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  • Springer  (700,794)
  • 2000-2004  (173,866)
  • 1990-1994  (314,761)
  • 1970-1974  (177,357)
  • 1950-1954  (34,810)
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  • 1
    Unknown
    Effects of Space Weather on Technology Infrastructure : Proceedings of the NATO ARW on Effects of Space Weather on Technology Infrastructure, Rhodes, Greece, from 25 to 29 March 2003. (2004)
    Springer
    Details
    Keywords: communication ; design ; dynamics ; environment ; network ; physics ; power transmission ; radio ; satellite ; simulation ; technology ; transmission
    Description / Table of Contents: The 17 chapters of this book grew out of the tutorial lectures given by leading world-class experts at the NATO Advanced Research Workshop “Effects of Space Weather on Technology Infrastructure” - ESPRIT, which was held in Rhodes on March 25-29, 2004. All manuscripts were refereed and subsequently meticulously edited by the editor to ensure the highest quality for this monograph. I owe particular thanks to the lecturers of the ESPRIT Advanced Research Workshop for producing these excellent tutorial reviews, which convey the essential knowledge and the latest advances in our field. Due to the breadth, extensive literature citations and quality of the reviews we expect this publication to serve extremely well as a reference book. Multimedia material referring to individual chapters of the book is accessible on the accompanying CD. The aim of ESPRIT was to assess existing knowledge and identify future actions regarding monitoring, forecasting and mitigation of space weather induced malfunction and damage of vital technological systems operating in space and on the ground.
    ISBN: 9781402027543
    URL: https://doi.org/10.1007/1-4020-2754-0
    Language: English
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  • 2
    Unknown
    The Conversion of Liquid Rocket Fuels : Risk Assessment, Technology and Treatment Options for the Conversion of Abandoned Liquid Ballistic Missile Propellants (Fuels and Oxidizers) in Azerbaijan (2004)
    Springer
    Details
    Description / Table of Contents: Prof. Dr. -Ing. Wolfgang Spyra Brandenburg University of Technology in Cottbus, Germany The demilitarization and conversion of military properties wor- wide has been a topic of growing importance since the end of the Cold War. The slowing of the arms race brought on by weapons treaties and relaxed tensions between NATO and Warsaw Pact nations caused sto- piles of conventional weapons to become superfluous. The need to process and dispose of such weapons began more quickly in NATO countries. This demilitarization process began shortly after the reunification of Germany and was largely completed by the mid to late 1990’s. The remaining process, no small task in itself, of converting lands formerly used by the military into safe and environmentally acceptable landscapes may continue for decades to come. Due to a lack of resources and technology, the process of demilitarization in the former Warsaw Pact countries has launched more slowly. In 2002 both Georgia and Moldova finished projects which destroyed their stocks of liquid ballistic missile components. Both these projects were carried out through the cooperative support of trans-national organizations, private contractors, and research institutions. The Republic of Azerbaijan now finds itself at the beginning of its demilitarization process. Stored at the country’s military depots are over 2000 tons of missile fuels, oxidizer, and chemical additives. This hazardous waste is kept in tanks intended only for temporary transport and storage.
    Pages: Online-Ressource (X, 148 pages)
    ISBN: 9781402023811
    URL: https://doi.org/10.1007/1-4020-2381-2
    Language: English
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  • 3
    Unknown
    Strategic decision making : applying the analytic hierarchy process (2004)
    London ; New York : Springer
    Decision engineering  
    Details
    Keywords: Decision making, Mathematical models. ; Decision making, Methodology.
    Pages: ix, 172 p.
    ISBN: 1-85233-864-4
    URL: http://www.netLibrary.com/urlapi.asp?action=summary&v=1&bookid=108180
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  • 4
    Unknown
    Web services, E-Business, and the Semantic Web : second international workshop, WES 2003, Klagenfurt, Austria, June 16-17, 2003 ; WES 2003 (2004)
    Berlin ; New York : Springer
    Lecture notes in computer science  
    Details
    Keywords: Semantic Web, Congresses.
    Pages: x, 145 p.
    ISBN: 3-540-25982-1
    URL: http://www.netLibrary.com/urlapi.asp?action=summary&v=1&bookid=130186
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  • 5
    Electronic Resource
    Electronic Resource
    Contributions to the theory of organismic sets, II: Aggressiveness and submissiveness (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 49-54 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the theory of organismic sets (Bull. Math. Biophysics,31, 159–198, 1969) we considered organisms as sets endowed with certain “activities,” the latter’s resulting in a set of “products.” Those products may be of a material nature, like a hormone secreted by a cell, or of a non-material nature, like a feeling or an attitude. In the present paper aggressiveness and submissiveness are considered as such non-material products of the activities of the brain cells. A general description of aggressiveness and submissiveness is given in terms of organismic sets. Cycles in “peck order” are thus naturally explained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476664
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  • 6
    Electronic Resource
    Electronic Resource
    Contribution to the theory of organismic sets, III (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 55-66 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In line with previous studies on organismic sets, the division of all organismic sets intogeneral autotrophic and heterotrophic is introduced. The first produce their food themselves from some external source of energy, which in general may be an energy of any kind. The others use other organismic sets as the source of their food and energy. On earth we know only one kind of generalgeneral autotrophic organismic sets, namely, the autotrophic plants which use solar radiation as their source of energy and for production of their own food. It is shown why autotrophic animals do not exist on earth except as microorganisms like, e.g.,Euglena. A rigorous proof of the previously derived theorem that in an organismic set of ordern〉1 no element can be completely specialized is given. It requires the introduction of new postulates. Finally, in considering the organic world as a whole, the notion of organismic sets ofmixed order is introduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476665
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  • 7
    Electronic Resource
    Electronic Resource
    “A stochastic solution of the 3-body problem in chemical kinetics. The termolecular stochastic process I” (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 67-81 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It appears to be axiomatic that termolecular and higher order reactions occur relatively rarely. The basis for this judgment seems to lie in the supposition that successful 3-Body collisions of 3 interactive species of molecules cannot occur frequently enought to account for chemical or biochemical transformation. In order to provide a more complete mathematical framework than now exists for examining this hypothesis the probability of effective termolecular “δ-collisions” as a function of time is derived. This amounts to adding to the class of reactions for which stochastic models are now available the termolecular reaction. In common with the unimolecular and bimolecular cases this process is seen to satisfy the criterion of consistency-in-the-mean with respect to deterministic formulations. It is planned next to use the termolecular process and the lower order processes in computer-assistedin numero experimental studies aimed at comparing alternative mechanisms of reaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476666
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  • 8
    Electronic Resource
    Electronic Resource
    Maximum likelihood estimation for stochastic first order reactions (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 83-96 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Small sample properties of the maximum likelihood estimator for the rate constant of a stochastic first order reaction are investigated. The approximate bias and variance of the maximum likelihood estimator are derived and tabulated. If observations of the system are made at timesiτ,i=1, 2, ...,N; τ〉0, the observational spacing τ which minimizes the approximate variance of the maximum likelihood estimator is found. The non-applicability of large sample theory to confidence interval derivation is demonstrated by examination of the relative likelihood. Bartlett’s method is employed to derive approximate confidence limits, and is illustrated by using simulated kinetic runs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476667
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  • 9
    Electronic Resource
    Electronic Resource
    Random walk with persistence and external bias (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 311-338 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The partial differential equation of the random walk problem with persistence of direction and external bias is derived. By persistence of direction or internal bias we mean that the probability a particle will travel in a given direction need not be the same for all directions, but depends solely upon the particle's previous direction of motion. The external bias arises from an anisotropy of the medium or an external force on the particle. The problem is treated by considering that the net displacement of a particle arises from two factors, namely, that neither the probability of the particle traveling in any direction after turning nor the distance the particle travels in a given direction need be the same for all directions. A modified Fokker-Planck equation is first obtained using the assumptions that the particles have a distribution of travel times and speeds and that the average time of travel between turns need not be zero. The fional equation incopporating the assumption of a persistence of direction and an external bias is then derived. Applications to the study of diffusion and to long-chain polymers are then made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476407
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  • 10
    Electronic Resource
    Electronic Resource
    Methods of statistical analysis (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 383-383 
    Details
    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/BF02476411
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  • 11
    Electronic Resource
    Electronic Resource
    The transmission of excitation from the membrane to actomyosin (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 385-385 
    Details
    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/BF02476412
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  • 12
    Electronic Resource
    Electronic Resource
