematical biology 41 (1979), S. 761-766 
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    Notes: Abstract We consider a method for selection among a collection of self-reproducing macromolecular information carriers. The information carriers are assumed subject to the general constraint in which the fluxes of the energy rich monomers used in the syntheses of the information carriers are controlled externally. The constraint forces a competition among the various macromolecular species and a Darwinian like selection takes place. We show that the overall selective behaviour is independent of the specific form of the constraint. A general criteria for selection is given and we show that the selection process may generally be characterized by an optimization principle.
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    The bifurcation diagram of a model chemical reaction—II. Two dimensional time-periodic patterns (1979)
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    Bulletin of mathematical biology 41 (1979), S. 767-790 
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    Notes: Abstract The bifurcation equations of a general reaction-diffusion system are derived for a circular surface. Particular attention is directed to the deformation of the circular boundary into an elliptic shape. This leads to a new bifurcation diagram which may involve secondary bifurcation, but which retains however the basic characteristics of the solutions for the circular case. Numerical simulations of the various coexisting, time-periodic and space-dependent solutions, are presented for a simple model reaction and circular geometry.
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    Some remarks on the dynamics of molecular self-organization (1979)
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    Bulletin of mathematical biology 41 (1979), S. 803-812 
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    Notes: Abstract The dynamics of a self-organizing molecular system is described in terms of its normal modes. Each normal mode is associated with a certain eigenvalue, the average of which reflects most directly the overall process of self-organization. For the temporal change of this quantity a maximum principle holds.
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    A simple anatomical model of muscle, and the effects of internal pressure (1979)
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    Bulletin of mathematical biology 41 (1979), S. 791-802 
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    Notes: Abstract The purpose of this study is to investigate the relationship between the structure of muscle and its function, especially with regard to the influence of the internal pressure when a muscle contracts. A model is constructed based on the anatomy of muscle. For difference shapes of muscle, but of equal volume, the muscle features (i.e. force exerted etc.) are computed after every contraction step. A function for the internal pressure is also calculated. The internal pressure influences the structure of the muscle which also depends in a certain way upon the function of the muscle.
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    Periodic auto-immune hemolytic anemia: An induced dynamical disease (1979)
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    Bulletin of mathematical biology 41 (1979), S. 829-834 
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    Notes: Abstract Experimentally induced auto-immune hemolytic anemia (AIHA) in rabbits is characterized either by constant depressed erythrocyte numbers, or by oscillatory erythrocyte numbers about a depressed level (periodic auto-immune hemolytic anemia). Here the experimetallys observed characteristics of AIHA are satisfactorily accounted for by a simple model for erythropoiesis, assuming only the peripheral erythrocyte destruction rate is elevated with all other parameters normal. The onset of periodic AIHA is identified with the occurrence of a Hopf bifurcation in the model dynamics for certain values of the erythrocyte destruction rate.
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    On the gating currents and the dipole transitions (1979)
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    Bulletin of mathematical biology 41 (1979), S. 841-848 
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    Notes: Abstract Gating current is considered to be due to the transition of dipoles, which are coupled with the membrane matrix. Based on previous theory of nerve excitation, the equation for gating current is derived; the charge displacement equation and the time constant of the gating current are also derived. Agreement with experimental data is good.
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    Explicit solutions of Fisher's equation for a special wave speed (1979)
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    Bulletin of mathematical biology 41 (1979), S. 835-840 
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    Notes: Abstract The travelling waves for Fisher's equation are shown to be of a simple nature for the special wave speeds $$c = \pm 5/\sqrt {(6)} $$ . In this case the equation is shown to be of Painlevé type, i.e. solutions admit only poles as movable singularities. The general solution for this wave speed is found and a method is presented that can be applied to the solution of other nonlinear equations of biological and physical interest.
