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  • Springer  (136,054)
  • Institute of Physics  (21,355)
  • American Meteorological Society
  • 1995-1999  (81,348)
  • 1990-1994
  • 1965-1969  (66,719)
  • 1955-1959  (11,831)
  • 1998  (81,348)
  • 1967  (36,853)
  • 1966  (29,866)
  • 1955  (11,831)
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  • 1995-1999  (81,348)
  • 1990-1994
  • 1965-1969  (66,719)
  • 1955-1959  (11,831)
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  • 1
    Electronic Resource
    Electronic Resource
    A multidimensional birth process and its application to some problems in the dynamics of biological populations (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 333-345 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper is a sequel to a paper by the author entitled “Restricted Transition Probabilities and Their Applications to Some Problems in the Dynamics of Biological Populations” (Bull. Math. Biophysics, 1966,28, 315–331). The paper is divided into two parts. In part one some aspects of the maximum size attained by the population during a finite time interval are studied for the case the stochastic process underlying the evolution of the population is a birth process. Two interesting by-products emerge from the study presented in part one; namely a combinatorial method of finding solutions to the Kolmogorov differential equations in special cases, and secondly, a set of criteria for the optimum allocation of genotypes in the host population of a host-pathogen system. The optimum allocation of genotypes in the host population is a problem of practical importance in controlling plant pathogens. In part two the theory of restricted transition probabilities developed in the companion paper is applied in finding the distribution of the time to the appearance of the first mutation for the case of a two dimensional birth process. The distribution of the time to the appearance of the first mutation is of importance in understanding the role mutation plays in the evolution of a population, particularly in the pathogen population of a host-pathogen system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476814
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  • 2
    Electronic Resource
    Electronic Resource
    The motion of the left ventricle. I (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 355-362 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The complex arrangement of the muscle fibers in the ventricular wall and the nonsymmetric contraction and expansion of the ventricle preclude the writing of a differential equation of motion for the ventricle as a whole. We can, however, describe the motion of the ventricle by describing the motion of the dimensional parameters length and diameter; the radius, circumference, cross-sectional area, and volume following naturally from these. The ventricle is assumed to be an ellipsoid of revolution and the dimensional parameters to be periodic functions of time. Each of the parameters is expressed as a Fourier series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476816
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  • 3
    Electronic Resource
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    Comparaison des modeles de neurone de Hodgkin-Huxley et de Nelson (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 347-354 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Le modèle de Nelson peut-être considéré comme une approximation du modèle de Hodgkin-Huxley. Moins précis, il est plus maniable. Le modèle de Nelson peut également être considéré comme une généralisation du modèle de Hodgkin-Huxley. En effet, il introduit des liaisons synaptiques localisées ou diffusantes, et un processus de facilitation. Le mécanisme des liaisons synaptiques ne se traduit pas facilement dans le langage de Hodgkin-Huxley. Par contre, le processus de facilitation s'interprète facilement. Nelson's model can be taken as an approximation of Hodgkin-Huxley's model. Its precision is lesser, but it is more usable. Nelson's model can also be taken as a generalization of Hodgkin-Huxley's one; for it introduces localized or diffusing synaptic connexions and a facilitating process. The mechanism of synaptic connexions cannot be easily translated into Hodgkin-Huxley's language. On the contrary, the facilitating process is easily interpreted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476815
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  • 4
    Electronic Resource
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    The theory of the left ventricular aneurysm (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 363-370 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A spherical model for the human left ventricle with two different types of aneurysms, circular and rectangular-square, is proposed and meaningful relations are derived between the parameters of the aneurysms and ventricle. Such ventricular parameters as stroke volume, end-diastolic volume, and end-systolic volume are given normal human values to compute values for end-systolic radius and percentage shortening of muscle for various sized circular and rectangular-square aneurysms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476817
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  • 5
    Electronic Resource
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    A note on crime control (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 375-378 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Volterra theory of two competing populations is extended to the contemporary social problem of crime control. Domains of stability for the time dependence of the numbers in the criminal and enforcement groups are exposed by a numerical example. Both augmentation and reduction of enforcement can produce a stable system. Average values of the ratio of members in each group show great sensitivity to the control policies adopted by the remaining sector of the total population.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476819
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  • 6
    Electronic Resource
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    Interactions in enzymatic reactions (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 379-390 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper deals with interactions of substances via an enzymatic reaction (Bull. Math. Biophysics,25, 141–154, 1963). The substances are the activators, inhibitors and/or substrates of the reaction. Due to the bimolecularity of the processes in the reaction, the quantitative relation between the steady state amount of complexes and the amounts of the substances assumes a typical form. In multiple enzymatic reactions this form is more complicated, though basically similar. Because the substances may influence the steady state amounts of the complexes in opposite directions, the compensation and blocking effects are the properties of enzymatic reactions. The substances with the same direction of influence may potentiate each other. In the enzymatic reaction here considered, the potentiation is always non-negative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476820
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  • 7
    Electronic Resource
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    Decay of cell synchronization: Solutions of the cell-growth equation (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 391-409 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Growth-rate functions in analytic form have been obtained for cell cultures in which the doubling times follow the Gaussian and Poisson distributions. The growth-rate functions are calculated by using Laplace transforms to solve an integral equation previously presented. Oscillatory solutions result if a substantial fraction of the cells in a culture are synchronized to divide at some particular time. The synchrony and, hence, the oscillatory character of the growth-rate function eventually disappear because of the non-zero variance of the doubling-time distribution. If their variances are sufficiently small, the Gaussian and Poisson doubling-time distributions lead to growth-rate functions that become identical in the limit of large time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476821
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  • 8
    Electronic Resource
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    On the derivation of a mean growth equation for cell cultures (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 411-416 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract IfN(t) is the expected number of cells in a culture at timet, $$\dot N(t)$$ the corresponding time derivative, andf(t−τ)dt the probability that a cell of aget−τ at timet will divide in the succeeding time intervaldt, then according to Hirsch and Engelberg (this issue) there obtains the integral equation $$\dot N(t) = 2\int_{ - \infty }^t {f(t - \tau )\dot N(\tau )d\tau }$$ for describing the dynamics of the cell population. It is the purpose of this note to give two alternative derivations of this equation, one based on the age density equation of Von Foerster, and the other based on a generalized form of the Harris-Bellman equation describing the first moment of an age dependent, branching process. In addition, a probability model is posed from which the Von Foerster equation and, hence, the Hirsch-Engelberg equation readily follows.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476822
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  • 9
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    A mathematical theory of enamel solubility and the onset of dental caries: I. The kinetics of dissolution of powdered enamel in acid buffer (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 417-432 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model of the dissolution kinetics of powdered enamel is developed based on the kinetic rate termq, $$q = K'H - k'C \cdot P_1$$ , whereH=[H +],C=[Ca ++] andP 1=[HPO 4 = ]. The differential equations describing the rate of mineral dissolution (and the linearly related rate of appearance of calcium and phosphate in solution) have been derived and solved for three basic cases: (1) when thepH of the solution and surface area of the enamel are considered constant, (2) when thepH is assumed constant, but the reduction in surface area during dissolution is considered, and (3) when the rise ofpH resulting from the buffering effect of the dissolved enamel is considered along with the change in surface area. Analytical solutions have been obtained for cases (1) and (2), while a numerical solution has been found for case (3). Data from a study on enamel dissolution are presented that agree with the theory of case (3), and it is noted that apH rise as large as 0.5 can occur, as has been shown elsewhere in the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476823
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  • 10
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    Reward and punishment in learning with possible reference to punishment for crime (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 477-481 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract On the basis of Landahl's theory of two-choice learning it is shown that application of punishment for wrong responses, without giving award for correct ones, does not lead to complete learning, no matter how many trials are used. If initially a “wrong response” was learned, then an attempt to inhibit it by punishment alone will in a class of cases lead only to a 50% suppression of that wrong response. Possible connection with the problem of effectiveness of punishment as a deterrent for crime is mentioned.
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    URL: http://dx.doi.org/10.1007/BF02476827
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  • 11
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    The use of two radiotracers for transfer-rate determinations in closed two compartment systems (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 483-483 
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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/BF02476828
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  • 12
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    Cooperative specific adsorption of iona at charged sites in an electric field (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 483-483 
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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/BF02476829
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  • 13
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    Operations research around the world meetings (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 485-485 
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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/BF02476830
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  • 14
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    Dimensional anlaysis and the equations of electrophoresis (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 501-510 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A set of characteristic parameters is given for electrophoresis accompanied by diffusion, followed by a method of simplification of the transport equation. The concept of electrophoretic similarity is introduced in connection with the presentation of solutions and the final section contains some dimensional considerations of the potential equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476857
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  • 15
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    Categories of (ℓ, ℛ)-systems (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 511-517 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We show that when we represent (ℓ, ℛ)-systems with fixed genome as automata (sequential machines), we get automata with output-dependent states. This yields a short proof that ((ℓ, ℛ)-systems from a subcategory of automata—and with more homomorphisms than previously exhibited. We show how ((ℓ, ℛ)-systems with variable genetic structure may be represented as automata and use this embedding to set up a larger subcategory of the category of automata. An analogy with dynamical systems is briefly discussed. This paper presents a formal exploration and extension of some of the ideas presented by Rosen (Bull. Math. Biophyss,26, 103–111, 1964;28, 141–148;28 149–151). We refer the reader to these papers, and references cited therein, for a discussion of the relevance of this material to relational biology.
