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  • Articles  (8,027)
  • Springer  (8,027)
  • 2020-2020
  • 1970-1974  (8,027)
  • 1945-1949
  • 1974  (4,080)
  • 1973  (3,947)
  • Mathematics  (7,727)
  • Nature of Science, Research, Systems of Higher Education, Museum Science  (300)
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  • Articles  (8,027)
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  • 2020-2020
  • 1970-1974  (8,027)
  • 1945-1949
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  • 1
    Electronic Resource
    Electronic Resource
    The structure of DNA as deduced from fiber X-ray crystallography (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 301-311 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract X-ray diffraction patterns obtained experimentally for fibers, together with their chemical structures, can be analyzed theoretically in terms of an integral equation. The partially unknown electron density function can be solved by iteration. This mathematical technique has been applied with success to study the secondary structures of DNA fibers.
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    URL: http://dx.doi.org/10.1007/BF02458338
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  • 2
    Electronic Resource
    Electronic Resource
    Information Processing in the Visual Systems of Arthropods (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 339-340 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461333
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  • 3
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    Optimality in the control of environmental systems (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 341-345 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract For an environmental system described by a system of nonlinear first-order differential equations, the problem of achieving specified terminal conditions in a given time with a minimum expenditure of resources is considered. The initial conditions and the minimum value are found numerically in a particular example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464612
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  • 4
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    Kinetic approach to neural systems: I (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 535-544 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A kinetic model of neural systems is introduced and discussed with statistical mechanics techniques. It is assumed that, for a macroscopic description of the model, it suffices to consider only the distribution for the velocity and position of the impulses, and the distribution for the excitation and position of the neurons, at any timet. Making use of Boltzmann's method for the study of a dilute gas, coupled differential equations for the rate of change with time of the distributions have been constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463265
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  • 5
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    Flow of a newtonian fluid through a permeable tube: The application to the proximal renal tubule (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 457-476 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Creeping flow of a Newtonian fluid through a rigid permeable tube is considered and the transmural seepage is assumed to obey Darcy's law. Closed-form solutions for the pressure and velocity fields are presented and equations describing the axial variation of the mean cross-sectional pressure, the axial volumetric flow and the transmural fluid flux are derived. Approximate solutions for small seepage rates are given and are applied to the flow in the proximal renal tubule. Probable values for the epithelium permeability and the intraluminal hydrostatic pressure drop are obtained.
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    URL: http://dx.doi.org/10.1007/BF02463260
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  • 6
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    Disseminated storage of information with sequential coding (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 663-688 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper demonstrates that it is possible to construct memory models where the information inserted is stored in disseminated form, using sequential coding, the changes in the units forming the models being determined by their geometrical connections and by the incoming stream of information. The models are shown to have large storage capacity and their efficiency can be made insensitive to loss of or damage to a large fraction of their units. The satisfactory verification by computer simulation of the analysis and results described in the present paper will be the subject of a future paper.
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    URL: http://dx.doi.org/10.1007/BF02458369
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  • 7
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    On knowledge and unpleasantness (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 605-605 
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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/BF02463273
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  • 8
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    The Kerner linearization method (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 67-76 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We examine in detail Edward Kerner’s method for linearizing the equations of enzyme kinetics. Our main result is the determination of canonical forms for systems which can be linearized by the method. This is done both in general and in the special cases of two and three dimensions where complete results are obtained. The practical problem of identifying linearizable systems is also considered and computable necessary criteria are presented.
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    URL: http://dx.doi.org/10.1007/BF02461192
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  • 9
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    Continuous determination of the volume of a space in a non steady state condition (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 59-66 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A general method for determination of the volume of a space in a non steady state condition, in case diffusion might be significant, is developed. Instantaneous mixing of indicators with native fluid is assumed in this first stage of investigation. Theoretical expressions are obtained for the volume of the space and the diffusion coefficient as a function of time. An analysis of feasibility of the method is also included.
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    URL: http://dx.doi.org/10.1007/BF02461191
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  • 10
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    Passive transfer of low-molecular nonelectrolytes across deformable semi-permeable membranes—II: Dynamics of a single muscle fiber swelling and shrinking and related changes of theT-system tubule form (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 379-401 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The theory of transfer of low-molecular nonelectrolytes across deformable semipermeable membranes of large curvature developed in Part I (Rubinstein, 1974) is used to describe the dynamics of swelling and shrinking of a muscle fiber at the influx and efflux of low-molecular nonelectrolytes. A large set of computations showed that the theory explains the experiments described in the literature.
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    URL: http://dx.doi.org/10.1007/BF02464616
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  • 11
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    Heat transfer in perfused biological tissue—I: General theory (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 403-415 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Green's function for heat and matter transport is calculated for an infinite medium in which a convection field v(r,t) makes a contribution to the total heat and matter current. It is given by a uniformly and absolutely convergent series in which every term is calculated from the preceding one merely by integration. The solution procedure is interpreted physically and illustrated by a simple problem in which v(r,t)=const. in space and time. Since the solution contains no intrinsic spatial symmetry, it can serve as a starting point for a theory of heat and mass transport in perfused biological tissue.
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    URL: http://dx.doi.org/10.1007/BF02464617
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  • 12
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    A long wavelength solution for a microorganism swimming in a channel (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 435-444 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The hydrodynamics of a microorganism swimming in a channel is investigated. The microorganism is modeled as a two-dimensional sheet swimming at low Reynolds numbers between two rigid walls. The wavelengths of the propulsive waves passing down the sheet are assummed to be very large compared to the channel spacing, but the amplitude of the propulsive waves is arbitrary. Explicit analytical solutions for the propulsive velocity and the rate of energy dissipated in terms of the wave amplitude, channel spacing, wave number, and wave speeds are given.
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    URL: http://dx.doi.org/10.1007/BF02464619
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  • 13
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    Mathematical models of conception and birth (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 455-456 
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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/BF02464621
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  • 14
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    Why are there so many species? (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 477-488 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown from the statistical-mechanical overview of Volterra's ecological model how to reckon the fluctuations of collective variables such as the total population of a genus: and that these fluctuations are much decreased (or that the collective populationsteadiness is enhanced) as the speciation is increased. (A niching of species in time, or phase-niching, is entailed here.) Secondly, it is shown how Preston's log-normal distribution describing the species-abundance relationship, as well as a generalization of such distributions, come forth simply and naturally from the statistical-Volterra-dynamics.
