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  • Springer  (96,943)
  • Wiley  (20,904)
  • 1985-1989  (63,659)
  • 1980-1984  (54,188)
  • 1925-1929
  • 1986  (63,659)
  • 1982  (54,188)
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  • 1985-1989  (63,659)
  • 1980-1984  (54,188)
  • 1925-1929
Year
  • 1
    Electronic Resource
    Electronic Resource
    An equation for flow in the renal proximal tubule (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 29-57 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460061
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  • 2
    Electronic Resource
    Electronic Resource
    Seventeenth Annual Meeting of the Classification Society of North America (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 105-105 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460066
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  • 3
    Electronic Resource
    Electronic Resource
    Editorial: Software Survey Section (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. I 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460067
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  • 4
    Electronic Resource
    Electronic Resource
    Dominance of geometric overelastic factors in pulse transmission through arterial branching (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 97-103 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460065
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  • 5
    Electronic Resource
    Electronic Resource
    Galerkin's finite element-Laplace transform technique to transient heat migration in human skin and subcutaneous tissues (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 125-136 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460018
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  • 6
    Electronic Resource
    Electronic Resource
    Multiple stable equilibria in a predator-prey system (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 137-148 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460019
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  • 7
    Electronic Resource
    Electronic Resource
    Servocontrol of the heart rate in homeothermic animals: On recognizing butterfly catastrophy models in biology (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 107-124 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460017
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  • 8
    Electronic Resource
    Electronic Resource
    Simulation of cellular compaction and internalization in mammalian embryo development as driven by minimization of surface energy (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 167-187 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460021
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  • 9
    Electronic Resource
    Electronic Resource
    Topological properties of binary trees grown with order-dependent branching probabilities (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 197-211 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460023
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  • 10
    Electronic Resource
    Electronic Resource
    Pattern formation and morphogenesis: A reaction-diffusion model (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 213-228 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460024
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  • 11
    Electronic Resource
    Electronic Resource
    Editorial: Software survey section (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. I 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460027
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  • 12
    Electronic Resource
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    SCoP: An interactive simulation control program for micro- and minicomputers (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 427-441 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459691
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  • 13
    Electronic Resource
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    Global stability of partially closed food-chains with resources (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 455-468 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462317
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  • 14
    Electronic Resource
    Electronic Resource
    Global stability in time-delayed single-species dynamics (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 485-492 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462319
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  • 15
    Electronic Resource
    Electronic Resource
    Predator-prey systems with group defence: The paradox of enrichment revisited (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 493-508 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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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    URL: http://dx.doi.org/10.1007/BF02462320
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  • 16
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    A class of general stochastic compartmental systems (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 509-523 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462321
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  • 17
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    Optimized homology searches of the gene and protein sequence data banks (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 569-583 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462324
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  • 18
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    Receptors and functional linkage in membrane permeability: A quantum mechanical model (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 545-567 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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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    URL: http://dx.doi.org/10.1007/BF02462323
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  • 19
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    A nonlinear measure of subalignment similarity and its significance levels (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 617-632 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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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    URL: http://dx.doi.org/10.1007/BF02462327
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  • 20
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    An equivalence result for integral equations with application to branching processes (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 1-15 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theorem is proved, concerning expected values of a multitype branching process in a varying environment. The consequence of the theorem is that the branching process can be treated (in the sense of expected values) as a dynamical system with control terms. This is of importance in situations where the process serves as an abstract model of the dynamics of malignant cells for use in chemotherapy. A simple example of this kind is given.
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    URL: http://dx.doi.org/10.1007/BF02459415
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  • 21
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    General solution for flow and stress phenomena in elastic vessles (Navier-Stokes) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 29-42 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method is developed for a full nonlinear evaluation of all velocities and stresses represented in the Navier-Stokes equations and in the general stress tensor. The information required is essentially that for solution of linearized forms. The solution is analytical except for the calculation of the axial velocity, which requires computer assistance to step through time and space. The treatment of the problem, although directed towards solutions involving fluid flow in elastic vessels, is also adaptable to solid deformations (strain vs rate of strain) where the general stress tensor applies. A special case for the distorting ellipse is presented as well as a limited, spatially analytic, solution.