    On the spread of information with time and distance (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 367-381 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The transmission of some information or behavior pattern is treated as a flow of “particles” which execute random motions over a population of individuals and which may multiply or disappear. Equations are derived for the number density of these “particles” and from this is calculated the number of individuals through which the “particles” have passed. The results are applied to a number of situations such as 1) uniform spatial distribution with multiplication factor decreasing with time because of loss of interest or confusion of the information, 2) multiplication factor constant but the rate of spreal decreasing with multiple hearings, 3) one-dimensional region with a small starting region with or without an absorbing barrier 4) two-dimensional region with absorbing barrier, 5) continous sources of information within a small region in one dimension, 6) uniform spatial distribution in which individuals do not respond to more than one hearing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476410
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  • 13
    Electronic Resource
    Electronic Resource
    A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 387-394 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A situation is considered in which a fluid containing a substance flows through a vessel at a constant rate, the substance being permeable to the vessel wall. In the region outside the vessel there is supposed to be rapid mixing in the direction perpendicular to the axis of the vessel but no mixing longitudinally. The solution for the spatial distribution at any time is given for the case of an arbitrary initial distribution along the vessel length in the absence of an input. The solution is also given for the case of a single impulsive input, the concentration being initially zero everywhere.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476432
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  • 14
    Electronic Resource
    Electronic Resource
    Organismic supercategories and qualitative dynamics of systems (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 339-354 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The representation of biological systems by means of organismic supercategories, developed in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–71;32, 539–561), is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Băianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete result concerning dynamics of genetic system, development, fertilization, regeneration, analogies, and oncogenesis are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476778
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  • 15
    Electronic Resource
    Electronic Resource
    Some realizations of (M, R)-systems and their interpretation (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 303-319 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some years ago (Rosen 1958a, b; 1959) we described a class of metaphorical, relational paradigms for cellular activity which we termed (M, R)-systems. A sizable amount of subsequent work, to be itemized below, has been devoted to an exploration of some of the properties of these systems. The main purpose of the present paper is to put this class of paradigms into a general system-theoretic perspective, with a particular view to appraising the relation between the type of system description embodied in the (M, R)-system and other kinds of physical and mathematical descriptions of cellular systems. Thus, the principal aim is to establish the relationships and connections between the global relational formalism embodied in the (M, R)-systems and the empirical descriptions which still represent the bulk of our biological knowledge.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476776
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  • 16
    Electronic Resource
    Electronic Resource
    Relational forces and structures produced by them (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 321-338 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract After giving a brief review of the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967;31, 159–198, 1969), in which the concept of relational forces, introduced earlier (Bull. Math. Biophysics,28, 283–308, 1966a) plays a fundamental role, the author discusses examples of possible different structures produced by relational forces. For biological organisms the different structures found theoretically are in general agreement with observation. For societies, which are also organismic sets as discussed in the above references, the structures can be described only in an abstract space, the nature of which is discussed. Different isomorphisms between anatomical structures, as described in ordinary Euclidean space, and the sociological structures described in an abstract space are noted, as should be expected from the theory of organismic sets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476777
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  • 17
    Electronic Resource
    Electronic Resource
    A mathematical contribution to the study of orientation of organisms (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 431-476 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Organisms orient themselves to a stimulus by two general methods. One method is by directed orientation (taxis); the other is by undirected locomotory reaction (kinesis). An equation, and the methods for finding the necessary parameters of this equation, is derived for the distribution of organisms within a container, with the following limitations: (1) the organisms have no accommodation, (2) they are always active, and (3) the stimulus changes slowly with position. Necessary modifications of the equation are then derived, so that the last two limitations may be eliminated. The equation cannot be solved excatly because of its complexity; hence an approximation method must be used. This method is discussed, an approximate solution is found, and a time constant for equilibrium to be established is derived. Applications tovarious experiments in the literature are then made with fairly satisfactory results. A new interpretation of the theory of klino-kinesis with accommodation is found upon application of the equations developed to experimental work. Further limitations and uses of these equations are then discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476435
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  • 18
    Electronic Resource
    Electronic Resource
    Structural parameters of communication networks (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 501-507 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Certain parameters are defined which roughly characterize the internal structure of networks. A given network structure uniquely determines the values of the parameters, but the reverse is not true. The parameters therefore define certain classes of networks. One of the parameters, thedispersion D(S) gives an indication of the “compactness” of the internal structure. Addition theorems and inequalities are derived relating the dispersions of sub-systems to the dispersion of the complete structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476438
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  • 19
    Electronic Resource
    Electronic Resource
    Determination of diffusion and permeability coefficients in nerve trunks (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 489-500 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.
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    URL: http://dx.doi.org/10.1007/BF02476437
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  • 20
    Electronic Resource
    Electronic Resource
    Enzyme localization as a mechanism of apparent active transport (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 509-522 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model based on enzyme localization is developed which gives rise to an apparent active transport of a metabolite into or out of cells. The model is applied to three simple situations, using Fick's equation and the Rashevsky approximation. It is shown that the apparent efficiency can be made as large as desired if, for constant reaction, the outer cell region is made sufficiently small, or, for autocatalytic reaction, if the metabolite concentration in the outer region is sufficiently small. The physical limitations imposed by this mechanism are developed for all three situations.
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    URL: http://dx.doi.org/10.1007/BF02476439
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  • 21
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    Spread of information through a population with socio-structural bias: I. Assumption of transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 523-533 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A previously derived iteration formula for a random net was applied to some data on the spread of information through a population. It was found that if the axon density (the only free parameter in the formula) is determined by the first pair of experimental values, the predicted spread is much more rapid than the observed one. If the successive values of the “apparent axon density” are calculated from the successive experimental values, it is noticed that this quantity at first suffers a sharp drop from an initial high value to its lowest value and then gradually “recovers”. An attempt is made to account for this behavior of the apparent axon density in terms of the “assumption of transitivity”, based on a certain socio-structural bias, namely, that the likely contacts of two individuals who themselves have been in contact are expected to be strongly overlapping. The assumption of transitivity leads to a drop in the apparent axon density from an arbitrary initial value to the vicinity of unity (if the actual axon density is not too small). However, the “recovery” is not accounted for, and thus the predicted spread turns out to beslower than the observed.
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  • 22
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    Spread of information through a population with socio-structural bias: II. Various models with partial transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 535-546 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The assumption of transitivity treated in part I is modified in various ways to describe an information-diffusion process, in which a certain amount of randomness of contact does occur. In one model a parameter is introduced which is indicative of a tendency to go beyond one's immediate vicinity to spread the information as the vicinity becomes saturated with knowers. In another model the randomness appears in the assumption that new knowers are uniformly distributed among the knowers. Two of the equations thus derived, each with two free parameters are in good agreement with experimental results.
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  • 23
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    Probabilistic and multiple regression modeling of the biologist’s decision processes and its implications for medical diagnosis (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 439-449 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Current psychological research into the inference (diagnostic) process is briefly reviewed, using as a vehicle an investigation of the prediction of the probability of success of hypothetical applicants to a graduate program in biology. Brunswik’s lens model and multiple regression analysis are used, as is a Bayesian approach. Four judges’ (biologists’) predictions are analyzed. Some general conclusions about inference, drawn from the current data in psychology, are presented.