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  • 15
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    A note on knowledge and unpleasantness (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 313-317 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Various philosophers have repeatedly denounced knowledge as a source of unpleasantness, thereby criticizing education. This paper presents a set theoretical approach to knowledge and education and tries to explain how they could lead occasionally to a feeling of unpleasantness.
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    URL: http://dx.doi.org/10.1007/BF02458339
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  • 16
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    An analysis of countercurrent exchange with emphasis on renal function (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 275-286 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An analysis of countercurrent exchange in a U-tube is presented for a single-solute, constant-volume flow rate system with spatially varying source fluxes and permeabilities. Analytical solutions are given for the steady-state equations and numerical solutions for the unsteady-state equations. The solutions indicate that an external source of solute delivered to the stream flowing away from the U-tube bend can be distributed by the exchanger so that the concentration in both limbs increases toward the bend. In particular, there exist source fluxes whose magnitude decreases monotonically toward the bend for which the maximum solute concentration occurs at the bend. The point at which a concentration maximum occurs is governed principally by the solute permeability of the barrier separating the two limbs and by the volume flow rate through the exchanger. The system dynamics depend strongly on the relative cross-sectional areas of the two limbs or, equivalently, on the flow velocities within them. The model is used as a basis for discussion of various functional aspects of the renal vasa recta system.
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    URL: http://dx.doi.org/10.1007/BF02458336
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  • 17
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    Mathematical analysis of circulatory mixing process (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 287-300 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The circulatory mixing process was analyzed as the time course of the dispersion of indicator after its injection into the heart. In simplified models, which had one or two lumped mixing chambers and circulatory pathways connected with them, it was suggested that the extent of dispersion could be evaluated by the variance of indicator distribution in the total circulating blood when the circulation time distributions between the chambers and the concentration curves in the chambers were known. The method of determining the circulation time distributions through the pulmonary, systemic and total circulations was derived and the actual distributions were obtained in dogs by indicator dilution techniques. With the use of these distributions, the time course of the circulatory mixing process was numerically calculated. The results showed that there was considerable difference in velocities of the process between the case of the right heart injection and the left heart injection of the indicator.
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  • 18
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    Reactions chimiques couplees considerees en tant que filtres passe-bande (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 319-337 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An investigation is made as to whether or not the existence of a band-pass filter function, analogous to that in electronics, can be proved from the fundamental laws of chemical kinetics. The problem is important for better understanding of the preference of certain biological rhythms to others. It is shown with simple examples that such behavior is possible for a number of systems of coupled chemical reactions far enough from the thermodynamic equilibrium. It is of interest to generalize this behavior since it could conceivably play a role in the transmission of “usable information” in biology.
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    URL: http://dx.doi.org/10.1007/BF02458340
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  • 19
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    Organismic sets. Scientific creativity, its spread and applications (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 339-344 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The phenomenon of mental creativity is considered from the standpoint of the theory of organismic sets, developed by the author in a series of previous publications. It is shown how the differences in creativity between different individuals may be interpreted on this basis, and why extreme creativity is rare. A parallel interpretation for facility in observation is given, and it is shown why facility in creativity and observation is much rarer than either individual facility. A further conclusion is drawn regarding the deducibility of the laws of nature by purely logical means.
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    URL: http://dx.doi.org/10.1007/BF02458341
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  • 20
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    Quantum theory of time-varying stimulation in nerve (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 359-374 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The equation for the quantum transitions (spontaneous and stimulated) of membrane dipoles is solved for the various forms of time-varying stimulation in nerve. From the condition of ever-increasing dipole population in the upper state, the threshold for excitation is determined in each case. The results obtained are in agreement with the established facts. The optimum frequency for stimulation is given asv 0=0.0615/T 2 whereT 2 is the dipole relaxation time. The feature of the theory is that the mathematical formulation is based upon a physical mechanism and the results can thus provide some understanding in the observed phenomena.
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    URL: http://dx.doi.org/10.1007/BF02458343
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  • 21
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    On gompertz curves (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 415-415 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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  • 22
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    Reorientation of membrane dipoles during nerve excitation (1973)
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    Bulletin of mathematical biology 35 (1973), S. 417-418 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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  • 23
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    Announcement (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 419-419 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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  • 24
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    Interfilament forces in striated muscle (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 565-575 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Evaluation of the Van der Waals energy per filament suggests that molecular dispersion forces should not be very important in determining the stability of the myofilament lattice in resting muscle. In order to explain the lattice stability and other important properties of the striated muscle, it is suggested that a balance between electrostatic forces and forces developed by some interfibrillar structures is mainly responsible.
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  • 25
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    A method for simultaneous determination of (I) the blood flows to the organs and (II) the cardiac output (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 549-563 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method is presented for the simultaneous determination of (i) the blood flow to the organs and (ii) the cardiac output. Part I of the paper deals with the analysis of ann compartment (organ) vascular system model. The data, employed in the analysis, consists of continuous monitoring of the amounts of indicatorM i in the organs (or compartments). An analysis for determination of the cardiac output and the absolute flows to the organs is presented. Since it is difficult to isolate certain organ systems and measure the amounts of indicator in them exclusively, a more realistic model of then compartment vascular system is presented in Part II. Herein, the analysis has accounted for the finite transit time, of the indicator, from one organ system to another. Further, estimation theory is employed to make estimates of blood flow to different organs by taking note of (i) the measurement errors due to the detectors' monitoring (for an organ system) some combination ofM i 's instead of theM i for the particulari th organ and (ii) noise uncertainties introduced by the measuring instruments.
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  • 26
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    Particle distribution for dilute suspension in flow (1973)
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    Bulletin of mathematical biology 35 (1973), S. 577-589 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Analytic expressions for the velocity profile and particle distribution of a dilute suspension in flow were obtained as functions of radial distance. Einstein's linear viscosity model and the hypothesis of “minimum energy dissipation” were used. The methods of variational calculus were applied during the mathematical development. A parabolic velocity profile, which is a modified form of that for Hagen-Poiseuille flow, and a uniform particle distribution were obtained. An attempt is made to explain the results in light of some of the widely held theories on suspension flow and the rather severe limitations of Einstein's viscosity model. A suggestion for future work is made for improving the results of the present.