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    URL: http://dx.doi.org/10.1007/BF02459417
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  • 22
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    Spatially localized interactive neural populations—II: Stability and dynamics of excitatory sets (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 43-56 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The stability characteristics and dynamical behavior of a system of mutually excitatory neurons in close spatial proximity are investigated with a mathematical model. The model predicts the existence of uniform, intermediate levels of activity other than those of no activity and maximal activity. The model also, yeilds a good explanation of data obtained from periglomerular neurons in the olfactory bulb of the cat.
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    URL: http://dx.doi.org/10.1007/BF02459418
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  • 23
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    Stochastic compartmental models with banching and immigrant particles (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 75-86 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A multicompartmental model in which particles enter the system from the environment and reproduce according to a Markov branching process has been considered. Explicit expressions have been obtained for the mean vector and the correlation structure for the numbers of particles in different compartments in different time points of the system. Growth rates of the mean vector and some special cases of the system are also discussed.
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  • 24
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    Mode analysis of physiological oscillators intercoupled via pure time delays (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 57-74 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The study of bi-directionally coupled oscillators is relevant in biological modelling of such systems as gastro-intestinal electrical activity, cardiac pacemarkers, cardiovascular and respiratory interactions and circadian rhythms. Interconnecting pathways in biological systems often exhibit pure time-delay characteristics. In this paper the multiple-mode limit-cycle behaviour of such systems is analysed using the method of harmonic blance. It is shown that the coupling time delay radically affects the number, frequency and amplitudes of entrained limit-cycles.
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    URL: http://dx.doi.org/10.1007/BF02459419
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  • 25
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    Bifurcation, stability diagrams, and varying diffusion coefficients in reaction-diffusion equations (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 87-102 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The effect of keeping all the parameters constant, except the diffusion coefficients, in a pair of reaction-diffusion equations is studied. It is shown that the stability of the constant solution and the bifurcation points can be easily established by constructing a simple stability diagram. The possible qualitatively different diagrams are enumerated.
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    URL: http://dx.doi.org/10.1007/BF02459421
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  • 26
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    Random ecological systems with structure: Stability-complexity relationship (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 103-117 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We have numerically examined more than one million Large Complex Systems (LCS) of interacting variables (interpretable as interacting populations) governed by Generalized Lotka-Volterra Equations (GLV), with self-regulation term. The scope was to have some insight on the stability-complexity relationship. We considered systems of prey-predator type, and we gave appropriate rules for constructing the model systems, rules that specify the behaviour of model systems in order to put them near the biological reality. The results show, among other things, a strict correlation between the stability and the prey-predator ratio (which, in our model, uniquely determines the connectedness of the system).
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    URL: http://dx.doi.org/10.1007/BF02459422
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  • 27
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    Remark on the article, “Applied catastrophe theory in the social and biological sciences” by M. A. B. Deakin (1980) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 149-150 
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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/BF02459425
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  • 28
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    Transient effects on the initial rate of oxygenation of red blood cells (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 119-134 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The rate-controlling process in the oxygenation of red blood cells is investigated using a Roughton-like model for oxygen diffusion and reaction with hemoglobin. The mathematical equations describing the model are solved using two independent techniques, numerical inversions of the Laplace transform of the equations and numerical solutions via an implicit-explicit finite difference form of the equations. The model is used to re-examine previous theoretical models that incorporate either a red cell membrane that is resistive to oxygen diffusion or an unstirred layer of water surrounding the cell. Although both models have been postulated to be equivalent, the results of the computer simulations demonstrate significant differences between the two models in the rate of oxygenation of the red cells, depending upon the values chosen for the diffusion coefficient for O2 in the membrane and the thickness of the water layer. The difference is apparently due to differences in the induction and transient periods of the water layer model relative to the membrane model.
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    URL: http://dx.doi.org/10.1007/BF02459423
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  • 29
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    Energy and biological evolution—II. The mathematical structure of equilibrium states (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 537-547 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We examine certain mathematical structures presented in Part I. The most important of these are the energy structures determined by the couple (ω×E, ψ) the space of causality defined by ψ-1(0) and the notion of collapsibility, i.e., the descent of a species from a higher to a lower equilibrium configuration as a result of energy loss.