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    URL: http://dx.doi.org/10.1007/BF02476858
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  • 16
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    The origin of lift forces in fluttering flight (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 487-500 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A two-dimensional nonlinear integro-differential equation with time-varying coefficients describing the behavior of the fluttering wing-body systems typical of natural flight mechanisms has been deduced from the Navier-Stokes equation which generalizes local pressure and velocity distributions in the externally oscillating air field. The resulting equation for the wing forces is combined with an analogous expression for the forces of gravitation and acceleration associated with the body. The air acceleration force, not previously considered in bio-physical models of insect and bird flight, is shown to arise from a formal analysis of unsteady or time-varying contributions to the velocity field, while the square form of the conventional steady state aerodynamic forces is derived from the intertial terms in the Navier-Stokes equation with the aid of the approximations of Newtonian impact theory. Previous calculations (Houghton, 1964) have indicated that the contribution to gravitational stability of air acceleration and aerodynamic life are roughly in the ratio of 3:1.
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    URL: http://dx.doi.org/10.1007/BF02476856
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  • 17
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    Evoked potentials arising from neural population elements excited at different times on a warped surface (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 519-536 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Certain types of cortical electrical events are non-propagated so that the associated electric fields must have standing wave characteristics. However, cortical electric events typically are generated by neurone populations which cannot be activated simultaneously on impulse driving. Hence the sum of the standing wave fields due to asynchronous activation of adjoining regions of cortical neurones must give the appearance of a traveling wave. Analysis of cortical waveforms is further complicated by curvature in cortical surfaces. A model is presented that shows the effects of curvature and time lag in activation on the form of the potential at points in space around a laminar array of elements simulating a population of cortical neurones. The results are compared with waveforms evoked by single-shock stimulation of the prepyriform cortex in cats.
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    URL: http://dx.doi.org/10.1007/BF02476859
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  • 18
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    A continuity equation for cell populations (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 545-554 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A continuity equation for cell-number density in a population of cells is derived, and a system of equations for eliminating parameters between the general solution and the initial distribution obtained.
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    URL: http://dx.doi.org/10.1007/BF02476861
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  • 19
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    The behavior of the weakening and failing myocardium (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 537-544 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Use of an electrical model of the left ventricle of the heart and the arterial system permits analysis of the changes which take place as the capacity of the myocardium for generation of force decreases. The model is simple in structure, and its construction and practical testing would not be difficult. It demonstrates that, as the heart muscle weakens, the peak of intracardiac force occurs later in systole, and the difference between the intracardiac pressure and the aortic pressure in the second half of systole is much greater than for the normal heart. The feedback mechanisms which are proposed to affect myocardial contractility would affect this compensation for cardiac weakening. Indices to categorize the behavior of the normal, compensated though weakened, and decompensated myocardium are proposed.
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    URL: http://dx.doi.org/10.1007/BF02476860
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  • 20
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    The frequency distribution of chromosome constituents in cells with chromosome-number dispersion (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 555-566 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The frequency distribution in a population of cells of the quantityCD (defined as the amount of some chromosomal substance in a cell which containsC chromosomes) is calculated using the distribution in the population of the amount per chromosome,D, and the distribution of chromosome number,C.
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    URL: http://dx.doi.org/10.1007/BF02476862
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  • 21
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    Calculation of rate of synthesis of chromosomal DNA in cells with chromosome-number dispersion (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 567-574 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The rate of chromosomal DNA synthesis in an exponentially growing population of cells having chromosome-number dispersion is calculated using DNA histogram data, chromosome-number distribution data, and the assumptions that the synthesis rate is constant and DNA double exactly.
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    URL: http://dx.doi.org/10.1007/BF02476863
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  • 22
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    Estimation of rate of synthesis of chromosomal DNA in ehrlich ascites tumor cells (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 575-584 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An estimate is made of the rate coefficient for linear DNA synthesis with exact doubling in an exponentially growing population of Ehrlich ascites tumor cells having chromosome-number dispersion. Comparison of calculated and experimental results suggest that the assumptions used in the calculation are tenable, but further experimental evidence is needed to prove this.
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    URL: http://dx.doi.org/10.1007/BF02476864
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  • 23
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    A sociological approach to biology (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 655-661 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper develops further some suggestions made previously (Bulletin of Mathematical Biophysics,28, 283–308, 1966) that certain biological phenomena may be more easily interpreted from a “sociological” point of view by considering the organism as a social aggregate of cells and a cell as a social aggregate of genes. In this light the problems of origin of life on earth, of aging, and of parasitism and symbiosis are discussed. The notion of social aggregates of different orders is introduced.
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    URL: http://dx.doi.org/10.1007/BF02476867
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  • 24
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    Theorems on random evolution (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 663-663 
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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/BF02476868
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  • 25
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    A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of intraocular pressure (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 585-643 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theoretical and experimental study was made of the mechanical behavior of the cornea. The theoretical analysis included an analytical solution for the symmetrical constraint of a thin, shallow, spherical shell by a rigid indenter. The experimental study investigated the rheology of the cornea with particular emphasis on its compliance with the requirements of the Boltzmann Superposition Principle. Representative results of tests on twenty enucleated hog eyes and two human eyes have been reported. The corneas of the human and hog eyes behaved as linear viscoelastic solids; the human eyes differed from the hog eyes in having a long term creep component. Several eyes were tested at the site of procurement, six to seven minutes after the animal's death, and it was established that creep is not an artifact due to aging or enucleation. The analytical and experimental results were combined to study some instruments used to detect the level of pressure in the eye. The theoretical analysis predicted that a type of elastic instability occurs during the process of flattening a small portion of the cornea; this is discussed with reference to the Goldmann and Mackay-Marg tonometers. The role of corneal creep was considered with reference to the response of the Schiøtz indentation tonometer during the time dependent process known as tonography.
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  • 26
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    Further studies on the shape of the tracking curve of an automobile and its dependence on biological parameters of the driver (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 645-654 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Following previous studies, differential equations are established which determine the variation of the stimulus towards a corrective turn of the steering wheel and its effect on the excitation of the centers in the brain which results in the production of the corrective turn. The equations are derived under the highly oversimplified assumption that all excitation thresholds are so small that they can be neglected. Under these assumptions it is found that the tracking curve of a car is a sinusoid with negative damping, that is, with an ever increasing amplitude. Driving under these assumptions is imposible since the car will always eventually jump off the road. The possible effects of the threshold as well as stimuli towards corrective turns other than the distance from the edge of the lane are very briefly discussed. In spite of the negative results of the paper, its interest lies in the circumstance that with the complication of the model, we find that driving depends not only on the reaction times as the only “purely biological” parameter, but on three other neurobiophysical constants. In a subsequent paper (Rashevsky, 1967) it is shown how the introduction of one or more purely biological parameters of the driver makes a stable driving regime possible.
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    URL: http://dx.doi.org/10.1007/BF02476866
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  • 27
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    The motion of thhe left ventriele: I (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 663-663 
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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/BF02476869
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  • 28
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    Bimolecular systems: I. Linear systems of complexes (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 1-16 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A vast number of biologically important processes are based upon bimolecular systems. In these systems intermediate complexes are formed. Bimolecular systems in which no complex-complex interactions occur are called linear systems of complexes. A definition and some characteristic properties of these systems are given here. There may exist a contradiction of Onsager's principle of detailed balancing in these systems; however, no principal differences are found between the steady state behavior of an open system and that of a closed system. It is shown that the steady state behavior of a linear system of complexes of arbitrary complexity has some similarities with the steady state behavior of a simple bimolecular system, e.g., Michaelis-Menten enzymatic reaction. Multiplicity of action of the substances participating in biomolecular processes may produce some qualitative differences in the steady state behavior of the system.
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  • 29
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    DNA histograms of irradiated cells: The case of prophase-trapping (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 17-32 
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    Notes: Abstract A time-dependent DNA histogram is calculated for an irradiated population of cells under the limiting assumption that the cells cannot pass through prophase due to the effects of the radiation. The population is assumed to increase exponentially prior to irradiation, but after irradiation to neither gain nor lose cells. Chromosome-number dispersion is taken into account in the calculation. The qualitative behavior of the calculated and experimental histograms are in reasonable agreement. The quantitative agreement between the two is relatively good at short post-irradiation times but is poor at long post-irradiation times (say, greater than half the doubling time). This suggests that recovery phenomena cannot be neglected at long post-irradiation times.