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  • 27
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    A semiclassical theory for nerve excitation by a low intensity electromagnetic field (1973)
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    Bulletin of mathematical biology 35 (1973), S. 591-605 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A possible mechanism for microwave-neuron interaction, when the nerve is irradiated by a thermally insignificant electromagnetic field, is described. The radiation field is treated classically, but the atomic system which interacts with this field is treated quantum mechanically using the density matrix approach. Attention is given to both homogeneous and inhomogeneous broadening effects, and the degrading influence of inhomogeneous broadening upon the neural membrane's ability to interact with the electromagnetic field is shown.
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  • 28
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    The epileptic neuron: I (1973)
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    Bulletin of mathematical biology 35 (1973), S. 709-714 
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    Topics: Biology , Mathematics
    Notes: Abstract Mathematical models of neurons are studied which exhibit spontaneous and repetitive firings in the absence of normally occurring substances. The activity of such neurons could result in the symptoms of epilepsy. The identification of such substances would be important in the treatment of the disease as well as in the understanding of their mode of action. The importance of the geometrical and physical parameters for the generation of spontaneous repetitive discharges is brought out.
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  • 29
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    The epileptic neuron: II (1974)
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    Bulletin of mathematical biology 36 (1974), S. 1-16 
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    ISSN: 1522-9602
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    Notes: Abstract Conditions under which a neuron can maintain repetitive discharges are studied with the view that some light may be shed on the problem of epilepsy. It is shown that if there are excitatory and inhibitory substances as well as binding substances in volved, then for repetitive discharges to occur, the formation of the substances must be intracellular. The geometric physical characteristics of the system are also determining factors. The role of a fatigue factor is considered in an attempt to understand the frequency and duration of mild and severe epileptic attacks.
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  • 30
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    On the number of phenotype structures in genetic systems (1974)
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    Bulletin of mathematical biology 36 (1974), S. 325-338 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Phenotype structures in genetic systems are carefully defined in an abstract setting so that a considerable amount of enumerative theory can be brought to bear on the problem of enumerating them. Recent results can be used to simplify the computations, and a natural correspondence is suggested which changes the problem of finding the number of phenotype structures to the problem of determining the numbers of certain graphs with colored points.
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  • 31
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    The interaction of diffusion and perfusion in homogeneous tissue (1974)
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    Bulletin of mathematical biology 36 (1974), S. 505-526 
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    Notes: Abstract A mathematical model is proposed to examine the interaction between blood perfusion and gas diffusion in the uptake of inert gases in tissue. The standard Haldane perfusion model is contrasted with the Hills radial bulk diffusion model in a variety of homogeneous tissue types used in decompression theory. It is the intention of the present analysis to fix ideas on the role of diffusion, perfusion and axial concentration and quantitative studies are given and seem to show that Haldane's perfusion theory is at best a poor approximation even at asymptotic times. It is shown that a strong interaction exists between diffusion and perfusion in muscle tissue and neither approach adequately describes the actual uptake half-time of an inert gas.
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  • 32
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    Necessary and sufficient condition for a model insect population to go to extinction (1974)
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    Bulletin of mathematical biology 36 (1974), S. 527-533 
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    Notes: Abstract A necessary and sufficient condition on the parameters for a model population to become extinct is presented. The mathematical model describes an insect population with overlapping generations where the females are polyandrous and the males are subject to autosterilization. The relationship between the values of the parameters of the model and the time to extinction is illustrated.
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  • 33
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    D'Arcy Thompson's theorems and the shape of the molluscan shell (1974)
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    Bulletin of mathematical biology 36 (1974), S. 567-575 
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    Notes: Abstract The paper deals with properties of mathematical models of biological systems. It is shown that under suitable conditions the number of parameters employed in the model depends only on the biological system and not on the particular model chosen. As an application the mathematical description of the formation of molluscan shells is discussed.
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    Molecular control systems: I—Temporal organization in cells revisited (1974)
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    Bulletin of mathematical biology 36 (1974), S. 595-599 
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    Notes: Abstract An analysis of Goodwin's fundamental nonlinear oscillator in the light of the requirement that concentrations must be intrinsically non-negative reveals that most of the phase plane is “forbidden”, and that there is one distinguished closed curve that has some of the properties of a limit cycle.
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    Note on oscillations of turbidity in a precipitation reaction system of thyroxine (1974)
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    Bulletin of mathematical biology 36 (1974), S. 601-604 
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    Notes: Abstract A model for a precipitation reaction system is presented in which all steps are reversible monomolecular or bimolecular reactions. Under certain conditions, quasi-stable oscillations in turbidity can occur, as has been observed in the precipitation of thyroxine.
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    Stabilité structurelle et morphogénèse (1974)
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    Bulletin of mathematical biology 36 (1974), S. 611-613 
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    Stochastic processes and applications in biology and medicine. Part 1—Theory. Part 2—Models (1974)
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    Bulletin of mathematical biology 36 (1974), S. 607-610 
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    A note on open linear systems (1974)
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    Bulletin of mathematical biology 36 (1974), S. 97-99 
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    Notes: Abstract A theorem is given which states a necessary and sufficient condition for the specific activity to be uniform throughout an open compartmental system in the steady state.
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    Introduction to Mathematics for Life Scientists (1974)
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    Bulletin of mathematical biology 36 (1974), S. 101-102 
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    A dynamic model of an environmental system withn interacting components andp degrees of freedom (1974)
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    Bulletin of mathematical biology 36 (1974), S. 91-96 
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    Notes: Abstract The nonlinear differential equations of growth proposed by Volterra (1931) are used as the basis for a dynamic model of ann-element system withp specified, terminal conditions andp missing initial conditions. The resulting two-point boundary-value problem can be solved, ifp is not large, by the shooting method used previously by Huddleston (1967). A numerical example withn=4 andp=2 is solved on a digital computer, and some results are presented.
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    Use of a heat transfer analogy for a mathematical model of respiratory tract deposition (1974)
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    Bulletin of mathematical biology 36 (1974), S. 105-116 
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    Notes: Abstract Mathematical models predicting the aerosol deposition in the respiratory tract are reviewed. Data in the literature indicated not only that the air flow in the trachea and major bronchi may not be laminar, but also that the entrance effect of the tube or airway has not been considered. A new approach to a mathematical model of respiratory tract deposition, based on the analogy of the heat and mass transfer, is discussed.