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  • 24
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    Anin numero study of glucose-insulin interaction (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 451-462 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model has been developed to simulate the glucose-insulin interaction following a glucose load such as occurs in an IVGTT. This model differs from earlier models in that the insulin response to glucose loading is a recurring all or none threshold response. The model has been simulated on a digital computer using the digital analog simulation language CSMP.
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  • 25
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    Wave propagation in bone media (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 463-479 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The composite nature of bone dictates the use of a model for bone which is transversely isotropic. We solve the associated sets of partial differential equations governing the dynamic elastic behavoor of a two-layered cylindrical-shaped bone. The solution is analyzed for long, short, and intermediate length waves. The special case of compact bone is treated for long and short wave lengths and a numerical example is worked out to determine the wave speeds (for short wave lengths) given a set of elastic constants, determined by ultrasonic methods, and the bone density, wave frequency, and radius.
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  • 26
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    Fourth International Biophysics Congress (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 481-481 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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  • 27
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    Obituary of Nicolas Rashevsky (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. i 
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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/BF02477019
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  • 28
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    On the stochastic theory of compartments: I. A single-compartment system (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 53-63 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A stochastic model is developed for a compartment with a single time-dependent input, and generalized to include inputs from several sources. With the number of particles of a given molecular species in the compartment as the random variable, the mean, variance and third central moment of this variable are calculated from its generating function, and compared with previous results. The behavior of the calculated moments is discussed, and the possibility of applying the model to chemical and biological systems is considered.
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  • 29
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    A remark on sensory deprivation from the point of view of organismic sets (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 439-441 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that from the definition of organismic sets (Rashevsky,Organismic Sets. Some Reflections on the Nature of Life and Society, Holland, Michigan, Mathematical Biology, Inc. and Grosse Pointe, Michigan, J. M. Richards Laboratory) a complete sensory deprivation of an organismic set of ordern=2 should result in malfunctioning of the set. A generalization to higher order sets is suggested.
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    Optimal branching structure of the vascular tree (1972)
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    Bulletin of mathematical biology 34 (1972), S. 431-438 
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    Notes: Abstract Optimality in branching structure of the vascular tree was studied. Analysis on its physiological roles as the duct system for blood supply to the capillaries predicted that the vascular tree should be constructed with minimum volume under restriction of determinant pressure, flow and location at the origin and the terminals. Mathematical derivations of this conditional extremum problem yielded some equations expressing the relations between the radii of the branches and their branching angles, which provided numerical solutions for branching points of bi- and poli-terminal minimum volume trees. Comparison of the peritoneal vascular tree in a dog with the minimum volume one computed under the same restrictive conditions showed good agreement in their branching structure.
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    First order kinetics in a distributed model (1972)
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    Bulletin of mathematical biology 34 (1972), S. 443-456 
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    Notes: Abstract In order to determine the kinetics of passage of a substance through an organ containing a tangle of vessels, we study the response of a tube to various inflows (perfusion, brief injection, ...). The introduction of the catabolic terms and of the spatial dependence between bulk concentration and surface concentration allows one to account for the difference of arteriovenous concentrations observed experimentally for many metabolites. The relationships between the physico-chemical parameters of the organ and the operational parameters of the model demonstrate the importance of the transit time through the considered vessels. If one considers the different pathways as independent, the introduction of the transit time distribution for an inert substance enables one to compute the response of the organ analytically or by recurrence, using convolution. The parameters of the model can be obtained by the moments method.
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    Stochastic simulation of the gas diffusion in the air phase of the human lung (1972)
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    Bulletin of mathematical biology 34 (1972), S. 457-466 
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    Notes: Abstract The solution of the diffusion equation in the gas phase of the human lung is very difficult because of the structure of the bronchial tree. It is shown by means of physical arguments, how one can reduce the diffusion equation to a simple one-dimensional form. The solution is then obtained by a stochastic simulation, which is easily realized on a digital computer.
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    A new mathematical model of the respiratory center (1972)
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    Bulletin of mathematical biology 34 (1972), S. 467-481 
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    Notes: Abstract A new mathematical model of the oscillatory behavior of the respiratory center has been developed based upon published records of neuronal activity during respiration in the pons and medulla. In contrast with a previous model, four, rather than two, networks are assumed to interact in the respiratory center so as to produce the respiratory oscillation. A mathematical description of this interaction, in the form of a set of four first-order, nonlinear, coupled differential equations, is derived; the behavior of the solutions of this system is studied qualitatively, and expressions for the durations of the inspiratory and expiratory phases are obtained in terms of some parameters. It is found that central and chemical influences drive the medullar neurons to a position somewhere between saturation and full cutoff, and the pontine neurons deeply into cutoff. The control of the duration of the different phases by these chemical and central means is discussed. In order to effect a decrease in the magnitude of the various times, the neurons have to be driven towards operating points of higher central facilitation.
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    A mathematical model for calcium homeostasis (1972)
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    Bulletin of mathematical biology 34 (1972), S. 483-502 
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    Notes: Abstract In vivo control of calcium is analysed under the assumption that hormonal influences via plasma levels of parathormone and calcitonin are of prime (but not absolutely dominating) importance. A brief review concerning the physiological significance of body calcium and the mode of action of these two hormones is presented as an introduction to the basic philosophy of the study. A theoretical quasi-linear lumped-parameter model is developed to describe variations in ionic calcium, parathormone and calcitonin plasma concentrations to specific input stimuli. Formal evaluation of the system response requires the determination of ten constants, together with quantitation of ingested calcium entry into the plasma compartment which isindependent of hormonal influences. Values for various parameters are deduced from published data and experimental procedures are outlined to facilitate determination of the remaining unknowns. It is suggested that the proposed model should prove useful for investigations concerning general hormonal actions on calcium homeostatic mechanisms in both normal and diseased states, with particular reference to calcitonin.
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    The struggle for life: III. A predator-prey chain (1972)
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    Bulletin of mathematical biology 34 (1972), S. 521-532 
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    Notes: Abstract Ann species predator-prey chain is analyzed to determine what oscillations occur in population sizes. It is found that only the populations of the first and second species in the chain must necessarily oscillate around the point of equilibrium if they do not come to equilibrium. The other species may or may not oscillate.
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    Mathematical models for exchange of substances in regional vascular beds— Measurement of the rates within vivo counters (1972)
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    Bulletin of mathematical biology 34 (1972), S. 503-520 
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    Notes: Abstract Sangren and Sheppard developed a mathematical model for first-order processes taking place in the regional circulation, applicable—for example—to tracer studies of potassium transport. It permits calculation of specific activity at any point along a “tube of flow” or in the cuff of tissue surrounding it as a function of time following a spike injection of tracer. In efforts to relate to the exchange a rate curves obtained within vivo counters pointed at the region of interest, we developed a compartment-system model of the process. In investigating the properties of the Sangren and Sheppard model integrated over an entire circulatory bed, as thein vivo counter would see it, we found that when the distribution of transit times of the “tubes of flow” can be approximated by an exponential sum, the solution reduces to that of the compartment system model. This results in an important simplification in the calculation, and insight into the assumptions underlying the two different models. A curve-fitting computer program for the compartment model has been written and applied to double-isotope studies of potassium transport in the hind leg of the dog.
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    A numerical experiment on the determination of kinetic rate constants in the presence of diffusion (1972)
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    Bulletin of mathematical biology 34 (1972), S. 547-558 
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    Notes: Abstract Two chemicals,A andB, are allowed to diffuse together and a reaction described by $$A + B\mathop \rightleftharpoons \limits_{K_{ - 1} }^{K_1 } C$$ is allowed to proceed. This system is described mathematically by a system of partial differential equations. A numerical procedure is presented to find the rate constants ofK 1 andK −1. A systematic analysis of the effects of errors is also presented.