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    A note on the mathematical biology of automobile driving (1967)
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    Bulletin of mathematical biology 29 (1967), S. 187-188 
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    Notes: Abstract It is pointed out that the three different stimuli for a corrective turn, namely the distance from the edge of the lane, the rate of approach to the edge, and the angle between the direction of the car and the direction of the lane (Bull. Math. Biophysics,28, 645–654, 1966,29, 181–186, 1967) may act all three simultaneously. It is found that in that case the tracking curve of the car is stable below a critical speed and becomes unstable above it.
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    Mathematical biology of automobile driving (1967)
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    Bulletin of mathematical biology 29 (1967), S. 181-186 
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    Notes: Abstract Continuing a previous study (Bull. Math. Biophysics, 28, 645–654, 1966), the biophysical mechanism of a corrective turn is investigated for the case where the stimulus for the corrective turn is produced not only by the perception of the nearness of an edge of the lane, but also by the rate of approach of the car towards the edge. In that case it is found that the tracking curve of the car may consist of a series of damped sinusoids and safe driving would be possible at any speed if it were not for the endogenous fluctuation in the driver's central nervous system. If the effect of the rate of approach increases sufficiently rapidly as the distance to the edge of the lane decreases, then a stable undamped oscillating tracking curve is possible. The case is also studied where the driver makes a corrective turn in response to a direct perception of the angle between the direction of the lane and the longitudinal axis of the car.
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    Angles of branching and diameters of branches in the human bronchial tree (1967)
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    Bulletin of mathematical biology 29 (1967), S. 245-259 
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    Notes: Abstract The principle of minimal work requires that the conducting airways of the human lung should have a maximum radius for minimal resistance to gas flow. At the same time there is a requirement that the airways should have a minimal volume for economy of space. These two opposing requirements have been investigated mathematically, and a method for calculating the angle of branching which produces minimal volume has been derived. The relationship of the radii of the parent and daughter branches to produce minimal resistance has been similarly defined. By measurement of a bronchial cast from a human lung the extent to which the predicted optimum structure is realized in practice has been shown. The change in structure associated with change of function at the transition from conducting airway to diffusion zone has been demonstrated.
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    Finite linnaean structures (1967)
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    Bulletin of mathematical biology 29 (1967), S. 191-206 
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    Notes: Abstract This paper considers a class of set-theoretical entities, calledn-rank Linnaean structures, which are intended as abstract models of the taxonomic classificatory systems of biology. In the first part, devoted to formalism, finite Linnaean structures are discussed in complete generality; but, in addition, eight distinct subclasses are noted and some of the properties of their elements are explored. In the second part, concerned with applications, it is shown that taxonomic systems may be recast in the form of finite Linnaean structures, and an effort is made to show that some undesirable features of earlier models are avoided without artificiality and without abandoning extensional mathematics.
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    Abstract power structures (APS) and related bumping orders (1967)
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    Bulletin of mathematical biology 29 (1967), S. 207-216 
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    Notes: Abstract Generalizing an idea of M. Richardson (Fundamentals of Mathematics, New York: Macmillan Co., 1958), an APS on a given populationP is a non-empty collection of non-empty subsets ofP such that ifA is in the collection andA⊆B, thenB is in the collection. From a structure of this kind a partial ordering ofP, called therelated bumping order, is derived. The question is raised as to what kinds of partial orderings can be so obtained. For structures determined by voting weights of the members of the population, a complete characterization of all possible bumping orders is obtained.
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    Stability analysis of a mathematical neuron model (1967)
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    Bulletin of mathematical biology 29 (1967), S. 217-226 
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    Notes: Abstract The “second method” of Liapunov is used to perform a stability analysis of a mathematical model of the neuron. This analysis is based on the hypothesis that the firing of the neuron coincides with a temporary state of instability of the system, and that the initiation of all-or-none process depends on the magnitude of membrane depolarization and its first time derivative. It is found that the stability (and hence the possibility of a second firing) is restored approximately when the rate of membrane repolarization is at a maximum. This result predicts that the duration of the period of absolute refractoriness in neurons would be about 75 per cent of the spike duration, and thus shorter than the value usually obtained from experimental measurements.
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    A neural net model for masking phenomena (1967)
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    Bulletin of mathematical biology 29 (1967), S. 227-232 
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    Notes: Abstract Some aspects of masking phenomena are considered in terms of the simplest possible model of two-factor neural elements. The effect of a number of variables can be accounted for, but the introduction of an internuncial element results in a masking function which need not be symmetric about zero delay interval. As an illustration, the results for a special case are compared with available data. In general, such a model results in a masking function which depends on the intensity, area, and duration of the stimuli, as well as on the temporal and spatial separation between them.
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    The struggle for life: I. Two species (1967)
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    Bulletin of mathematical biology 29 (1967), S. 377-388 
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    Notes: Abstract The general equations are discussed describing two species in competition or in symbiosis or feeding one on the other.
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    A note on Rashevsky’s postulate of relational forces (1967)
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    Bulletin of mathematical biology 29 (1967), S. 403-404 
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    Organismic sets and biological epimorphism (1967)
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    Bulletin of mathematical biology 29 (1967), S. 389-393 
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    Notes: Abstract It is shown that the principle of biological epimorphism (Rashevsky,Mathematical Principles in Biology and Their Applications, Springfield, Ill.: Charles Thomas, 1960) is contained in the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967) if an additional postulate not directly connected to mappings is made.
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    Out-of-print volumes and back issues of the Bulletin of Mathematical Biophysics (1967)
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    Bulletin of mathematical biology 29 (1967), S. 407-407 
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    Model of urethra under uniform circumferential tension (1967)
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    Bulletin of mathematical biology 29 (1967), S. 409-409 
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    Bimolecular systems: II. Nonlinear systems of complexes (1967)
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    Bulletin of mathematical biology 29 (1967), S. 605-613 
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    Notes: Abstract This paper deals with bimolecular systems in which also complex-complex interactions occur. Because of the complexity of the problem, an approximation in a form of coupled linear systems of complexes (Bull. Math. Biophysics,29, 1–16, 1967) is considered. Two types of couplings, serial and parallel, are studied. In the serial coupling the nonlinear system of complexes has the same behavior as its subsystems. An entity, initial sensitivity, has interesting properties: in serial coupling it is at most equal to the product and in parallel coupling, at most equal to the sum of partial initial sensitivities.
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    Bimolecular systems: III. Catalytic systems (1967)
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    Bulletin of mathematical biology 29 (1967), S. 615-623 
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    Notes: Abstract Amplification effect in the catalytic bimolecular systems is a consequence of the kinetic characteristic of the catalyst. Two types of the coefficient of amplification are defined. The applicability of these definitions is given by the type of the bimolecular system. In a simple example it is shown that the concept of amplification is meaningful in these systems. Furthermore, two rules, analogous to those for a coupling of amplifiers, are derived for the two basic modes of coupling of catalytic systems. Thus, in biological systems the catalytic reactions may be regarded as biologically effective amplifiers.
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    A theory of cell hydration governed by adsorption of water on cell proteins rather than by osmotic pressure (1967)
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    Bulletin of mathematical biology 29 (1967), S. 583-596 
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    Notes: Abstract It is postulated that cell hydration is governed by adsorption of water on cell proteins in accord with the Bradley adsorption isotherm, and that the action of a solute in the surrounding solution is to lower the vapor pressure of the solution so that cell water adsorption is decreased by moving down the Bradley isotherm. From these concepts, it is derived that cell volume (V) should be related to solute concentration (x) by the equationV=−E log10 x+F whereE andF are constants which are independent of type of solute. For a non-adsorbed solute this agrees well with experimental data. For solutes which are adsorbed by cell proteins, a correction in the above equation may be necessary at higher solute concentrations, which is shown to be compatible with various experimental data. The types of experiments which are generally used to support the osmotic pressure theory of cell hydration agree equally well with the adsorption theory. The virtue of the adsorption theory is that, unlike the osmotic pressure theory of cell swelling, it is compatible with permeability of the cell membrane to solutes, which has been experimentally observed for various solutes.
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    Considerations of quasi-stationarity in electrophysiological systems (1967)
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    Bulletin of mathematical biology 29 (1967), S. 657-664 
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    Notes: Abstract Conditions under which a time varying electromagnetic field problem (such as arises in electrophysiology, electrocardiography, etc.) can be reduced to the conventional quasistatic problem are summarized. These conditions are discussed for typical physiological parameters.
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    The dead space in a compartmental lung model (1967)
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    Bulletin of mathematical biology 29 (1967), S. 711-718 
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    Notes: Abstract A compartmental lung model with any number of synchronously filling and emptying functional chambers and a common dead space or conducting region is considered. It is shown that the model gives rise to an output, in an open circuit washout determination, which is a weighted sum of exponentials. From estimates of these weights and exponential components, estimates of the model parameters can be recovered. Relations giving the unique correspondence between the output parameters and the model parameters are derived and the existence and uniqueness of solutions established.
