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  • 1982  (44,622)
  • 1
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    Bulletin of mathematical biology 44 (1982), S. 1-15 
    ISSN: 1522-9602
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    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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    Bulletin of mathematical biology 44 (1982), S. 29-42 
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    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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    Bulletin of mathematical biology 44 (1982), S. 43-56 
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    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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    Bulletin of mathematical biology 44 (1982), S. 75-86 
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    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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    Bulletin of mathematical biology 44 (1982), S. 57-74 
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    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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    Bulletin of mathematical biology 44 (1982), S. 87-102 
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    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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    Bulletin of mathematical biology 44 (1982), S. 103-117 
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    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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    Bulletin of mathematical biology 44 (1982), S. 149-150 
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    Bulletin of mathematical biology 44 (1982), S. 119-134 
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    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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    Bulletin of mathematical biology 44 (1982), S. 537-547 
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    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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    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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    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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    Bulletin of mathematical biology 44 (1982), S. 593-593 
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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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    Bulletin of mathematical biology 44 (1982), S. 594-595 
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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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    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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    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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    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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    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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    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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    Bulletin of mathematical biology 44 (1982), S. 899-900 
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    Bulletin of mathematical biology 53 (1991), S. 281-312 
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    Bulletin of mathematical biology 53 (1991), S. 253-279 
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    Bulletin of mathematical biology 53 (1991), S. 313-326 
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    Bulletin of mathematical biology 53 (1991), S. I 
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    Bulletin of mathematical biology 53 (1991), S. 345-353 
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    Notes: Abstract The statistical correlation of nucleotides in a DNA sequence is described by a set of redundanciesD 1,D 2,D 3,... By calculation of {D n} of 2341 coding regions of nucleic acid sequences it is demonstrated that about 2/3 of sequences has correlation length ≤2, 10% of sequences—correlation with 3-periodicity and others—long range aperiodic correlations. The implications of the results from the interactions of random mutation and natural selection are discussed briefly.
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    Bulletin of mathematical biology 53 (1991), S. 327-343 
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    Notes: Abstract A basic characteristic of biological memory is that it has a graded duration, which, even for socalled short-term memory, can vary from minutes to days (i.e. over about three orders of magnitude), depending on the training protocol, which one can think of as determining the “strength” of the memory. Furthermore, the molecular analysis of simple learning in invertebrates has revealed many examples where “learning” is produced by adecrease in an appropriate membrane conductance. This paper provides a quantitative analysis of a simple kinetic scheme where by a conductance decrease can be produced by repetitive nerve impulses, with a duration that varies with stimulus frequency. The simplest model considered is based on the actual kinetics of the naturally-occurring ionophore Monazomycin. This model yields durations ranging only over a factor of about 10, for reasonable parameter values. However, a simple modification of the model yields memory durations ranging over three or more orders of magnitude. We also show that Monazomycin-like kinetics can appear as the result of a combination of simple uni- and bi-molecular reactions, thus making more plausible the possibility that the effects described here may operate in actual biological systems.
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    Bulletin of mathematical biology 53 (1991), S. 579-589 
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    Notes: Abstract A mathematical model (Kliemann, W. 1987.Bull. math. Biol. 49, 135–152.) that predicts the quantitative branching pattern of dendritic tree was evaluated using the apical and basal dendrites of rat hippocampal neurons. The Wald statistics for χ2-test was developed for the branching pattern of dendritic trees and for the distribution of the maximal order of the tree. Using this statistic, we obtained a reasonable, but not excellent, fit of the mathematical model for the dendritic data. The model's predictability of branching patterns was greatly enhanced by replacing one of the assumptions used for the original model “splitting of branches for all dendritic orders is stochastically independent”, with a new assumption “branches are more likely to split in areas where there is already a high density of branches”. The modified model delivered an excellent fit for basal dendrites and for the apical dendrites of hippocampal neurons from young rats (30–34 days postpartum). This indicates that for these cells the development of dendritic patterns is the result of a purely random and a systematic component, where the latter one depends on the density of dendritic branches in the brain area considered. For apical dendrites there is a trend towards decreasing pattern predictability with increasing age. This appears to reflect the late arrival of afferents and subsequent synaptogenesis proximal on the apical dendritic tree of hippocampal neurons.