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    URL: http://dx.doi.org/10.1007/BF02459407
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  • 30
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    A stochstic model for a two-compartment reversible system (1982)
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    Bulletin of mathematical biology 44 (1982), S. 557-570 
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    Notes: Abstract This paper discusses a general stochastic model for a two-compartment reversible system with non-homogeneous Poisson inputs, arbitrary residence times at each of the compartments and time-dependent transition probabilities. The probability distributions of the number of particles in each compartment and in the system are obtained together with the number of particles which depart from the system. In addition, various covariance functions with a time lag are obtained. Some of the above obtained results are deduced for time-independent arrivals, exponential residence times and time-independent transition probabilities. Fluctuations of the particles present in the system are also analysed. Similar analysis is provided for the model into which some particles are initially introduced at the system. Some possible applications are discussed at the end.
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    Effects of dispersion on stability of multispecies prey-predator systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 571-578 
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    Notes: Abstract The general multispecies prey-predator system with Gompertz's antisymmetric interactions is nonlinearly stable in the absence of dispersion and continues to remain stable with dispersion under both homogeneous reservoir and zero flux boundary conditions in a region containing the equilibrium state. It is proved that a general multispecies food-web model without antisymmetric interactions is stable in the absence of dispersion and remains stable with dispersion in the above-mentioned region.
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    Repeatability of experiments (1982)
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    Bulletin of mathematical biology 44 (1982), S. 593-593 
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    Graph theoretical criteria for stability and boundedness of predator-prey systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 579-585 
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    Notes: Abstract We introduce a graphical approach in the study of the qualitative behavior ofm species predator-prey systems. We prove that tree graphs imply global stability for Volterra models and local stability for general models; furthermore, we derive sufficient conditions so that loop graphs imply stability and boundedness of the solutions.
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    A reply to “repeatability of experiments” by R. B. Campbell (1982)
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    Bulletin of mathematical biology 44 (1982), S. 594-595 
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    An epizootic model of an insect-fungal pathogen system (1982)
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    Bulletin of mathematical biology 44 (1982), S. 731-739 
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    Notes: Abstract A system of integro-differential equations is derived to describe epizootics of a fungal pathogen in an insect population. Because of piecewise continuous behavior under some parametric conditions, it is concluded that standard phase orbits can be misleading. Using a different analytic approach yields a simple system of finite difference equations. Both the continuous and discrete versions are compared to classical forms. The continuous version differs from a classical one in possessing a second derivative dependent on population density. The discrete version differs in maintaining positive, non-zero populations of both infectives and susceptibles in finite time.
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    On feedback control of gonadotropin secretion (1982)
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    Bulletin of mathematical biology 44 (1982), S. 741-748 
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    Notes: Abstract This note is an attempt to demonstrate that hypothalamic pulsatile GnRH secretion is not the result of a short-term, negative steroid hormone feedback. Clarification of this point is of importance for further modelling the control of gonads.
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    The development of largangians for biological models (1982)
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    Bulletin of mathematical biology 44 (1982), S. 749-760 
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    Notes: Abstract A modern theory of the calculus of variations is used to form necessary and sufficient conditions for the existence of a Lagrangian representation of a system of first-order ordinary differential equations. There exists a theorem to the effect that when a system of ordinary differential equations is variationally self-adjoint, the fulfillment of such conditions is guaranteed. In addition, self-adjointness, allows establishement of an algorithm by which a Lagrangian for the system may be explicitly constructed. Examples in mathematical biology are given to illustrate the use of the stated theorem.
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    An optimal control model of diabetes mellitus (1982)
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    Bulletin of mathematical biology 44 (1982), S. 793-808 
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    Notes: Abstract Engineering optimal control theory is applied to equations describing insulin and glucose interactions. The nature of the optimal controller is established. It is shown how the results can be utilized in a closed loop feedback control system.
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    Biological optimality: Comparison of generalized feasibility and optimality conditions for linear, error-minimizing systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 777-791 
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    Notes: Abstract An attempt is made to compare the conditions for the general error-optimality of linear systems developed by Kalman with the conditions for feasibility of linear models of neuromuscular and physiological control systems. Models of three actual physiological systems are tested for both the above criteria. Theoretical analysis presented here shows that there are no simple relationships between the two sets of conditions. Analysis carried out on the physiological systems models suggests the need for a general set of conditions for other optimality criteria, such as time and energy minimization, similar to Kalman's condition for error minimization.