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    A charge transfer process in the visual pigments (1967)
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    Bulletin of mathematical biology 29 (1967), S. 677-690 
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    Notes: Abstract A physical model that incorporates all the experimental information on the formation of the visual pigment rhodopsin is presented. The visual pigments consist of a chromophore bound to an appropriate protein. Thus rhodopsin (λm 505 mμ) is formed by a Schiff’s base linkage C19H27CH=NH+-opsin (λm 440 mμ) between 11-cis retinal (λm 380 mμ) and the protein opsin (λm 280 mμ). It is found that there exists a red shift in the spectrum of rhodopsin from the Schiff’s base. The model brings an explanation for this red shift. It is shown that such a shift may be due to a charge transfer process (R. S. Mulliken,J. Am. Chem. Soc.,74, 811–824, 1952) between an electron at the double bond of carbons C11−C12 and an atomic orbital of the sulphur present in cysteine. This provides an explanation of the presence of SH-groups in the protein after the absorption of light. A one-electron approximation is used and the dipole momentμ NV ; hence, the oscillator strengthf of the transitionNV is estimated and compared with the experimentally determined extinction coefficient ∈m by mixing 3.5×10−3 M of 11-cis retinal with 8.3×10−5 M of cysteine at pH ranges 6 through 8. Reasonable agreement is found. Solvent, concentration and temperature dependence are shown also.
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    Optimal models for social change (1967)
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    Bulletin of mathematical biology 29 (1967), S. 841-862 
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    Notes: Abstract By assigning coordinates to the environmental function space comprising all physical and mental stimuli, mathematical interpretations can be based on such terms as adaptability, and reactivity which relate to individuals interacting with their environment within a society. These psychometric concepts are incorporated into a framework of functional analysis, which permits the optimization of social change by maximizing the satisfaction integral through the use of variational or dynamic programming methods in conjunction with some optimal social policy. The approach provides a mathematical connection between psychology and sociology, and further demonstrates that existing forms of government are simulated by differential equations belonging to the same general class. The synthesis of new classes of functional equations describing social progress is visualized as a legitimate objective for abstract mathematical sociology.
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    A suggestion for a new approach to the mathematical theory of imitative behavior (1967)
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    Bulletin of mathematical biology 29 (1967), S. 863-877 
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    Notes: Abstract The theory of imitative behavior as developed hitherto by the author was based on the assumption that each individual has a natural preference for one of the two mutually exclusive behaviors. The endogenous fluctuations in the central nervous system then result in the individual’s exhibiting the two behaviors alternately with a relative frequency determined by the natural preference. Imitation shifts the natural preference towards one or the other of the two mutually exclusive behaviors. In the present approach it is suggested that the relative frequency of the two mutually exclusive behaviors exhibited alternately is determined by maximizing the “satisfaction function” of the individual, that is by hedonistic factors rather than by purely random fluctuations. Corresponding equations are developed. It is shown that in certain cases, even when the imitation effect is absent, a sort of “pseudoimitation” may occur. Another situation leads, in the case of two individuals only, to a complete “division of labor” between them, with respect to the two behaviors. Each one exhibits only one behavior. After that imitation is introduced explicitly by assuming that imitation by one individual or another increases the satisfaction function of the imitating individual. Results thus obtained show similarities to the results of the old theory.
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    Book review (1998)
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    Bulletin of mathematical biology 60 (1998), S. 195-196 
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    A mathematical model for fibroblast and collagen orientation (1998)
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    Bulletin of mathematical biology 60 (1998), S. 101-129 
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    Notes: Abstract Due to the increasing importance of the extracellular matrix in many biological problems, in this paper we develop a model for fibroblast and collagen orientation with the ultimate objective of understanding how fibroblasts form and remodel the extracellular matrix, in particular its collagen component. The model uses integrodifferential equations to describe the interaction between the cells and fibers at a point in space with various orientations. The equations are studied both analytically and numerically to discover different types of solutions and their behavior. In particular we examine solutions where all the fibroblasts and collagen have discrete orientations, a localized continuum of orientations and a continuous distribution of orientations with several maxima. The effect of altering the parameters in the system is explored, including the angular diffusion coefficient for the fibroblasts, as well as the strength and range of the interaction between fibroblasts and collagen. We find the initial conditions and the range of influence between the collagen and the fibroblasts are the two factors which determine the behavior of the solutions. The implications of this for wound healing and cancer are discussed including the conclusion that the major factor in determining the degree of scarring is the initial deposition of collagen.
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    Extinction times and phase transitions for spatially structured closed epidemics (1998)
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    Bulletin of mathematical biology 60 (1998), S. 215-230 
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    Notes: Abstract This paper considers the time to extinction for a stochastic epidemic model of SEIR form without replacement of susceptibles. It first shows how previous rigorous results can be heuristically explained in terms of the more transparent dynamics of an approximating deterministic system. The model is then extended to include a host population structured into patches, with weak nearest-neighbour mixing of infection. It is shown, by considering the approximating deterministic system, that the expected time to extinction in a population of n + 1 patches each of size N is of the form a log N + bn, provided that N 〉 N c where N c is a critical patch size below which transits are unlikely to occur. This corresponds to the simple decomposition of the time of an epidemic into the time it takes to spread through one patch plus the time it takes to transit to each of n successive patches. Expressions for this threshold and the coefficients of the time to extinction are given in terms of the transmission parameters of infection and the coupling strength between patches. These expressions are compared with numerical results using parameters relevant to a study of phocine distemper virus in North Sea seals, and the agreement is found to be good for large and small N. In the region when N ≈ N c , where transits may or may not occur, interesting transitional behaviour is seen, leading to a non-monotonicity of the extinction time as a function of N.
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    Book reviews (1998)
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    Bulletin of mathematical biology 60 (1998), S. 409-415 
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    The loss of immunity in directly transmitted infections modeling: Effects on the epidemiological parameters (1998)
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    Bulletin of mathematical biology 60 (1998), S. 355-372 
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    Notes: Abstract When directly transmitted infectious diseases are modeled assuming an everlasting induced immunity (and constant contact rate), there are well-established formulas to deal with, which is not true if we include the loss of induced immunity. In general, the immunity induced by the disease is everlasting. We propose a model considering the loss of immunity and present methods for the estimation of two epidemiological parameters: the force of infection and the basic reproduction ratio. We also analyze the effects of the loss of immunity on these parameters. Based on these results, we conclude that reinfection can play an important role in highly vaccinated populations.
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    Models for the length distributions of actin filaments: I. Simple polymerization and fragmentation (1998)
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    Bulletin of mathematical biology 60 (1998), S. 449-475 
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    Notes: Abstract We studied mathematical models for the length distributions of actin filaments under the effects of polymerization/depolymerization, and fragmentation. In this paper, we emphasize the effects of these two processes acting alone. In this case, simple discrete and continuous models can be derived and solved explicitly (in several special cases), making the problem interesting from a modeling and pedagogical point of view. In a companion paper (Ermentrout and Edelstein-Keshet, 1998, Bull. Math. Biol. 60, 477–503) we investigate what happens when the processes act together, with particular attention to fragmentation by gelsolin, and with a greater level of biological detail.
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    Parallel dose-response curves in combination experiments (1998)
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    Bulletin of mathematical biology 60 (1998), S. 197-213 
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    Notes: Abstract A possible experimental design for combination experiments is to compare the doseresponse curve of a single agent with the corresponding curve of the same agent using either a fixed amount of a second one or a fixed dose ratio. No interaction is then often defined by a parallel shift of these curves. We have performed a systematic study for various types of doseresponse relations both for the dose-additivity (Loewe additivity) and for the independence (Bliss independence) criteria for defining zero interaction. Parallelism between doseresponse curves of a single agent and those of the same agent in the presence of a fixed amount of another one is found for the Loewe-additivity criterion for linear doseresponse relations. For nonlinear relations, one has to differentiate between effect parallelism (parallel shift on the effect scale) and dose parallelism (parallel shift on the dose scale). In the case of Loewe additivity, zero-interaction dose parallelism is found for power, Weibull, median-effect and logistic doseresponse relations, given that special parameter relationships are fulfilled. The mechanistic model of competitive interaction exhibits dose parallelism but not effect parallelism for Loewe additivity. Bliss independence and Loewe additivity lead to identical results for exponential doseresponse curves. This is the only case for which dose parallelism was found for Bliss independence. Parallelism between single-agent doseresponse relations and Loewe additivity mixture relations is found for examples with a fixed doseratio design. However, this is again not a general property of the design adopted but holds only if special conditions are fulfilled. The comparison of combination doseresponse curves with single-agent relations has to be performed taking into account both potency and shape parameters. The results of this analysis lead to the conclusion that parallelism between zero interaction combination and single-agent doseresponse relations is found only for special cases and cannot be used as a general criterion for defining zero-interaction in combined-action assessment even if the correct potency shift is taken into account.
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    Pattern formation in a generalized chemotactic model (1998)
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    Bulletin of mathematical biology 60 (1998), S. 1-26 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate, numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development.