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    Notes: Abstract In order for immune cells to carry out many of their functions, including clearance of infectious agents from tissue, they must first encounter their targets in the tissue. This encounter process is often the rate-limiting step in the overall function. Most immune cells exhibit chemotactic ability, and previous continuum models for encounter rates and dynamics have shown that chemotaxis can be a great advantage to cells by greatly increasing encounter rates relative to those for randomly moving cells. This paper describes computer simulations of discrete cell-target encounter events in two dimensions, for the two cases considered by the continuum models: where only a single cell and a single target are present, and where many cells and targets are present. The results of these simulations verify our previous model predictions that a small amount of chemotactic bias dramatically decreases the encounter time, while further increases in the amount of bias have a much smaller effect. Chemotactic ability is shown to be an important determinant of the kinetics of target clearance, and its effects depend on the initial cell-target ratio and the initial distributions of cells and targets. To the best of our knowledge, this work provides the first computer simulations of particle-target encounter in which there is biased motion of particles toward their targets, and is therefore of general interest beyond specific application to immune cell function.
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    Bulletin of mathematical biology 53 (1991), S. 657-663 
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    Bulletin of mathematical biology 53 (1991), S. 881-899 
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    Notes: Abstract The concept of a one-way block, arising from a region of depressed tissue, has remained central to theories for cardiac arrhythmias. We show that both the geometry of a depressed region and spatial heterogeneities in depression are key factors for inducing such a block. By using an asymptotic approximation, known as the eikonal equation, to model qualitatively the movement of a depolarization wave-front down a Purkinje fibre bundle, we show how a one-way block in conduction may result from asymmetric constriction in the width of a depressed bundle. We demonstrate that this theory is valid for biologically relevant parameters and simulate a one-way block by numerically solving the eikonal approximation. We consider the case of non-uniform depression, where the planar travelling wave speed is spatially dependent. Here, numerical simulations indicate that such a spatial dependency may, in itself, be sufficient to produce a one-way block.
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    Bulletin of mathematical biology 53 (1991), S. 911-940 
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    Notes: Abstract The MacArthur-Wilson equilibrium theory of island biogeography has been one of the more influential concepts in modern biogeography and ecology. In this paper, we synthesize the theory and examine effects of different immigration/extinction rate-species diversity curves on original predictions from the theory by using the System Dynamics simulation modeling approach. Moreover, we develop a comprehensive and generic System Dynamics model to incorporate a variety of recent modifications and extensions of the theory, including area effect, distance effect, competition effect, habitat diversity effect, target effect, and rescue effect. Through computer simulation with STELLA, a more profound understanding of the theory of island biogeography can be gained. The System Dynamics modeling approach is especially appropriate for such a study because it maximizes the utilization of the ecological data by incorporating qualitative information so that a complex, imprecisely-defined ecological system can be studied quantitatively, effectively, and comprehensively. Our simulation results show that different monotonic rate-species diversity curves do not affect the essence of the theory of island biogeography, while the magnitude of equilibrium species diversity may be greatly affected. Non-monotonic rate-species diversity curves may result in potential multiple equilibria of species diversity. In addition, our model suggests that a non-monotonic relationship may exist between the equilibrium turnover rate and island area and between the equilibrium turnover rate and distance.
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    Bulletin of mathematical biology 53 (1991), S. 665-678 
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    Notes: Abstract A method to estimate a lower bound of the Kolmogorov entropy—the so calledK 2-entropy—from a time series is presented which avoids use of the generalized correlation integral. The influence of the norm is studied. The method is demonstrated on some standard examples. The entropy of the attractor apparent in the EEG of the foetal sheep is estimated and the results are compared with results obtained from synthesized data featuring some basic properties of EEG. This gives an insight into the limitations of the procedure.
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    Bulletin of mathematical biology 53 (1991), S. 685-700 
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    Notes: Abstract The autonomous oscillations in yeast continuous cultures are investigated analytically and related to the behaviour of the single cell by means of a suitable modified version of Monod’s classical chemostat model. Two main cell phases or states are considered to account for the experimentally observed changes occurring in the cell growth course: the budded phase and the unbudded one. Thus, a sort of two compartment structure is given to the total biomass. The model so far obtained allows one to analyse the local properties of the predicted steady states under various assumptions, both on the yield coefficients and the specific growth rates. Necessary conditions for the local instability are derived and the existence of stable limit cycles is shown by computer simulation. With respect to the qualitative changes in the metabolic parameters, this analysis agrees with the results obtained by simulation of complex structured and segregated models. However, the oscillation period is too long compared with the experimental one and this fact may be mainly due to the strong simplifying assumptions on the dynamic evolution of the transfer rates between the two compartments. The model’s usefulness seems until now restricted to the identification of the relationships between the cell cycle regulation and the oscillation triggering.
