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  • Springer  (100,817)
  • 2010-2014
  • 1985-1989  (100,817)
  • 1940-1944
  • 1986  (52,321)
  • 1985  (48,496)
Collection
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  • 2010-2014
  • 1985-1989  (100,817)
  • 1940-1944
Year
  • 1
    Electronic Resource
    Electronic Resource
    Coupling of a slow and a fast oscillator can generate bursting (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 1-21 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A general mechanism underlying bursting is proposed and described. It consists of two coupled nonlinear oscillators with different frequencies, where the slower oscillator alternatively switches the faster one on and off. This mechanism is shown to work in an extended Bonhoefer-van der Pol oscillator as well as in a modified version of the Hodgkin-Huxley equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459643
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  • 2
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    Analytical bounding functions for diffusion problems with michaelis-menten kinetics (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 145-153 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Pointwise upper and lower bounds for the solution of a class of nonlinear diffusion problems with Michaelis-Menten kinetics are presented. Simple analytical bounding curves are obtained and for an illustrative case the calculated values bound the recent numerical solution of P. Hiltmann and P. Lory, 1983.Bull. math. Biol. 45, 661–664.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459650
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  • 3
    Electronic Resource
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    Cell mass concentration variance resulting from fluctuations in the incoming nutrient concentration to a chemostat (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 337-342 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The cellular response in terms of steady-state variance of cell mass concentration to fluctuations in incoming nutrient concentration to a chemostat has been examined. A white noise process is assumed to describe incoming nutrient concentration fluctuations and the variance of cell mass concentration has been found to depend on cell yield (a lumped measure of nutrient concentration fluctuation magnitude and lifetime) and two system time constants.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459920
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  • 4
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    Chaotic dynamics of information processing: The “magic number seven plus-minus two” revisited (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 343-365 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a well-known collection of his essays in cognitive psychology Miller (The Psychology of Communication. Penguin, 1974) describes in detail a number of experiments aiming at a determination of the limits (if any) of the human brain in processing information. He concludes that the ‘channel capacity’ of human subjects does not exceed a few bits or that the number of categories of (one-dimensional) stimuli from which unambiguous judgment can be made are of the order of ‘seven plus or minus two’. This ‘magic number’ holds also, Miller found, for the number of random digits a person can correctly recall on a row and also the number of sentences that can be inserted inside a sentence in a natural language and still be read through without confusion. In this paper we propose a dynamical model of information processing by a self-organizing system which is based on the possible use of strange attractors as cognitive devices. It comes as an amusing surprise to find that such a model can, among other things, reproduce the ‘magic number seven plus-minus two’ and also its variance in a number of cases and provide a theoretical justification for them. This justification is based on the optimum length of a code which maximizes the dynamic storing capacity for the strings of digits constituting the set of external stimuli. This provides a mechanism for the fact that the ‘human channel’, which is so narrow and so noisy (of the order of just a few bits per second or a few bits per category) possesses the ability of squeezing or ‘compressing’ practically an unlimited number of bits per symbol—thereby giving rise to a phenomenal memory.
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    URL: http://dx.doi.org/10.1007/BF02459921
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  • 5
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    The extension of two-dimensional cable theory to arteries and arterioles (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 409-424 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Electrical polarization of an artery or an arteriole may be modeled by the use of equations developed for two-dimensional cable theory. Two special cases have previously been solved: those corresponding to the case in which the radius is either zero (one-dimensional cable theory) or infinite. This paper presents the general solution.
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    URL: http://dx.doi.org/10.1007/BF02459923
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  • 6
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    On the computation of the tertiary structure of globular proteins—IV. Use of secondary structure information (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 367-407 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The distance geometry approach for computing the tertiary structure of globular proteins emphasized in this series of papers (Goelet al., J. theor. Biol. 99, 705–757, 1982) is developed further. This development includes incorporation of some secondary structure information—the location of alpha helices in the primary sequence—in the algorithm to compute the tertiary structure of alpha helical globular proteins. An algorithm is developed which estimates the interresidue distances between chain-proximate helices. These distances, in conjunction with the global statistical average distances obtainable from a database of real proteins and determined by the primary sequence of the protein under study, are used to determine the tertiary structure. Five proteins, parvalbumin, hemerythrin, human hemoglobin, lamprey hemoglobin, and sperm whale myoglobin, are investigated. The root mean square (RMS) errors between the calculated structures and those determined by X-ray diffraction range from 4.78 to 7.56 Å. These RMSs are 0.21–2.76 Å lower than those estimated without the secondary structure information. Contact maps and three-dimensional backbone representations also show considerable improvements with the introduction of secondary structure information.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459922
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  • 7
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    Editorial: Software survey section (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. I 
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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/BF02459925
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  • 8
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    The unidirectional flux transient as a tool for quantifying parallel diffusional pathways through membranes. Exact solution for two pathways (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 425-434 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract If a plane membrane consists of patches, each with a given area and a given diffusion coefficient, then the transient of the total unidirectional flux of a diffusing substance (as defined experimentally by Ussing) is predictable. Here the inverse problem is studied: given only the observed transient of the total unidirectional diffusion flux, the unknown membrane heterogeneity transverse to the flux is to be quantified. The ratio of the arithmetic and of the harmonic means (both area-weighted) of the diffusion coefficients, evaluated over the membrane, is expressed in terms of the observed transient alone and is used to characterize the heterogeneity. A unique exact solution of the inverse problem for two kinds of patches is obtained in closed form. A singular limit of this solution pertains to currently postulated models of endothelial membranes, for which a characteristically shaped transient is predicted.
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    URL: http://dx.doi.org/10.1007/BF02459924
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  • 9
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    Editor's comments (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 435-435 
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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/BF02460005
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  • 10
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    Sequence similarity (‘Homology’) searching for molecular biologists (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 437-474 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Major types of sequence similarity searching (often, and incorrectly, called ‘homology’ searching) are reviewed and examples of each are presented. The features and limitations of each type of program, and individual implementations of each type are discussed. Two pairs of sequences are used as examples to show how implementations of each type differ in their results and their presentation. Both local and global alignment programs are examined, and the programs reviewed run on many different types of computer architectures, from laboratory computers such as the IBM PC, minicomputers such as the VAX, to large mainframe computers such as DEC-10/20 series.
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    URL: http://dx.doi.org/10.1007/BF02460006
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  • 11
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    The existence of stable equilibria in Volterra predator-prey systems represented by loop graphs (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 489-494 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Criteria for the existence of globally stable equilibria in classical Volterra predator-prey systems represented by loop graphs are provided by comparing the community matrix with a matrix belonging to matrix classS W .
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    URL: http://dx.doi.org/10.1007/BF02460008
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  • 12
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    Pattern regulation in reaction-diffusion systems-the problem of size invariance (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 475-487 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Ordinary reaction-diffusion mechanisms do not account for size invariance properties of morphogenetic fields. We show that such a failure results from ignoring cell individuality. By considering purely topological factors, such as the number of intercellular contacts or the extent of the cell surface in contact with neighbouring cells, size invariance exists in reaction-diffusion systems. Our results are general, model independent and may be applied to any multi-unit ensemble exhibiting coherent behaviour.
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    URL: http://dx.doi.org/10.1007/BF02460007
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  • 13
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    Effects of twist on pulse waves in arteries (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 495-502 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The artery is treated as a thick-walled cylindrical shell. Using the large deformation theory, an analytical expression for the pulse wave speed is obtained and the effect of twist on the wave speed is discussed. Numerical results indicate that although phase velocity increases with pressure, it decreases with increasing twist angle.
