ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Springer  (146,830)
  • American Physical Society  (19,011)
  • American Geophysical Union  (5,550)
  • 1965-1969  (171,391)
Collection
Keywords
Publisher
Years
Year
  • 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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Comparaison des modeles de neurone de Hodgkin-Huxley et de Nelson (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 347-354 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    The theory of the left ventricular aneurysm (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 363-370 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    A note on crime control (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 375-378 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Interactions in enzymatic reactions (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 379-390 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Decay of cell synchronization: Solutions of the cell-growth equation (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 391-409 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    On the derivation of a mean growth equation for cell cultures (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 411-416 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    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 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Reward and punishment in learning with possible reference to punishment for crime (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 477-481 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476827
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476828
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    Cooperative specific adsorption of iona at charged sites in an electric field (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 483-483 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476829
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 13
    Electronic Resource
    Electronic Resource
    Operations research around the world meetings (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 485-485 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476830
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 14
    Electronic Resource
    Electronic Resource
    Dimensional anlaysis and the equations of electrophoresis (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 501-510 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 15
    Electronic Resource
    Electronic Resource
    Categories of (ℓ, ℛ)-systems (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 511-517 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476858
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 16
    Electronic Resource
    Electronic Resource
    The origin of lift forces in fluttering flight (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 487-500 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476856
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 17
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476859
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 18
    Electronic Resource
    Electronic Resource
    A continuity equation for cell populations (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 545-554 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476861
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 19
    Electronic Resource
    Electronic Resource
    The behavior of the weakening and failing myocardium (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 537-544 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476860
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 20
    Electronic Resource
    Electronic Resource
    The frequency distribution of chromosome constituents in cells with chromosome-number dispersion (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 555-566 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476862
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 21
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476863
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 22
    Electronic Resource
    Electronic Resource
    Estimation of rate of synthesis of chromosomal DNA in ehrlich ascites tumor cells (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 575-584 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476864
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 23
    Electronic Resource
    Electronic Resource
    A sociological approach to biology (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 655-661 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476867
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 24
    Electronic Resource
    Electronic Resource
    Theorems on random evolution (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 663-663 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476868
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 25
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476865
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 26
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476866
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 27
    Electronic Resource
    Electronic Resource
    The motion of thhe left ventriele: I (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 663-663 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476869
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 28
    Electronic Resource
    Electronic Resource
    Bimolecular systems: I. Linear systems of complexes (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 1-16 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476958
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 29
    Electronic Resource
    Electronic Resource
    DNA histograms of irradiated cells: The case of prophase-trapping (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 17-32 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476959
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 30
    Electronic Resource
    Electronic Resource
    A note on the mathematical biology of automobile driving (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 187-188 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476971
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 31
    Electronic Resource
    Electronic Resource
    Mathematical biology of automobile driving (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 181-186 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476970
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 32
    Electronic Resource
    Electronic Resource
    Angles of branching and diameters of branches in the human bronchial tree (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 245-259 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476898
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 33
    Electronic Resource
    Electronic Resource
    Finite linnaean structures (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 191-206 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476893
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 34
    Electronic Resource
    Electronic Resource
    Abstract power structures (APS) and related bumping orders (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 207-216 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476894
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 35
    Electronic Resource
    Electronic Resource
    Stability analysis of a mathematical neuron model (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 217-226 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476895