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    Notes: Abstract The mathematical model developed by Riveroet al. (1989,Chem. Engng Sci. 44, 2881–2897) is applied to literature data measuring chemotactic bacterial population distributions in response to steep as well as shallow attractant gradients. This model is based on a fundamental picture of the sensing and response mechanisms of individual bacterial cells, and thus relates individual cell properties such as swimming speed and tumbling frequency to population parameters such as the random motility coefficient and the chemotactic sensitivity coefficient. Numerical solution of the model equations generates predicted bacterial density and attractant concentration profiles for any given experimental assay. We have previously validated the mathematical model from experimental work involving a step-change in the attractant gradient (Fordet al., 1991Biotechnol. Bioengng.37, 647–660; For and Lauffenburger, 1991,Biotechnol. Bioengng,37, 661–672). Within the context of this experimental assay, effects of attractant diffusion and consumption, random motility, and chemotactic sensitivity on the shape of the profiles are explored to enhance our understanding of this complex phenomenon. We have applied this model to various other types of gradients with successful intepretation of data reported by Dalquistet al. (1972,Nature New Biol. 236, 120–123) forSalmonella typhimurum validating the mathematical model and supportin the involvement of high and low affinity receptors for serine chemotaxis by these cells.
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    Bulletin of mathematical biology 53 (1991), S. 797-804 
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    Bulletin of mathematical biology 53 (1991), S. 845-851 
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    Notes: Abstract Disconnected recurrences of the stop signal, serine and arginine appear in the original representation of the genetic code, and of the stop signal, arginine, serine and leucine in the codon ring representation. To achieve connectedness along with structural continuity, arook’s tour representation is presented here. On the basis of structural similarities and disparities in their side groups, each of the 20 amino acids is associated with a domain comprised of from one to six contiguous squares on the chess board. As the rook moves on the chess board, it reaches all 64 squares in the ordering of the codon numbers, which prescribe the codons by a simple formula based on the position and size of the nucleotides in a triplet. Recurrences of the stop signal, arginine and serine occur naturally on the tour as the rook enters each of the latter domains for the second time. A mathematical equivalent of the rook’s tour may enter as a programming device in the implementation of the code by the RNAs.
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    Circuits, systems and signal processing 1 (1982), S. 93-104 
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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Circuits, systems and signal processing 1 (1982), S. 137-169 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Circuits, systems and signal processing 1 (1982), S. 267-268 
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    Circuits, systems and signal processing 1 (1982), S. 433-445 
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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Circuits, systems and signal processing 10 (1991), S. 71-89 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We consider general input-output systems, which need not be of a feedback type, that are governed by nonlinear operator equations which relate the input, state, and output. Assuming that these equations depend on a parameterA which is allowed to vary in a neighborhood of a “nominal value”A 0 , we study the dependence of the output onA when the input is fixed. Essentially, we call a system insensitive if the output depends continuously onA. Two insensitivity concepts are introduced, and it is shown that certain monotonicity-like conditions ensure insensitivity. Also, several particular cases of the governing equations are studied. As examples, a control system described by a singular system of ordinary differential equations and a nonlinear feedback system are discussed.
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    Circuits, systems and signal processing 10 (1991), S. 153-161 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The relationship between the elements in the vector of any limit cycle due to rounding in ann-order direct-form digital filter is established. Some bounds on the elements in such vectors are also determined. Sufficient conditions for the accessibility of period-r limit cycles due to rounding inn-order digital filters are presented.
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    Circuits, systems and signal processing 10 (1991), S. 327-342 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper analyzes two direction-of-arrival (DOA) estimation algorithms used in the presence of multipath propagation and with very few snapshots. The conditional maximum likelihood (CML) algorithm and the method of direction estimation (MODE) are discussed. The estimates provided by these algorithms are shown to coincide for large number of snapshots or large signal-to-noise ratio. Necessary and sufficient conditions are derived for the algorithms to yield unique estimates. It is shown that their uniqueness conditions coincide with the minimal uniqueness condition on the array, that is independent of the algorithm used (if the array does not satisfy this minimal condition, no DOA estimation method can give unique estimates). Numerical examples are presented to demonstrate the theoretical results.