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    The development of anoxia following occlusion (1982)
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    Bulletin of mathematical biology 44 (1982), S. 851-877 
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    Notes: Abstract Following arteriolar occlusion, tissue oxygen concentration decreases and anoxic tissue eventually develops. Although anoxia first appears in the region most distal to the capillary at the venous end, it eventually spreads throughout the entire region of supply. In this paper the changing oxygen concentration, from the time of occlusion until the tissue is entirely anoxic, is examined mathematically. The equations governing oxygen transport to tissue are solved by iterating a nonlinear integral equation. This solution is valid until anoxia first appears. After anoxia develops it is necessary to solve a moving boundary problem. This is done using the method of matched asymptotic expansions, and accurate solutions are obtained for a wide range of physiological conditions.
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    Announcements (1982)
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    Bulletin of mathematical biology 44 (1982), S. 899-900 
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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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    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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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Comparative performance of polynomial signal extraction (1982)
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    Circuits, systems and signal processing 1 (1982), S. 93-104 
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    Notes: Abstract A stochastic approximation problem for polynomic operators is formulated. The performance of polynomic operators of various degrees is compared. The effect of causality constraints is also examined.
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    Feedback system design: The single-variate case — Part I (1982)
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    Circuits, systems and signal processing 1 (1982), S. 137-169 
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    Notes: Abstract A recently developed algebraic approach to the feedback system design problem is reviewed via the derivation of the theory in the single-variate case. This allows the simple algebraic nature of the theory to be brought to the fore while simultaneously minimizing the complexities of the presentation. Rather than simply giving a single solution to the prescribed design problem we endeavor to give a complete parameterization of the set of compensators which meet specifications. Although this might at first seem to complicate our theory it, in fact, opens the way for a sequential approach to the design problem in which one parameterizes the subset of those compensators which meet the second specification...etc. Specific problems investigated include feedback system stabilization, the tracking and disturbance rejection problem, robust design, transfer function design, pole placement, simultaneous stabilization, and stable stabilization.
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    Editorial (1982)
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    Circuits, systems and signal processing 1 (1982), S. 267-268 
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    Rational approximation via selective modal analysis (1982)
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    Circuits, systems and signal processing 1 (1982), S. 433-445 
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    Notes: Abstract We describe a recently developed framework for exploring the structure of linear time-invariant models of large systems, and for constructing interpretable or physically-based, reduced-order models that reproduce selected modes of the original systems to a desired accuracy. Application of this framework to constructing lumped approximations for interconnections of lumped and distributed systems is briefly explored.
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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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    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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    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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    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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    Future directions in computer simulation (1986)
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    Bulletin of mathematical biology 48 (1986), S. 405-415 
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    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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    Strategies for computer modeling (1986)
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    Bulletin of mathematical biology 48 (1986), S. 417-426 
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    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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    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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    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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    Selection under random mutations in stochastic eigen model (1982)
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    Bulletin of mathematical biology 44 (1982), S. 17-28 
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    Notes: Abstract The concept of natural selection is examined, which is one of basic principles for the Darwinian interpretation of evolution. In this model selection is defined as a solution of the deterministic Eigen equation. Next, the random effect is introduced through the mutation term. However, the probability of finding the solution expressing the selection is shown to be smallest. The validity of the model and its applicability to polynucleotide replication are discussed.
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    Factors defining the rate of oxygen uptake by the red blood cell (1982)
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    Bulletin of mathematical biology 44 (1982), S. 135-147 
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    Notes: Abstract Using numerical methods, the initial rates of oxygen uptake by the red blood cell have been computed. The methods accommodate both a water layer and membrane which may act as diffusive impedance to gas influx. The differential solubilities of the gas in these two layers have also been incorporated in the methods. The presence of a 0.50–0.65 μm deoxygenated water layer has been calculated to simulate the experimental results by Roughton (1959). Experimental studies of CO and NO uptake by the red cell could also be simulated. Although a membrane-only model with given parameters can also account for the observed rates of oxygenation of the red cell (Weingardenet al., submitted for publication), the additional incorporation of differential solubilities of oxygen in the different layers of the RBC yields results that indicate a three layer model to be more plausible. Using a thin layer-red cell oxygenation system, the rates of oxygenation were determined for red cells surrounded by a 4.2 μm deoxygenated water layer. The rates were found to compare favorably to the results of the theoretical model.