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    Isotherms forr species adsorbed at linear polymers with nearest neighbor cooperative interaction (1974)
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    Bulletin of mathematical biology 36 (1974), S. 117-126 
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    Notes: Abstract The equation of the cooperative specific isotherm is derived for the general case ofr species interacting cooperatively at nearest neighboring sites. Explicit expressions for the special casesr=2–5 are given.
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    Pseudo-sound generation at atherosclerotic constrictions in arteries (1974)
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    Bulletin of mathematical biology 36 (1974), S. 143-155 
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    Notes: Abstract Sounds and murmurs have long been employed to qualitatively diagnose cardiovascular disease. However, quantitative diagnosis has been hindered by the lack of understanding of the sound generation and transmission mechanisms. Clinical phonoangiographic studies have shown that simple assumptions about low frequency sound transmission through tissue surrounding an artery are inadequate for obtaining meaningful quantitative diagnosis. Therefore, a theory is developed which relates internal turbulent flow in constricted peripheral arteries to the sound observed at the surface of the skin by means of assumptions of similarity and local axial homogeneity of the internal turbulence. It is found that the spectrum of pressure at the wall of the artery is related to the spectrum of the pressure at the surface of the skin by a filtering factor approximately proportional to ω-2. This arises not because of frequency dependent volumetric absorption in the surrounding medium, as with ultrasound, but because of the manner in which stochastic signals add when observed.
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    Measuring a mitotic oscillator: The ARC discontinuity (1974)
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    Bulletin of mathematical biology 36 (1974), S. 171-182 
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    Notes: Abstract Mitosis occurs synchronously in up to 108 nuclei in the syncytial plasmodium ofPhysarum polycephalum. Any two phases of the mitotic cycle may be mixed by fusing plasmodial pairs. A topological property of the synchronized phase of the fused pair as a function of parental phases, the arc discontinuity, characterizes the underlying oscillator, and indicates mitosis is controlled by a moderate relaxation oscillator which rotates more rapidly near its singularity than its limit cycle. A model oscillator is briefly described.
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    Genetic nets and dissipative structures: An algebraic approach (1974)
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    Bulletin of mathematical biology 36 (1974), S. 183-196 
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    Notes: Abstract Genetic nets represent an attempt to model genome structure. Depending on the interaction dynamics assumed, they can constitute highly non-linear chemical systems having multiple steady states; hence their relevance to the theory of dissipative structures. Their typical size and possible complexity makes it difficult to study them by means of customary analytical techniques based on differential equations. We have therefore considered an algebraic approach derived from regarding the nets as finite-state automata. This view has revealed a surprisingly rich algebraic structure which can be used to investigate problems concerned with the relation between biological structure and function. This algebraic structure is described with particular reference to the genetic nets of Tsanev and Sendov.
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    Finite fluctuations and multiple steady states far from equilibrium (1974)
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    Bulletin of mathematical biology 36 (1974), S. 205-213 
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    Notes: Abstract The role of finite fluctuations in transitions between nonequilibrium steady states in nonlinear systems is investigated. Attention is focused on a model biochemical system for which the usual deterministic chemical kinetics predicts a far-from-equilibrium region of multiple steady states. A stochastic approach to chemical kinetics is adopted to study explicitly the effect of fluctuations around the coexisting stable states on a predicted hysteresis in the transition between those states. A numerical solution of the stochastic master equation for the system yields results which differ qualitatively from predictions of the purely macroscopic theory. Possible implications of these results are considered, and several important aspects of the computational scheme are discussed in some detail.
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    The global asymptotic stability of prey-predator systems with second-order dissipation (1974)
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    Bulletin of mathematical biology 36 (1974), S. 215-217 
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    Notes: Abstract Models of biological development, evolution and control should take into account that very small numbers of cells or chemicals or individuals eventually grow into stable, large populations. The simplified two-component model used in these studies includes the following: (1) first-order decay; (2) first-order autocatalysis; (3) negative feedback; (4) positive feedback; (5) second-order decay; (6) second-order autocatalysis. A positive definite Lyapunov function is constructed and shown to have a negative definite total derivative. The stationary statex〉0,y〉0, therefore possesses global asymptotic stability. This means that sustained oscillations cannot occur. Another stationary state,x=y=0, is shown to be unstable. This means that infinitesimally small perturbations ofx=y=0 will result in evolution of the variables to the stable stationary state. This result contrasts with that obtained with the Lotka-Volterra model in that small perturbations ofx=y=0 for that model result in sustained, oscillating excursions; the smaller the initial perturbations, the larger these excursions will be. A simulation illustrates that stable populations of 1020 x's andy's can arise from a singlex andy.x grows more or less continuously, buty remains extremely small for 80 per cent of the time interval required for the variables to approach their stable populations.
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    Semiconductor theory of ion transport in thin lipid membranes: II. Surface recombination (1974)
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    Bulletin of mathematical biology 36 (1974), S. 247-264 
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    Notes: Abstract Following the theory of surface recombination in semiconductors, we have derived an expression for the rate of ion recombination at the membrane surface. The surface recombination rate is used in the boundary conditions of current flows at the interfaces. Expressions for the ion fluxes are then derived as functions of environmental variables and membrane parameters. Our analysis strongly suggests that the ion flow through a thin lipid membrane consists of two major components: the surface barrier jumping current and the surface recombination current that are controlled decisively by surface barrier height, surface trap density and surface recombination rates. These general formulations are useful not only for the calculation but also for the understanding of ion transport in thin lipid membranes under a variety of experimental conditions. The implications of this theory to biological membranes and its possible extensions are discussed.
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    Transport of O2 along a model pathway through the respiratory region of the lung (1974)
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    Bulletin of mathematical biology 36 (1974), S. 275-303 
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    Notes: Abstract A pathway through the system of branching in the respiratory region of the lung is modelled by a circular cylinder, closed at one end, with partitions which define the component respiratory units. In this model the transport of O2 during inspiration, generated by diffusion is compared with that produced by diffusion together with convection and the importance of convection in the respiratory region in promoting oxygen uptake at the alveolar wall is discussed. For this discussion it is only necessary to consider inspiration. The equations are solved numerically for flow rates of 10, 85 and 200 liters/min. O2 uptake at the wall and curves of constant O2 concentration are shown to illustrate the influence of convection. It is found that after a 2 sec inspiration from an O2 tension of 98 mm Hg and a lung volume of 2300 ml, convection is about 12 per cent as important as diffusion at a flow rate of 85 liters/min, whereas at 10 liters/min convection is only about 0.4 per cent as important as diffusion.