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    Circuits, systems and signal processing 10 (1991), S. 361-389 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In Part I of this paper we consider a general model of an input-output system governed by nonlinear operator equations that relate the system's input, state, and output, all of which are elements in extended spaces. This model encompasses feedback systems as a special case. Assuming that the equations governing the system depend on a parameterA that is allowed to vary in a neighborhoodN r (A 0) of a nominal valueA 0 in a linear space, we study conditions under which the system is stable for everyA ε Nr(A0), i.e., when the system exhibits robust stability. By stability we essentially mean that the input-output operator is continuous. Depending on the type of continuity of a map between two extended spaces, four concepts of robustness are introduced. The main results, Theorems 1 and 2, furnish sufficient conditions for a system to be robust in the respective sense. Basically, they show that if the nominal system satisfies a certain condition guaranteeing its stability, and the operators appearing in the governing equations depend continuously on the parameterA, then we have robust stability. As examples illustrating the applications of our results we discuss (1) a feedback-feedforward system, in particular the case when the extended space consists of locally square-integrable functions or functions continuous on [0, ∞), and (2) a time-varying dynamical system described by a linear vector differential equation, whose variables are continuous functions on [0, ∞) which decrease exponentially to zero ast → ∞. At the end of the paper some modifications of the presented theory are discussed.
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    Circuits, systems and signal processing 10 (1991), S. 485-511 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Higher-than-second-order statistics-based input/output identification algorithms are proposed for linear and nonlinear system identification. The higher-than-second-order cumulant-based linear identification algorithm is shown to be insensitive to contamination of the input data by a general class of noise including additive Gaussian noise of unknown covariance, unlike its second-order counterpart. The nonlinear identification is at least as optimal as any linear identification scheme. Recursive-least-squares-type algorithms are derived for linear/nonlinear adaptive identification. As applications, the problems of adaptive noise cancellation and time-delay estimation are discussed and simulated. Consistency of the adaptive estimator is shown. Simulations are performed and compared with the second-order design.
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    The Geneva risk and insurance review 16 (1991), S. 59-74 
    ISSN: 1554-9658
    Keywords: Unemployment Insurance ; Risk Sharing ; Social Security
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    Topics: Economics
    Notes: Abstract Two models of spot labor markets are presented in which labor suppliers have heterogeneous attitudes towards effort and in which uncertainty prevails on labor productivity and growth. The problem of selecting efficient rules to manage unemployment insurance (UI) systems is considered. We show that there does not exist any system which combines an efficient allocation of labor with an efficient allocation of risks among employees, unemployed workers and capital-owners. Pareto-efficient policy rules are a best compromise between these two conflicting objectives. It implies that productive efficiency could be improved in periods of mass unemployment by reducing UI benefits. That would be at the expense of more inefficiencies in the sharing of macroeconomic risks. At the optimum, the UI benefit is positively correlated to growth and it is negatively correlated to labor productivity.
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    The Geneva risk and insurance review 16 (1991), S. 137-138 
    ISSN: 1554-9658
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    Topics: Economics
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    The Geneva risk and insurance review 16 (1991), S. 139-141 
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    Topics: Economics
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    The Geneva risk and insurance review 16 (1991), S. 143-165 
    ISSN: 1554-9658
    Keywords: Social Insurance ; Redistribution ; Incentives
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    Topics: Economics
    Notes: Abstract We extend the familiar income taxation model à la Mirrlees, so as to include income uncertainty, due for instance to a risk of illness. Following a line of research initiated by Blomqvist and Horn [1984] we prove that the existence of a Social Health Insurance system may be justified even when the insurance market is efficient. Moreover, if there is a negative statistical dependence between probability of illness and labor productivity, then the optimum of a Utilitarianist Social Welfare function implies that Social Insurance provides a complete coverage for every household.
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    The Geneva risk and insurance review 16 (1991), S. 167-177 
    ISSN: 1554-9658
    Keywords: Risk Taking ; Taxation ; Complete Conventional Securities Markets
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    Topics: Economics
    Notes: Abstract In general equilibrium, with complete conventional securities markets and endogenous asset supply, taxes on risk remuneration are ineffective but harmless. They do not alter the real allocation of goods or the distribution of wealth, they impose no excess burden, and, in particular, have no impact on risk taking.