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    Book review (1982)
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    Bulletin of mathematical biology 44 (1982), S. 151-151 
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    Role of the hypergeometric distribution in the transmission of excitation through sympathetic Ganglia (1982)
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    Bulletin of mathematical biology 44 (1982), S. 152-152 
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    On a class of finite deformations of elastic soft tissues (1982)
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    Bulletin of mathematical biology 44 (1982), S. 175-192 
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    Notes: Abstract Due to the complicated physiological structure of soft biological tissues, stresses can only be measured after the specimen has been stretched to many times of its related length. Therefore, the classical constitutive equations of finite elasticity developed for vulcanized, rubbery materials and the linear theories developed for most engineering materials cannot be applied to soft tissues which are highly elastic in nature. In this article, utilizing a mechanical model developed by Demiray for soft tissues, a class of finite deformations of some tissues is studied and the results are compared with experiment and the existing literature. These problems are the simultaneous extension and twisting of a circular cylindrical bar, the bending of a rectangular block, and the pure shear of a rectangular prism. It is believed that solutions to these problems may find some applications in plastic surgery.
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    Effects of convective and dispersive migration on the linear stability of a two species system with mutualistic interactions and functional response (1982)
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    Bulletin of mathematical biology 44 (1982), S. 271-282 
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    Notes: Abstract In this paper, effects of convective and dispersive migration on the linear stability of the equilibrium state of a two species system with mutualistic interactions and functional response have been investigated. In both finite and semi-infinite habitats, it has been shown that the otherwise stable equilibrium state without dispersal remains so with dispersal also, both under flux and reservior conditions. In the case of finite habitat, the degree of stability increases as dispersal coefficients of the two species increase. The effect of convective migration also is to stabilize the equilibrium state in this case.
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    Announcements (1982)
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    Bulletin of mathematical biology 44 (1982), S. 307-307 
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    A model of the spatial-temporal characteristics of the alpha rhythm (1982)
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    Bulletin of mathematical biology 44 (1982), S. 283-305 
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    Notes: Abstract A linear spatially distributed model of a chain of neurons and interneurons was investigated in relation to the generation of propagated alpha rhythmic activity. It was assumed that the elements of the chain were interconnected by means of recurrent collaterals and inhibitory fibres in such a way that the connectivity functions were assumed to be homogeneous and their strength was an exponentially decreasing function of distance. It was found that such a neuronal chain shows propagation properties for frequencies in the alpha band. The results obtained with the model are in agreement with the phase velocities encountered experimentally. In this way, it was possible to estimate the length of the neural fibres responsible for the phenomenon of propagated activity. The estimates obtained are in good agreement with recent quantitative neuroanatomical data on the circuitry of the neocortex.
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    A behavioral summary for completely random nets (1982)
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    Bulletin of mathematical biology 44 (1982), S. 309-320 
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    Notes: Abstract This paper characterizes the cycle structure of a completely random net. Variables such as number of cycles of a specified length, number of cycles, number of cyclic states and length of cycle are studied. A square array of indicator variables enables conveninent study of moment structure. Additionally, exact and asymptotic distributional results are presented.
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    Eigensolutions of nonlinear wave equations in one dimension (1982)
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    Bulletin of mathematical biology 44 (1982), S. 321-337 
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    Notes: Abstract A class of nonlinear equations describing the steady propagation of a disturbance on the infinite interval in one dimensional space are shown under certain conditions to admit solution with a unique velocity of propagation. The class of equations describe both initial and final homogeneous steady states which are asymptotically stable with respect to uniform perturbations, in contrast to the Fisher equation, which does not.
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    Comparison of models of insulin release (1982)
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    Bulletin of mathematical biology 44 (1982), S. 399-409 
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    Notes: Abstract A model for insulin secretion with a storage and a labile compartment, as well as a provisionary factor, is combined with a signal model in which the signal can be the difference between an excitation and an inhibition, or the difference in concentrations inside and outside some cell components. The model, using a single set of values for the parameters, accounts in a semiquantitative manner for all of the regularly appearing features of the insulin secretion from thein vitro perfused pancreas to a wide range of patterns of glucose and tolbutamide stimulation. Among the features which can be accounted for are: early and late secretion of insulin as a function of glucose in terms of a single parameter; the apparent depletion and recovery during a pulsed pattern of stimulation by tolbutamide; the hypersecretion following a short period of rest during a prolonged stimulation by glucose; the negative spike which occurs when the concentration of glucose, which has been maintained for a period of time, is suddenly reduced to a lower level; and the appropriate responses to slow and fast ramp functions of glucose concentration.