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    URL: http://dx.doi.org/10.1007/BF02460009
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  • 14
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    Effects of the shape of stenosis on the resistance to blood flow through an artery (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 545-550 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The effect of the shape of stenosis on the resistance to blood flow through an artery with mild local narrowing has been studied. It is shown that the resistance to flow decreases as the shape of stenosis changes and the maximum resistance is attained in the case of symmetric stenosis.
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    URL: http://dx.doi.org/10.1007/BF02460013
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  • 15
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    A method for numbering binary rooted and unrooted phylogenies and their hypothetical taxonomic units (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 535-543 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A set of 2n−2 relations (edges) and a set ofn−1 hypothetical taxonomic units (HTUs) derive from the estimation of a binary phylogeny of a set ofn operational taxonomic units (OTUs). We propose an easy way for numbering thesen−1 hypothetical taxonomic units, as well as for then−2 interior points of an unrooted binary phylogeny. We also present an alternative method to the one proposed by Rohlf (Bull. math. Biol. 45, 33–40, 1983) for numbering the π i=1 n (2i−3) possible rooted binary phylogenies and the π i=1 n−1 (2i−3) possible unrooted binary phylogenies conerning a set ofn operational taxonomic units. An illustrative example of the method is presented. It is hoped that some studies in phylogenetics will become more accessible, from the viewpoint of computational economy, by the use of this method.
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    URL: http://dx.doi.org/10.1007/BF02460012
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  • 16
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    Mathematical modeling of opiate binding to mouse brain membrane (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 503-512 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The heterogeneity of rat brain opiate receptors was examined by analyzing competition data. The binding of three prototypical tritiated opioid agonists, [3H]-dihydromorphine ([3H]-DHM), [3H]-D-ala2-D-leu5-enkephalin ([3H]-DADLE), and [3H]-ethylketocyclazocine ([3H]-EKC) was determined in the presence of varying concentrations of each of these unlabeled ligands, generating nine displacement curves. A computer program was then used to find the best fit of a model system to these data, assuming two, three or four independent binding sites. The best fit was a four-site model. One of these sites is specific for DHM; two are relatively selective for DHM and DADLE respectively, but also bind EKC. The remaining site binds only EKC with high affinity. These results, together with displacement data using naloxone, FK33824, and D-ala2-met5-enkephalinamide, are discussed in terms of current opiate receptor models.
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    URL: http://dx.doi.org/10.1007/BF02460010
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  • 17
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    Capillary operators—II (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 651-668 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This work continues with an examination of capillary exchange models as operators, namely the operatorsO k andK αk relating extravascular and intravascular concentration to input for the Krogh cylinder model of a single capillary, a model basic to many organ models. Fundamental algebraic and analytic properties are presented: the operators belong to a commutative Banach algebra; an addition theorem holdsK αk +K βk =K α+β,k ; the operatorK αk has an inverse;K αk -1 , (as an operator on LebesgueL p space or on the locally integrable functions); partial derivatives are given forK αk [f](t) andO k [f](t) (sensitivity functions); and inequalities are established for the derivatives. Dominance relations between model curves are inferred. Error bound formulas are presented forK andO as bounds on ‖K αk f-K βl f‖ p and ‖O k f-O l f‖ p for allL p . Consequent limitations on relative errors are shown. The implications for operators on a finite time interval are deduced.
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    URL: http://dx.doi.org/10.1007/BF02460131
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  • 18
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    A theoretical analysis for determining the nonlinear hydraulic permeability of a soft tissue from a permeation experiment (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 669-683 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The nonlinear nature of the hydraulic permeability, as well as the corresponding pressure and displacement fields, in a soft tissue are studied for steady-state permeation. From a two-phase continuum model analytical expressions are derived that can be used with the results from a permeation experiment to determine the dependence of the permeability on the strain. In the process it is found that, because of the compaction of the tissue arising from fluid flow, it is necessary to distinguish between the apparent and intrinsic permeability. The former, which is an averaged quantity, is the permeability usually obtained in permeation studies. However, as shown from the analysis, it can differ substantially from the latter, which is the local permeability in the tissue.
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    URL: http://dx.doi.org/10.1007/BF02460132
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  • 19
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    Editorial: Software survey section (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), 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/BF02460134
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  • 20
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    Editor's comments (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 695-695 
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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/BF02469298
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  • 21
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    Chaotic phenomena (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 697-738 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
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    URL: http://dx.doi.org/10.1007/BF02469299
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  • 22
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    Effects of the torso boundary and internal conductivity interfaces in electrocardiography: An evaluation of the ‘Infinite medium’ approximation (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 685-694 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The analytic, eccentric spheres model of the torso was used to examine the validity of approximating the ‘infinite medium’ potential by integrating ‘finite medium potentials’ over the torso surface. Although idealized, the analytic model is sophisticated enough for all important torso conductivity and geometry parameters to be preserved in the formulation. The model generates both ‘finite medium’ potentials (for which the torso is surrounded by air) and also ‘infinite medium’ potentials (for which the outermost layer of the torso extends outward to infinity). The finite medium torso potentials were integrated over the torso surface in accordance with the approximation used by many investigators in an effort to make the surface distribution more representative of the primary cardiac sources. The resulting potential distribution was compared with the true infinite medium potential, in which the effects of internal inhomogeneities (secondary sources) were taken into account. The difference between the two representations was found to be significant, and caution should be used when interpreting such data.
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    URL: http://dx.doi.org/10.1007/BF02460133
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  • 23
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    An environ analysis for nonlinear compartment models (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 739-748 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Environ analysis, an input-output analysis for models of ecological systems, has been previously formulated for linear systems. This note has a twofold purpose: first, we indicate that a variation of parameters technique can be applied, at least in principle, to computeboth input and output environs; and second, we show that this technique may be used for computation of environs in nonautonomous, nonlinear compartment models. This nonlinear theory, obtained as a direct extension of dynamical system developments, allows the traditional environ partitioning of compartmental storages and flows. An example of a nonlinear nutrient-producer-consumer system whose output environs can be computed asymptotically is presented to illustrate these concepts.
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  • 24
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    Dependence of tetanic hyperpolarization on pump conductance in the cyanide-treatedXenopus node (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 749-755 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract Prolonged exposure to cyanide leads to a delayed but reversible disappearance of tetanic hyperpolarization in theXenopus node (G. M. Schoepfle,Am. J. Physiol. 231, 1033–1038, 1976). This effect is attributed to a pronounced decline in the absolute values of the ATP and ADP concentrations, such that the ATP-driven ion translocation is no longer possible, regardless of the existing values for (Na)i, (K)i and the (ATP)/(ADP) ratio. Mathematically, this would imply a vanishing of a constant pump conductance gp in the exression for electrogenic pump current densitityJ p, whereJ p=g p (V m −E p) in whichV m is membrane potential andE p is an ATP-and sodium-dependent e.m.f.
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    Stress-strain behavior for curved exponential strips (1985)
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    Bulletin of mathematical biology 47 (1985), S. 757-764 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract For the two-parameter (A, α) exponentially-stiffening constituitive relation, typical of many biological materials, it is shown that the uniaxial stress-strain behavior of an initially curved strip is significantly changed by the residual bending stresses. Closedform theoretical results depend on the thickness to radius ratio (h/R) and the relative strain level ε(h/R). The bending stresses tend to obscure accurate measurement ofA and α unless care is taken. However, it is shown that by changing co-ordinates to (dℝ/d∈, ℝ)-space, bothA and α can be recovered from the high stress data, and α alone can be recovered from the low stress data. This has practical application to the mechanics of cornea, sclera, and heart muscle.