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  • 54
    ISSN: 1476-5535
    Keywords: Actinomycete ; Biotransformation ; pH control ; Magnesium sulfate ; MK-733 ; Simvastatin
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary An actinomycete (MA 6474, ATCC 53828) isolated from a soil sample (Mutare, Zimbabwe) was found to biotransform the sodium salt of Simvastatin (MK-733) to 6-α-hydroxymethyl MK-733, 6-β-hybroxymethyl MK-733, and 6-ring-hydroxy MK-733. The bioconversion efficiency to the desired compound, 6-α-hydroxymethyl MK-733, was enhanced by optimizing the physico-chemical parameters of the process. In shake flask cultures, addition of magnesium (0.125 mg/l Mg SO4·7H2O) to the medium resulted in a five-fold increase in the rate of bioconversion to the α diastereomer. The ratio of bioconversion products (6-α-hydroxymethyl, 6-β-hydroxymethyl, and 6-ring-hydroxy MK-733) was regulated by pH. Process improvements and scale up in 23-1 fermentors, which consisted of a controlled addition of substrate (MK-733), resulted in a 2-fold increase in alpha diastereomer Production (42 vs. 79 U/ml) and a 23-fold rate increase in the formation of α-diastereomer. A high diastereomeric ratio (α: β=9∶1) facilitated downstream processing.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 147-156 
    ISSN: 1476-5535
    Keywords: Methanol ; Yeast extract ; Two-phase process ; Periplasmic antigen ; Intracellular antigen
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    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Various physico-chemical parameters have been studied in order to improve the production of hepatitis B virus pre-S2 antigen (middle surface antigen) by the methylotrophic yeastHansenula polymorpha. Antigen production was done in two steps: first, production of cells on glycerol (Phase 1), followed by induction of antigen expression with methanol (Phase 2). Dense cultures ofH. polymorpha, equivalent to 35–40 g/l (dry weight), were readily obtained in small fermenters using minimal medium containing glycerol as carbon source. Antigen expression in this minimal medium, after induction with methanol, was however low and never exceeded 1.6 mg/l of culture. Antigen production was greatly enhanced by adding complex organic nitrogen sources along with methanol at induction time; yeast extract was the best of all the sources tested. In shake flasks, antigen production was proportional to yeast extract concentration up to 7% (w/v) yeast extract. it became clear that the nutritional conditions for good antigen expression were different from those for good biomass production. The effects of yeast extract were reproduced in small fermenters: antigen levels reached 8–9 mg/l in medium containing 6% (w/v) yeast extract during induction with methanol. The mechanisms of yeast extract's effects are still unknown but are probably nutritional. The recombinantH. polymorpha strain produced both periplasmic and intracellular antigen. The periplasmic antigen was shown to be present as 20–22-nm particles and was therefore immunogenic. Immunoblotting indicated that part of the pre-S2 antigen was present as a 24-kDa degradation product. These studies have led to a 140-fold increase in volumetric productivity of antigen and to a 4.6-fold increase in specific production.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 171-178 
    ISSN: 1476-5535
    Keywords: EPA ; Omega-3 ; Arachidonic acid ; Polyunsaturated fatty acid
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    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary The effect of culture conditions upon lipid content and fatty acid composition of mycelia ofPythium irregulare was investigated with particular attention to increasing the yield of 5,8,11,14,17-eicosapentaenoic acid (20∶5; ω−3) (EPA). All experiments were done by shake flask culture using a yeast extract + malt extract medium. The maximum growth rate was obtained at 25°C, but maximum EPA production was obtained at 12°C. The highest EPA production was 76.5 μg EPA/ml 13 days fermentation at 12°C. Addition of glucose during fermentation increased the yield considerably. The highest yield was 112 μg/ml, obtained at 13 days fermentation with spiking on day 11. Fermentation time could be shortened by initial incubation at 25°C for 2 days, followed by incubation at 12°C for 6 days. The culture also produced arachidonic acid and other ω-6 polyunsaturated fatty acids. EPA production was also obtained with lactose or sweet whey permeate, a by-product of cheese manufacture that contains lactose as the main carbohydrate.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 179-185 
    ISSN: 1476-5535
    Keywords: Mortierella alpina ; Arachidonic acid ; Polyunsaturated fatty acid ; Fungal lipid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary WhenMortierella alpina ATCC 32222 was incubated in a glucose salts medium at 25°C the biomass (17.5 g/l) contained 9.62% arachidonic acid which amounted to 54% (w/w) of total biomass lipids. When the glucose concentration in the medium was varied from 0 to 150 g/l, the percentage of arachidonic acid in biomass and in lipids was highest at a glucose concentration of 30 g/l, but highest yield of arachidonic acid per litre of culture broth was observed at a glucose concentration of 100 g/l. While production of biomass reached a plateau of 17 g/l after a 3-day incubation at 25°C, the percentage of arachidonic acid in lipids and biomass increased dramatically from 3 to 6 days with a concurrent arachidonic acid yield increase from 0.89 to 1.63 g/l. Optimum initial culture pH for arachidonic acid production was in the range 6.0–6.7. By increasing the concentration of the glucose salts medium three-fold, yields of biomass and arachidonic acid were increased to 35.8 g/l and 3.73 g/l, respectively.