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    URL: http://dx.doi.org/10.1006/bulm.1997.0010
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    A continuum mechanics approach to determining the cellular velocity field within a wool follicle (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 79-100 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract A model, based on the principles of continuum mechanics, is presented for the analysis of cell-velocity fields within wool follicles. The model requires specification of three follicle characteristics in the form of spatially varying fields: viscosity, cell density and cell production rate. The viscosity is introduced as an attempt to model both complex intercellular interactions and individual cell deformation as the cells move. It is demonstrated that the distribution of cell production is more important than axial variation in viscosity in determining the overall flow pattern.
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    URL: http://dx.doi.org/10.1006/bulm.1997.0025
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    Modelling the metabolic versatility of a microbial trichome (1998)
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    Bulletin of mathematical biology 60 (1998), S. 131-150 
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    Notes: Abstract A microbial trichome extracts nutrients from its immediate surroundings. It may also oxidize electron donors, reduce electron acceptors, and exude the ‘waste’ products of endogenous redox metabolism. Finally, it may effect light harvesting. These exchange fluxes are summed up in a generic model, which covers photoautotrophs as well as chemoheterotrophs. The focus is on endogenous metabolism and the cellular homeostasis of both reducing and phosphorylating equivalents. A novel result is the formulation of four ‘rules’, akin to the Pasteur effect, which govern the compatibility of endogenous metabolism with various assimilatory processes.
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    URL: http://dx.doi.org/10.1006/bulm.1997.0026
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    Optimal harvesting for a predator-prey metapopulation (1998)
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    Bulletin of mathematical biology 60 (1998), S. 49-65 
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    Topics: Biology , Mathematics
    Notes: Abstract In this paper we present a deterministic, discrete-time model for a two-patch predator-prey metapopulation. We study optimal harvesting for the metapopulation using dynamic programming. Some rules are established as generalizations of rules for a single-species metapopulation harvesting theory. We also establish rules to harvest relatively more (or less) vulnerable prey subpopulations and more (or less) efficient predator subpopulations.
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    URL: http://dx.doi.org/10.1006/bulm.1997.0005
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    Wavelet-based analysis of human blood-flow dynamics (1998)
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    Bulletin of mathematical biology 60 (1998), S. 919-935 
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    Notes: Abstract To analyze signals measured from human blood flow in the time-frequency domain, we used the wavelet transform which gives good time resolution for high-frequency components and good frequency resolution for low-frequency components. Five characteristic frequency peaks, corresponding to five almost periodic rhythmic activities, were found on the time scale of minutes. These oscillations were characterized by time and spatial invariant measures. The potential of this approach in studying the blood-flow dynamics was illustrated by revealing differences between the groups of control subjects and athletes.
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    URL: http://dx.doi.org/10.1006/bulm.1998.0047
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    Book review (1998)
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    Bulletin of mathematical biology 60 (1998), S. 997-998 
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    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1006/bulm.1998.0065
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    Diffusively coupled bursters: Effects of cell heterogeneity (1998)
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    Bulletin of mathematical biology 60 (1998), S. 1167-1200 
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    Topics: Biology , Mathematics
    Notes: Abstract The interaction of a pair of weakly coupled biological bursters is examined. Bursting refers to oscillations in which an observable slowly alternates between phases of relative quiescence and rapid oscillatory behavior. The motivation for this work is to understand the role of electrical coupling in promoting the synchronization of bursting electrical activity (BEA) observed in the β-cells of the islet of Langerhans, which secrete insulin in response to glucose. By studying the coupled fast subsystem of a model of BEA, we focus on the interaction that occurs during the rapid oscillatory phase. Coupling is weak, diffusive and non-scalar. In addition, non-identical oscillators are permitted. Using perturbation methods with the assumption that the uncoupled oscillators are near a Hopf bifurcation, a reduced system of equations is obtained. A detailed bifurcation study of this reduced system reveals a variety of patterns but suggests that asymmetrically phase-locked solutions are the most typical. Finally, the results are applied to the unreduced full bursting system and used to predict the burst pattern for a pair of cells with a given coupling strength and degree of heterogeneity.
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    Modeling actin filament reorganization in endothelial cells subjected to cyclic stretch (1998)
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    Bulletin of mathematical biology 60 (1998), S. 1017-1037 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Hemodynamic forces affect endothelial cell morphology and function. In particular, circumferential cyclic stretch of blood vessels, due to pressure changes during the cardiac cycle, is known to affect the endothelial cell shape, mediating the alignment of the cells in the direction perpendicular to stretch. This change in cell shape proceeds a drastic reorganization at the internal level. The cellular scaffolding, mainly composed of actin filaments, reorganize in the direction which later becomes the cell’s long axis. How this external mechanical stimulus is ’sensed’ and transduced into the cell is still unknown. Here, we develop a mathematical model depicting the dynamics of actin filaments, and the influence of the cyclic stretch of the substratum based on the experimental evidence that external stimuli may be transduced inside the cell via transmembrane proteins which are coupled with actin filaments on the cytoplasmic side. Based on this view, we investigate two approaches describing the formulation of the transduction mechanisms involving the coupling between filaments and the membrane proteins. As a result, we find that the mechanical stimulus could cause the experimentally observed reorganization of the entire cytoskeleton simply by altering the dynamics of the filaments connected with the integral membrane proteins, as described in our model. Comparison of our results with previous studies of cytoskeletal dynamics reveals that the cytoskeleton, which, in the absence of the effect of stretch would maintain its isotropic distribution, slowly aligns with the precise direction set by the external stimulus. It is found that even a feeble stimulus, coupled with a strong internal dynamics, is sufficient to align actin filaments perpendicular to the direction of stretch.
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    Emergence of donor control in patchy predator—prey systems (1998)
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    Bulletin of mathematical biology 60 (1998), S. 1149-1166 
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    Topics: Biology , Mathematics
    Notes: Abstract We study a general predator—prey system in a spatially heterogeneous environment. The predation process, which occurs on a behavioural time-scale, is much faster than the other processes (reproduction, natural mortality and migrations) occurring on the population dynamics time-scale. We show that, taking account of this difference in time-scales, and assuming that the prey have a refuge, the dynamics of the system on a slow time-scale become donor-controlled. Even though predators may control the prey density locally and on a behavioural fast time-scale, nevertheless, both globally and on a slow time-scale, the prey dynamics are independent of predator density: the presence of predators generates a constant prey mortality. In other words, in heterogeneous environments, the prey population dynamics depend in a switch-like manner on the presence or absence of predators, not on their actual density.
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    Mean oscillation of functions and the Paley-Wiener space (1998)
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    The journal of Fourier analysis and applications 4 (1998), S. 283-297 
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    ISSN: 1531-5851
    Keywords: Primary 42B25 ; 30D10 ; Secondary 26A16 ; 46B45 ; 47B10 ; 47B35 ; Mean oscillation ; Paley-Wiener space ; Besov spaces ; wavelets ; commutators ; Hankel operators ; Schatten-von Neumann ideals
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    Topics: Mathematics
    Notes: Abstract The oscillatory behavior of functions with compactly supported Fourier transform is characterized in a quantified way using various function spaces. In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points. Several open questions about spaces of sequences are answered and applications in the study of commutator operators on the Paley-Wiener space are shown.
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    Wavelets on fractals and besov spaces (1998)
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    The journal of Fourier analysis and applications 4 (1998), S. 329-340 
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    ISSN: 1531-5851
    Keywords: 42C15 ; 46E35 ; Wavelets ; function spaces ; fractals
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    Topics: Mathematics
    Notes: Abstract Wavelets on self-similar fractals are introduced. It is shown that for certain totally disconnected fractals, function spaces may be characterized by means of the magnitude of the wavelet coefficients of the functions.
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    Gibbs' phenomenon for sampling series and what to do about it (1998)
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    The journal of Fourier analysis and applications 4 (1998), S. 357-375 
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    ISSN: 1531-5851
    Keywords: 42C15 ; 94A12 ; wavelets ; interpolation ; orthogonal expansions
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    Topics: Mathematics
    Notes: Abstract Gibbs' phenomenon occurs for most orthogonal wavelet expansions. It is also shown to occur with many wavelet interpolating series, and a characterization is given. By introducing modifications in such a series, it can be avoided. However, some series that exhibit Gibbs' phenomenon for orthogonal series do not for the associated sampling series.
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    A space-time-filtered Viterbi receiver for CCI/ISI reduction in TDMA systems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 85-102 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, we present a hybrid space-time-filtered Viterbi receiver using multiple antennas for co-channel interference (CCI) reduction and intersymbol interference (ISI) equalization in a slow Rayleigh fading channel. In this approach, a space-time filter is first applied at the antenna outputs to maximize the signal-to-interference-plus-noise ratio (SINR), and the scalar output is then sent to a Viterbi equalizer. We propose a closed-form solution to jointly determine the weight vector for the space-time filter and the channel vector for the Viterbi equalizer. We also examine the need for a whitening filter prior to the Viterbi equalizer and show that it only marginally improves the performance. Simulation results are provided to validate our approach and to compare the performance of our receiver with that of different existing receivers.