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 36
    Electronic Resource
    Electronic Resource
    A neural net model for masking phenomena (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 227-232 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476896
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 37
    Electronic Resource
    Electronic Resource
    The struggle for life: I. Two species (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 377-388 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The general equations are discussed describing two species in competition or in symbiosis or feeding one on the other.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476909
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 38
    Electronic Resource
    Electronic Resource
    A note on Rashevsky’s postulate of relational forces (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 403-404 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476912
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 39
    Electronic Resource
    Electronic Resource
    Organismic sets and biological epimorphism (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 389-393 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476910
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 40
    Electronic Resource
    Electronic Resource
    Out-of-print volumes and back issues of the Bulletin of Mathematical Biophysics (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 407-407 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476914
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 41
    Electronic Resource
    Electronic Resource
    Model of urethra under uniform circumferential tension (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 409-409 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476915
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 42
    Electronic Resource
    Electronic Resource
    Bimolecular systems: II. Nonlinear systems of complexes (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 605-613 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476597
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 43
    Electronic Resource
    Electronic Resource
    Bimolecular systems: III. Catalytic systems (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 615-623 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476598
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 44
    Electronic Resource
    Electronic Resource
    A theory of cell hydration governed by adsorption of water on cell proteins rather than by osmotic pressure (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 583-596 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476595
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 45
    Electronic Resource
    Electronic Resource
    Considerations of quasi-stationarity in electrophysiological systems (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 657-664 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476917
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 46
    Electronic Resource
    Electronic Resource
    The dead space in a compartmental lung model (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 711-718 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476922
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 47
    Electronic Resource
    Electronic Resource
    A charge transfer process in the visual pigments (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 677-690 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476919
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 48
    Electronic Resource
    Electronic Resource
    Optimal models for social change (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 841-862 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476932
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 49
    Electronic Resource
    Electronic Resource
    Note from the editor (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 1-1 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476935
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 50
    Electronic Resource
    Electronic Resource
    A suggestion for a new approach to the mathematical theory of imitative behavior (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 863-877 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476933
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 51
    Electronic Resource
    Electronic Resource
    Erythrocyte distribution in arterial blood flow: IV. Simplification of the proposed equations (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 27-32 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a previous paper (Bull. Math. Biophysics,29, 565–574, 1967) the author developed equations to represent velocity and hematocrit profiles in quasi-Poiseuille flow of blood. It was assumed that energy dissipation was minimized and that the viscosity depended on hematocrit and shear rate according to the Casson formula. These equations are simplified considerably, placed in a form more suitable for numerical solution and shown to depend on a single dimensionless parameter. Typicalin vivo values for this parameter are calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476937
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 52
    Electronic Resource
    Electronic Resource
    Éléments d’une théorie générale de la croissance d’une population (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 33-46 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper, discrete models of reproduction are studied. In part one, definitions are given, particularly on order of the reproduction; part two concerns the growth of the population; part three, the phenomena of delay or acceleration; and part four, the consequences of mortality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476938
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 53
    Electronic Resource
    Electronic Resource
    Neuroendocrine control of thyroid secretion in living systems: A feedback control system model (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 3-26 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model of the regulation of thyroid hormone in the bloodstream of living systems is formulated and analyzed. The portion of this model defined as theregulator includes components representing the thyroid, anterior pituitary and hypothalamic organs and their intercommunicating channels, that is, the peripheral plasma and hypophysial portal circulations and certain neuro-secretory connections. The loss of hormones from the plasma in the living system associated with physiological mechanisms within the peripheral tissue space and the excretory pathways is represented in the model by a lumpedload on the regulator. The model is reduced to a system of differential equations involving eleven parameters and variables, all of which are identified with certain physiological structures and states. Five of these are currently observable by available laboratory techniques and two others are computable explicity from the equations of the model; the remaining four can be computed in the same way to within a multiplicative constant. Procedires for carrying out ten of these measurements and calculations are suggested. On the basis of the equations and parameters of the model, a discussion of the normal behavior and the response of this system to certain types of disturbances is presented. A systematic effort has been made in the development of this model to include all relevant physiological data and relationships reported in the biological literature. A summary of this literature, reflecting the views and interpretations made by the authors of this paper, is included for completeness and ease of reference.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476936