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  • 58
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    Keywords: Dopamine receptor ; Agonist and antagonist ; Ligand ; Dihydroxy acetanilide
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    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A natural product, Sch 42029, isolated from the fermentation of anActinoplanes sp. (SCC 1971) was found to displace Sch 23390 from the dopamine-1 (D1) receptor. The compound was isolated from the fermentation broth by adsorption of the filtrate on XAD-16 resin, elution with water-methanol, followed by purification by gel-permeation chromatography and HPLC. Using spectroscopic analysis, the structure was determined to be 2,5-dihydroxy acetanilide. The pure compound displaced Sch 23390, a D1-selective ligand, at aK i of 1.6 μm and spiperone, a D2-selective ligand, at aK i of 200 μm.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 193-199 
    ISSN: 1476-5535
    Keywords: Organic hazardous waste ; Leachate ; Landfill management
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Co-disposal of 12 compounds representing major organic classes (aromatic hydrocarbons, halogenated hydrocarbons, pesticides, phenols, and phthalate esters) with shredded municipal solid waste was tested using a laboratory-scale column and pilot-scale lysimeter to characterize transport and transformation phenomena including sorption, volatilization and bioassimilation. Leachate and gases emitted from the lysimeters were examined for identifiable products of biotransformation. The results of this investigation provided a mechanistic evaluation of the attenuating and assimilative capacity of municipal solid waste landfills for specific organic compounds. Physical/chemical organic compound characteristics were related to refuse characteristics and composition to predict compound fate. Such knowledge is useful in developíng landfill management and operational strategies consistent with the need for control of pollutant releases.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 201-207 
    ISSN: 1476-5535
    Keywords: Diffusion chamber ; Cadmium-sensitive ; Cadmium-resitant ; Sediment ; Bacteria ; Cadmium-sorption
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Sorption of cadmium by sediment bacteria and freshwater sediment was investigated using diffusion chambers to simulate the water-sediment interface. Diffusion chambers were constructed to provide two compartments separated by a dialysis membrane. Diffusion of cadmium across the membrane was monitored after pure cultures of sediment bacteria or lake sediments were added to the sediment side of a diffusion chamber. Cellular accumulation of cadmium by cadmium-sensitive and cadmium-resistant bacteria removed between 20% and 80% of the dissolved cadmium from the simulated water column and pore water. Cellular accumulation of cadmium was greatest for cadmium-sensitive isolates that were tested. Sediment with an intact microbial community sequestered 80% of the cadmium added to sediment, whereas autoclaved sediment retained 97% of the metal that was added. Addition of glucose to cadmium-amended sediment decreased retention of cadmium by untreated and autoclaved sediments, resulting in elevated concentrations of dissolved cadmium in the simulated water column.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 209-212 
    ISSN: 1476-5535
    Keywords: Biodegradation ; Direct method ; Indirect method ; Method comparison ; BOD method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Degradation of 10 organic chemicals by pre-acclimated microorganisms in BOD dilution water was determined directly by UV spectrophotometry and indirectly by a modified BOD method. Residual chemical concentrations were periodically measured and pseudo-first-order biodegradation rate constants (k 1) were calculated. Thek 1 spectrophotometry values ranged from 0.006/h to 0.077/h andk 1-BOD values from 0.002/h to 0.043/h for 1-methylnaphthalene and indole, respectively. The ratios ofk spectrophotometry to k1-BOD were between 1.5 for salicylic acid and 3.0 for 1-methylnaphthalene with a mean of 2.7. A significant (α=0.001) linear correlation (r 2=0.854,F=46.630) existed between the two sets of rate constants. Results from this study suggest that the modified BOD method may be used to estimate chemical biodegradation rates in synthetic media.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 213-221 
    ISSN: 1476-5535
    Keywords: Biofilm ; Scanning electron microscope ; Environmental scanning electron microscope
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Descriptions of biofilms and their elemental compositions based on scanning electron micrographs and energy dispersive x-ray analysis cannot be related to the original condition of the biofilm on the surface. Solvent replacement of water removes extracellular polymeric material and reduces the concentration of elements bound within the biofilm. In the wet state, bacteria and microalgae are enmeshed in a gelatinous film that is either removed or dried to a thin inconspicuous residue during sample preparation for scanning electron microscopy. The environmental scanning electron microscope provides a fast, accurate image of biofilms, their spatial relationship to the substratum and elemental composition.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 223-227 