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    Example of a system which is computation universal but not effectively programmable (1982)
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    Bulletin of mathematical biology 44 (1982), S. 443-447 
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    Notes: Abstract The incorporation of a chaotic component in a computing system is incompatible with its being effectively programmable. The example presented shows that concepts of programming suitable for biological systems may differ from those which have grown out of our experience with present day digital computers.
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    Primary events in odour detection (1982)
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    Bulletin of mathematical biology 44 (1982), S. 411-423 
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    Notes: Abstract An analysis of the interaction between stimulus molecules and the olfactory receptor cell membrane is presented. The model is based upon a sequence of events, i.e. stimulus delivery at the olfactory epithelium, absorption of molecules in the mucus layer, diffusion of the molecules towards the receptor cells and molecule-receptor cell membrane interaction. The mathematical analysis considers the situation during electrophysiological experiments, where an odour puff is delivered at an exposed olfactory mucosa. Such a situation resembles sniffing of odour samples. The analysis is discussed in relation to experimental evidence.
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    Analytical model of hygroscopic particle behavior in human airways (1982)
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    Bulletin of mathematical biology 44 (1982), S. 425-442 
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    Notes: Abstract A model is developed to calculate the deposition of hygroscopic aerosols in the human tracheobronchial (TB) tree. The TB airflow pattern assumed is consistent with experimental observations and accounts for anatomical features such as the larynx and cartilaginous rings in large airways. Some original deposition efficiency formulae are presented for laminar and turbulent airstreams. Stepwise growth is simulated by changes in particle size and density at each TB generation. The dose distribution of NaCl aerosols is studied as a function of inhaled particle size and flow rate. Two NaCl growth rate curves are used which differ in the mode of aerosol-air mixing in the trachea. The initial rate of aerosol mixing in the human due to the laryngeal jet is shown to be an important factor affecting the deposition of hygroscopic aerosols. Total TB deposition of NaCl exceeds that for nonhygroscopic particles of the same inhaled aerodynamic size. Hygroscopic growth can also influence the regional TB distribution of dose when submicron NaCl particles grow rapidly enough to deposit by impaction and sedimentation.
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    Remark on the letter by Zhitomirsky and Kagna (1980) (1982)
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    Bulletin of mathematical biology 44 (1982), S. 449-449 
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    Announcements (1982)
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    Bulletin of mathematical biology 44 (1982), S. 451-452 
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    Mathematical model for the study of fertility and viability in inbreeding populations (1982)
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    Bulletin of mathematical biology 44 (1982), S. 491-500 
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    Notes: Abstract Granted that a single or complex gene is responsible for inbreeding depression, theoretical expressions for fertility and viability are obtained in different diploid populations: brother-sister, half-brother-sister, cousins and double-cousins. The conclusions of the study of viability variations according to the coefficient of parentage are proved by the results of experiments and lead to a new view of genetic load.
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    Energy and biological evolution—I. The equilibrium states of biochemical processes (1982)
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    Bulletin of mathematical biology 44 (1982), S. 501-535 
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    Notes: Abstract The Thom gradient model of morphogenesis poses the followinga posteriori problem: “From the observed morphology of a given natural process (effect) determine the dynamics of the process (cause)”. In this paper we consider the classicala priori problem: “Given the cause (dynamics) determine the effect (resultant morphology)”. We find that in biochemical processes the mechanisms for energy activation, energy-matter interaction and energy dissipation determine the dynamics. Furthermore there exists basic energy mechanisms which drive the equilibrium states through the elementary catastrophes of Thom. A comparison with current theories shows that our models describe open ecological food chains and their dynamical systems generalize the equations of organisation posed by M. Eigen.
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    Energy and biological evolution—III. Theoretical ecology and macromolecular self-organization (1982)
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    Bulletin of mathematical biology 44 (1982), S. 549-555 
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    Notes: Abstract We show that the elementary models of biochemical evolutionary processes are the bases for the study of open ecological systems and macromolecular self-organisation. We deduce a biochemical analogue for the basic closed phytoplankton-zooplankton food chain. The perturbation of the Michaelis-Menten mechanism which determines the nutrient-dependent growth rate of the phytoplankton species leads to higher catastrophes for the nutrient equilibrium manifold. The umbilic models are generalizations of the equations of organization of Eigen.