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 54
    Electronic Resource
    Electronic Resource
    Linear bulk diffusion into heterogeneous tissue (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 47-59 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper an expression is derived which describes the transient overall uptake of an inert solute by a section of tissue excised with parallel faces and placed upon an impermeable base. The approach diverges from the conventional analyses for perfused tissue (Morales and Smith,Bull. Math. Biophysics,6, 125–141, 1944;7, 47–99, 1945) because the extravascular zone is regarded as a heterogeneous diffusion medium. Account for this is taken by regarding tissue as effectively composed of two phases—a continuous (extracellular) phase similar to water, and a dispersed phase comprising cells of irregular profile. In both phases the relevant mode of uptake is taken as bulk diffusion rather than surface permeation, thus emphasizing the influence of the internal geometry of the tissue upon its overall exchange response.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476939
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 55
    Electronic Resource
    Electronic Resource
    The identification of recirculating systems in the frequency domain (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 87-104 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method for the identification of flow systems by frequency domain analysis has been extended to include systems with recirculation and truncated data curves. Application of the technique to clinical indicator-dilution curves indicates that the method may be useful in the quantitation of intracardiac shunts. A number of numerical examples which demonstrate the accuracy of the method are included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476941
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 56
    Electronic Resource
    Electronic Resource
    A systems-mathematical interpretation of psychoanalytic theory (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 61-86 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By assigning time-varying coordinates to all environmental stimuli, it has been possible to axiomatize psychoanalytic theory on the five principles of multiple causation, growth-aging influence, genetic influence, historic influence and conscious-unconscious activity. The theorems of summation of response and the inevitability of conscious-unconscious conflict with their corollaries follow directly from the axiomatic foundations, as does the existence of an adaptation-defense mechanism. The interpretation of the defense mechanism in terms of an ego-id feedback system provides the basis for the structural existence of conscious-conscious and unconscious-unconscious conflict.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476940
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 57
    Electronic Resource
    Electronic Resource
    Cellular systems as sequential machines: Stability properties (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 117-122 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In previous studies of (M,R) (Rosen, 1961; Demetrius, 1966), it was assumed that changes in the structure of (M,R) which were induced by environmental alternations occurred without error. Here, the effect of both “genetic” and “metabolic” malfunctions on the behavior of (M,R) is examined and a subclass of these systems whose behavior is invulnerable to such errors is specified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476943
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 58
    Electronic Resource
    Electronic Resource
    Cellular systems as graphs (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 105-116 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The definition of an (M,R) is formulated in a way that emphasizes its mathematical properties. Neglecting interactions between the components, it is shown that: (1) An (M,R) contains only one non-reestablishable component. (2) If an (M,R) contains only one non-reestablishable component, then that component is central. Examples are given to illustrate the biological significance of these two results. The notion of “lag-independence” is introduced, and it is shown that if a system possesses only one non-reestablishable component which is “lag-independent” then all components are lag-independent. The concepts of reestablishability, centrality and lag-independence are applied in order to suggest various criteria for optimal organization of (M,R).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476942
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 59
    Electronic Resource
    Electronic Resource
    A theoretical model for the control mechanisms in biochemical reactions (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 123-133 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical representation for the analysis of control mechanisms in biochemical reactions is presented. First, the theoretical concept of concentration in biological systems is developed. Then a system consisting of two functions λ and τ is constructed as a network of single output automata. The range of λ is taken to be formed by a set of twostates qualitatively different from the “repair function” Φ f of a mappingf: A→B in the stimulated Φ1 and unstimulated state Φ0. Likewise, the range of τ is formed by the set δ={f o ,f 1} wheref 1 means the mappingf in its stimulated state andf o in the unstimulated one. It is demonstrated that the mathematical structure described acts as a control mechanism over thef and Φ f , so that two biochemical components,A→B, are transformed at a controlled rate. Some of the biological applications of this model are briefly examined. The Jacob-Monod model, the enzymatic adaptation phenomenon, and the “rheon unit” hypothesis are discussed within our framework. Eventually, a concrete model for the RNA-polymerase mechanism, based on the above discussion, is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476944
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 60
    Electronic Resource
    Electronic Resource
    A contribution to Rashevsky’s mathematical theory of development (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 135-151 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The application of Rashevsky’s transformationT to a primordial graph yields a set of graphs corresponding to different stages in the development of the organism. However, sinceT is multiple-valued the graphs obtained are not ordered. To obtain an ordering, it is first shown that the set of graphs under consideration is equivalent to a well defined setO (for “organism”) ofn-tuples. A metric is then introduced which is based on a biological consideration discussed by Rashevsky (Bull. Math. Biophysics,16, 317–348, 1954). Since a metric implies an ordering of the setO, with a knowledge of the structure of the primordial, one can obtain the developmental sequence. Unfortunately, at present, the structure of the primordial graph is unknown which makes the direct application of the above principle impossible. Consequently, an indirect approach which makes use of more accessible biological phenomena is discussed as well. The hypothesis thatrate of development decreases exponentially and the implications this has with regard to the metric onO are discussed. It is shown that if the hypothesis is accepted the search for the developmental sequence is narrowed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476945