    ISSN: 1476-5535
    Keywords: Deionized water ; Ultra-pure water ; Ozone ; Ultra-violet sterilization ; Oligotroph ; Bacteria ; R2A medium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Presently, tryptic soy agar (TSA) medium is used in the semiconductor industry to determine the concentration of viable oligotrophic bacteria in ultra-pure water systems. Deionized water from an ultra-pure water pilot plant was evaluated for bacterial growth at specific locations, using a non-selective medium (R2A) designed to detect injured heterotrophic as well as oligotrophic bacteria. Results were compared to those obtained using Tryptic Soy Agar. Statistically greater numbers of bacteria were observed when R2A was used as the growth medium. Total viable bacterial numbers were compared both before and after each treatment step of the recirculating loop to determine their effectiveness in removing bacteria. The reduction in bacterial numbers for the reverse osmosis unit, the ion exchange bed, and the ultraviolet sterilizer were 97.4%, 31.3%, and 72.8%, respectively, using TSA medium, and 98.4%, 78.4%, and 35.8% using R2A medium. The number of viable bacteria increased by 60.7% based on TSA medium and 15.7% based on R2A medium after passage of the water through an in-line 0.2-μm pore size nylon filter, probably because of the growth of bacteria on the filter. Our results suggest that R2A medium may give a better representation of the microbial water quality in ultra-pure water systems and therefore a better idea of the effectiveness of the various treatment processes in the control of bacteria.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 229-236 
    ISSN: 1476-5535
    Keywords: Mannanase ; Sporotrichum cellulophilum ; Galactomannan ; Hemicellulase
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Extracellular mannanase activity produced bySporotrichum cellulophilum was purified into two components using acetone precipitation, SP-Sephadex C50 ion exchange chromatography and preparative polyacrylamide gel electrophoresis. The purified mannanse components, M1 and M2, had molecular weights of 108 000–112 000 and 32 200–36 000 respectively. Component M1 was shown to contain 2 subunits having molecular weights of 62 000 and 50 000. M1 and M2 had similar pH-activity profiles with pH optima of 5.5 and 6.0 respectively. M1 was more thermostable than M2: half lives of the enzymes at 70°C were 30 and 9 min for M1 and M2 respectively.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 237-245 
    ISSN: 1476-5535
    Keywords: Microbial emulsifier ; Biosurfactant ; Bioemulsifier
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Biosurfactants have potential for use in enhancement of in situ biorestoration by increasing the bioavailability of contaminants. Microorganisms isolated from biostimulated, contaminated and uncontaminated zones at the site of an aviation fuel spill and hydrocarbon-degrading microorganisms isolated from sites contaminated with unleaded gasoline were examined for their abilities to emulsify petroleum hydrocarbons. Emulsifying ability was quantified by a method involving agitation and visual inspection. Biostimulated-zone microbes and hydrocarbon-degrading microorganisms were the best emulsifiers as compared to contaminated and uncontaminated zone microbes. Biostimulation (nutrient and oxygen addition) may have been the dominant factor which selected for and encouraged growth of emulsifiers; exposure to hydrocarbon was also important. Biostimulated microorganisms were better emulsifiers of aviation fuel (the contaminant hydrocarbon) than of heavier hydrocarbon to which they were not previously exposed. By measuring surface tension changes of culture broths, 11 out of 41 emulsifiers tested were identified as possible biosurfactant producers and two isolates produced large surface tension reductions indicating the high probability of biosurfactant production.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 247-252 
    ISSN: 1476-5535
    Keywords: Invertase ; Entrapped yeast ; Ethanol pretreatment ; Heat pretreatment
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Gel-entrapped, non-viable yeast biomass with specific invertase activity has been produced by two different pretreatment protocols: a short-time thermal treatment and a brief contact with concentrated ethanol solutions. Four yeast strains were most promising:K. fragilis L-293,C. utilis L-282,S. cerevisiae L-170 and L-209. Of these, the ethanol-tolerant L-282 and the ethanol-tolerant and heat-resistant L-170 gave the most active gel-entrapped biocatalysts: around 2 mg of reducing sugars produced per mg dry yeast per min.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 253-258 
    ISSN: 1476-5535
    Keywords: Cholesterol ; 4-Cholesten-3-one ; Cholesterol oxidation ; Heterologous gene expression ; Streptococcal vector