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    A mathematical note on the fahraeuslindqvist effect in power law fluid (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 765-769 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract An axisymmetric flow of a power law fluid through circular tubes under constant pressure gradient with the flow parameters varying radially is analyzed theoretically. The main finding is that for the Fahraeus-Lindqvist (F-L) effect to occur, it is necessary to have at least one of the parametersK (consistency) andn (index) as a discontinuous function ofr in the absence of wall slip; and with slip condition the parameters could be continuous functions ofr under specific conditions. In both the cases the existence of more than one discontinuity cannot be ruled out. The results obtained are consistent with experimental findings of blood flow through narrow tubes.
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    URL: http://dx.doi.org/10.1007/BF02469303
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    Zygotic algebra for two linked loci with sexually different recombination rates (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 771-782 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This is a study of the properties of a zygotic algebra of two linked autosomal loci with different recombination rates in males and females, without selection or mutation and with random mating. The above-mentioned zygotic algebra contains a genetic subalgebra. A canonical basis of this subalgebra is constructed and the train roots are calculated.
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    URL: http://dx.doi.org/10.1007/BF02469304
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    Third International Summer School on Mathematical Modelling in Physiology and Clinical Medicine (1985)
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    Bulletin of mathematical biology 47 (1985), S. 799-799 
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    ISSN: 1522-9602
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    URL: http://dx.doi.org/10.1007/BF02469307
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  • 29
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    The possible role of solitonic processes during A to B conformational changes in DNA (1985)
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    Bulletin of mathematical biology 47 (1985), S. 783-789 
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    ISSN: 1522-9602
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    Notes: Abstract Among the conformations which the DNA molecule can adopt, the transition beween the A and B families, controlled by water content (relative humidity), seems to be implicated in the transcription process. Focusing on the main structural difference involved (tilting of base normals with respect to the helix axis), a model is constructed, solitary wave solutions of the resulting equation of motion are demonstrated and possible experimental implications indicated.
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    On the distribution of the time required to remove white balls from an URN (1985)
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    Bulletin of mathematical biology 47 (1985), S. 791-797 
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    ISSN: 1522-9602
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    Notes: Abstract Balls are removed one-at-a-time at equal time intervals from an urn initially containingw 0 white balls and a large number b of black balls and each black or white ball is immediately replaced by a black ball. The distribution of the number of white balls remaining aftert iterations (under certain limiting operations) is taken from the literature. The problem is to use this result to find the time required to remove a fixed number of white ballsw 1 from the urn. We then find the mean and variance of this distribution and also look at the special case whenw 1 =w 0.
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    Editorial: Software survey section (1985)
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    Bulletin of mathematical biology 47 (1985), S. I 
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    An equation for flow in the renal proximal tubule (1986)
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    Bulletin of mathematical biology 48 (1986), S. 29-57 
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    Notes: Abstract Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.
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    Seventeenth Annual Meeting of the Classification Society of North America (1986)
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    Bulletin of mathematical biology 48 (1986), S. 105-105 
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    Editorial: Software Survey Section (1986)
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    Bulletin of mathematical biology 48 (1986), S. I 
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    Dominance of geometric overelastic factors in pulse transmission through arterial branching (1986)
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    Bulletin of mathematical biology 48 (1986), S. 97-103 
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    Notes: Abstract The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.
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    Galerkin's finite element-Laplace transform technique to transient heat migration in human skin and subcutaneous tissues (1986)
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    Bulletin of mathematical biology 48 (1986), S. 125-136 
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    Notes: Abstract Galerkin's finite element-Laplace transform technique (GAFELTTE) has been used to study transient temperature distribution in human skin and subcutaneous tissues. This study incorporates heat conduction, heat carried by perfusion of blood in the capillary beds and metabolic heat generation in the tissues. Different values of various quantities have been considered in all three parts, namely epidermis, dermis and subcutaneous tissues, depending on physiological considerations. The GAFELTTE provides interface temperatures for a wide range of the values of skin surface temperatures. These values have been used to obtain temperature profiles in the region considered. Steady-state temperature distribution has been deduced from the solution obtained by GAFELTTE and has been compared with the results obtained by using different methods.
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    Multiple stable equilibria in a predator-prey system (1986)
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    Bulletin of mathematical biology 48 (1986), S. 137-148 
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    Notes: Abstract Necessary and sufficient conditions are given for three equilibria to occur in a predatorprey model and conditions are given for two of these to be stable. The existence of two stable equilibria requires predator intraspecific competition for either space or food, and the lower the prey growth rate the stronger this predator self-regulation must be. A prey growth rate that is skewed to the right, the ability of a few predators to survive at low prey densities, and predators with high searching effectiveness, long handling times, and large maximum per capita rate of increase all make two stable equilibria more likely.
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    Servocontrol of the heart rate in homeothermic animals: On recognizing butterfly catastrophy models in biology (1986)
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    Bulletin of mathematical biology 48 (1986), S. 107-124 
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    Notes: Abstract Drawing evidence from a variety of cardiovascular studies on the heart rate in homeothermic animals, the author establishes the following thesis. The servocontrol (i.e. the autonomic and reflex control) by the medulla oblongata of the heart (rate) is a negative feedback dynamic which is isomorphic (i.e. ‘diffeomorphic’) to the dyamic underlying the heat rate control in those animals (cf. Kuyk,Bull. math. Biol. 46, 81–102, 1984). In fact, unlike in the heat rate case, the qualitative evidence supporting this thesis can not be fully complemented by quantitative data stemming from experiments, because of a lack of pertinent experiments—which, indeed, should measuresimultaneously the heart rate state parameter and thefour control parameters at the input side of the medulla. The results of some of the existing experiments on animal preparations can nevertheless be adduced to recognize that this dynamic can be graphed by the five-dimensional butterfly catastrophe type. The theory leads to new ways of looking at experiments in the field and/or setting up such experiments in the future.
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    Simulation of cellular compaction and internalization in mammalian embryo development as driven by minimization of surface energy (1986)
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    Bulletin of mathematical biology 48 (1986), S. 167-187 
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    Notes: Abstract A model based upon minimization of surface energy is proposed as an explanation for compaction and internalization of cells during mammalian embryo development. The model is used to simulate and graphically display these phenomena on a computer.
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    Topological properties of binary trees grown with order-dependent branching probabilities (1986)
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    Bulletin of mathematical biology 48 (1986), S. 197-211 
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    Notes: Abstract This paper describes a growth model for binary topological trees. The model defines the branching probability of all segments in the tree. The branching probability of a segment is formulated as a function of two variables, one indicating its type (intermediate or terminal), the other representing its order, i.e. the topological distance to the root segment. The function is determined by two parameters, namely the ratio of branching probabilities of intermediate and terminal segments and the strength of the order dependency, implemented in an exponential form. Expressions are derived for the calculation of symmetry properties of the partitions and it is indicated which part of the parameter domain results in predominantly symmetrical trees.
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    Pattern formation and morphogenesis: A reaction-diffusion model (1986)
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    Bulletin of mathematical biology 48 (1986), S. 213-228 
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    Notes: Abstract The problem of cellular differentiation and consequent pattern generation during embryonic development has been mathematically investigated with the help of a reaction-diffusion model. It is by now a well-recognized fact that diffusion of micromolecules (through intercellular gap junctions), which is dependent on the spatial parameter (r), serve the purpose of ‘positional information’ for differentiation. Based on this principle the present model has been constructed by coupling the Goodwin-type equations for RNA and protein synthesis with the diffusion process. The homogeneous Goodwin system can exhibit stable periodic solution if the value of the cooperativity as measured by the Hill coefficient (ρ) is greater than 8, which is not biologically realistic. In the present work it has been observed that inclusion of a negative cross-diffusion can drive the system into local instability for any value of ρ and thus a time-periodic spatial solution is possible around the unstable local equilibrium, eventually leading to a definite pattern formation. Inclusion of a negative cross-diffusion thus makes the system biologically realistic. The cross-diffusion can also give rise to a stationary wave-like dissipative structure.