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    Nonlinear generalizations of the Kedem-Katachalsky equations for ionic fluxes (1982)
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    Bulletin of mathematical biology 44 (1982), S. 761-775 
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    Notes: Abstract The transport equation of Kedem and Katchalsky for the flux of ions through a membrane is generalized to demonstrate explicitly the role of impermeant ions in determining its mathematical form. Whereas the Kedem-Katchalsky equation is linear in the salt concentrations in the bathing solutions, the more general equation is bilinear (and symmetric) in the ionic concentrations of the permeant species. The Kedem-Katchalsky flux equation is further generalized to include explicitly a term for ion-exchange in systems having more than a single permeant salt. This additional term is also bilinear (and antisymmetric) in the concentrations of the exchanging ionic species. Flux equations are derived for systems having (1) a single mono-monovalent salt, (2) two mono-monovalent salts and (3) an arbitrary number of salts with no restriction upon the valencies of the ionic components. Since it has no effect upon the form of concentration-dependent terms in the flux equations, coupling to volume flow is neglected.
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    Some applications of the concept of body forces for the myocardium (1982)
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    Bulletin of mathematical biology 44 (1982), S. 819-840 
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    Notes: Abstract A mathematical theory of the dynamics of the myocardium based on the concept of body forces is applied to account for two different experimental results. The first result consists of a relation between oxygen consumption and the kinetic energy of the myocardium. The second set of results provides a consistent interpretation of the relationship between different indices used to assess the ventricular performance.
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    On the stochastic theory of compartments: A semi-Markov approach for the analysis of theK-compartmental systems (1982)
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    Bulletin of mathematical biology 44 (1982), S. 809-817 
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    Notes: Abstract In this paper a semi-Markov process approach is developed to analyse stochastic compartmental systems using straightforward probabilistic arguments. Explicit expressions for several characteristics of thek-compartmental systems with a Poisson process input are derived and various models found in the literature arising from biological applications are generalised here using the semi-Markov process technique.
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    Analysis of a nonlinear diffusion problem With Michaelis-Menten kinetics by an integral equation method (1982)
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    Bulletin of mathematical biology 44 (1982), S. 841-849 
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    Notes: Abstract A mathematical model for oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics is analyzed by means of an intergral equation method. It is shown that an integral equation formulation can be used to obtain a numerical solution associated with this boundary and initial value problem. Through an illustrative numerical calculation we are able to obtain an accurate solution for both the steady and transient problems. Finally, a comparison is made with the numerical solution of McElwain and the variational solution of Anderson and Arthurs for the steady state and Lin's result concerning the unsteady state.
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    A note on exact solutions of two prey-predator equations (1982)
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    Bulletin of mathematical biology 44 (1982), S. 893-897 
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    Notes: Abstract Exact solutions are obtained and discussed for classes of Lotka-Volterra and Leslie-Gower systems governing the interaction of two species. The classes are defined by certain constraints which are imposed on the time-dependent parameters of the equations. A general result for such systems is that each species is characterised by two time-scales: one representing natural growth and the other, the interdependence of the species.
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    Diffusion along intercellular spaces: An analysis of a transient situation (1982)
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    Bulletin of mathematical biology 44 (1982), S. 879-891 
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    Notes: Abstract We present an analysis of the diffusion of a tracer in a model of a cell-intercellular space system. The problem reduces to the resolution of a system of a linear partial differential equation and of a linear integral differential equation. The mathematical results have been obtained in terms of their Laplace transforms, which have been inverted by a numerical procedure for some parameter values. The importance of considering gradients of concentrations in intercellular spaces instead of lumping them with the external mediums has been discussed together with the possibility of extending Ussing's relation to transient cases, in order to detect active transports. Some possible implementations of the model to take into account more general situations have been considered.
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    The asymptotic behavior of Hermite-Padé polynomials (1982)
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    Circuits, systems and signal processing 1 (1982), S. 305-309 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We present speculations on the asymptotic behavior of Hermite-Padé polynomials of type I constructed from a set of functions with common branch points. The proposed form is consistent with all known results and numerical work.