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    Sydney Richard Parker 1923–1996 (1998)
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    Circuits, systems and signal processing 17 (1998), S. i 
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    Topics: Electrical Engineering, Measurement and Control Technology
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    Parametric signal processing of anechoic data from prosthetic heart valve testing (1998)
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    Circuits, systems and signal processing 17 (1998), S. 123-136 
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    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Prosthetic heart valves have been responsible for extending the life spans and improving the quality of life of many people with serious heart conditions. Even though the heart valves are extremely reliable, eventually they are susceptible to the long-term fatigue and structural failure effects expected for mechanical devices operating over long periods of time. In [2] a classification procedure was developed using spectral features obtained from acoustic signals to determine the condition of the prosthetic heart valve. Although this classification procedure has produced very encouraging results, this method still lacks a fundamental physical description of the sounds produced by the valve during normal operation. In order to obtain a better understanding of the valve acoustic response, we have performed a set of anechoic tests. In this paper, we describe the anechoic experiment and also present limited transient response results. This transient information will eventually be used to identify and improve the features used to classify the valve condition.
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    On neural network design — Part I: Using the MVQ algorithm (1998)
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    Circuits, systems and signal processing 17 (1998), S. 195-218 
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    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this two-part study we present a new design methodology for neural classifiers. The design procedure utilizes a multiclass vector quantization (MVQ) algorithm for information extraction from the training set. The extracted information suffices to specify the hidden layer in a canonical neural network architecture. The extracted information also leads to the specification of neuron inhibition rules and subsequently the design of the hidden layer-to-output map. In Part I of the study we focus attention on the MVQ algorithm and how it is used to extract information from a training set. The extracted information is referred to as thecodebook. The codebook is used to directly specify the hidden layer. This specification can take the form of a perceptron layer, a radial basis layer, or a heterogeneous layer involving a mixture of neuron types. These and otherh-layer specifications are determined directly from the same extracted information. The MVQ codebook also suffices to scale the activation function of each neuron. In Part II we consider the nonsimplistic hidden layer-to-output map design. We note that the MVQ algorithm, as it extracts information, decomposes the design set into disjoint neighborhoods. For each neighborhood we identify subsets of the hidden layer neurons, which are significant sensors for the neighborhood. For each such subset we construct an output map. Inhibition rules are established to ensure that the proper output map is activated. In benchmark simulations the overall design exhibits excellent performance, to the extent that we are hard pressed to identify bounds on performance, if any.
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    A holographic transform domain image watermarking method (1998)
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    Circuits, systems and signal processing 17 (1998), S. 361-389 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A transform domain image tagging orwatermarking method that survives image cropping (and, hence, is “holographic”) was proposed at Bell Labs in September 1994. This report analyzed in detail the various properties of this method and introduces an optimal procedure for watermark recovery.
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    A sectoring algorithm for exact computation of the frequency response of linear interval systems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 483-493 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract An algorithm for the exact computation of the frequency responses of linear interval systems is obtained. For the computation a sectoring stage is added to an elimination algorithm to eliminate interior curves. It is shown that the intersection of a ray and the frequency response set is an empty set or a line segment whose endpoints are extrema of the functions defined. Required mathematical analysis tools for the development of the sectoring algorithm and an illustrative example are provided.
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    The fundamental subspace sequences of matrix pencils: A toeplitz matrix unified characterization (1998)
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    Circuits, systems and signal processing 17 (1998), S. 559-574 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The geometric theory of the domain of an ordered pair (F, G) of matrices or the geometry associated with matrix pencils provides a unifying framework for the study of algebraic, dynamic and feedback properties of linear singular systems. The key concepts and tools of the geometry are the notions of the (F, G)-, (G, F)-invariance and a set of subspace sequences. In this paper, an alternative characterization of these sequences is given based on the properties of the partitioned null spaces of appropriate sequences of Toeplitz matrices defined by the (F, G) pair. The results provide a simple procedure for the computation of the limit spaces of these sequences and clearly cover corresponding problems of the singular, implicit systems theory.
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    Active noise compression systems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 667-682 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a new concept of narrowband and broadband active noise compression (ANCom) systems which improves the conventional active noise equalization (ANE) technique to meet some practical requirements. By using a variable equalization coefficient, the narrowband ANCom system can automatically switch among the four different operating modes of narrowband ANE, according to the primary noise power. As a result, it can “compress” the narrowband noise into a desired power range when the primary noise power varies drastically. Compared to a conventional broadband ANE system, the novel broadband ANCom system not only has the ability to shape the residual noise power spectrum, but can also compress the residual noise power into a predetermined dynamic range as the narrowband AN-Com does. Theoretical analyses are conducted for both the narrowband ANCom and broadband ANCom systems. Simulation results show that the proposed algorithms work well in both static and dynamic situations.
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    A note on representation theorems for linear discrete-space systems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 703-708 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The cornerstone of the theory of discrete-space single-input single-output linear systems is the idea that every such system has an input-output mapH that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight, which, for the case of bounded inputs mapped continuously into bounded outputs, was recently corrected by adding an additional term to the representation. Here we give a more general result that addresses an important larger family of inputs.
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    Robust stabilization of singular systems withH ∞-bounded uncertainty (1998)
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    Circuits, systems and signal processing 17 (1998), S. 737-755 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper the problem of robust stabilizing a linear, time-invariant singular system is studied. The characterization is given in terms ofH ∞-bounded perturbations to the numerator and denominator factors of its normalized left coprime factorization. An optimal stability margin is provided in terms of the definition of the Hankel norm of a singular system. The Hankel norm is computed using two generalized Lyapunov equations.
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    Design of sharp linear-phase FIR bandstop filters using the frequency-response-masking technique (1998)
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    Circuits, systems and signal processing 17 (1998), S. 1-27 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A novel computationally efficient realization of sharp linear-phase finite impulse response (FIR) bandstop filters is proposed. The synthesis scheme for the bandstop filters is derived from variations of the frequency-response-masking technique. Five realization structures are presented in this paper for the synthesis of five different classes of bandstop filters. Approximate expressions for the optimal value of the impulse response up-sampling ratio (M) and the corresponding number of multipliers are derived.
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    Capon estimation of covariance sequences (1998)
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    Circuits, systems and signal processing 17 (1998), S. 29-49 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Estimating the covariance sequence of a wide-sense stationary process is of fundamental importance in digital signal processing (DSP). A new method, which makes use of Fourier inversion of the Capon spectral estimates and is referred to as theCapon method, is presented in this paper. It is shown that the Capon power spectral density (PSD) estimator yields an equivalent autoregressive (AR) or autoregressive moving-average (ARMA) process; hence, theexact covariance sequence corresponsing to the Capon spectrum can be computed in a rather convenient way. Also, without much accuracy loss, the computation can be significantly reduced via an approximate Capon method that utilizes the fast Fourier transform (FFT). Using a variety of ARMA signals, we show that Capon covariance estimates are generally better than standard sample covariance estimates and can be used to improve performances in DSP applications that are critically dependent on the accuracy of the covariance sequence estimates.
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    Signal processing based on parameter structural modeling and separation of highly correlated signals of known structure (1998)
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    Circuits, systems and signal processing 17 (1998), S. 51-68 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Results in the study of signal processing based on the use of parameter structural modeling (PSM) are presented. First, we introduce a special form of time-series modeling based on signal-dependent building blocks. Such modeling is used in the design of a nestedform transversal structure, known as a composite filter, based on a shift-invariant finite impulse resonse (FIR) as well as infinite impulse response (IIR) building blocks. The newly proposed composite PSM model (CPSM) possesses a unique feature, namely, its ability to suppress one signal of a given structure, while at the same time being ideally transparent to another one. The intrinsic property of this proposed CPSM is its enhanced insensitivity with respect to noise as well as its ability to fast track, in contrast to the commonly used linear line-enhancer based on conventional autoregressive moving average (ARMA), thus leading to a more practically sound processing of short-duration signals. It is shown that the proposed time-series modeling based on CPSM can be effectively applied towards the separation of superimposed signals of heavily overlapping spectra. Next, the parameter-invariant nonlinear structural signal representation based on shift-invariant CPSM is presented. The use of this model in the design of annihilation operators (AO) is described, and composite parameter-free structural modeling (CPFSM) is developed. Based on this model, two canonical forms of the parameter-invariant null filters (PINF) are presented, and their use in the suppression of a given class of signals, independently of the values of theira priori unknown parameters, is illustrated. The paper also presents some simulation examples illustrating the application of the proposed CPSM and CPFSM in solving problems of detection and parameter estimation in the presence of highly non-Gaussian, mainly signal-like interferences.