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    Editorial: Software survey section (1986)
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    Bulletin of mathematical biology 48 (1986), S. I 
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    SCoP: An interactive simulation control program for micro- and minicomputers (1986)
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    Bulletin of mathematical biology 48 (1986), S. 427-441 
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    Notes: Abstract A nes software system is described for building simulation programs on micro- and minicomputers. Model equations are written as C subroutines, compiled and linked to the SCoP package to produce a menu-driven, interactive program. The system maintains a database of names, values, and units for all model parameters and variables. Run-time options include several methods for interactive parameter modification and both graphic and tabular outputs, with output values presented as they are calculated. Simulation output values can be compared with experimental data graphically and a companion program SCoPFit is provided for formal optimization of parameter values.
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    Global stability of partially closed food-chains with resources (1986)
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    Bulletin of mathematical biology 48 (1986), S. 455-468 
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    Notes: Abstract We consider the existence and global stability of aq-member equilibrium (1≤q≤n) in partially closed food-chains of lengthn having an abiotic component as resource. We observe that such existence demands bounds of resource supply rate and these bounds are weighted sums of interaction coefficients. Particular results of global sector-stability of partially feasible equilibria of simple food-chains obeying Lotka-Volterra dynamics are shown. Lastly the elasticity of such food-chains when a new species is introduced at the highest trophic level is investigated.
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    Global stability in time-delayed single-species dynamics (1986)
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    Bulletin of mathematical biology 48 (1986), S. 485-492 
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    Notes: Abstract Criteria are established for three classes of models of single-species dynamics with a single discrete delay to have a globally asymptotically stable positive equilibrium independent of the length of delay.
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    Predator-prey systems with group defence: The paradox of enrichment revisited (1986)
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    Bulletin of mathematical biology 48 (1986), S. 493-508 
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    Notes: Abstract The main concern of this paper is with survival or extinction of predators in models of predator-prey systems exhibiting group defence of the prey. It is shown that if there is no mutual interference among predators, enrichment could result in their extinction. However, if there is mutual interference, the predator population survives (at least deterministically).
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    A class of general stochastic compartmental systems (1986)
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    Bulletin of mathematical biology 48 (1986), S. 509-523 
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    Notes: Abstract In this paper a general class of semi-Markov compartmental systems is studied. Two models for different input processes are analysed. Attention has been paid to the recurrence times associated with each compartment and to the distribution of the number of particles in each compartment. As an example, a three-compartment system is discussed to study the movement between three health states of patients with chronic diseases.
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    Optimized homology searches of the gene and protein sequence data banks (1986)
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    Bulletin of mathematical biology 48 (1986), S. 569-583 
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    Notes: Abstract A strategy is presented for searching the gene and protein sequence data banks which combines the use of two previously described algorthms. The implementation of this strategy is thoroughly evaluated with respect to sensitivity, specificity and speed. The establishment of standard benchmarks for comparing programs that rearch the sequence data banks for homology is proposed.
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    Receptors and functional linkage in membrane permeability: A quantum mechanical model (1986)
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    Bulletin of mathematical biology 48 (1986), S. 545-567 
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    Notes: Abstract During functional linkage, ligand receptors are coupled to other receptors and to the cell's metabolic-transport apparatus. The linkage guides the cellular processing of matter, energy and information. Previous conceptions of functional linkage have used the ideas of classical physics appropriate to macroscopic objects. This study presents an initial quantum mechanical model of functional linkage in the case of ligands moving through lipid bilayers and hydrophilic transmembrane channels (‘pores’) of molecular dimensions. On the basis of permeability data, energy surfaces consisting of piecewise-constant potential regions are used to model the lipid bilayers and transmembrane channels. The centre-of-mass wavefunction for a ligand on such energy surfaces is analysed and the permeability coefficients calculated from the wavefunction's transmission characteristics. It is found that quasi-bound states in the several ligand-binding regions of a bilayer or pore system can functionally link to facilitate the passage of the molecule across the permeability barrier. Appearance of the linkage is a sensitive function of the ligand's energy. If the centre-of-mass energies are distributed as in a thermalized fluid, the flux via the quantum functional linkage can equal or exceed that of a classical flux for proton transport through rigid pores in which the intrasite barriers are relatively high (0.25–1 eV) and narrow (0.1–1 Å). The functional linkage plays a less important role in bilayer (rather than pore) energy surfaces and at higher molecular weights. If the ligand-receptor interaction is accompanied by energy transfer to or from ligands, the flux via the quantum functional linkage can equal or exceed the classically expected flux at all relevant ligand molecular weights. These findings are discussed in relation to earlier work and the limitations of the model emphasized.
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    A nonlinear measure of subalignment similarity and its significance levels (1986)
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    Bulletin of mathematical biology 48 (1986), S. 617-632 
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    Notes: Abstract A new measure of subalignment similarity is introduced. Specifically, similaritys(l,c) is defined as the logarithm to the basep of the probability of findingc or fewer mismatches in a subalignment of lengthl, wherep is the probability of a match. Previous algorithms can not use this measure to find locally optimal subalignments because, unlike Needleman-Wunsch and Sellers similarities, this measure is nonlinear. A new pattern recognition algorithm is described for finding all locally optimal subalignments of two nucleotide sequences. The DD algorithm can uses(l, c) or any other reasonable similarity function to assess the relative interest of subalignments. The DD algorithm searches only the diagonal graph, which lacks insertions and deletions. This search strategy greatly decreases the computation time and does not require an arbitrary choice of gap cost. The paths of the resulting DD graph usually draw attention to likely locations for insertions and deletions. A heuristic formula is derived for estimating significance levels fors(l, c) in the context of the lengths of the two aligned sequences. The DD algorithm has been used to find interesting subalignments between the nucleotide sequences for human and murine interleukin 2.
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    Locally optimal subalignments using nonlinear similarity functions (1986)
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    Bulletin of mathematical biology 48 (1986), S. 633-660 
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    Notes: Abstract Nonlinear similarity functions are often better than linear functions at distinguishing interesting subalignments from those due to chance. Nonlinear similarity functions useful for comparing biological sequences are developed. Several new algorithms are presented for finding locally optimal subalignments of two sequences. Unlike previous algorithms, they may use any reasonable similarity function as a selection criterion. Among these algorithms are VV-1, which finds all and only the locally optimal subalignments of two sequences, and CC-1, which finds all and only the weakly locally optimal subalignments of two sequences. The VV-1 algorithm is slow and interesting only for theoretical reasons. In contrast, the CC-1 algorithm has average time complexityO(MN) when used to find only very good subalignments.
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    Adaptability: The significance of variability from molecule to ecosystem (1986)
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    Bulletin of mathematical biology 48 (1986), S. 701-703 
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    Convergence in a resource-based competition system (1986)
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    Bulletin of mathematical biology 48 (1986), S. 681-699 
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    Notes: Abstract A resource-based competition model of two consumer species and one resource species is formulated in the form of a Lotka-Volterra system. The competition involves both exploitation and interference. By a method of asymptotic estimates, sufficient conditions are derived for the three species system to converge ast→∞ to an equilibrium point with all three species present; a generalization of the result forn≥2 and single resource species is indicated. The strong form of equilibrium perisistence of the three species consumer-resource system is achieved by the ability of each of the consumer species to exploit the resource and interfere with others in such a way which will avoid exclusion by the other.