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    Nested-feedback-loops realization of 2-D systems (1982)
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    Circuits, systems and signal processing 1 (1982), S. 321-343 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Algorithms are derived for representation of double power series by branched continued fractions. Some properties of the branched continued fractions are given. Two new alternative structures for realization of a two-dimensional, zero memory nonlinear transfer characteristic are proposed. These structures permit the design of 2-D systems with relatively low sensitivity of the transfer function to coefficient errors. Generalized equivalence transformations of branched continued fractions are also presented. Illustrative examples are included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01599016
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  • 94
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    Port properties of nonlinear reciprocal networks (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 77-92 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Time-invariantn-port networks are considered which are constructed from linear resistors and transformers, and nonlinear inductors and capacitors. A port property is sought which is analogous to the symmetry of the impedance matrix obtained in the linear case. Such a property is found using a stochastic characterization: with all resistors assumed to be at the one temperature and modelled to include the usual thermal noise, a fluctuating noise voltage will be observed at the ports of the networks. With some reasonable restrictions on the nature of the nonlinearities in the reactive elements, the vector of such noise voltages is shown to constitute what is known as a reversible stochastic process; in the linear case, reversibility holds if and only if the impedance matrix is symmetric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01600035
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  • 95
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    Continuation algorithms for the eigenvalue problems (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 123-134 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Three algorithms for the solution of the eigenvalue problem for a continuously parameterized family of sparse matrices are presented; a continuousLU (orLR) algorithm, a continuousQR algorithm, and a continuous Hessenberg algorithm. Each of the three algorithms may be implemented recursively and the sparsity of the given matrices is preserved throughout the numerical process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01600038
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  • 96
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    Stability analysis of complex dynamical systems (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 171-202 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We present two new algorithms to estimate the domain of attraction of the equilibriumx=0 of a nonlinear systemx=f(x). One of these algorithms utilizes quadratic Lyapunov functions while the second algorithm makes use of norm Lyapunov functions. Both of these procedures yield estimates for the domain of attraction which are comparable to those obtained by existing methods; however, the present algorithms appear to be significantly more efficient than existing algorithms. We also show how sometimes the applicability of the above results can be extended to high order systems by invoking the comparison principle. In doing so, we establish some results for the comparison principle which are of interest in their own right. Specifically, we relate the domain of attraction of a low order comparison system to the domain of attraction of a higher order system and we give an interpretation of the comparison principle in terms of stability preserving maps. In order to demonstrate the applicability of the present results, and in order to compare the present results with existing results, several specific examples are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01600051
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  • 97
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    A block matrix representation of permutation networks (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 251-266 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This work provides a mathematical framework for topologically-independent analysis of permutation networks. First, a structure-dependent representation is provided using matrices whose entries are switching expressions. Then, a transformation is presented which maps these matrices into structure-independent representations which are matrices whose entries are 0/1 matrices. Algebraic tools for manipulating the second type of matrices are also provided. Notions such as permutations realizable by a network, the rearrangeability property, and series and parallel connections of networks are defined and discussed with regard to the proposed representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01600055
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  • 98
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    Toeplitz equations and Kronecker's algorithm (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 289-304 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A reliable algorithm, similar to the modifed Kronecker algorithm, is provided for the solution of the Polish polynomial approximation problem. Implicit in this solution is an efficient and reliable method for the algebraic solution of Toeplitz equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01599013
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  • 99
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    Stieltjes series and soliton interaction (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 311-320 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract TheKdV andMkdV multisoliton solutions are found to be generated by rational Stieltjes functions of the non-linearity parameter, each pole of which can be associated with a soliton. The well-known asymptotic emergence of the separate solitons follows at once from the motion of the poles. Successive (n-1/n) Padé approximants to theN-soliton series are considered to show how the solitons are reconstructed from an increasing number of perturbation terms (n ≤N). Their asymptotic behaviour is particularly striking: as time increases the behaviour of then th approximation becomes that of an actualn-soliton solution, constituted by then leading solitons. Furthermore, it turns out that each such Padé approximation satisfies a conservation law: the mass of the approximated solution, equal to that of then solitons included, is conserved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01599015
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  • 100
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    A remark on the numerics of rational approximation and the rate of convergence of equally spaced interpolation of ¦x ¦ (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 367-377 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this note we review the technique for rational Chebyshev approximation as given by the generalization of the Remes algorithm and point out its connection to the generalized eigenvalue problem for symmetric Hankel matrices. By a classical example and some recent work it can be shown that interpolation with rational functions (even) on equidistant knots may lead to results that are superior to Chebyshev approximation by means of polynomials for comparable numerical work.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01599018
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