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    Nonlinear digital filters mimicking cellular neural networks (1998)
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    Circuits, systems and signal processing 17 (1998), S. 69-83 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This work is motivated by the need forFaithful digital simulation of cellular neural networks (CNNs) that maintains most of their qualitative properties of stability and convergence. An interconnection of nonlinear digital filters mimicking behaviors of the analog CNNs is proposed, and the main properties are studied in detail. The discrete model obtained is proven to have the same convergence properties as the original analog network. The key to this development is the use of anAppropriate discretization scheme. Our discrete approximation to the nonlinear state-space representation of cellular neural networks is such that the Lyapunov function used to show convergence in analog cellular neural networks is still a Lyapunov function (when appropriately discretized) for our nonlinear digital filter network. This is in contrast to other digital simulations of CNNs, which have not been proven to preserve the convergence properties. The network of nonlinear digital filters so introduced thus adds another item to the catalog of digital filters obtained viaappropriate discretization of analog circuits, e.g., wave digital filters, orthogonal filters, and certain other of their more recently studied nonlinear counterparts.
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    Direct multiple-channel blind equalization (1998)
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    Circuits, systems and signal processing 17 (1998), S. 117-122 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, the problem of blind channel identification and equalization is reviewed, and some recent results are presented.
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    URL: http://dx.doi.org/10.1007/BF01213973
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    Halfband filters and Hilbert transformers (1998)
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    Circuits, systems and signal processing 17 (1998), S. 137-164 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents in summarizing form a description of halfband filters and the related symmetrical Hilbert transformers. It starts with the two complemetary relations by which halfband filters are defined and the consequences for their impulse responses. The idealized versions of the frequency responses of halfband lowpasses and Hilbert transformers are introduced, and the related tolerance schemes that realized systems must satisfy are described. Using their frequency responses, the transformation of one filter type into the other is presented in general form. The design of finite impulse response (FIR)-halfband filters and their relation to corresponding Hilbert transformers are recalled, using maximally flat and Chebyshev approximations as examples. It is shown that the relation between both types of systems can be used for the infinite impulse response (IIR) case as well. The design of IIR-halfband filters is presented for systems with approximately linear phase and for those with minimum phase again for maximally flat and Chebyshev approximations. The design methods are partly new. The general procedure for the transformation into Hilbert transformers yields noncausal solutions, one of which is already known from the literature. By modifying this operation, phase-splitting systems are obtained, one of them related to corresponding continuous ones, discussed in papers published around 1950. Another system with approximately linear phase corresponds to a paper presented in 1987. Finally, the coupled form of these phase splitting allpasses is found to be a Hilbert transformer with precise phase difference, but with deviations of the magnitudes of the frequency responses.
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    URL: http://dx.doi.org/10.1007/BF01202851
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    Computationally efficient, robust algorithm for matched field processing (1998)
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    Circuits, systems and signal processing 17 (1998), S. 165-193 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The matched field processing (MFP) localization performance of very low frequency (VLF) arrays operated in the deep ocean basins appears to be limited more by uncertainty in the sound velocity profile (SVP) than by low signal-to-noise ratio (SNR). We present a new robust variation of MFP designed to be less sensitive to velocity error in weakly inhomogeneous environments. We analyze the computational requirements of this and other MFP algorithms. When either the search volume is large of the acoustic array is large, computational efficiency is an issue. We present an efficient MFP implementation for the conventional MFP algorithm and our robust algorithm. We show that parallel implementation of these algorithms may allow real-time performance.
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    URL: http://dx.doi.org/10.1007/BF01202852
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    Global asymptotic stability of a class of feedback neural networks with an application to optimization problems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 219-241 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract By applying results from homotopy theory, new conditions are obtained for the existence and uniqueness of an equilibrium for a class of continuous-time feedback neural networks which contains the Hopfield model as a special case. Next, new criteria are established for the global asymptotic stability of the unique equilibrium of this class of neural networks by utilizing Lur'e-type Lyapunov functions and the stability theory for systems of differential inequalities. Several practical stability testing conditions are given. As a special case, criteria are derived for the global asymptotic stability of Hopfield neural networks. This is followed by a robustness analysis of the class of neural networks considered. The results obtained are then applied to an optimization problem.
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    URL: http://dx.doi.org/10.1007/BF01202854
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    Optimal interpolating and smoothing functional artificial neural networks (FANNs) based on a generalized fock space framework (1998)
    Springer
    Circuits, systems and signal processing 17 (1998), S. 271-287 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Functional artificial neural networks (FANNs) are artificial neural networks (ANNs) in which the synaptic weights are “functions” rather than numbers. Thus the signals in such networks are analog, and the action of a synapse on a signal passing through it takes place in the form of a scalar product inL 2 between the functional weight and the signal. In this paper, four classes of FANNs are introduced. They result from the solution of a nonparametric optimization problem in a generalized Fock space (GFS) of abstract Volterra series under interpolating or smoothing input-output training data constraints. Two of these classes of FANNs correspond to the interpolating case and are represented by what we call the (two-layer)optimal interpolating (OI) FANN and theoptimal multilayer neural interpolating (OMNI) FANN. The remaining two classes correspond to the smoothing case. We name their representations as the (two-layer)optimal smoothing (OS) FANN and theoptimal smoothing multilayer artificial neural (OSMAN) FANN. In addition to providing the background and the derivation of these FANNs, this paper presents a novel approach to their implementation. This approach does away with the computationally cumbersome use of functional weights. Instead, the effect of these weights is provided by linear time-invariant differential equation models of which those weights are impulse responses. These are implemented by a linear filter bank. This approach thus leads to simple and meaningful causal realizations of FANNs which we call Dynamical FANNs or simply D-FANNs.
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    URL: http://dx.doi.org/10.1007/BF01202856
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    Are analog neural networks better than binary neural networks? (1998)
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    Circuits, systems and signal processing 17 (1998), S. 243-270 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, we study the problem of maximizing an objective function over the discrete set {−1, 1} n using a neural network. It is now known that a binary (two-state) Hopfield network can take, in the worst case, an exponential number of time steps to find even a local maximum of the objective function. In this paper, we carry this argument further by studying theradius of attraction of the global maxima of the objective function. If a binary neural network is used, in general there is no guarantee that a global maximum has a nonzero radius of attraction. In other words, even if the optimization process is started off with the neural network in an initial state that isadjacent to the global maximum, the resulting trajectory of the network may not converge to the nearby maximum, but may instead go off to another maximum. At the same time, another set of recent results shows that, if ananalog neural network is used to optimize the same objective function, thenevery local maximum of the objective function has a nontrivial domain of attraction, and conversely, the only equilibria that are attractive are the local maxima of the objective function. This raises the question as to whether analog neural networks offer some advantages over binary neural networks for optimizing the same objective function. As a motivation for this line of inquiry, we study the problem of decoding an algebraic block code using a neural network. It is shown that the binary neural network implementation has the undesirable property thatall the global maxima of the objective function have azero radius of attraction. In contrast, if an analog neural network is used to maximize exactly the same objective function, the region of attraction of each maximum contains not only the associated “orthant” of the state space, but also some points not in this orthant. In other words, the analog implementation exhibits the desired tolerance to transmission errors, whereas the binary neural network does not have this property. With this motivation, two open questions are posed that provide a program of research for studying the possible superiority of analog neural networks over binary neural networks.
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    URL: http://dx.doi.org/10.1007/BF01202855
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    Average power analysis of sequential circuits using an autoregressive model (1998)
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    Circuits, systems and signal processing 17 (1998), 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 We present a new statistical technique for average power estimation in sequential circuits. Because of the feedback loops, power dissipations of sequential circuits in consecutive clock cycles are temporally correlated. The existence of data correlation makes it unsuitable to apply conventional techniques to average power inference, because the sample variance is no longer a maximum likelihood estimator. The convergence criterion derived from the biased variance estimation will be overly optimistic, causing power simulation to stop prematurely at a lower-than-specified estimation accuracy. To overcome this problem, we propose a systematic approach for modeling the power dissipation behavior of sequential circuits as an autoregressive random process. An accurate process variance can be obtained by the model parameters, which enables the derivation of a robust confidence interval of the average power. The interval is checked for convergence against a user-specified accuracy criterion. An iterative procedure is developed to invoke these steps repeatedly until the convergence specification is met. For a set of benchmark sequential circuits, this technique yields high accuracy and efficiency.
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    URL: http://dx.doi.org/10.1007/BF01202857
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    An algebraic technique for designing active filters in the frequency domain for control and signal processing (1998)
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    Circuits, systems and signal processing 17 (1998), S. 391-400 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a straightforward algebraic method for designing feedback loops in the frequency domain. The emphasis here is on control system design, but the technique is applicable to active filter design as well. The object is to produce a practical analog filter with a minimum of design effort. The algebraic solution to the design problem is presented, and several examples are explored.