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    Magnetostatic wave devices for UHF band applications (1985)
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    Circuits, systems and signal processing 4 (1985), S. 285-300 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Magnetostatic surface wave (MSSW) devices made with pure and gallium-substituted yttrium-iron garnet (Ga:La-YIG) films are described. These devices include nondispersive and dispersive delay lines, band-pass filters, oscillators, and resonators. By controlling the magnitude of the bias magnetic field and the temperature of operation, it is possible to tune these devices over a wide frequency range extending from 0.3 to 4 GHz and from 3 to 18 GHz using Ga:La-YIG and pure YIG films, respectively. These devices could be used in pulse compression radar, microscan receivers, complicated Fourier transform processors, and fundamental oscillator circuits. In this paper, we briefly show results for pure YIG devices tunable in C and X bands and discuss, in detail, the performance of the Ga:La-YIG devices for UHF applications.
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    MSW devices for EW receiver applications (1985)
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    Circuits, systems and signal processing 4 (1985), S. 301-316 
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    Notes: Conclusion Significant improvements are required in the performance of MSW dispersive delay lines and filter banks before they are ready for systems application. Typically delay lines with bandwidths of 1 GHz or greater, differential delays in the range 200 ns to 1μs, and minimum phase errors (〈±1 °) are required for large (∿40 dB) dynamic range compressive receivers. However, techniques are evolving (see rest of this issue) in this relatively new area of technology which will allow systems performance requirements on phase errors to be met. Possible approaches to low phase error dispersive delay lines include reflective arrays, stepped ground planes, and multiple YIG films. The stepped ground plane technique is the most advanced and uses an optimization approach to the delay-line design, which results in a minimum phase error [20]. Ultimately the minimum achievable phase error will be limited by reflections from transducers and multiple mode effects in the delay lines. The MSW compressive receiver requires parallel advances in high-speed digital processing techniques to achieve its full potential. The MSW filter bank provides a simple channelization technique applicable up to approximately 20 GHz. Narrowband channels with 10 dB insertion loss, 3 dB bandwidths of 10 to 40 MHz, and 50 dB bandwidths of 30 to 120 MHz are possible with the already demonstrated techniques. Broader bandwidth channels in the range 50 to 200 MHz with flat passband response require improved transducer design techniques. The channelized receiver does not require extremely high-speed operations but, since a large number of channels are involved, size and cost become very significant.
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    On the mechanism of transient instability of power systems (1985)
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    Circuits, systems and signal processing 4 (1985), S. 413-434 
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    Notes: Abstract In recent studies, it has been verifiedheuristically andexperimentally (via simulations) that instability in power systems due to a fault occurs when one machine or a group of machines, called thecritical group, loses synchronism with the remaining machines. Using energy functions associated with a critical group (rather than system-wide functions), transient stability results which are less conservative than other existing results, have been obtained. The existence and identity of a critical group is ascertained in these studies byoff-line simulations. In this paper, we present results, for power systems with uniform damping, which establishanalytically theexistence and theidentity of the critical group of machines due to a given fault. We also present a result to determine estimates of the domain of attraction of asymptotically stable equilibrium points in power systems. The results presented herein can potentially be usedon-line to determine which machines belong to a critical group, and to use this information for corrective action (e.g.,shedding of the critical generators orfast valving for these generators). The applicability of the present results is demonstrated by means of a specific example (a 162-bus, 17-generator model of the power network of the State of Iowa).
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    A survey of linear singular systems (1986)
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    Circuits, systems and signal processing 5 (1986), S. 3-36 
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    Notes: Abstract This paper is a brief historical review of linear singular systems, followed by a survey of results on their solution and properties. The frequency domain and time domain approaches are discussed together to sketch an overall picture of the current status of the theory.
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    Arma spectral estimation based on partial autocorrelations — Part II: Statistical analysis (1985)
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    Circuits, systems and signal processing 4 (1985), S. 367-383 
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    Notes: Abstract In a previous paper [1], a new algorithm for ARMA spectral estimation of stationary time series has been presented. The algorithm is based on nonlinear least squares fit of the sample partial autocorrelations to the partial autocorrelations generated by the assumed ARMA model. This paper explores the statistical properties of the above algorithm, including some numerical examples of the asymptotic variance of the estimated parameters, as compared to the Cramer-Rao bound. The results confirm the good performance of the algorithm and suggest an improvement in its implementation.
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    MSW applications for phased array antennas (1985)
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    Circuits, systems and signal processing 4 (1985), S. 335-350 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A potential application of MSW technology lies in the area of time delay for future low-sidelobe wide-bandwidth phased array antennas. High-precision MSW electronically tunable analog time-delay units in transmit/receive modules in phased arrays have the potential of greatly enhancing antenna system capabilities, by increasing instantaneous operating bandwidth and decreasing sidelobe levels, over phased array systems using only phase shifters or switched lines for beam steering and control. This paper provides a status report of MSW time delays for such arrays.
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    Arterial flow under periodic body acceleration (1985)
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    Bulletin of mathematical biology 47 (1985), S. 35-52 
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    Notes: Abstract The present study deals with the effect of externally-imposed body accelerations on blood flow in arteries. Body accelerations may be caused deliberately, for example making the subjecs lie down on vibrating tables: or unintentionally during travel in road vehicles, aircraft or spacecraft. A mathematical model of flow in single arteries subject to a pulsating pressure gradient as well as body acceleration is presented. The resulting equations are solved by using the technique of Laplace transforms. Computational results are presented for the effects of body accelerations on flow variables namely flow rate, velocity of flow, acceleration and shear stress corresponding to typical arteries of human subjects.
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    Distribution of stresses in the left ventricular wall of the intact heart (1985)
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    Bulletin of mathematical biology 47 (1985), S. 53-70 
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    Notes: Abstract The left ventricle is modelled as a prolate spheroid of viscoelastic material with an aim to demonstrate the qualitative effects of anistropy and nonhomogeneity in the calculation of intact ventricular wall stresses. The pericardial pressure is accounted for in the analysis and an attempt is made to examine to what extent this influences the ventricular stresses. Numerical results are also obtained by computing the analytical expressions derived through the analysis.
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    Monte carlo simulation of an ecosystem: A matching between two levels of observation (1985)
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    Bulletin of mathematical biology 47 (1985), S. 111-122 
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    ISSN: 1522-9602
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    Notes: Abstract A Montes Carlo computer simulation is designed in order to described the evolution of an ecosystem under imposed environmental conditions of energy. Some preliminary results of a simple situation show a suggestive matching between the detailed random behaviors of individuals and a global deterministic model. This fact may provide a new insight into the understanding and control of biomass production processes and represents a new tool for the evaluation of the reliability of the classical treatments.
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    Mode analysis of a tubular structure of coupled non-linear oscillators for digestive-tract modelling (1985)
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    Bulletin of mathematical biology 47 (1985), S. 71-110 
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    ISSN: 1522-9602
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    Notes: Abstract A commonly accepted mathematical model for the slow-wave electrical activity of the gastro-intestinal tract of humans and animals comprises a set of interconnected nonlinear oscillators. Using a van der Pol oscillator with third-power conductance characteristics as the unit oscillator a number of structures have been analysed using a matrix Krylov-Bogolioubov method linearisation. The mode analysis of one-dimensional chains and two-dimensional arrays has been reported. In this paper the method has been extended to consider a tubular structure which is relevant to modelling small-intestinal rhythms. It is shown that this structure is capable of producing stable single models, non-resonant double modes and degenerated modes. General expressions are obtained for anm×n structure and examples given of two special conditions of 3×4 (i.e. odd numbers of oscillators in a ring) and 4×3 cases. The analytical results obtained for these two cases have been vertified experimentally using an electronic implementation of coupled van der Pol oscillators. Results obtained using fifth-power non-linear oscillators are summarised.