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 61
    Electronic Resource
    Electronic Resource
    Compartmental systems and generating functions (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 49-63 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Compartmental systems can be represented by direct graphs in which each node corresponds to a generating function and each arm to a transfer generating function. A homomorphism is established between a compartmental system and this representation, in analogy with that obtained through the use of the Laplace transformation. From the values obtained experimentally in a given compartment, through the solution of a difference equation, the generating function for the corresponding node can be calculated and the graph of the system can be built up within the degrees of freedom of the model. From the graph it is possible to calculate the transfer generating function between any two connected nodes, the mean permanence time in a given node, the mean transit time between two nodes, and their precursor-successor order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477261
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 62
    Electronic Resource
    Electronic Resource
    On the competitive exclusion principle (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 85-89 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Competitive Exclusion Principle, formulated by V. Volterra (Memorie del R. Comitato Talassografico Italiano,131, 1–142, 1927) for a number of species competing for a common ecological niche, is extended to a number of species competing for many ecological niches.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477264
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 63
    Electronic Resource
    Electronic Resource
    Periodic and aperiodic phases of circulatory mixing (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 65-70 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A modification is presented of an earlier theory of the mixing of dye following injection into the circulation. Approximate theoretical relations are given for the concentration of dye in the right heart and in the aorta following right atrial injection. It is shown that when the probability distribution of transit times around the circulation has a prolonged tail, mixing waves are now inscribed about a quasi-exponential relation. Later in time the relation levels off to a uniform asymptotic concentration corresponding to an equilibrium volume of dilution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477262
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 64
    Electronic Resource
    Electronic Resource
    Cooperative specific adsorption of ions at charged sites in an electric field (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 91-104 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The adsorption of two cations at the anionic sites of a polymer (e.g., such as a protein) in an electric fields is discussed, taking into account cooperative interaction of the cations mediated through the backbone of the polymer. The calculation of the grand partition function explicitly considers the vacant negative sites of the polymer. As in the case without cooperative interaction, the problem reduces to the determination of the largest eigenvalue of asymmetric matrices. The weights of the different neighbor configurations are determined. Approximate formulae for the grand partition function and for those weights are derived. The formal analogy of these cooperative phenomena and those occurring in quantum (bio)chemistry is pointed out exemplifying an earlier suggestion about the basis of quantum biology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477265
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 65
    Electronic Resource
    Electronic Resource
    A proposed mechanism for the sol-gel transformation (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 105-112 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The transformation from gel to sol in cell cytoplasm is treated as the transition from a lattice of macromolecules linked by Ca++ ions to a random distribution of the macromolecules. The transition is a cooperative process, whose probability is expressed in terms of the theory of runs. The process is related to cell metabolism by the assumption that available Ca++ concentration is regulated by metabolically produced endogenous chelating agents.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477266
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 66
    Electronic Resource
    Electronic Resource
    Kinetic criteria of solid state mechanisms in biology (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 113-118 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Kinetic criteria for solid state physical mechanisms of electron and ion transport in biological systems are summarized, and the mechanisms are discussed. A reaction which is rate-limited by electron or ion transport across a particle or membrane in accord with Ohm's law will show first order kinetics, with an hyperbolic relationship between rate constant and the sum of substrate plus product. Larger initial substrate concentrations produce smaller rate constants, thus giving the appearance of substrate inhibition. Examples are cytochrome oxidase and peroxidase, and pyruvate carboxylase. Ohmic transport mechanisms may be caused by electron conduction or superconduction through protein, by electron conduction through water, or by conduction of ions through membranes. A reaction which is rate-limited by charge transport across an activation energy barrier at an interface in accord with a logarithmic voltage-current law will show reaction kinetics conforming to the Elovich equation, and will have the appearance of a pair of simultaneous first order processes. Examples include decay of photogenerated free radicals in eye melanin particles and in photosynthetic particles of bacteria, and sodium and potassium ion transport across cell surfaces. The logarithmic voltage-current law may be regarded as an empirical relationship describing behavior of interfaces, justified by extensive experimental data on many types of interfaces, or it may be derived theoretically for individual cases from statistical mechanical and/or solid state physical considerations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477267
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 67
    Electronic Resource
    Electronic Resource