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    Observations on cardiac energetics: I. Theoretical introduction (1972)
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    Bulletin of mathematical biology 34 (1972), S. 533-546 
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    Notes: Abstract Equations are developed to describe the energy expenditure of the human heart. As well as the external potential and kinetic energy terms, general consideration is given to other possible avenues of energy consumption. Emphasis is placed upon using mathematical variables which are readily available for experimental verification. The errors involved in assuming that mean values for the physiological parameters give reasonable estimations for the external mechanical performance are examined, and a theoretical estimation for the discrepancy in the kinetic component is presented. Logical extension of the mathematical derivation leads to a determination of cardiac external mechanical efficiency and clearly demonstrates the significance of the ventricular pressure-volume loop in this context. Finally, experimental procedures are suggested to clarify further some of the conclusions reached through the theoretical analysis.
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    Organismic sets. Sex in animal and human societies (1972)
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    Bulletin of mathematical biology 34 (1972), S. 559-563 
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    Topics: Biology , Mathematics
    Notes: Abstract The question is discussed as to the reason why some animal societies, such as bees or ants, are sexually differentiated, that is, onlysome of its members are exhibiting reproducing activities. It is indicated that human society may be on its way to such a sexual differentiation which may eventually come.
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    Some biochemical threshold mechanisms (1972)
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    Bulletin of mathematical biology 34 (1972), S. 565-565 
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    Announcement (1972)
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    Bulletin of mathematical biology 34 (1972), S. 567-567 
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    The structure of DNA as deduced from fiber X-ray crystallography (1973)
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    Bulletin of mathematical biology 35 (1973), S. 301-311 
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    Notes: Abstract X-ray diffraction patterns obtained experimentally for fibers, together with their chemical structures, can be analyzed theoretically in terms of an integral equation. The partially unknown electron density function can be solved by iteration. This mathematical technique has been applied with success to study the secondary structures of DNA fibers.
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    Composting of explosives and propellant contaminated soils under thermophilic and mesophilic conditions (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 137-144 
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    ISSN: 1476-5535
    Keywords: Composting ; Explosives ; Propellants ; Thermophilic ; Mesophilic ; Bioremediation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Composting was investigated as a bioremediation technology for clean-up of sediments contaminated with explosives and propellants. Two field demonstrations were conducted, the first using 2,4,6-trinitrotoluene (TNT), octahydro-1,3,5,7-tetranitro-1,3,5,7-tetraazocine (HMX), hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), and N-methyl-N,2,4,6-tetranitroaniline (tetryl) contaminated sediment, and the second using nitrocellulose (NC) contaminated soil. Tests were conducted in thermophilic and mesophilic aerated static piles. Extractable TNT was reduced from 11840 mg/kg to 3 mg/kg, and NC from 13090 mg/kg to 16 mg/kg under thermophilic conditions. Under mesophilic conditions, TNT was reduced from 11 190 mg/kg to 50 mg/kg. The thermophilic and mesophilic half-lives were 11.9 and 21.9 days for TNT, 17.3 and 30.1 days for RDX, and 22.8 and 42.0 days for HMX, respectively. Known nitroaromatic transformation products increased in concentration over the first several weeks of the test period, but decreased to low concentrations thereafter.
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    Purification and properties of extracellularβ-fructofuranosidases fromAureobasidium sp. ATCC 20524 (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 145-147 
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    ISSN: 1476-5535
    Keywords: Fructo-oligosaccharide ; 1-Kestose ; Glycoprotein ; Fructosyl-transferring activity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Two extracellular β-fructofuranosidases (E-1 andE-2) fromAureobasidium sp. ATCC 20524, producing 1-kestose (1F-β-fructofuranosyl-sucrose) from sucrose, were purified to homogeneity. Molecular weights of the enzymes were estimated to be about 304000 (E-1) and 315000 (E-2) Da by gel filtration. The enzymes contained 33% (w/w) (E-1) and 27% (w/w) (E-2) carbohydrate. TheK m values for sucrose ofE-1 andE-2 andE-2 were 0.34 and 0.28 M, respectively. were 0.34 and 0.28 M, respectively. The enzymatic profiles of these enzymes were almost identical to intracellular enzymesP-1 andP-2 except for the differences in carbohydrate content andK m values ofE-2 andP-2.
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    Insect fungal symbionts: A promising source of detoxifying enzymes (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 149-161 
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    ISSN: 1476-5535
    Keywords: Toxin ; Secondary plant metabolite ; Allelochemical ; Insecticide ; Mycotoxin ; Endocytobiont
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Many species of insects cultivate, inoculate, or contain symbiotic fungi. Insects feed on plant materials that contain plant-produced defensive toxins, or are exposed to insecticides or other pesticides when they become economically important pests. Therefore, it is likely that the symbiotic fungi are also exposed to these toxins and may actually contribute to detoxification of these compounds. Fungi associated with bark beetles, ambrosia beetles, termites, leaf-cutting ants, long-horned beetles, wood wasps, and drug store beetles can variously metabolize/detoxify tannins, lignins, terpenes, esters, chlorinated hydrocarbons, and other toxins. The fungi (Attamyces) cultivated by the ants and the yeast (Symbiotaphrina) contained in the cigarette beetle gut appear to have broad-spectrum detoxifying abilities. The present limiting factor for using many of these fungi for large scale detoxification of, for example, contaminated soils or agricultural commodities is their slow growth rate, but conventional strain selection techniques or biotechnological approaches should overcome this problem.
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    Biosensors for process monitoring (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 163-172 
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    ISSN: 1476-5535
    Keywords: Biosensors ; Process control ; Enzyme thermistor ; Immunoassay ; Bio-field effect transistor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A short review about the biosensor research activities for bioprocess monitoring in the F.R.G. after its reunification is given. The principles of biosensor applications are presented. In situ sensors and sensors based on the principles of flow injection analysis are studied. Some applications of a four-channel enzyme thermistor, bio-field effect transistors, and immunoanalysis systems for real process monitoring are presented.
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    Ecology ofVibrio vulnificus in Galveston Bay oysters, suspended particulate matter, sediment and seawater: Detection by monoclonal antibody — immunoassay — most probable number procedures (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 219-223 
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    ISSN: 1476-5535
    Keywords: Vibrio vulnificus ; Oyster ; Monoclonal antibody ; Most probable number ; Enzyme immunoassay
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Oysters, suspended particulate matter (SPM), sediment and seawater samples were collected from West Galveston Bay, Texas over a 16-month period and analyzed for the presence ofVibrio vulnificus, a naturally-occurring human marine pathogen. Detection and enumeration ofV. vulnificus was performed using a species-specific monoclonal antibody (mAb FRBT37) in an enzyme immunoassay (EIA)-most probable number (MPN) procedure capable of detecting as few as 2000 target organisms.V. vulnificus was not detected in seawater, oyster or SPM samples during the cold weather months, but was detected at low levels in several sediment samples during this time period. Increased levels of the organism were first observed in early spring in the sediment, and then in SPM and oysters. The major increase inV. vulnificus occurred only after the seawater temperature had increased above 20°C and the winter-spring rainfall had lowered the salinity below 16‰. The highestV. vulnificus levels at each site were associated with suspended particulate matter. These results are consistent with the hypothesis that (1)V. vulnificus over-winters in a floc zone present at the sediment-water interface, (2) is resuspended into the water column in early spring following changes in climatic conditions, (3) colonizes the surfaces of zooplankton which are also blooming during early spring and (4) are ingested by oysters during their normal feeding process.