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    The theory and practice of distance geometry (1985)
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    Bulletin of mathematical biology 47 (1985), S. 157-157 
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    Applications of game-theoretic concepts in biology (1985)
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    Bulletin of mathematical biology 47 (1985), S. 161-192 
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    Editor's comments (1985)
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    Bulletin of mathematical biology 47 (1985), S. 159-159 
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    Study of age dependent half-life of iodine in man: A reinforcement-depletion urn model (1985)
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    Bulletin of mathematical biology 47 (1985), S. 205-213 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract An urn contains balls ofs different colors. The problem of the reinforcement of a specified color and random depletion of balls has been considered by Shenton (1981, 1983). In this paper, the theory is applied to the biological age dependent half-life of radioactive iodine in man; the data of Cook and Snyder (1965) is used. The intake of radioactive iodine and its retention subsequently is studied.
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    Non-linear compartmental systems: extensions of S. R. Bernard's urn model (1985)
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    Bulletin of mathematical biology 47 (1985), S. 193-204 
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    Notes: Abstract One of the limitations of stochastic, linear compartmental systems is the small degree of variability in the contents of compartments. S. R. Bernard's (1981) urn model (S. R. Bernardet al., Bull. math. Biol. 43, 33–45.) which allows for bulk arrivals and departures from a one-compartment system, was suggested as a way of increasing content variability. In this paper, we show how the probability distribution of the contents of an urn model may be simply derived by studying an appropriate set of exchangeable random variables. In addition, we show how further increases in variability may be modeled by allowing the size of arrivals and departures to be random.
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    Expansion of the master equation for a biomolecular selection model (1985)
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    Bulletin of mathematical biology 47 (1985), S. 231-238 
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    Notes: Abstract A stochastic model based on Eigen and Schuster's theory of biomolecular self-replication is studied by treating the master equation with the system-size expansion technique. The steady-state results are found to be in good agreement with the previous results and with those derived from the principle of detailed balancing. Multispecies competition and coexistence are studied carefully with the conclusions that a stable steady state is predicted for the former and a metastable state for the latter. The stochastic selection processes are also analyzed and discussed.
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    A formalization of consensus index methods (1985)
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    Bulletin of mathematical biology 47 (1985), S. 215-229 
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    Notes: Abstract A consensus in dex method comprises a consensus method and a consensus index that are defined on a common set of objects (e.g. classifications). For each profile of objects, the consensus method returns a consensus object representing information or structure shared among profile objects, while the consensus index returns a quantitative measure of agreement among profile objects. Since the relationship between consensus method and consensus index is poorly understood, we propose simple axioms prescribing it in the most general terms. Many taxonomic consensus index methods violate these axioms because their consensus indices measure consensus object invariants rather than profile agreement. We propose paradigms to obtain consensus index methods that measure agreement and satisfy the axioms. These paradigms salvage concepts underlying consensus index methods violating the axioms.
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    Polynucleotide evolution and branching processes (1985)
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    Bulletin of mathematical biology 47 (1985), S. 239-262 
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    Notes: Abstract The theory of multitype branching processes is applied to the kinetics of polynucleotide replication. The results obtained are compared with the solutions of the deterministic differential equations of conventional chemical kinetics.
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    Moments and order statistics of extinction times in multitype branching processes and their relation to random selection models (1985)
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    Bulletin of mathematical biology 47 (1985), S. 263-272 
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    Notes: Abstract We investigate the circumstances under which the moments of the order statistics of the extinction times of a set of independent branching processes exist. This extends a result of Schuster and Sigmund,Bull. math. Biol. 46, 11–17, 1984, which was found in a special random selection model. Furthermore we discussed existence of the expectation of extinction times of multitype branching processes and extend well known results for irreducible processes to the reducible case.
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    On linear stochastic compartmental models in discrete time (1985)
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    Bulletin of mathematical biology 47 (1985), S. 287-293 
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    Notes: Abstract This note presents a general time-dependent study of linear stochastic compartmental models in discrete time. The transient distribution of the state of the system is obtained by adapting methods used in the continuous time analysis. Covariance functions with and without a time lag are then deduced by a simple probabilistic argument. Results are derived in the Markov case and are partly extended to the semi-Markov case.
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    Fractals and the analysis of growth paths (1985)
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    Bulletin of mathematical biology 47 (1985), S. 273-286 
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    Notes: Abstract A simple practical method exists for classifying and comparing planar curves composed of connected line segments. This method assigns, a single numberD, the fractal dimension, to each curve.D=log(n)/[log(n)+log(d/L)], where:n is the number of line segments,L is the total length of the line segments, andd is the planar diameter of the curve (the greatest distance between any two endpoints). At one end of the spectrum, for straight line curves,D=1; at the other end of the spectrum, for random walk curves,D→2. Standard statistics are done on the logarithms of the fractal dimension [log(D)]. With this measure, trails of biological movement, such as the growth paths of the cells and the paths of wandering organisms, can be analyzed to determine the likelihood that these trails are random walks and also to compare the straightness of the trails before and after experimental interventions.
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    Modeling persistence and mutual interference among subpopulations of ecological communities (1985)
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    Bulletin of mathematical biology 47 (1985), S. 295-304 
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    Topics: Biology , Mathematics
    Notes: Abstract A model is proposed of an ecological community where some (or all) of the subpopulations exhibit mutual interference. Mutual interference introduces sublinearities which makes the persistence analysis of the community more complex since the model is no longer a dynamical system. A transformation is introduced which yields a dynamical system, thereby making a persistence analysis more tractable. The results are applied to determining top-predator persistence of a simple food chain and to the question of invasibility of a stable community by a new subpopulation.
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    Flow in an arteriosclerotic blood vessel with rigid permeable wall (1985)
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    Bulletin of mathematical biology 47 (1985), S. 613-627 
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    Topics: Biology , Mathematics
    Notes: Abstract This paper concerns the fluid-mechanical study of the effects of permeability of the wall of an arteriosclerotic blood vessel by idealizing the tissue space as a porous medium bounding the blood vessel and the arteriosclerotic blood vessel as a constricted axisymetric tube of slowly but arbitrarily varying cross-secton. An analytical solution in the general case is obtained by perturbation technique and several important particular geometries of constriction are discussed as special cases. Numerical results for the effects of permeability on the wall shear stress and filtration velocity are shown graphically.
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    A mathematical approach to semantic network development (1985)
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    Bulletin of mathematical biology 47 (1985), S. 629-650 
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    Notes: Abstract Beginning from the notion of semantic network structure, we develop a quantitative description of how much can be learned by an animal whose developmental programme is a set of co-acting epigenetic rules. In the model considered, the activity of the rules regulates the size, connectivity and innate information content of the semantic network. The network itself is associated with a behavioral repertoire. The modeling approach shows how to begin accounting for the effects of both genetic and environmental information, in a manner that quantifies the roles of specific epigenetic rules for psychological development. In previous models the Shannon-Weaver information contentI of a semantic network follows power lawsI ∞N ξ, withN the number of interrelated concept elements in the network and ξ a scaling exponent labeling a universality class of semantic networks. Our calculations provide evidence that epigenetic rules of the type considered, involving both innate and learned semantic network components, sustain a new universality class for which ξ=1.