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    An exact analysis of the sliding motion in contractile system: A simplified model of muscle system (1979)
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    Bulletin of mathematical biology 41 (1979), S. 813-828 
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    Notes: Abstract A system involving two kinds of sliding filaments is analysed with special attention to the actomyosin system. Rigorous results are obtained about the statistical effect originating from many active sites distributed on both filaments. It is necessary for the occurrence of smooth motion in sliding filament that the spatial periods of active sites on both filaments are relatively incommensurable, and that the number of active sites on each filament is large enough. Sufficient conditions for smooth contraction are derived under the assumption that both filaments are rigid; this is called rigid rod approximation in the present paper. The elastic mode of the filaments, during the sliding process, is analysed by perturbation theory based on the rigid rod approximation. A stochastic theory is briefly discussed in reference to the cooperative generation of contractile force, which is concerned in Hill's relation of muscle contraction.
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    Some models for selection of biological macromolecules with time varying constraints (1979)
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    Bulletin of mathematical biology 41 (1979), S. 849-859 
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    Notes: Abstract We consider some models for selection in self-reproducing macromolecular systems subject to time varying environmental constraints. We show that many of the results concerning selection obtained previously for stationary constraints may be generalized and that the over-all selective behaviour even in complex enzyme coupled systems is basically the same under the time varying external conditions as it is in the stationary case.
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    Some stability conditions for discrete-time single species models (1979)
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    Bulletin of mathematical biology 41 (1979), S. 861-875 
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    Notes: Abstract Standard results relating to the stability of autonomous first order difference equations are restated here with slight modifications so as to apply directly to equations in which the state variable remains positive. Some simple and effective tests for both local and global stability of these first order difference equations are presented. The main results are illustrated with examples drawn from population biology.
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    A teleological explanation of Weber's law and the motor unit size law (1979)
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    Bulletin of mathematical biology 41 (1979), S. i 
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    Analytical considerations on a new class of functions for the mathematical description of the human Erythrocyte's profile during the osmotic, “disk-sphere” transition (1979)
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    Bulletin of mathematical biology 41 (1979), S. 899-904 
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    Notes: Abstract An analytical procedure is used to derive a class of functions for the shapes of the cross section of the human red cell during its osmotic swelling.
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    Tenth International Symposium on Mathematical Programming (1979)
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    Mathematical programming 16 (1979), S. 261-261 
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    On a class of least-element complementarity problems (1979)
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    Mathematical programming 16 (1979), S. 111-126 
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    Keywords: Least Element ; Linear Complementarity ; Quadratic Programs ; Special Structure ; Applications ; Computational Experience
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    Notes: Abstract The present paper studies the linear complementarity problem of finding vectorsx andy inR + n such thatc + Dx + y ≧ 0,b − x ≧ 0 andx T (c + Dx + y) = y T (b − x) = 0 whereD is aZ-matrix andb 〉 0. Complementarity problems of this nature arise, for example, from the minimization of certain quadratic functions subject to upper and lower bounds on the variables. Two least-element characterizations of solutions to the above linear complementarity problem are established first. Next, a new and direct method to solve this class of problems, which depends on the idea of “least-element solution” is presented. Finally, applications and computational experience with its implementation are discussed.
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    Editorial policy (1979)
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    Mathematical programming 16 (1979), S. 139-139 
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    An algorithm for a piecewise linear model of trade and production with negative prices and bankruptcy (1979)
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    Mathematical programming 16 (1979), S. 190-209 
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    Keywords: Algorithm ; Piecewise Linear ; Complementary Pivot ; Equilibrium Model ; Trade ; Production Prices ; Linear Programming ; Fixed Point Methods
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    Notes: Abstract The general equilibrium model is approximated as a piecewise linear convex model and solved from the point of view of welfare economics using linear programming and fixed point methods.
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    Referees 1978 (1979)
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    Mathematical programming 16 (1979), S. 260-260 
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    The Mathematical Programming Society (1979)
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    Mathematical programming 16 (1979), S. 263-263 
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