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    Conversion of sodium cyanide to carbon dioxide and ammonia by immobilized cells ofPseudomonas putida (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 235-238 
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    ISSN: 1476-5535
    Keywords: Biodegradation ; Pseudomonas putida ; Immobilization ; Sodium cyanide
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Pseudomonas putida, isolated from contaminated industrial wastewaters and soil sites, was found to utilize sodium cyanide (NaCN) as a sole source of carbon and nitrogen. Cells, immobilized in calcium alginate beads (1–2 mm diameter) were aerated in air-uplift-type fluidized batch bioreactor containing 100–400 ppm of NaCN. Degradation of NaCN was monitored for 168 h by analyzing gaseous and dissolved ammonia (NH3), CO2, pH and optical density. The results indicated that the alginate-immobilized cells ofP. putida were able to degrade NaCN into NH3 and CO2 in a time-dependent manner.
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    Changes in protein composition ofSaccharomyces brewing strains in response to heat shock and ethanol stress (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 229-234 
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    ISSN: 1476-5535
    Keywords: Heat shock protein (HSP) ; Yeast ; Saccharomyces ; Viability ; Thermotolerance ; Ethanol tolerance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Heat shock and ethanol stress of brewing yeast strains resulted in the induction of a set of proteins referred to as heat shock proteins (HSPs). At least six strongly induced HSPs were identified in a lager brewing strain and four HSPs in an ale brewing strain. Four of these HSPs with molecular masses of approximately 70, 38, 26 and 23 kDa were also identified in two laboratory strains ofSaccharomyces cerevisiae. The appearance of HSPs correlated with increased survival of strains at elevated temperatures and high concentrations of ethanol. These results suggest that HSPs may play a role in the ethanol and thermotolerance of yeasts. The properties of these proteins and membrane fatty acids in relation to heat and ethanol shock are being investigated.
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    Isolation and characterization of a novel polysaccharide fromBacillus licheniformis NCIB 11634 (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 239-245 
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    ISSN: 1476-5535
    Keywords: Novel polysaccharide ; Bacillus licheniformis ; Raffia venifera ; d-Glucose ; d-Mannose ; d-Xylose
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A polysaccharide producing strain ofBacillus licheniformis was isolated from exudate of raffia palm,Raffia vinifera. The optimum conditions for growth and polysaccharide production have been investigated and established. No appreciable polysaccharide was formed on glucose. It grew best in Czapek-Dox media with sucrose as the carbon source. The polysaccharide has been characterized as a heteropolymer containingd-glucose,d-mannose andd-xylose.
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    Announcement from the publisher (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 269-269 
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    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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    Effect of deglycosylation on the properties of β-fructofuranosidaseP-1 fromAureobasidium sp. ATCC 20524 (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 251-255 
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    ISSN: 1476-5535
    Keywords: β-Fructofuranosidase ; Deglycosylation ; Aureobasidium ; Enzymatic stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Most of the carbohydrate moiety of β-fructofuranosidaseP-1 fromAureobasidium sp. ATCC 20524 was removed by endo-β-N-acetylglucosaminidase F. A subunit of 94000 Da was observed in SDS-PAGE after deglycosylation. TheK m value for sucrose was not changed by deglycosylation but the stability at pH 4–5 and 50°C was decreased. The deglycosylated enzyme was more sensitive to proteases such as pronase E and subtilisin than the native enzyme. It is considered that the carbohydrate moiety of β-fructofuranosidaseP-1 contributes to the stability of the enzyme but is not essential in its catalytic function.
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    Information Processing in the Visual Systems of Arthropods (1974)
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    Bulletin of mathematical biology 36 (1974), S. 339-340 
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    Topics: Biology , Mathematics
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    Optimality in the control of environmental systems (1974)
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    Bulletin of mathematical biology 36 (1974), S. 341-345 
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    Topics: Biology , Mathematics
    Notes: Abstract For an environmental system described by a system of nonlinear first-order differential equations, the problem of achieving specified terminal conditions in a given time with a minimum expenditure of resources is considered. The initial conditions and the minimum value are found numerically in a particular example.
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    Kinetic approach to neural systems: I (1974)
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    Bulletin of mathematical biology 36 (1974), S. 535-544 
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    Notes: Abstract A kinetic model of neural systems is introduced and discussed with statistical mechanics techniques. It is assumed that, for a macroscopic description of the model, it suffices to consider only the distribution for the velocity and position of the impulses, and the distribution for the excitation and position of the neurons, at any timet. Making use of Boltzmann's method for the study of a dilute gas, coupled differential equations for the rate of change with time of the distributions have been constructed.
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    Flow of a newtonian fluid through a permeable tube: The application to the proximal renal tubule (1974)
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    Bulletin of mathematical biology 36 (1974), S. 457-476 
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    ISSN: 1522-9602
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    Notes: Abstract Creeping flow of a Newtonian fluid through a rigid permeable tube is considered and the transmural seepage is assumed to obey Darcy's law. Closed-form solutions for the pressure and velocity fields are presented and equations describing the axial variation of the mean cross-sectional pressure, the axial volumetric flow and the transmural fluid flux are derived. Approximate solutions for small seepage rates are given and are applied to the flow in the proximal renal tubule. Probable values for the epithelium permeability and the intraluminal hydrostatic pressure drop are obtained.
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    Disseminated storage of information with sequential coding (1973)
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    Bulletin of mathematical biology 35 (1973), S. 663-688 
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    Notes: Abstract The paper demonstrates that it is possible to construct memory models where the information inserted is stored in disseminated form, using sequential coding, the changes in the units forming the models being determined by their geometrical connections and by the incoming stream of information. The models are shown to have large storage capacity and their efficiency can be made insensitive to loss of or damage to a large fraction of their units. The satisfactory verification by computer simulation of the analysis and results described in the present paper will be the subject of a future paper.
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    On knowledge and unpleasantness (1974)
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    Bulletin of mathematical biology 36 (1974), S. 605-605 
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    The Kerner linearization method (1974)
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    Bulletin of mathematical biology 36 (1974), S. 67-76 
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    Notes: Abstract We examine in detail Edward Kerner’s method for linearizing the equations of enzyme kinetics. Our main result is the determination of canonical forms for systems which can be linearized by the method. This is done both in general and in the special cases of two and three dimensions where complete results are obtained. The practical problem of identifying linearizable systems is also considered and computable necessary criteria are presented.
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    Continuous determination of the volume of a space in a non steady state condition (1974)
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    Bulletin of mathematical biology 36 (1974), S. 59-66 
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    Notes: Abstract A general method for determination of the volume of a space in a non steady state condition, in case diffusion might be significant, is developed. Instantaneous mixing of indicators with native fluid is assumed in this first stage of investigation. Theoretical expressions are obtained for the volume of the space and the diffusion coefficient as a function of time. An analysis of feasibility of the method is also included.
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    Passive transfer of low-molecular nonelectrolytes across deformable semi-permeable membranes—II: Dynamics of a single muscle fiber swelling and shrinking and related changes of theT-system tubule form (1974)
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    Bulletin of mathematical biology 36 (1974), S. 379-401 
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    Notes: Abstract The theory of transfer of low-molecular nonelectrolytes across deformable semipermeable membranes of large curvature developed in Part I (Rubinstein, 1974) is used to describe the dynamics of swelling and shrinking of a muscle fiber at the influx and efflux of low-molecular nonelectrolytes. A large set of computations showed that the theory explains the experiments described in the literature.
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    Heat transfer in perfused biological tissue—I: General theory (1974)
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    Bulletin of mathematical biology 36 (1974), S. 403-415 
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    Notes: Abstract Green's function for heat and matter transport is calculated for an infinite medium in which a convection field v(r,t) makes a contribution to the total heat and matter current. It is given by a uniformly and absolutely convergent series in which every term is calculated from the preceding one merely by integration. The solution procedure is interpreted physically and illustrated by a simple problem in which v(r,t)=const. in space and time. Since the solution contains no intrinsic spatial symmetry, it can serve as a starting point for a theory of heat and mass transport in perfused biological tissue.