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    Theoretical relationship between the optimal models of the vascular tree (1974)
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    Bulletin of mathematical biology 36 (1974), S. 311-323 
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    Notes: Abstract Two models of optimal branching structure of the vascular tree are compared. Murray’s minimum work model derived from minimum energy loss due to flow and volume in the duct system is proved to be included as a mathematical group in the authors’ model defined by the minimum volume under determinant pressure, flow and position at the terminals. The problem about heterotypical trees which are identical at the terminal conditions but different in the topological order of branch combinations are discussed, applying the results of analyses on the equivalent duct of uniform terminal pressure trees. It is proved that the minimum work tree has the least energy loss compared with its heterotypical minimum volume trees and is a better model of branching structure of the vascular tree.
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    A morphogenetic system matched to a group (1973)
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    Bulletin of mathematical biology 35 (1973), S. 615-625 
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    Notes: Abstract A period of morphogenesis is operationally defined as a system. This period precedes cell differentiation and is axially expressed. Six interacting elements of structure are defined utilizing Spemann and Mangold's heteroplastic transplantation experiments. The system generates thirty-six interactions, given a rule of composition and specific premises. The element set and operation is matched to the symmetric group S3.
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    Asymptotic behavior in a deterministic epidemic model (1973)
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    Bulletin of mathematical biology 35 (1973), S. 607-614 
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    Notes: Abstract The effects of a periodic contact rate and of carriers are considered for a generalization of Bailey's simple epidemic model. In this model it is assumed that individuals become susceptible again as soon as they recover from the infection so that a fixed population can be divided into a class of infectives and a class of susceptibles which vary with time. If the contact rate is periodic, then the number of infectives as time approaches infinity either tends to zero or is asymptotically periodic depending on whether the total population size is less than or greater than a threshold value. The behavior for large time of the number of infectives is determined for three modifications of the model which involve carriers.
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    Electron-phonon (trapped photon) coupling and infrared coaxial transmission line theory of energy transport in mitochondria and nerve (1973)
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    Bulletin of mathematical biology 35 (1973), S. 627-644 
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    Notes: Abstract This paper develops quantitatively for the kinetics of mitochondrial oxidation the implications of the hypothesis that phosphorylation is accomplished by phonons in the mitochondrial solid. The concept is used that the phonon acts like a trapped photon to produce a reverse photocurrent, which inhibits oxidation, in the absence of phonon dissipation due to phosphorylation or uncoupling. The same conceft in reverse is shown to explain qualitatively the generation or membrane potentials in nerve axon. Infrared optical phonons generated in the above processes are expected to have limited mibility, but it is shown that the structure and geometry of the lipid bilayer membrane are well adapted to the rapid and efficient dissemination of this energy throughout the mitochondrion or nerve axoni n the form of infrared electromagnetic waves by a coaxial transmission line mechanism. The mitochondrion may act like an infrared coaxial resonant cavity.
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    Mathematical analysis of the asymptotic behavior of the Leslie population matrix model (1973)
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    Bulletin of mathematical biology 35 (1973), S. 645-661 
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    Notes: Abstract LetL be a Leslie population matrix. Leslie (1945) and others have shown that the matrixL has a leading positive eigenvalueλ 0 and that in general: (1) $$\mathop {\lim }\limits_{t \to \infty } \frac{{L^t X}}{{\lambda _0^t }} = \gamma X_{\lambda _0 } $$ whereX λ 0 is an eigenvector corresponding toλ 0,X is any initial population vector, and γ is a scalar quantity detormined byX. In this article we generalize (1) exhaustively by removing the mild restrictions on the fertility rates which most writers impose. The result is an oscillatory limit of a kind first noted by Bernardelli (1941) and Lewis (1942) and described by Bernardelli as “population waves”. We calculate in terms ofλ 0 and the entries of the matrixL the values of this oscillatory limit as well as its time-independent average over one period. This calculation includes as its leading special case the result of (1), confirming incidentally that γ is nonzero. To stabilize a population, the matrixL must be adjusted so thatλ 0=1. The limits calculated for the oscillatory and non-oscillatory cases then have maximum significance since they represent the limiting population vectors. We discuss a simple scheme for accomplishing stanbilization which yields as a byproduct an easily accessible scalar measure ofL's tendency to promote population growth. The reciprocal of this measure is the familiar net reproduction rate.
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    The Danziger-Elmergreen theory of periodic catatonic schizophrenia (1973)
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    Bulletin of mathematical biology 35 (1973), S. 689-707 
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    Notes: Abstract Properties of the solutions of the mathematical model introduced by Danziger and Elmergreen for the study of periodic catatonic schizophrenia are studied, and it is shown that the properties established suggest that the model can be used to study other forms of catatonic schizophrenia besides periodic catatonic schizophrenia.
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    On the stochastic theory of compartments: Solution forn-compartment systems with irreversible, time-dependent transition probabilities (1974)
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    Bulletin of mathematical biology 36 (1974), S. 489-504 
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    Notes: Abstract The bivariate distribution of a two-compartment stochastic system with irreversible, time-dependent transition probabilities is obtained for any point in time. The mean and variance of the number of particles in any compartment and the covariance between the number of particles in each of the two compartments are exhibited and compared to existing results. The two-compartment system is then generalized to ann-compartment catenary and to ann-compartment mammillary system. The multivariate distributions of these two systems are obtained under two sets of initial conditions: (1) the initial distribution is known; and (2) the number of particles in each compartment of the system at timet=0 is determined. The moments of these distributions are also produced and compared with existing results.
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    Dustbathing as a regulatory mechanism (1974)
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    Bulletin of mathematical biology 36 (1974), S. 545-553 
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    Notes: Abstract Three mathematical models were developed to describe how some species of birds, such as bobwhite quail (Colinus virginianus) regulate the amount of oil on their plumage. The models assume that dustbathing plays a significant role in this regulatory process. They differed primarily in their assumptions about the relationship between oiling and dustbathing behavior. Several experiments were run to check on the implications of the models.
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    Observations on the hydrodynamics and swimming motions of mammalian spermatozoa (1974)
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    Bulletin of mathematical biology 36 (1974), S. 555-565 
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    Notes: Abstract An asymptotic solution of the Stokes Flow equations for a self-propelling filament is presented. An explicit expression for the propulsive velocity is obtained for the case of an infinite filament undergoing small amplitude sinusoidal motions. The asymptotic solution is then used to obtain drag coefficients to be used in a simpler approximate analysis which can be applied to experimentally observed motions.