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    An isoclinal approach to the comparative statics of biological communities (1986)
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    Bulletin of mathematical biology 48 (1986), S. 59-75 
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    Notes: Abstract An understanding of the comparative statics of biological communities is important both as a means of explaining the long-term effects of changes in environmental conditions, and as a framework for viewing community time trajectories. A general formulation of community dynamics is presented here which, given full information about a particular community's dynamic behavior, describes the impact of a change in environmental conditions on the community steady state. However, since such full information is often lacking in studies of biological communities, various approaches to partial information analysis of comparative statics are presented and compared, including a generalized protocol for isocline analysis. The suggested isocline protocol is shown to be a useful tool for both full and partial information analyses, as well as for both general and partial equilibrium studies.
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    An interpretation of Fujita's frequency diagrams in phyllotaxis (1986)
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    Bulletin of mathematical biology 48 (1986), S. 77-86 
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    Notes: Abstract Fujita's diagrams in phyllotaxis, showing the frequencies of divergence angles as a function of these angles for low phyllotactic patterns such as (2, 1) and (3, 2), which are approximately normal curves centered at the limitdivergence angle of 137.51°, are shown to be puzzling when compared to results and observations in the field. An analysis of these diagrams is proposed, in the context of Fujita's methodology, of data from other sources, of a mathematical theorem on lattices, and of the contact pressure theory of phyllotaxis.
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    Existence of steady-state probability distributions in multilocus models for genotype evolution (1986)
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    Bulletin of mathematical biology 48 (1986), S. 87-95 
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    Notes: Abstract It is shown that a representative Fisher-Wright model withn(≥3) diallelic loci admits a necessary condition for existence of a time-independent steady-state probability distribution. This necessary condition states that a global integral depending on the phenotype fitness functions of natural selection must be larger than a certain quantity depending on the parameters associated with genetic drift.
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    Transient phase kinetics of activation of human plasminogen (1986)
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    Bulletin of mathematical biology 48 (1986), S. 149-166 
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    Notes: Abstract Equations for the time-dependent concentrations of all species involved in the general mechanism of human plasminogen activation proposed by Wohlet al. (J. biol. Chem. 255, 2005–2013, 1980) have been derived. These equations are valid for the whole course of the reaction: for both the transient phase and the steady state. In addition, we compare our results with the ones obtained by the above-mentioned authors for the steady state assuming rapid equilibrium conditions. Finally, we propose a method for the determination of all velocity constants.
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    Interval graphs and maps of DNA (1986)
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    Bulletin of mathematical biology 48 (1986), S. 189-195 
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    Notes: Abstract A special class of interval graphs is defined and characterized, and an algorithm is given for their construction. These graphs are motivated by an important representation of DNA called restriction maps by molecular biologists. Circular restriction maps are easily included.
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    On mathematical modeling of critical variables in cancer treatment (goals: Better understanding of the past and better planning in the future) (1986)
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    Bulletin of mathematical biology 48 (1986), S. 253-278 
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    Notes: Abstract Over the past 25 years stepwise improvement in the cure of disseminated cancers has been good, fair or very poor depending on the particular cancer one is discussing. “Cancer chemotherapy provides variably effective treatment for the majority of forms of human cancer and curative treatment for some 12 categories.” We have been slow to gain and learn how to apply quantitative information on the biologic phenomena that underlie the responsiveness, or lack of responsiveness, of many different cancers to single drugs and combinations of drugs delivered in different ways. I am of the opinion that continuing development and integration of rational biomathematical models based on principles already identified, and testing them for compatibility with much already available experimental and clinical data, will lead to models that will help in planning more effective treatment regimens for cancers now classified as moderately refractory or very refractory to chemotherapy. Some of the critical variables are considered briefly. My advice, for what it is worth, is “try to be sure that the biologic concepts that you use in modeling are almost as good as the arithmetic.”
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    Physiological pharmacokinetics (1986)
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    Bulletin of mathematical biology 48 (1986), S. 309-322 
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    Notes: Abstract A discussion of the bases of physiological pharmacokinetics is followed by a brief review of the fundamental mass balance equations of the models. Some examples are outlined, together with a listing of published reviews which give many more references and detailed examples. Finally, some thoughts on future research directions are presented.
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    Cell kinetics simulation languages (1986)
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    Bulletin of mathematical biology 48 (1986), S. 323-336 
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    Notes: Abstract The use of stochastic simulation languages in cell kinetics research is discussed. Two special purpose simulation languages; CELLSIM and CELLGROW are described and example problems are presented.
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    Chemical carcinogenesis and toxicity models: Matching complexity to objectives (1986)
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    Bulletin of mathematical biology 48 (1986), S. 293-307 
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    Notes: Abstract Mathematical models predicting tissue doses of chemical toxicants can be either highly complex or simple, depending upon the end results needed. As an example of a highly complex mathematical model, the Miller Model of the distribution of reactive gases in human and animal lungs is described. The Miller Model accounts for the convection, the radial and axial diffusion, and the chemical reactions of gases as an inhaled breath passes down the airways. The geometry and physiology of human and animal lungs are used to calculate the convection and diffusion likely in each generation or bifurcating series of airways commencing with the trachea and extending 24 generations in humans. The chemical reactivity of ozone, an air pollutant, is accounted for by simulating second-order chemical reactions with the fluid lining materials of the lung and tissue biological molecules. The flux of ozone into three compartments (pulmonary tissue, overlying liquid layer and capillary blood) in each generation of the lung is calculated to provide molecular doses of ozone reaching each region of the lung. These results of calculated molecular dose are then used to construct dose-response curves for a variety of biological endpoints. A much simpler model is also described which recognizes the saturable or Michaelis-Menten type of kinetics controlling the removal of nickelous ion (nickel) from the lung. This model is used to calculate the chronic lung burden of the human lung for occupational, environmental and cigarette smoking exposure scenarios. In both the complex Miller Model and the simpler nickel lung burden model, the results can be used to calculate molecular doses at the potential site of action of these environmental chemicals and to unify a wide variety of studies. The predictions made are more likely to be valid since multiple investigators using a variety of animal species have participated in generation of the primary data. As a methodology, mathematical modeling based on physiological, physicochemical and anatomical principles provides a means of eliminating non-scientific considerations from the important process of regulating and recognizing toxic or cancer causing chemicals in the human environment.
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    Kinetic simulation of anticancer drug effects on metabolic pathway fluxes: Two case studies (1986)
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    Bulletin of mathematical biology 48 (1986), S. 337-351 
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    Notes: Abstract This paper presents a brief review of applications of kinetic simulation of multi-enzyme networks to the study of antimetabolite drugs used as anticancer agents. Kinetic models consist of systems of nonlinear differential equations that describe changes in concentrations of cellular metabolites with respect to time. Such models have been used to predict the effect of changes in activity of enzymes, or changes in enzyme kinetic parameters, on sensitivity to inhibition. Kinetic simulation has provided insight into several aspects of the biochemical pharmacology of antimetabolites, including drug sensitivity and resistance, and drug-drug interactions. Two specific studies are described in detail. The first concerns the importance of the ratio of competing enzymes in determining the selectivity of inhibitors of one of the competing enzymes, studied by a simple model. The second case study examines the effect of alternative biosynthetic pathways, thede novo and salvage pathways of pyrimidine nucleotide biosynthesis, on the selectivity of antipyrimidine drugs, as studied by a detailed model of 27 reactions of pyrimidine metabolism.
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    Cancer chemotherapy: Optimal control using the Verhulst-Pearl equation (1986)
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    Bulletin of mathematical biology 48 (1986), S. 381-404 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract General (deterministic) ordinary differential equations for the representation of cancer growth are presented when the growth is perturbed due to the action of a chemotherapeutic agent. The Verhulst-Pearl equation is introduced as a particular example of a growth equation applicable to human tumors. An optimal control problem with general performance criterion and state equation is formulated and shown to possess a novel feedback control relationship. This relationship is used in two continuous drug delivery problems involving the Verhulst-Pearl equation.