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A streptomycete gene coding for extracellular cholesterol oxidase (choA) was subcloned and expressed inEscherichia coli. The pUCO series recombinants were obtained by inserting thechoA gene into the uniqueKpnI site of pUC19 vector. Expression was observed with pUCO192A and pUCO193 constructs in which the cloned gene(s) were aligned with the upstreamlacZ promoter. Isopropyl β-d-thioglucopyranoside (IPTG) enhanced this expression up to 2.5-fold. Specific Cho activity in the cell extracts of the stable pUCO193 transformant were 0.004 U and 0.007 U per mg protein without and with IPTG induction, respectively. Cho activity was detected in the spent medium of this culture, suggesting possible secretion of the enzyme.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 273-276 
    ISSN: 1476-5535
    Keywords: Bacterial resistance ; Isothiazolone, Quarternary ammonium compounds ; Thiocarbamate ; Water cooling system ; Pseudomonas cepacia ; Pseudomonas stutzeri ; Bacillus subtilis ; Bacillus cereus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Bacteria from water cooling systems developed resistance to three different bactericides i.e. quarternary ammonium compound (QAC), isothiazolone and thiocarbamate. Resistance was induced by exposing isolates to increasing sublethal concentrations for a period of 10 weeks.Bacillus subtilis became resistant to 1000 mg l−1 QAC. Cross-resistance was also detected, e.g. isothiazolone induced resistance to QAC and thiocarbamate.
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 265-271 
    ISSN: 1476-5535
    Keywords: Efrotomycin ; Nocardia lactamdurans ; Uracil catabolism
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    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Nocardialactamdurans has been shown to catabolyse uracil via the reductive pathway. The end product of this pathway, β-alanine, is incorporated into the pyridone ring of efrotomycin. Support for this proposal includes: (1) reversal of thymine inhibition of efrotomycin biosynthesis by dihydrouracil andN-carbamoyl-β-aline, two intermediates of the catabolic pathway; (2) incorporation of [5,6-3H]-uracil into efrotomycin with a relative molar specific activity of approximately 0.5, close to the theoretical maximum; and (3)13C coupling at C4 and C5 of efrotomycin after feeding resting cells with [4,5-13C]-uracil. Our results do not rule out the possibility of an alternative source of β-alanine or the coexistence of uracil catabolism via oxidative reactions.
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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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    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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    Bulletin of mathematical biology 44 (1982), S. 151-151 
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    Bulletin of mathematical biology 44 (1982), S. 152-152 
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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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    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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    Bulletin of mathematical biology 44 (1982), S. 307-307 
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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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    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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    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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    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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    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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    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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    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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    Bulletin of mathematical biology 44 (1982), S. 449-449 
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    Bulletin of mathematical biology 44 (1982), S. 451-452 
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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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    Circuits, systems and signal processing 1 (1982), S. 321-343 
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    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.
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    Circuits, systems and signal processing 1 (1982), S. 77-92 
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    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.
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    Circuits, systems and signal processing 1 (1982), S. 123-134 
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    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.
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    Circuits, systems and signal processing 1 (1982), S. 171-202 
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    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.
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    Circuits, systems and signal processing 1 (1982), S. 251-266 
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    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.
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