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    Stochastic theory of compartments: One and two compartment systems (1974)
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    Bulletin of mathematical biology 36 (1974), S. 577-587 
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    Notes: Abstract Previous work on compartmental systems is generalized (i) to allow the particles present at time zero to have a different lifetime distribution than those which arrive after time zero, and (ii) to allow a particle which enters the system at timet to have a lifetime distribution which is a function oft but is otherwise quite general. The one and two compartment models are analyzed under the above conditions and compared to previous results of Thakuret al. (1974), Purdue (1974) and Cardenas and Matis (1974). Finally, some results for the two compartment, reversible system are given. The analysis used is a blend of direct random variable and queueing theoretic techniques.
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    Bounds on the total particle number for species governed by reaction-diffusion equations in the infinite spatial domain (1974)
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    Bulletin of mathematical biology 36 (1974), S. 589-593 
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    Notes: Abstract Differential inequality methods are developed for establishing upper and lower bounds on the total particle numberN(t)=∫θ(x,t) d3 x associated with solutions to nonlinear reaction-diffusion equations of the form ∂θ/∂t=D∇2θ+fθ-gθ n+1 , whereD(〉0),n(〉0),f andg are constant parameters. If finite in a neighborhood oft=0,N(t) is bounded below for allt≥0 by a certain derived function oft for equations withg≥0. An upper bound onN(t) is obtained for equations withn=1,f〈0 andg〈0. These results provide general preservation and extinction criteria for the total particle number.
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    A neuron field theory: Mathematical approaches to the problem of large numbers of interacting nerve cells (1973)
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    Bulletin of mathematical biology 35 (1973), S. 345-357 
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    Notes: Abstract A field theoretical approach to the problem of continuously distributed and simultaneously active nerve cells is presented, starting with a differential-integral field equation of the form $$\frac{\partial }{{\partial t}}\psi (r,t) = H\psi (r,t) + F(r,t)$$ which relates the field ψ to its inhibitory and excitatory sourcesF by means of the field operatorH. General solutions are represented with the aid of Green's functions. The Green's function, giving the response of the system to a very short point stimulation, is calculated in the absence of interaction between neurons and for a special case of non-local interaction. Possible applications of the theory are demonstrated for receptive fields and neuronal mechanisms in the vertebrate retina.
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    Some proposals in cardiac muscle mechanics and energetics (1973)
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    Bulletin of mathematical biology 35 (1973), S. 375-399 
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    Notes: Abstract Based on A. V. Hill's three-component model, mechanical properties of the contractile element (CE), such as velocity and tension, were determined as muscle shortening and loads in quick-release or afterloaded isotonic contraction. The method is applicable for studying cardiac mechanics, to obtain force-velocity data of the same CE length at varous afterloads. Analysis of the energetics of cardiac muscle was based on simulation studies of cardiac mechanics (Wong 1971, 1972). By proper derivation, the conventional contractile element work (CEW) was found to be a minor energy determinant. The tension-time integral and tension-independent heat (Ricchiuti and Gibbs, 1965) represent energy utilization for activation and maintenance of tension, the primary energy determinant.
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    The effect of the torso boundary in electrocardiography (1973)
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    Bulletin of mathematical biology 35 (1973), S. 401-405 
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    Notes: Abstract This paper outlines and contrasts three different (external) “infinite medium” potential fields which may be obtained (in principle) from known geometry, conductivities, and bounded medium torso potentials. Their electrocardiographic implications are considered.
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    An attitude to nucleic acid models (1973)
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    Bulletin of mathematical biology 35 (1973), S. 407-409 
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    Nucleic acid structure (1973)
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    Bulletin of mathematical biology 35 (1973), S. 411-413 
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    Passive transfer of low-molecular nonelectrolytes across deformable semipermeable membranes—I: Equations of convective-diffusion transfer of nonelectrolytes across deformable membranes of large curvature (1974)
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    Bulletin of mathematical biology 36 (1974), S. 365-377 
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    Notes: Abstract The passive transfer of a low-molecular nonelectrolytes mixture across a semipermeable deformable membrane of large curvature is considered. The equations obtained here make it possible to describe the concentration of species redistribution and the change of the membrane shape.
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    A new model for interacting populations—II: Principle of competitive exclusion (1974)
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    Bulletin of mathematical biology 36 (1974), S. 355-364 
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    Notes: Abstract The principle of competitive exclusion is investigated within the framework of the solvable model proposed earlier for two-species systems. The results elucidate the recent controversy over the interpretation of experimental data onDrosophila equilibrium. It is shown that the necessary and sufficient conditions for stable coexistence of competing species is that the product of intraspecific rate constants be greater than the product of interspecific rate constants. Inequalities between rate constants for the occurrence of stable equilibriumbelow andabove the line joining single species equilibria are derived. The availability of larger domain of coexistence suggests that the model presented here has the potential to accommodate a wider class of phenomena than the Gause—Volterra model according to which coexistence is possible only above the line of single species equilibrium.
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    Théorie chromosimique de l'inbreeding: Modèle probabiliste (1974)
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    Bulletin of mathematical biology 36 (1974), S. 417-434 
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    Notes: Abstract A molecular theory of inbreeding involving interactions between zones of gametic recognition (ZRG) localized on the chromosomal sets of male and female gametes is developed. This theory accounts for inbreeding effects and heterosis and raises the problem of control of embryonic development and the biological validity of the inbreeding coefficient. The mathematical analysis of this interaction system with sib matings permits the estimation of viability depression in inbred organisms. The biological validity of the model is discussed.
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    On the probability of reaching a threshold in a stochastic mammillary system (1974)
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    Bulletin of mathematical biology 36 (1974), S. 445-454 
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    Notes: Abstract The multivariate distribution over time of a particular stochastic mammillary compartmental model is obtained for any point in time. The maximum expectation of the peripheral compartments is then derived and used to determine lower bounds on the probability that the maximum of the peripheral compartments reaches any arbitrary threshold level. A bound on the probability is illustrated by an example and some of its implications are explored.
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    Dynamics of populations ofBiomphalaria glabrata and the von forerster equation (1974)
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    Bulletin of mathematical biology 36 (1974), S. 29-37 
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    Notes: Abstract Changes in time of populations ofBiomphalaria glabrata due to changes in the rate of infection bySchistosoma mansomi are investigated. This is done by applying Von Foerster equations with boundary conditions derived from experiment. The resulting equation is solved in some simplified cases and applications of the formalism to ecological problems is suggested.