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    URL: http://dx.doi.org/10.1007/BF01202299
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    Parameter estimation using RELAX with a COLD array (1998)
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    Circuits, systems and signal processing 17 (1998), S. 471-481 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This correspondence presents a RELAX (RELAXation-based) algorithm for angle, polarization, and waveform estimation of completely polarized narrowband electromagnetic plane waves arriving at a uniform linear co-centered orthogonal loop and dipole (COLD) array. We use numerical examples to demonstrate the performance of the RELAX algorithm for parameter estimation with the COLD array and compare it with the performance of the MODE (Method of Direction Estimation) algorithm. We show that this RELAX algorithm can outperform MODE and yet be computationally faster than MODE.
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    URL: http://dx.doi.org/10.1007/BF01201503
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    Coordinate logic filters and their applications in image processing and pattern recognition (1998)
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    Circuits, systems and signal processing 17 (1998), S. 517-538 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we present a number of image processing applications using coordinate logic filters, which execute coordinate logic operations among the pixels of the image. These filters are very efficient in various 1D, 2D, or higher-dimensional digital signal processing applications, such as noise removal, magnification, opening, closing, skeletonization, and coding, as well as in edge detection, feature extraction, and fractal modeling. In this paper we present some typical image processing applications using coordinate logic filters. The key issue in the coordinate logic analysis of images is the method of fast successive filtering and managing of the residues. The desired processing is achieved by executing only direct logic operations among the pixels of the given image. Coordinate logic filters can be easily and quickly implemented using logic circuits or cellular automata; this is their primary advantage.
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    URL: http://dx.doi.org/10.1007/BF01201506
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    Discretization of cascaded continuous-time controllers and uncertain systems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 591-611 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a new method for the digital modeling of a continuous-time uncertain system and a new method for the digital redesign of a sampled-data uncertain system. The system matrices characterizing the state-space representation of the original uncertain system are assumed to be interval matrices. The Chebyshev quadrature formula together with the interval arithmetic are used for the digital interval modeling, and a dual concept of digital interval modeling is utilized to discretize a predesigned cascaded analog controller for robust digital control of a continuous-time uncertain system. Using the newly developed digital interval models and digitally redesigned controllers, the resulting dynamic states of the digitally controlled sampled-data uncertain systemsare able to closely match those of the originally analogously controlled continuous-time uncertain systems for a relatively longer sampling period.
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    URL: http://dx.doi.org/10.1007/BF01203107
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    Eyes Closed: Simple, Intuitive, Statistically Sound, and Efficient Methods for Estimating Parameters of Clonal Growth Cancer Models (1998)
    Springer
    Risk analysis 18 (1998), S. 529-534 
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    ISSN: 1539-6924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/B:RIAN.0000006255.30436.ff
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    A Risk Assessment for Consumers of Mourning Doves (1998)
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    Risk analysis 18 (1998), S. 563-573 
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    ISSN: 1539-6924
    Keywords: Risk assessment ; mourning doves ; hunting ; radionuclides ; heavy metals ; lead shot ; cesium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Recreational and subsistence hunters and anglers consume a wide range of species, including birds, mammals, fish and shellfish, some of which represent significant exposure pathways for environmental toxic agents. This study focuses on the Department of Energy's (DOE's) Savannah River Site (SRS), a former nuclear weapons production facility in South Carolina. The potential risk of contaminant intake from consuming mourning doves (Zenaida macroura), the most popular United States game bird, was examined under various risk scenarios. For all of these scenarios we used the mean tissue concentration of six metals (lead, mercury, cadmium, selenium, chromium, manganese) and radiocesium, in doves collected on and near SRS. We also estimated risk to a child consuming doves that had the maximum contaminant level. We used the cancer slope factor for radiocesium, the Environmental Protection Agencies Uptake/Biokinetic model for lead, and published reference doses for the other metals. As a result of our risk assessments we recommend management of water levels in contaminated reservoirs so that lake bed sediments are not exposed to use by gamebirds and other terrestrial wildlife. Particularly, measures should be taken to insure that the hunting public does not have access to such a site. Our data also indicate that doves on popular hunting areas are exposed to excess lead, suggesting that banning lead shot for doves, as has been done for waterfowl, is desirable.
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    URL: http://dx.doi.org/10.1023/B:RIAN.0000005931.39844.35
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    An Empirical Approach for Deriving Information on Total Duration of Exposure from Information on Historical Exposure (1998)
    Springer
    Risk analysis 18 (1998), S. 611-619 
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    ISSN: 1539-6924
    Keywords: Exposure duration ; survey data ; longevity bias ; angler populations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Exposure duration is an important component in determining long-term dose rates associated with exposure to environmental contaminants. Surveys of exposed populations collect information on individuals' past behaviors, including the durations of a behavior up to the time of the survey. This paper presents an empirical approach for determining the distribution of total durations that is consistent with the distribution past durations obtained from surveys. This approach is appropriate where the rates of beginning and ending a behavior are relatively constant over time. The approach allows the incorporation of information on the distribution of age in a population into the determination of the distribution of durations. The paper also explores the impact of “longevity” bias on survey data. A case study of the application of this approach to two angler populations is also provided. The results of the case study have characteristics similar to the results reported by Israeli and Nelson (Risk Anal. 12, 65–72 (1992)) from their analytical model of residential duration. Specifically, the average period of time for the total duration in the entire population is shorter than the average period of time reported for historical duration in the surveyed individuals.
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    URL: http://dx.doi.org/10.1023/B:RIAN.0000005935.81670.61
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    A Quantitative Test of the Cultural Theory of Risk Perceptions: Comparison with the Psychometric Paradigm (1998)
    Springer
    Risk analysis 18 (1998), S. 635-647 
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    ISSN: 1539-6924
    Keywords: Risk perceptions ; cultural theory ; psychometric paradigm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This paper seeks to compare two frameworks which have been proposed to explain risk perceptions, namely, cultural theory and the psychometric paradigm. A structured questionnaire which incorporated elements from both approaches was administered to 129 residents of Norwich, England. The qualitative risk characteristics generated by the psychometric paradigm explained a far greater proportion of the variance in risk perceptions than cultural biases, though it should be borne in mind that the qualitative characteristics refer directly to risks whereas cultural biases are much more distant variables. Correlations between cultural biases and risk perceptions were very low, but the key point was that each cultural bias was associated with concern about distinct types of risks and that the pattern of responses was compatible with that predicted by cultural theory. The cultural approach also provided indicators for underlying beliefs regarding trust and the environment; beliefs which were consistent within each world view but divergent between them. An important drawback, however, was that the psychometric questionnaire could only allocate 32% of the respondents unequivocally to one of the four cultural types. The rest of the sample expressed several cultural biases simultaneously, or none at all. Cultural biases are therefore probably best interpreted as four extreme world views, and a mixture of qualitative and quantitative research methodologies would generate better insights into who might defend these views in what circumstances, whether there are only four mutually exclusive world views or not, and how these views are related to patterns of social solidarity, and judgments on institutional trust.
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    URL: http://dx.doi.org/10.1023/B:RIAN.0000005937.60969.32
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    Etude des premiers etages sensoriels (1966)
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    Bulletin of mathematical biology 28 (1966), S. 1-10 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Résumé Les premiers étages sensoriels sont étudiés en utilisant notre modèle de neurone et en supposant que les réseaux responsables de la perception sont particulièrement solides, stables, économiques. Nous montrons que les premiers neurones doivent être spontanément périodiques et autorégulés. La nécessité fonctionnelle des premiers étages de la voie visuelle est démontrée. Par analogie, nous étudions la voie auditive.
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    URL: http://dx.doi.org/10.1007/BF02476387
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    The flow of a viscous liquid in a converging tube (1966)
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    Bulletin of mathematical biology 28 (1966), S. 11-24 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of the viscous flow of an incompressible Newtonian liquid in a converging tapered tube has been solved in spherical polar coordinates. The method of the solution involves the Stokes' stream function and a technique introduced by Stokes in the study of a sphere oscillating in a fluid. The theory for the flow in a rigid tube includes: (1) the pulsatile flow with both radial and angular velocity components; (2) the steady state flow with both radial and angular velocity components and (3) the very slow steady state flow with only a radial velocity component present. For a tapered elastic tube, the velocity of the propagated pulse wave is determined. The solution given is in terms of the elastic constants of the system and the coordinates for this type of geometry. The pulse velocity is then related to the velocity in an elastic cylindrical tube with the necessary correction terms to account for the tapered tube.
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    URL: http://dx.doi.org/10.1007/BF02476388
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    Some multi-dimensional branching processes as motivated by a class of problems in mathematical genetics I (1966)
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    Bulletin of mathematical biology 28 (1966), S. 25-50 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper a class of branching processes applicable to populations reproducing by some asexual means or by a simple selfing system of mating is studied. The paper is divided into three parts. In part one the mathematical model is introduced, part two is a mathematical analysis of the model, and in part three concrete applications and examples are given. Many of the proofs of the theorems in part two are omitted but will appear in a subsequent issue of theBulletin.
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    URL: http://dx.doi.org/10.1007/BF02476389
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