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    URL: http://dx.doi.org/10.1007/BF02459688
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    Use of the circuit simulation program SPICE2 for analysis of the metabolism of anticancer drugs (1986)
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    Bulletin of mathematical biology 48 (1986), S. 353-380 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Complex networks of biological processes are analogous to electrical circuits. For each step in a biological or electrical network, flow is dependent on the driving force and the conductivity of the step. The relationship between biological flows and their driving forces can therefore be expressed as relationships between analogous currents and voltages. The time dependence of approach to equilibrium or a steady state is determined by the rates of depletion of material in various compartments. Electrical capacitance is therefore analogous to compartment volume. Once these generalized concepts of flow, force and capacitance are recognized, it becomes clear that computer programs designed for analysis of electrical circuits may be used for simulation of biological networks. A set of simple mathematical descriptions of the individual steps and a diagram showing how the steps are arranged with respect to each other are all that is necessary to perform a simulation; there is no need for computer programming skills or differential equations. The use of SPICE2 for simulation of the cellular and plasma pharmacokinetics of cytosine arabinoside (araC) is described as an example. A network model is developed which considers cellular pharmacokinetics (membrane transport, intracellular phosphorylation and dephosphorylation), and plasma pharmacokinetics following infusions of araC.
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    URL: http://dx.doi.org/10.1007/BF02459687
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    Future directions in computer simulation (1986)
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    Bulletin of mathematical biology 48 (1986), S. 405-415 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Developments in computer hardware and software are making significant improvements in the availability of simulation for biomedical researchers. This paper reviews past and present techniques for digital computer simulation and looks at improvements likely in the near future. In the area of hardware, personal computers are making computing and simulation more widely available and at the same time, supercomputers and special-purpose numerical processors are making it possible to solve larger problems. Software developments for simulation are reducing the time, effort and special skills required to produce a simulation program. A new hierarchical linker is proposed to make it easy to synthesize a global model by combining existing submodels. In the more distant future, computer models may be constructed graphically and with the assistance of intelligent programs capable of analysis and information retrieval.
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    URL: http://dx.doi.org/10.1007/BF02459689
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    Strategies for computer modeling (1986)
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    Bulletin of mathematical biology 48 (1986), S. 417-426 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Modeling is a ubiquitous and often misunderstood enterprise in which data from diverse disciplines are analyzed by techniques from other diverse disciplines in an attempt to confirm or falsify a set of hypotheses about the real world. Guidelines are offered for designing models to match the goals of modeling biological systems. Techniques for the construction and interpretation of models are discussed. The requirements for credibility of models are detailed, and tests are suggested for their validation.
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    First Conference of the International Federation of Classification Societies (1986)
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    Bulletin of mathematical biology 48 (1986), S. 453-453 
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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/BF02459693
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    Conference retrospective: An appropriate modeling infrastructure for cancer research (1986)
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    Bulletin of mathematical biology 48 (1986), S. 443-452 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Presentations and discussions at the symposium illustrate some general issues in biomedical modeling for cancer research. Given the motivations for modeling and assumptions concerning who should be involved in the modeling process, one can identify some basic needs to be met in supports to modelers. These concern both the models themselves and ways of presenting them to users. In conclusion, some thoughts are offered on economic and educational issues that may affect the infusion of modeling into biomedical research.
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    Editorial: Software survey section (1986)
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    Bulletin of mathematical biology 48 (1986), S. I 
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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/BF02459694
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    Theory of MSW transducers (1985)
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    Circuits, systems and signal processing 4 (1985), S. 41-62 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This is a review of two electrical equivalent circuits for multi-element magnetostatic wave transducers. The two circuit models are identified as a transmission line and a two terminal model. Both models have been extended to all three principal MSW modes of propagation to the point where computer programs have been written to plot phase and amplitude response as measured by commercial network analyzers. A review is provided of the basic assumptions, similarities and differences, advantages and disadvantages, and limitations of the two models. The useful range of them covers many cases of practical interest in the one to twelve Ghz frequency range.
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    URL: http://dx.doi.org/10.1007/BF01600072
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    Magnetostatic surface wave straight-edge resonators (1985)
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    Circuits, systems and signal processing 4 (1985), S. 201-209 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The performance of the magnetostatic surface wave straight-edge resonator (MSSW-SER) is presented. The resonator uses a rectangular YIG film to propagate MSSWs where the straight edge serves as a reflector. Problems arising from coupling to width mode resonances and their effect on the main resonance are investigated. Through a careful choice of YIG and transducer parameters, the interference effects of the width mode resonances with the main resonance are minimized. As a result, highQ tunable microwave resonators with a tuning range from 2–20 GHz, insertion loss less than 10 dB, and spurious rejection better than 10 dB could be designed and fabricated. This MSSW resonator could be used to construct a tunable low-phase-noise feedback oscillator. However, the tuning range of this MSW feedback oscillator is limited by the phase change of the external amplifier circuit.
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    URL: http://dx.doi.org/10.1007/BF01600080
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    The technology of YIG film growth (1985)
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    Circuits, systems and signal processing 4 (1985), S. 89-103 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents in a condensed form, a review of information regarding the technology of yttrium iron garnet (Y3Fe5O12 — YIG) film growth for MSW applications. The method used for film growth is liquid phase epitaxy from a molten solution of PbO/B2O3 into which Y2O3 and Fe2O3 have been added. There are five sections to the paper. The first is an introduction to the crystalline and magnetic features found in YIG. A short second section deals with growth techniques and apparatus. In a third section the melt composition, conditions of growth and homogeneity of as grown material are explored. Growth temperatures varying from 848° C to 998° C have been shown to successfully produce YIG films. Possible sources of MSW loss are explored in the fourth section. It is seen that material contamination and physical irregularities may have a negative effect onΔH. The final section summarizes the state in which YIG film production now stands. The finding is that although usable films are producible routinely, intrinsic performance is not yet achievable on a regular basis.
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    URL: http://dx.doi.org/10.1007/BF01600074
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    Special issue on magnetostatic waves and applications to signal processing (1985)
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    Circuits, systems and signal processing 4 (1985), S. 5-7 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01600070
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    Dispersive delay at gigahertz frequencies using magnetostatic waves (1985)
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    Circuits, systems and signal processing 4 (1985), S. 115-135 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Magnetostatic waves are intrinsically suited for use in microwave dispersive delay lines, because they are readily generated at high frequencies and their velocity is frequency dependent. Here we review progress toward meeting the systems requirement that the delay time be linear in frequency. Magnetostatic waves can approach this condition if a ground plane is nearby or if two or more ferrite layers are present; with forward volume waves one may also use a dispersive reflecting array, as is done with surface acoustic waves. The use of a properly shaped ground plane gives the lowest phase errors so far measured (±16° over 0.6 GHz); multiple ferrite layers show promise of allowing the greatest delay.
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    URL: http://dx.doi.org/10.1007/BF01600076
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    Q-factor for an MSW delay-line based oscillator (1985)
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    Circuits, systems and signal processing 4 (1985), S. 221-225 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A theoretical derivation of theQ-factor of an MSW delay-line based oscillator is presented which is based on a rigorous, classical definition of theQ-factor of a resonator. The theory takes into account (1) the propagation loss in the delay line, (2) the transduction losses at the input and output transducers of the delay line, (3) the delay times in the delay line and the circuit external to the delay line, and (4) the loading of the oscillator. While the present work was done with MSW in mind, the results are generally applicable to all delay-line based oscillators and would, for instance, apply to the SAW delay-line based oscillators.
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    URL: http://dx.doi.org/10.1007/BF01600082
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