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    Electrically induced phase transitions via the dipole model in excitable membranes (1974)
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    Bulletin of mathematical biology 36 (1974), S. 17-28 
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    Notes: Abstract Calculations based upon the membrane dipole model have been carried out and indicate the possibility of cooperative behavior during the membrane excitation process. An explicit expression is obtained for the critical electric field,E, which must be present to initiate the cooperative structural transition assumed to occur during membrane excitation. An hypothesis concerning the occurrence of two distinct phase transitions in the membrane resulting in the rapid influx of sodium ions and sodium ion inactivation, respectively, is presented.
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    A note on the shape of the erythrocyte (1974)
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    Bulletin of mathematical biology 36 (1974), S. 55-58 
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    Notes: Abstract Variational calculus is used to derive an equation for the shape of the cross section of a human red blood cell, the objective being the maximization of the surface area/volume ratio. Comparison to previous work is presented.
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    An intergral method for the analysis of flow in arterial stenoses (1974)
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    Bulletin of mathematical biology 36 (1974), S. 39-53 
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    Notes: Abstract An approximate solution is presented to the problem of incompressible flow through an axisymmetric constriction. The geometry is intended to simulate an arterial stenosis, and the solution is applicable to both mild and severe stenoses for Reynolds numbers below transition. Theoretical results obtained for specific geometries are given for the velocity distribution, pressure drop, wall shearing stress, and separation phenomena. These results reveal the significant alterations in flow caused by a stenosis. Experiments using model stenoses are described and compared with the theoretical results. Theoretical predictions of pressure drop and separation characteristics are in reasonably good agreement with the experimental observations.
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    Matematicheskie problemy v biologii (1974)
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    Bulletin of mathematical biology 36 (1974), S. 615-616 
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    The University of Texas Health Science Center at Houston, Division of Continuing Education and The Region V of IEEE announces Eleventh Symposium on Biomathematics and Computer Science in the Life Sciences (1974)
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    Bulletin of mathematical biology 36 (1974), S. 617-617 
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    The simulation of multi-neurone networks: Modelling of the lateral inhibition of the eye and the generation of respiratory rhythm (1974)
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    Bulletin of mathematical biology 36 (1974), S. 77-89 
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    Notes: Abstract We describe a model of a single neurone, and a method of interconnecting such neurone models suitable for multi-neurone network simulations on a digital computer. Two simulations are described; the lateral inhibition in the eye of the Limulus and the generation of respiratory rhythm in the brain stem of the cat.
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    Pulse velocities in cylindrical, tapered and curved anisotropic elastic arteries (1974)
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    Bulletin of mathematical biology 36 (1974), S. 103-103 
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    Interaction of peristaltic motion with Poiseuille flow (1974)
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    Bulletin of mathematical biology 36 (1974), S. 127-141 
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    Notes: Abstract The effect of Poiseuille flow on peristaltic transport has been investigated in a two-dimensional mathematical model of peristalsis for the case when the wall of the channel executes a sinusoidal motion of small amplitude. Closed-form solutions have been obtained for limiting values of Reynolds number and the Poiseuille flow parameter, while the method of Frobenius series solution has been used for the general case. It is found that the mean flow reversal is strongly dependent on the Poiseuille flow. The position of flow reversal may change drastically from the center of the channel to the boundaries. Numberical results are reported for various values of the physical parameters of interest.
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    Enzyme kinetics in cells (1974)
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    Bulletin of mathematical biology 36 (1974), S. 157-169 
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    Notes: Abstract Classical enzymology ignores the role which cellular membranes may play in regulating reaction kineticsin vivo. The correct description of cellular metabolic processes must derive from a mass balance equation for each reacting species. An elementary mathematical model, called the “continuous flow stirred tank reactor” in the chemical engineering literature, has been applied to Michaelis-Menten kinetics, substrate inhibition kinetics, and kinetics involving hydrogen ion as a byproduct. A number of remarkable phenomena, including multiple stationary states, threshold effects, temporal patterns, homeostatic regulation, amplification, and irreversible differentiation can result. Predictions of the model are in qualitative accord with experimental and theoretical studies of insolubilized enzymes, which are conventionally modeled by a more difficult mathematical formalism.
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    Stability and enzyme separation: Integral representation of the solutions (1974)
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    Bulletin of mathematical biology 36 (1974), S. 197-203 
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    Notes: Abstract Two enzymes, cross-coupled through their respective products, are membrane-bound and thereby separated from each other. The cross-coupling is of opposite character and diffusion limited, i.e. an activation-inhibition couple with a diffusion-induced time-lag. In this paper an integral representation for the solutions of the dynamic equations is developed using the Green's function technique, and an application to morphological changes in the mitochrondrion is discussed.
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    Stochastic kinetic models for small irreversible systems (1974)
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    Bulletin of mathematical biology 36 (1974), S. 219-227 
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    Notes: Abstract The probability distribution of the process level is derived for a general class of irreversible reaction systems. A method of approximating the mean and variance of the process level is developed and shown to be more accurate for small irreversible systems than other approximations used in the stochastic approach to kinetics.
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    Semiconductor theory of ion transport in thin lipid membranes: I. Potential and field distributions (1974)
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    Bulletin of mathematical biology 36 (1974), S. 229-246 
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    Notes: Abstract In the theory as presented in this paper and the following one, we shall attempt to apply the semiconductor principles and methods to the study of ion transport in thin lipid membranes. Detailed formulations are given on the potential energy barriers at the interfaces, voltage drops in the polar and non-polar regions, and potential and field distributions in the diffuse double layer and within a charged membrane. These results will be used mainly as the boundary conditions for the solution of ion flow as to be given in the following paper. The analysis clearly indicates that the ion transport is interface-limited and is profoundly influenced by the presence of surface charges. An explanation of Na+ extrusion in nerve membrane is given based on the field distribution analysis. The theory also suggests that the “membrane potential” depends mainly on surface charges but not necessarily on ion permeation through the membrane.