    Analysis of some effects of aortic smooth muscle onin vivo aortic pressure curves (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 119-130 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract When aortic pressure curves were predicted previously on the basis of a newly developed model of visco-elastic properties of the aorta, it was necessary to use published viscoelastic constants. These were usually obtained from longitudinal strips of blood vessels long removed from the animal, and therefore probably containing deteriorated smooth muscle. The predicted curves had the same form as actual tracings, substantiating the analysis somewhat, but the pressure levels were low. These low levels, if due to inadequate visco-elastic constants, could be attributed to the use of longitudinal rather than circumferential segments as well as to the use of segments with deteriorated muscle. The present analysis uses data collected by the author testing circumferential viscoelastic properties of fourteen different aortic regions in a way suggested by the author's model of an aortic wall. Moreover, the constants were measured on segments containing muscle relaxed by EDTA solutions and on similar segments containing muscle contracted by neosynephrine. These visco-elastic constants were used in the author's nonlinear differential equation of motion of the aortic wallin vivo to predictin vivo pressure curves. The predicted curves were low in any given aortic region if relaxed constants were used, but at normal levels with contracted constants. In fact, pressure curves predicted using constants obtained from aortic segments containing contracted muscle resembled actual tracings in form and pressure levels. Even the observed variations in the form of the systolic pressure curve down the aorta were predicted by this analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477268
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 68
    Electronic Resource
    Electronic Resource
    Biological similarity relative to allometric quantities (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 131-133 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is an empirical finding that an allometric quantity with dimensional exponents α, β and γ relative to mass, length, and time, respectively, has a value for its allometric exponentb satisfying the relation $$\tfrac{1}{3}(3\alpha + \beta + {\gamma \mathord{\left/ {\vphantom {\gamma 2}} \right. \kern-\nulldelimiterspace} 2}) \leqslant b \leqslant \tfrac{1}{3}(3\alpha + \beta + \gamma ).$$ A theoretical derivation is given of this double inequality using only the fact of constant density and the plausible assumption that metabolic rate is a dominant allometric quantity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477269
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 69
    Electronic Resource
    Electronic Resource
    The entropy of a continuous distribution (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 135-143 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract C. Shannon's definition (Bell System Technical Journal,27, 379–423, 1948) of the entropy of a continuous distribution is dimensionally incorrect and does not have the same significance as the corresponding definition in the discrete case. A new definition is proposed: this modified entropy is more like the entropy of a discrete distribution in one way, in another more like Shannon's “transmission rate.” The ideas are illustrated by reference to Wright's study of the hereditary influence on the coat pattern of the guinea pig.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477270
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 70
    Electronic Resource
    Electronic Resource
    Theorems on random evolution (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 145-150 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the following paper, a possible mode of evolution is described which differs from the traditional modes in not being selective in the Darwinian sense.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477271
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 71
    Electronic Resource
    Electronic Resource
    Information theory and genetics (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 177-181 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A description of the kinds of systems susceptible to information theoretical analysis is given. By means of an example, certain common fallacies in the application of communication theory to biology are illustrated. The entropy-information analogy is discussed. *** DIRECT SUPPORT *** A01E2109 00008
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477274
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 72
    Electronic Resource
    Electronic Resource
    A note on equivalent mathematical models (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 161-175 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model of a process contains parameters supposedly characterizing the system which manifests the process. If the parameters are statistically distributed in a population of such systems, the process manifested by the entire population will in general be described by a different mathematical model. Thus a choice is always at hand between two or more mathematical models, depending on which parameters (if any) are assumed to be distributed and, if so, how. Examples of such alternative interpretations are given for mathematical models of some behavioral processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477273
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 73
    Electronic Resource
    Electronic Resource
    Superimposed random coding of stimulus-response connections (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 191-202 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of economically linking a large number of stimuli with a large number of potential responses is considered to resemble a problem of efficient retrieval of documents (the responses) on the basis of their characterization by descriptors (the stimuli to which the responses are appropriate). In this retrieval problem, a method whereby the codes for descriptors are random positions in a coding field, and whereby codes for all applicable descriptors are superimposed in the same field, seems to be the simplest way of avoiding serious difficulties of retrieval. After a review of this method, the possibility is considered that very simple neural mechanisms could embody the essential features of the method. The aim of the discussion is to learn whether very simple structures and patterns of reinforcement would be adequate to carry out useful information processing in the brain, and to show some conceivable functions of simple neural networks which the experimenter might keep in mind. The discussion also shows how the structure of a simple “perceptron”-like network is suggested by the requirements of a retrieval task.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477276
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 74
    Electronic Resource
    Electronic Resource
    Studies on the electroretinogram. II. Model of an a-wave regenerator mechanism (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 223-233 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model is proposed to relate the regeneration of the ERGa-wave after partial light adaptation to the level of the light adaptation. The model assumes that thea-wave amplitude is a function of some reactive substance associated with ana-wave generator. The maximuma-wave amplitude occurs when the eye is fully dark adapted, and thea-wave generator initiator concentration is at a maximum. Thea-wave generator initiator concentration can be decreased by interacting with a product of the rhodopsin-light energy reaction, and increased by removal of this inhibitor. The removal of the inhibitor depends upon the isomerization of the all-trans-retinene to the 11-cis form. An excess of inhibitory material overa-wave generator initiator would cause a delay in the appearance of thea-wave until the excess inhibitory material is removed. This delay is a linear function of the logarithm of the adapting energy. The agreement of this model with the experimental ERG data is very good.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477279