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    A long wavelength solution for a microorganism swimming in a channel (1974)
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    Bulletin of mathematical biology 36 (1974), S. 435-444 
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    Notes: Abstract The hydrodynamics of a microorganism swimming in a channel is investigated. The microorganism is modeled as a two-dimensional sheet swimming at low Reynolds numbers between two rigid walls. The wavelengths of the propulsive waves passing down the sheet are assummed to be very large compared to the channel spacing, but the amplitude of the propulsive waves is arbitrary. Explicit analytical solutions for the propulsive velocity and the rate of energy dissipated in terms of the wave amplitude, channel spacing, wave number, and wave speeds are given.
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    Mathematical models of conception and birth (1974)
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    Bulletin of mathematical biology 36 (1974), S. 455-456 
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    Why are there so many species? (1974)
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    Bulletin of mathematical biology 36 (1974), S. 477-488 
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    Notes: Abstract It is shown from the statistical-mechanical overview of Volterra's ecological model how to reckon the fluctuations of collective variables such as the total population of a genus: and that these fluctuations are much decreased (or that the collective populationsteadiness is enhanced) as the speciation is increased. (A niching of species in time, or phase-niching, is entailed here.) Secondly, it is shown how Preston's log-normal distribution describing the species-abundance relationship, as well as a generalization of such distributions, come forth simply and naturally from the statistical-Volterra-dynamics.
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    The chemical basis of morphogenesis (1990)
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    Bulletin of mathematical biology 52 (1990), S. 153-197 
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    Notes: Abstract It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns onHydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.
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    Book reviews (1990)
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    Bulletin of mathematical biology 52 (1990), S. 319-334 
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    SIAM 1990 Annual Meeting and Short Course 15–20 July 1990 Hyatt Regency Hotel, Chicago, IL (1990)
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    Bulletin of mathematical biology 52 (1990), S. 335-337 
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    Editorial: Software survey section (1990)
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    Bulletin of mathematical biology 52 (1990), S. I 
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    The cellular computer DNA: Program or data (1990)
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    Bulletin of mathematical biology 52 (1990), S. 335-348 
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    Notes: Abstract The classical metaphor of the genetic program written in the DNA nucleotidic sequences is reconsidered. Recent works on algorithmic complexity and logical properties of computer programs and data are used to question the explanatory value of that metaphor. Structural properties of strings are looked for which would be necessary to apply to DNA sequences if the metaphor is to be taken literally. The notion of sophistication is used to quantify meaningful complexity and to distinguish it from classical computational complexity. In this context, the distinction between program and data becomes relevant and an alternative metaphor of DNA as data to a parallel computing network embedded in the global geometrical and biochemical structure of the cell is discussed. An intermediate picture of an evolving network emerges as the most likely where the output of the cellular computing network can produce, at a different time scale, changes in the structure of the network itself by means of changes in the DNA activity patterns.
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    Distribution of the number of matches between nucleotide sequences (1990)
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    Bulletin of mathematical biology 52 (1990), S. 349-358 
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    Notes: Abstract When two strings of symbols are aligned it is important to know whether the observed number of matches is better than that expected between two independent sequences with the same frequency of symbols. When strings are of different lengths, nulls need to be inserted in order to align the sequences. One approach is to use simple approximations of sampling for replacement. We describe an algorithm for exactly determining the frequencies of given numbers of matches, sampling without replacement. This does not lead to a simple closed form expression. However we show examples where sampling with, or without, replacement give very similar results and the simple approach may be adequate for all but the smallest cases.
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    Consistency of optimal sequence alignments (1990)
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    Bulletin of mathematical biology 52 (1990), S. 509-525 
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    Notes: Abstract Pairwise optimal alignments between three or more sequences are not necessarily consistent as a whole, but consistent and inconsistent residues are usually distributed in clusters. An efficient method has been developed for locating consistent regions when each pairwise alignment is given in the form of a “skeletal representation” (Bull. math. Biol. 52, 359–373). This method is further extended so that the combination of pairwise alignments that gives the greatest consistency is found when possibly many alignments are equally optimal for each pairwise comparison. A method for acceleration of simultaneous multiple sequence alignment is proposed in which consistent regions serve as “anchor points” limiting application of direct multi-way alignment to the rest of “inconsistent” regions.
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    Conditions for the unlimited growth in multitype population size dependent galton-watson processes (1990)
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    Bulletin of mathematical biology 52 (1990), S. 527-534 
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    Notes: Abstract Sufficient conditions are given for the unlimited growth or otherwise in multitype population size dependent Galton-Watson processes. These conditions are given in terms of moments of offspring distributions and extend known conditions for processes with one type.
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    A deterministic model of the cell cycle (1990)
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    Bulletin of mathematical biology 52 (1990), S. 535-547 
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    Notes: Abstract The variability of the duration of the cell cycle is explained by the phenomenon of sensitive dependence upon initial conditions; as may occur in deterministic non-linear systems. Chaotic dynamics of a system is the result of this sensitive dependence. First a deterministic system is formulated that is equivalent to the Smith-Martin transition probability model of the cell cycle. Next the model is extended to a dynamic process that ranges over the cell generations. A deterministic non-linear relationship between the cycle time of the mother and daughter cell is established. It clarifies the variability of mother-daughter correlation for the different cell types. The model is fitted to two different cell cultures; it shows that the graph of the non-linear relation has the same shape for different cell types.
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    Bulletin of mathematical biology 52 (1990), S. 583-596 
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    Editorial: Software survey section (1990)
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    Bulletin of mathematical biology 52 (1990), S. I 
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    Diffusion regulated growth characteristics of a spherical prevascular carcinoma (1990)
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    Bulletin of mathematical biology 52 (1990), S. 549-582 
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    Notes: Abstract Recently a mathematical model of the prevascular phases of tumor growth by diffusion has been investigated (S. A. Maggelakis and J. A. Adam,Math. Comput. Modeling, in press). In this paper we examine in detail the results and implications of that mathematical model, particularly in the light of recent experimental work carried out on multicellular spheroids. The overall growth characteristics are determined in the present model by four parameters:Q, γ, b, andδ, which depend on information about inhibitor production rates, oxygen consumption rates, volume loss and cell proliferation rates, and measures of the degree of non-uniformity of the various diffusion processes that take place. The integro-differential growth equation is solved for the outer spheroid radiusR 0(t) and three related inner radii subject to the solution of the governing time-independent diffusion equations (under conditions of diffusive equilibrium) and the appropriate boundary conditions. Hopefully, future experimental work will enable reasonable bounds to be placed on parameter values referred to in this model: meanwhile, specific experimentally-provided initial data can be used to predict subsequent growth characteristics ofin vitro multicellular spheroids. This will be one objective of future studies.
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    Synchronization of the behaviour within nests of the antleptothorax acervorum (fabricius)—I. Discovering the phenomenon and its relation to the level of starvation (1990)
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    Bulletin of mathematical biology 52 (1990), S. 597-612 
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    Notes: Abstract Workers of the speciesLeptothorax acervorum show age-polyethism, they start their life as broodworkers and later on they become nestworkers and foragers. Nestworkers and foragers of this ant species are inactive for 72% and 15% of the total time respectively. The short bursts of activity within the nest do not occur randomly but are synchronized so that the whole nest population exhibits nonperiodic pulses of activity: the ants were seen to wake each other actively. In addition starvation experiments were done to assess whether ants react upon food availability. In appeared that during a longlasting period of starvation the proportion of active ants in the nest is at a higher approximately constant level.