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    Flagellar elongation as a moving boundary problem (1974)
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    Bulletin of mathematical biology 36 (1974), S. 265-273 
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    Notes: Abstract Movement of a proposed controlling factor along the growing flagellum is considered as a special case of one-dimensional diffusion with a moving boundary. Flagellar elongation, which involves polymerization of the building units at the distal tip, is viewed as taking place in a series of steps. The concentration of the controlling factor at the tip is computed as a function of the distance of the tip from the base, and the time between polymerization reactions. It is proposed that the concentration of this factor at the tip is responsible for regulating the flagellar growth rate and final length.
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    Stochastic theory of compartments (1974)
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    Bulletin of mathematical biology 36 (1974), S. 305-309 
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    Notes: Abstract The stochastic model of a compartment developed by Thakur, Rescigno and Schafer is discussed without using generating functions. The behavior of the mean and variance of the number of particles present as a function of time is also discussed. We also allow both the input and output to be time dependent.
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    A new model for interacting populations—I: Two-species systems (1974)
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    Bulletin of mathematical biology 36 (1974), S. 347-353 
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    Notes: Abstract The exact solvable model presented here describes two interacting species whose populations oscillate periodically in time in the absence of self-interaction and attain saturation with fluctuations if self-interactions are included. While sharing broad features of the classical Volterra system, the model proposed here has the advantage of possessing exact solutions. The model thus provides a testing ground for general principles employed in the study of dynamics of populations.
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    Books received (1973)
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    Mathematical programming 4 (1973), S. 118-119 
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    A computational comparison of some non-linear programs (1973)
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    Mathematical programming 4 (1973), S. 144-154 
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    Notes: Abstract This article deals mainly with a comparison of certain computational techniques used for the solution of non-linear constrained mathematical programming problems.
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    Two commodity network flows and linear programming (1973)
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    Mathematical programming 4 (1973), S. 1-20 
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    Notes: Abstract This paper shows that the linear programming formulation of the two-commodity network flow problem leads to a direct derivation of the known results concerning this problem. An algorithm for solving the problem is given which essentially consists of two applications of the Ford—Fulkerson max flow computation. Moreover, the algorithm provides constructive proofs for the results. Some new facts concerning feasible integer flows are also given.
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    Matching, Euler tours and the Chinese postman (1973)
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    Mathematical programming 5 (1973), S. 88-124 
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    Notes: Abstract The solution of the Chinese postman problem using matching theory is given. The convex hull of integer solutions is described as a linear programming polyhedron. This polyhedron is used to show that a good algorithm gives an optimum solution. The algorithm is a specialization of the more generalb-matching blossom algorithm. Algorithms for finding Euler tours and related problems are also discussed.
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    The Mathematical Programming Society (1973)
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    Mathematical programming 5 (1973), S. 127-127 
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    Mathematical programming 5 (1973), S. 381-384 
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    Editorial policy (1973)
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    Mathematical programming 5 (1973), S. 386-386 
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    Referees 1973 (1973)
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    Mathematical programming 5 (1973), S. 387-387 
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    The Mathematical Programming Society (1973)
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    Mathematical programming 5 (1973), S. 388-388 
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    Mathematical programming 5 (1973), S. 385-385 
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    Pivot selection methods of the Devex LP code (1973)
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    Mathematical programming 5 (1973), S. 1-28 
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    Notes: Abstract Pivot column and row selection methods used by the Devex code since 1965 are published here for the first time. After a fresh look at the iteration process, the author introduces dynamic column weighting factors as a means of estimating gradients for the purpose of selecting a maximum gradient column. The consequent effect of this column selection on rounding error is observed. By allowing that a constraint may not be positioned so exactly as its precise representation in the computer would imply, a wider choice of pivot row is made available, so making room for a further selection criterion based on pivot size. Three examples are given of problems having between 2500 and 5000 rows, illustrating the overall time and iteration advantages over the standard simplex methods used today. The final illustration highlights why these standard methods take so many iterations. These algorithms were originally coded for the Atlas computer and were re-coded in 1969 for the Univac 1108.
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    Stability of the solution of definite quadratic programs (1973)
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    Mathematical programming 5 (1973), S. 41-53 
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    Notes: Abstract This paper studies how the solution of the problem of minimizingQ(x) = 1/2x T Kx − k T x subject toGx ≦ g andDx = d behaves whenK, k, G, g, D andd are perturbed, say by terms of size∈, assuming thatK is positive definite. It is shown that in general the solution moves by roughly∈ ifG, g, D andd are not perturbed; whenG, g, D andd are in fact perturbed, much stronger hypotheses allow one to show that the solution moves by roughly∈. Many of these results can be extended to more general, nonquadratic, functionals.
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    Edmonds polytopes and weakly hamiltonian graphs (1973)
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    Mathematical programming 5 (1973), S. 29-40 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Jack Edmonds developed a new way of looking at extremal combinatorial problems and applied his technique with a great success to the problems of the maximal-weight degreeconstrained subgraphs. Professor C. St. J.A. Nash-Williams suggested to use Edmonds' approach in the context of hamiltonian graphs. In the present paper, we determine a new set of inequalities (the “comb inequalities”) which are satisfied by the characteristic functions of hamiltonian circuits but are not explicit in the straightforward integer programming formulation. A direct application of the linear programming duality theorem then leads to a new necessary condition for the existence of hamiltonian circuits; this condition appears to be stronger than the ones previously known. Relating linear programming to hamiltonian circuits, the present paper can also be seen as a continuation of the work of Dantzig, Fulkerson and Johnson on the traveling salesman problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580109
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  • 99
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    On L1 and Chebyshev estimation (1973)
    Springer
    Mathematical programming 5 (1973), S. 73-87 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The problem considered here is that of fitting a linear function to a set of points. The criterion normally used for this is least squares. We consider two alternatives, viz., least sum of absolute deviations (called the L1 criterion) and the least maximum absolute deviation (called the Chebyshev criterion). Each of these criteria give rise to a linear program. We develop some theoretical properties of the solutions and in the light of these, examine the suitability of these criteria for linear estimation. Some of the estimates obtained by using them are shown to be counter-intuitive.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580112
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  • 100
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    Electronic Resource
    A revised simplex method for linear multiple objective programs (1973)
    Springer
    Mathematical programming 5 (1973), S. 54-72 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For linear multiple-objective problems, a necessary and sufficient condition for a point to be efficient is employed in the development of a revised simplex algorithm for the enumeration of the set of efficient extreme points. Five options within this algorithm were tested on a variety of problems. Results of these tests provide indications for effective use of the algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580111
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