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 75
    Electronic Resource
    Electronic Resource
    On the quantitative relationship between survival rate of larvae and their food supply (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 215-222 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The survival rate of fishes in their earlier stages of development and the influencing factors present one of the most fundamental problems of fish population dynamics. After I. Hjort's (Cons. L.'explor. Ner.,20, 3–228, 1914) work, there have been many investigators in this field and there is no doubt about the very important role of ova and larvae mortality in the fate of a given fish generation. Less clear are the ideas concerning factors determining the high mortality of fishes in their earlier stages of development; especially the factor of food supply of larvae during the period of transition to exogenic nutrition. The value of this factor has been estimated differently from different points of view. For example, R. J. H. Beverton and S. J. Holt (On the Dynamics of Exploited Fish Population, 1957) have given to the food supply factor its deserved importance. On the other hand, T. V. Dekhnik (Trudy Sevastopolskoi Biologicheskoi Stantsii,13, 216–244, 1960;Ibid.,14, 222–243, 1961) has proved in her investigations that at least for pelagic larvae of Black Sea fishes there is an excessive amount of food, and that therefore food cannot play an important role in larva survival. Not wanting to stop to review the literature of the problem (see Dekhnik,Trudy Sevastopolskoi Biologicheskoi Stantsii,13, 216–244, 1960), we will only remark that the problem as a whole needs further investigation. Not only new data are needed, but also methods for following up analysis have to be worked out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477278
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 76
    Electronic Resource
    Electronic Resource
    Learning fluctuations and hysteresis phenomena (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 253-259 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The investigation described here is anexperimental one which brings to light some new facts and confirms others already reported. They partly concern the hysteresis phenomena handled by N. Rashevsky (Mathematical Biophysics, 1960) and partly provide a point of departure for future biophysical research to be undertaken by biomathematicians.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477281
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 77
    Electronic Resource
    Electronic Resource
    An analysis of aortic pressure curves taking into account visco-elastic properties of the aorta and variations in peripheral resistance (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 27-52 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The aortic pressure curve necessarily reveals the mechanical properties of the aorta and peripheral resistance as well as of the dynamics of blood flow. The present study uses a reasonable model of visco-elastic properties of the aorta, a reasonable form for variations in peripheral resistance and blood flow to predict an aortic pressure tracing. Numerical values of constants measured experimentally were available in the published literature. These were used in the nonlinear differential equations of motion of the system under analysis. The equations yielded to piece-wise solution, giving the aortic circumference and the aortic pressure as functions of time. The form of both curves resembles clinical tracings, but numerical values of circumference were higher and of pressure lower thanin vivo. The discrepancies between predicted and clinical curves may reveal certain inadequacies in published measurements on visco-elastic constants. These measurements have been made on longitudinal rather than circumferential strips often containing dead rather than living muscle. The discrepancies, therefore, indicate specific gaps in our knowledge of aortic behaviorin vitro. The suggested model of the system aided in the design of experiments which could supply data necessary to substantiate or to revise the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476466
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 78
    Electronic Resource
    Electronic Resource
    The venous circulation (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 373-377 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some aspects of the circulation through the veins remain unexplained. The pressure gradient which ordinarily exists across a large vein, for example, is much greater than that necessary to maintain the same flow through a rigid tube of identical diameter (Brecher, 1956; Starling and Evans, 1962). During inspiration, blood flow through the thoracic portion of the inferior vena cava increases markedly, while that through the distal abdominal portion does not change. Furthermore, an active source of pressure drop in the chest is necessary to maintain venous flow. For the open chest the pressure drop occurs mainly during ventricular contraction, while in the closed chest it is produced chiefly by inspiration. The present study indicates that the high distensibility of the veins accounts in significant degree for the behavior characteristic of the venous circulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476842
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 79
    Electronic Resource
    Electronic Resource
    A logical model for growth and differentiation in multi-celled organisms (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 379-387 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper is an attempt to provide a logical model for the process of growth and differentiation in a multi-cellular organism. More specifically it is intended to show how genetic information relating to macroscopic structure and coded in the form of a logical tree could be progressively embodied in the organism as it develops by repeated division from a single cell. The aim is to establish biological analogies rather than mathematical interest, and reproduction, adaption, and the coordinating action of hormones are discussed within the general logical framework.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476843
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 80
    Electronic Resource
    Electronic Resource
    A mathematical model of the urethra (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 407-415 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Models having the form of surfaces of revolution may be used to represent the urethra under pre-voiding pressure. From such models are derived formulas for calculating muscle tension from the shape of a urethragram.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476845
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 81
    Electronic Resource
    Electronic Resource