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    The economics of exhaustible resources (1991)
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    Bulletin of mathematical biology 53 (1991), S. 281-312 
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    Some aspects of the dynamics of populations important to the management of the commercial Marine fisheries (1991)
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    Bulletin of mathematical biology 53 (1991), S. 253-279 
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    Bulletin of mathematical biology 53 (1991), S. 313-326 
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    Editorial: Software survey section (1991)
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    Bulletin of mathematical biology 53 (1991), S. I 
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    Resource management and behavioural ecology: A Conference in Celebration of the 60th Birthday of Colin Clark 24–26 July 1991 University of British Columbia, Cancouver, B.C. (1991)
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    Bulletin of mathematical biology 53 (1991), S. 327-327 
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    The statistical correlation of nucleotides in protein-coding DNA sequences (1991)
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    Bulletin of mathematical biology 53 (1991), S. 345-353 
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    Notes: Abstract The statistical correlation of nucleotides in a DNA sequence is described by a set of redundanciesD 1,D 2,D 3,... By calculation of {D n} of 2341 coding regions of nucleic acid sequences it is demonstrated that about 2/3 of sequences has correlation length ≤2, 10% of sequences—correlation with 3-periodicity and others—long range aperiodic correlations. The implications of the results from the interactions of random mutation and natural selection are discussed briefly.
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    Autocatalytic membrane conductance and memory (1991)
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    Bulletin of mathematical biology 53 (1991), S. 327-343 
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    Notes: Abstract A basic characteristic of biological memory is that it has a graded duration, which, even for socalled short-term memory, can vary from minutes to days (i.e. over about three orders of magnitude), depending on the training protocol, which one can think of as determining the “strength” of the memory. Furthermore, the molecular analysis of simple learning in invertebrates has revealed many examples where “learning” is produced by adecrease in an appropriate membrane conductance. This paper provides a quantitative analysis of a simple kinetic scheme where by a conductance decrease can be produced by repetitive nerve impulses, with a duration that varies with stimulus frequency. The simplest model considered is based on the actual kinetics of the naturally-occurring ionophore Monazomycin. This model yields durations ranging only over a factor of about 10, for reasonable parameter values. However, a simple modification of the model yields memory durations ranging over three or more orders of magnitude. We also show that Monazomycin-like kinetics can appear as the result of a combination of simple uni- and bi-molecular reactions, thus making more plausible the possibility that the effects described here may operate in actual biological systems.
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    Statistical evaluation of dendritic growth models (1991)
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    Bulletin of mathematical biology 53 (1991), S. 579-589 
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    Notes: Abstract A mathematical model (Kliemann, W. 1987.Bull. math. Biol. 49, 135–152.) that predicts the quantitative branching pattern of dendritic tree was evaluated using the apical and basal dendrites of rat hippocampal neurons. The Wald statistics for χ2-test was developed for the branching pattern of dendritic trees and for the distribution of the maximal order of the tree. Using this statistic, we obtained a reasonable, but not excellent, fit of the mathematical model for the dendritic data. The model's predictability of branching patterns was greatly enhanced by replacing one of the assumptions used for the original model “splitting of branches for all dendritic orders is stochastically independent”, with a new assumption “branches are more likely to split in areas where there is already a high density of branches”. The modified model delivered an excellent fit for basal dendrites and for the apical dendrites of hippocampal neurons from young rats (30–34 days postpartum). This indicates that for these cells the development of dendritic patterns is the result of a purely random and a systematic component, where the latter one depends on the density of dendritic branches in the brain area considered. For apical dendrites there is a trend towards decreasing pattern predictability with increasing age. This appears to reflect the late arrival of afferents and subsequent synaptogenesis proximal on the apical dendritic tree of hippocampal neurons.
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    Computer simulations of cell-target encounter including biased cell motion toward targets: Single and multiple cell-target simulations in two dimensions (1991)
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    Bulletin of mathematical biology 53 (1991), S. 591-621 
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    Notes: Abstract In order for immune cells to carry out many of their functions, including clearance of infectious agents from tissue, they must first encounter their targets in the tissue. This encounter process is often the rate-limiting step in the overall function. Most immune cells exhibit chemotactic ability, and previous continuum models for encounter rates and dynamics have shown that chemotaxis can be a great advantage to cells by greatly increasing encounter rates relative to those for randomly moving cells. This paper describes computer simulations of discrete cell-target encounter events in two dimensions, for the two cases considered by the continuum models: where only a single cell and a single target are present, and where many cells and targets are present. The results of these simulations verify our previous model predictions that a small amount of chemotactic bias dramatically decreases the encounter time, while further increases in the amount of bias have a much smaller effect. Chemotactic ability is shown to be an important determinant of the kinetics of target clearance, and its effects depend on the initial cell-target ratio and the initial distributions of cells and targets. To the best of our knowledge, this work provides the first computer simulations of particle-target encounter in which there is biased motion of particles toward their targets, and is therefore of general interest beyond specific application to immune cell function.
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    Bulletin of mathematical biology 53 (1991), S. 657-663 
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    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458634
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    One-way blocks in cardiac tissue: A mechanism for propagation failure in purkinje fibres (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 881-899 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The concept of a one-way block, arising from a region of depressed tissue, has remained central to theories for cardiac arrhythmias. We show that both the geometry of a depressed region and spatial heterogeneities in depression are key factors for inducing such a block. By using an asymptotic approximation, known as the eikonal equation, to model qualitatively the movement of a depolarization wave-front down a Purkinje fibre bundle, we show how a one-way block in conduction may result from asymmetric constriction in the width of a depressed bundle. We demonstrate that this theory is valid for biologically relevant parameters and simulate a one-way block by numerically solving the eikonal approximation. We consider the case of non-uniform depression, where the planar travelling wave speed is spatially dependent. Here, numerical simulations indicate that such a spatial dependency may, in itself, be sufficient to produce a one-way block.
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    URL: http://dx.doi.org/10.1007/BF02461489
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    A system dynamics model of island biogeography (1991)
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    Bulletin of mathematical biology 53 (1991), S. 911-940 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The MacArthur-Wilson equilibrium theory of island biogeography has been one of the more influential concepts in modern biogeography and ecology. In this paper, we synthesize the theory and examine effects of different immigration/extinction rate-species diversity curves on original predictions from the theory by using the System Dynamics simulation modeling approach. Moreover, we develop a comprehensive and generic System Dynamics model to incorporate a variety of recent modifications and extensions of the theory, including area effect, distance effect, competition effect, habitat diversity effect, target effect, and rescue effect. Through computer simulation with STELLA, a more profound understanding of the theory of island biogeography can be gained. The System Dynamics modeling approach is especially appropriate for such a study because it maximizes the utilization of the ecological data by incorporating qualitative information so that a complex, imprecisely-defined ecological system can be studied quantitatively, effectively, and comprehensively. Our simulation results show that different monotonic rate-species diversity curves do not affect the essence of the theory of island biogeography, while the magnitude of equilibrium species diversity may be greatly affected. Non-monotonic rate-species diversity curves may result in potential multiple equilibria of species diversity. In addition, our model suggests that a non-monotonic relationship may exist between the equilibrium turnover rate and island area and between the equilibrium turnover rate and distance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461491
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    Modularity and reliability in the organization of organisms (1992)
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    Bulletin of mathematical biology 54 (1992), S. 1-20 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An organism persists only if it satisfies internal and external constraints. Within the organism networks of processes meet the constraints. In such networks a principle of matching often obtains: the pattern of coupling among processes matches the correlation among constraints. That is, a module—a cluster of coupled processes—meets a constraint. Dissociable modules meet dissociàble constraints. A hierarchy of modules meets a hierarchy of constraints. We have inquired whether such matching is predicted by an optimality criterion in a simple example. We find that in an ensemble of networks with unreliable processes, the networks that meet the constraints with highest reliability obey the principle of matching. The difference in reliability between modular and nonmodular networks that meet the same constraints is a function of the probability of success per process. Our results suggest that this difference is maximal at a probability of success that increases monotonically with the number of processes in the network.