    Estimation of secretory rates of hormones from the specific activities of metabolites which have multiple secreted precursors (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 389-406 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The calculation of rates of entry of material into an open system of multiple pools in the steady state from the specific activities of end products, which may be derived from several pools, is described. This analysis may be applied to estimate the rates of secretion of steroid hormones from the specific activities of urinary metabolites which may have various hormones as common precursors. In a previous publication (Gurpideet al., 1963) formulae have been presented by which secretory rates could be calculated after a single injection of the tracers assuming that each of the urinary metabolites was uniquely derived from one of the pools in the system. In the present article similar formulae were derived without this assumption. Consequently, it is shown that, under certain circumstances, non-uniquely derived metabolites can be used to estimate secretory rates, and that it may be unnecessary to consider the pathways of conversion of the hormones to the metabolites or the sites where these conversion occur.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476844
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 82
    Electronic Resource
    Electronic Resource
    The use of two radiotracers for transfer-rate determinations in closed two compartment systems (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 431-434 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The sensitivity and “specificity” of measurements for the determination of transferates are enhanced by the use of an additional radiotracer, serving to trace the unlabelled substance. This method presents advantages mostly in systems outside their steady state but only exeptionally in steady state systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476847
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 83
    Electronic Resource
    Electronic Resource
    Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 417-429 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation: $$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB 1(t) is the first order initial entry function for the tracer material,P(t1) the perturbation function.T(t 2) is the tracer input function, andB 1(t−t 2 ,t 1 −t 2 ) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476846
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 84
    Electronic Resource
    Electronic Resource
    Correlation “waves” in brain-like structures (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 435-447 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A correspondence is established between a tangible model of brain structure (and function) and a system of observer-observed interactions. The observed quantities are “stimuli” in the form of signal amplitude distributions in a mass of neuron-like units; the observer is a set of neurons (not circumscribed in a local region) in which a distributed parameter mirrors the stimulus history of the set, i.e., represents a “memory”. Utilizing the theory of the Perceptron, a contemporary brain model, it is demonstrated that large systems composed of many observer-observed interactions exhibit quantum mechanical behavior on a “macroscopic” scale. This behavior entails wave-like phenomena and the need of applying the superposition mechanics to system information content calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476848
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 85
    Electronic Resource
    Electronic Resource
    Mathematical models for cellular systems. The von foerster equation. Part II (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 449-471 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This is the continuation of Part I, which was published in the September, 1965, issue of theBulletin. The birth rate, α(t), is now assumed to be a linear functional of the age density,n. This gives a simple model of self-replenishing stem cell compartments, and leads to a necessary condition for the existence of a steady state. Some examples are presented to illustrate the formalism. They include: (a) An equivivant population with life spanD and no losses from death or migration. The total number of cells is multiplied by 2 in each time intervalD. As a special case, frequently realized in practice, the population may be increasing exponentially with time (“log-phase” of growth). (b) A compartment with “random” emigration of cells and gamma distribution of life spans. (c) An oversimplified version of L. G. Lajtha’s model describing stem cell kinetics. In section IV a simple case in which the loss function depends explicitly onn is discussed very briefly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476849
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 86
    Electronic Resource
    Electronic Resource
    Mathematical models of nonuniform intrapulmonary gas distribution (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 473-476 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary Mathematical models of nonuniform gas distribution in the lungs which assume a two-chambered lung to be ventilated through a third chamber, i.e. a common dead space, have led to diverging results. A breath-by-breath analysis of such a system results in a two-exponential solution whereas a continuous ventilation analysis gives a three-exponential solution. This is caused by the different assumptions made in the two models about the composition of dead space gas. In the breath-by-breath analysis one assumes that theN 2 content of the dead space is zero at the end of inspiration. In the continuous ventilation model one assumes that theN 2 content in the dead space is unknown at all instants during the breathing cycle. No physical significance should be attached to any chamber in this type of analysis. The continuous ventilation model provides a more general solution than the cyclical ventilation model, because the former treats the common dead spaces as an independent unknown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476850
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 87
    Electronic Resource
    Electronic Resource
    On the electrocardiographic field equation (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 493-495 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476852
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 88
    Electronic Resource
    Electronic Resource
    The representation of organisms in terms of predicates (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 477-491 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The different approaches to relational biology developed by N. Rashevsky and R. Rosen consider essentially binary relations between various components of biological functions of the organism. Actually an organism is represented by a set of differentn-ary relations. The present paper is an attempt to outline a possible approach to this more realistic situation. Inasmuch asn-ary relation is ann-place predicate, it is attempted to describe the basic known properties of an organism in terms ofn-place predicates, in which the variables represent the different “components” of the organism. Some possible forms of such predicates are discussed and some general properties of systems of such predicates are studied. It is shown that if the organism is described by predicates of the type discussed here, statements can be derived about the conditions “of reestablishability” of different components. Conclusions similar to those obtained previously by R. Rosen are reached now on a very different basis. A description of the process of cell differentiation in multicellular organisms in terms of predicates studied here is briefly outlined. A comparison of similarities and differences between the approach and Rosen’s description of organisms in terms of the theory of categories is made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476851
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 89
    Electronic Resource
    Electronic Resource
    Temporal organization in cells (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 497-500 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476853
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 90
    Electronic Resource
    Electronic Resource
    29th National Meeting of the Operations Research Society of America (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 503-503 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476855
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 91
    Electronic Resource
    Electronic Resource
    Harold A. White March 4, 1933–July 27, 1965 Obituary notice (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 501-502 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476854
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 92
    Electronic Resource
    Electronic Resource
    Etude des premiers etages sensoriels (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 1-10 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476387
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 93
    Electronic Resource
    Electronic Resource
    The flow of a viscous liquid in a converging tube (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 11-24 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476388
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 94
    Electronic Resource
    Electronic Resource
    Some multi-dimensional branching processes as motivated by a class of problems in mathematical genetics I (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 25-50 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476389
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 95
    Electronic Resource
    Electronic Resource
    Design of neural nets with intermittent response and certain other relevant studies (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 51-74 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The application of the earlier results (Pavlidis, T. 1965. “A New Model for Simple Neural Nets and its Application in the Design of a Neural Oscillator.”Bull. Math. Biophysics,27, No. 2, 215–229) to the design of more complex neural nets is attempted. The following cases are considered: 1. Chains of neurons where it is proven that the frequency of the output pulses does not depend on the value of the input as long as it is above a certain threshold. 2. Groups of neurons with backward inhibition which present an intermittent mode of operation. 3. Neural nets with periodic facilitation which permit time sharing of certain components for different functions. 4. A neural net which can detect the sign of the input even if the main receptor is sensitive only to the absolute value of it, is presented. 5. A velocity estimating neural net which in combination with one of the nets with intermittent response provides a model for the smooth eye tracking movements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476390
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 96
    Electronic Resource
    Electronic Resource
    Academic learning, a variational model (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 75-90 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By assigning coordinates to the information space comprising all knowledge, rigorous mathematical interpretations can be placed on such terms as academic ability, memory and creativity such that these psychometric concepts can be incorporated into a framework of functional analysis which then permits the optimization of long-term academic learning processes through the location of the teaching trajectories in information space which will maximize the knowledge accumulated in a generalized educational system composed of a complex of subject-pupil-teacher interactions. The concepts of discrete and continuous information spaces are discussed in connection with subject-subject, subjectpupil and pupil-pupil interactions, and the advantages of using variational versus dynamic programming methods of optimizing alternative educational systems are evaluated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476391
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 97
    Electronic Resource
    Electronic Resource
    On chains of related sets (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 103-106 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract IfK is a partition of a setK which is partially ordered by the relationR andR is a collection of pairs of sets ofK such that the sets of each pair are related byR in the sense of Rashevsky, thenR is a relation which partially ordersK. Necessary and sufficient conditions thatK be a chain are obtained, and ifK is a chain under these conditions, it is shown thatK is unique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476393
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 98
    Electronic Resource
    Electronic Resource
    On multipole theory in electrocardiography (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 161-166 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper continues a comparison of the Taylor series and spherical harmonic forms of multipole representations initiated by Yeh (Bull. Math. Biophysics,24, 197–207, 1962). It is shown that while transformations from Taylor series form into spherical harmonic form is always possible, the inverse cannot be accomplished as suggested by Yeh; corrected transformation equations are given. It is also shown that direct measurement of Taylor coefficients, as outlined in Yeh, Martinek, and de Beaumont (Bull. Math. Biophysics,20, 203–216, 1958), is actually not possible. Accordingly, only the spherical harmonic coefficients can be determined by measurement of surface potentials, as in electrocardiography.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476990
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 99
    Electronic Resource
    Electronic Resource
    Some multi-dimensional branching processes as motivated by a class of problems in mathematical genetics II (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 181-190 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper is a continuation of a paper, “Some Multi-Dimensional Branching Processes as Motivated by a Class of Problems in Mathematical Genetics I,” by C. J. Mode, which appeared in a previous issue of theBulletin. Its purpose is two-fold; namely to discuss the mathematical existence of the model and to supply the mathematical proofs of some theorems in section two of the paper mentioned above. This paper should be read in conjunction with the previous paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476992
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 100
    Electronic Resource
    Electronic Resource
    A resolution of Rosen’s paradox for self-reproducing automata (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 191-194 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Rosen (Bull. Math Biophysics. 1959) has argued that a self-reproducing automaton of the type originally described by von Neumann is impossible because of a logical paradox inherent in its definition. The paradox is resolved by explicitly allowing errors (mutations) in the system and thus introducing evolution. There is no paradox in an automaton, originating from a slightly different ancestor through mutation. The von Neumann model thus becomes realistic and useful for a discussion of biological phenomena.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476993
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...