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    URL: http://dx.doi.org/10.1007/BF02458617
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    Maximum-likelihood estimation of the statistical distribution of Smith-Waterman local sequence similarity scores (1992)
    Springer
    Bulletin of mathematical biology 54 (1992), S. 59-75 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method is described for estimating the distribution and hence testing the statistical significance of sequence similarity scores obtained during a data-bank search. Maximum-likelihood is used to fit a model to the scores, avoiding any costly simulation of random sequences. The method is applied in detail to the Smith-Waterman algorithm when gaps are allowed, and is shown to give results very similar to those obtained by simulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458620
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    A general theory for host seeking decisions in mosquitoes (1992)
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    Bulletin of mathematical biology 54 (1992), S. 401-412 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We develop a theory for host seeking decisions in mosquitoes that explicitly considers the tradeoffs mosquitoes face in allocation to somatic and gametic function. Specifically, we consider conditions under which mosquitoes should seek out nectar and blood hosts upon encountering host odours. Results from development of a dynamic model that considers free and crop energy states suggest that mosquitoes should seek out blood hosts under a wide variety of conditions but that decisions to seek nectar depends upon crop volume, concentration and free energy. This pattern arises because mosquitoes carrying large crop loads are constrained in their ability to obtain large blood meals due to space limitations in the abdomen. The predicted patterns of behaviour are supported by published observations of mosquito behaviour.
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    URL: http://dx.doi.org/10.1007/BF02464840
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    Rate maximizing and state variable theories of diet selection (1992)
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    Bulletin of mathematical biology 54 (1992), S. 413-422 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In behavioral ecology, diet selection is often predicted by using a theory in which it is assumed that behaviors have evolved to maximize the rate of intake of energy. In this theory, it is assumed that fitness is a monotonic function of energy intake. An alternative is to deal directly with fitness, measured in terms of expected reproduction, and thus connect short term behavior with reproduction. Following the usual assumptions of the theory of diet choice, fitness satisfies a partial differential-difference equation. Conditions under which rate maximizing and state variable theories of diet selection yield identical predictions are identified. When predation, as well as starvation, is a source of mortality, the identification is not as complete.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464841
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    Components of uncertainty in clutch-size optimization (1992)
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    Bulletin of mathematical biology 54 (1992), S. 445-464 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Environmental uncertainty can be both a cause and consequence of chance variation in many of the phenotypic factors associated with the control of clutch size in birds. When such uncertainty inflates or otherwise influences the variance associated with expected reproductive success for any genotype, it will also influence the resulting phenotypic optima. Random variation that affects the evolution of clutch size optima explicitly may occur both within (intra-) and across (inter-) generations. Examples of intra-generational uncertainty could include chance variation in: (1) the quality and quantity of offspring, (2) parental quality, and (3) temporal resources like food. Inter-generational uncertainty would include chance variation in demographic and population characters. With respect to clutch (or litter) size, almost all forms of uncertainty tend to favor an optimum (genetic) strategy with a clutch that is smaller than the clutch associated with the apparent or actual maximal fitness of an individual parent. The overall effect of all the components of uncertainty can be evaluated through the integration of all this phenotypic variation: however each step of the integration is a conditional expectation of each component. Therefore, a single factor analysis may indicate a false optimum, and an integrated analysis of all components is necessary to evaluate the importance of their individual and joint effects on the adaptive evolution of clutch size.
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    URL: http://dx.doi.org/10.1007/BF02464843
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    Intra-specific competition and density dependent juvenile growth (1992)
    Springer
    Bulletin of mathematical biology 54 (1992), S. 503-519 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A difference equation model for the dynamics of a semelparous size-structured species consisting of juvenile and adult individuals is derived and studied. The adult population consists of two size classes, a smaller class and a larger more fertile class. Negative feedback occurs through slowed juvenile growth due to increased total population levels during the developmental period and consequently a smaller adult size at maturation. Intra-specific competition coefficients are size dependent and measure the strength of intra-specific competition between juveniles and adults. It is shown that equilibrium states in which adults and juveniles occur together at all times are in general destabilized by significantly increased juvenilevs adults competition with the result that stable periodic cycles appear, in which the generations alternate in time and hence avoid competition. This result supports the tenet that intra-specific competition between juveniles and adults is destabilizing. Exceptions to this destabilization principle are found, however, in which populations exhibiting non-equilibrium, aperiodic dynamics can be equilibrated by increase competition between juveniles and adults. This occurs, for example, when adult fertility and competition coefficients are significantly size class dependent.
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    URL: http://dx.doi.org/10.1007/BF02459632
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    Analysis of volume regulation in an epithelial cell model (1992)
    Springer
    Bulletin of mathematical biology 54 (1992), S. 537-561 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An epithelial cell is modeled as a single compartment, bounded by apical and basolateral cell membranes, and containing two nonelectrolyte solute species, nominally NaCl and KCl. Membrane transport of these species may be metabolically driven, or it may follow the transmembrane concentration gradients, either singly (a channel) or jointly (a cotransporter). To represent the effect of stretch-activated channels or shrinkage-activated cotransporters, the membrane permeabilities and cotransport coefficients are permitted to be functions of cell volume. When this epithelium is considered as a dynamical system, conditions are indicated which guarantee the uniqueness and stability of equilibria. Experimentally, many epithelial cells can regulate their volume, and such volume regulatory capability is defined for this model. It is clearly distinct from dynamical stability of the equilibrium and requires more stringent conditions on the volume-dependent permeabilities and cotransporters. For a previously developed model of the toad urinary bladder (Strieteret al., 1990,J. gen. Physiol. 96, 319–344) the uniqueness and stability of its equilibria are indicated. The analysis also demonstrates that under some conditions a second stable equilibrium may appear, along with a saddle-node bifurcation. This is illustrated numerically in a modified model of the epithelium of the thick ascending limb of Henle.
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    URL: http://dx.doi.org/10.1007/BF02459634
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    Book reviews (1992)
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    Bulletin of mathematical biology 54 (1992), S. 687-694 
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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/BF02459640
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    Modeling immune reactivity in secondary lymphoid organs (1992)
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    Bulletin of mathematical biology 54 (1992), S. 649-672 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Models of the dynamical interactions important in generating immune reactivity have generally assumed that the immune system is a single well-stirred compartment. Here we explicitly take into account the compartmentalized nature of the immune system and show that qualitative conclusions, such as the stability of the immune steady state, depend on architectural details. We examine a simple model idiotypic network involving only two types of B cells and antibody molecules. We show, for model parameters used by De Boeret al. (1990,Chem. Eng. Sci. 45, 2375–2382), that the immune steady state is unstable in a one compartmental model but stable in a two compartment model that contains both a lymphoid organ, such as the spleen, and the circulatory system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459638
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    On the kinetics and optimal specificity of cytotoxic reactions mediated by T-lymphocyte clones (1992)
    Springer
    Bulletin of mathematical biology 54 (1992), S. 839-873 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Using the chromium release assay and the single cell assay in agarose, we study the cytotoxic reaction of the MHC-restricted T lymphocyte clones P89:15 and P1:3, which recognize distinct but specific tumour antigens on the surface of syngeneic P815 mastocytoma cells. We propose a mathematical model which describes these experiments, accounts for the strongly non-Michaelian behaviour of the reaction and permits us to estimate the kinetic parameters characterizing effector-target conjugation and lethal hit delivery. The results show that the binding and lytic activity of effector cells is modulated by the number of targets bound to them. The binding of a second target by an effector having already a target bound is facilitated; on the other hand, an effector having bound two targets delivers a lethal hit more slowly than one with a single target bound. We investigate the role of these kinetic properties in the competition between the process of tumour progression due to cancer cell replication and the process of tumour regression due to T lymphocyte cytotoxic activity. For both clones, we estimate the effector-target ratio beyond which rejection prevails. This ratio is nine times larger for P1:3 than for P89:15. Furthermore, our analysis suggests that there exists an optimal specificity minimizing this ratio. Deviations from this optimum, be it in the sense of an increase or decrease of specificity, tendsto stabilize the tumoural state: a situation which in the broader context of the immune response evolution and regulation can be viewed as animmune response dilemma.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459933
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