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1.
John Z. Hearon 《Bulletin of mathematical biology》1953,15(2):111-119
On the basis of a previous general formulation (Bull. Math. Biophysics,15, 21–29, 1953a) a discussion is given of the error in the approximation method of N. Rashevsky. This error, inherent in the
method when the metabolic rate is different at each point in the cell, is discussed in detail and numerical values are presented
for two particular cases: the rate proportional to the concentration and the rate a prescribed function of the spatial coordinates.
It is shown that the formulation for the first case also applies to several other cases, that the error is negligible provided
the rate is sufficiently small, and that the error is fairly sensitive to the cell size. If the rate depends upon the coordinatesalone a small rate is not sufficient to insure a negligible error. The relations between the exact method, the standard approximate
method, an earlier approximate method (Physics,7 260, 1936), and a more recent refinement (Bull. Math. Biophysics,10, 201, 1948) of the standard method are discussed.
This work was performed while the author was a research participant, Oak Ridge Institute of Nuclear Studies, assigned to the
Mathematics Panel, Oak Ridge National Laboratory. 相似文献
2.
N. Rashevsky 《Bulletin of mathematical biology》1969,31(3):591-603
A previous study (Bull. Math. Biophysics,30, 735–749) is generalized to the case of active transport, which acts together in general with ordinary diffusion. The basic
results obtained are the same except for an additional important conclusion. In principle it is possible to obtain sustained
oscillations even when the secretions of the different glands do not affect the rates of formation or decay of each other
at all, but affect the “molecular pumps,” which are responsible for the active transports in various parts of the system.
Thus no biochemical interactions need necessarily take place between then-metabolites to make sustained oscillations possible in principle. This is an addition to a previous finding (Bull. Math. Biophysics,30, 751–760) that due to effects of the secreted hormones on target organs, non-linearity of biochemical interactions is not
needed for production of sustained oscillations. 相似文献
3.
N. Rashevsky 《Bulletin of mathematical biology》1971,33(4):555-559
In combining the author's theories of organismic sets (Rashevsky,Bull. Math. Biophysics,31, 159–198, 1969a) and Robert Rosen's theory of (M, R)-systems (Bull. Math. Biophysics,20, 245–265, 1958), a conclusion is reached that the number of either normal or pathological phenomena in organismic sets may
occur. Those phenomena are characterized by occurring spontaneously once in a while but are not exactly periodic. Some epilepsies
are an example of such pathological phenomena in the brain. 相似文献
4.
N. Rashevsky 《Bulletin of mathematical biology》1960,22(1):73-84
The principle of biotopological mapping (Rashevsky, 1954,Bull. Math. Biophysics,16, 317–48) is given a generalized formulation, as the principle of relational epimorphism in biology. The connection between
this principle and Robert Rosen’s representation of organisms by means of categories (1958,Bull. Math. Biophysics,20, 317–41) is studied. Rosen’s theory of (M,R)-systems, (1958,Bull. Math. Biophysics,20, 245–60) is generalized by dropping the assumption that only terminalM
i
components are sending inputs into theR
i
components. It is shown that, if the primordial organism is an (M,R)-system, then the higher organisms, obtained by a construction well discussed previously (1958,Bull. Math. Biophysics,20, 71–93), are also (M,R)-systems. Several theorems about such derived (M,R)-systems are demonstrated.
It is shown that Rosen’s concept of an organism as a set of mappings throws light on phenomena of synesthesia and also leads
to the conclusion that Gestalt phenomena must occur not only in the fields of visual and auditory perception but in perceptions
of any modality. 相似文献
5.
Gordon C. K. Yeh 《Bulletin of mathematical biology》1962,24(2):197-207
In Yeh, Martinek, and de Beaumont (Bull. Math. Biophysics,20, 203–216, 1958), multipole representations of current generators in a volume conductor are used, based upon the Taylor series
expansion of the potential function. In Yeh, (Bull. Math. Biophysics,23, 263–276, 1961) multipole representations of current generators in a spherical volume conductor are used, based upon the
spherical harmonic expansion. This paper correlates these two systems of multipole representations so that formulations in
terms of one system of the representations may be readily transformed into formulations in terms of the other system. Since
the Taylor series representation is more graphic, whereas the spherical harmonic representation is more compact, such a transformation
between these two systems of formulations can serve useful purposes in the application of the theory of electrocardiography.
This investigation was supported by the National Heart Institute under Research Grant H-2263 (c-4). 相似文献
6.
N. Rashevsky 《Bulletin of mathematical biology》1971,33(3):321-338
After giving a brief review of the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967;31, 159–198, 1969), in which the concept of relational forces, introduced earlier (Bull. Math. Biophysics,28, 283–308, 1966a) plays a fundamental role, the author discusses examples of possible different structures produced by relational
forces. For biological organisms the different structures found theoretically are in general agreement with observation. For
societies, which are also organismic sets as discussed in the above references, the structures can be described only in an
abstract space, the nature of which is discussed. Different isomorphisms between anatomical structures, as described in ordinary
Euclidean space, and the sociological structures described in an abstract space are noted, as should be expected from the
theory of organismic sets. 相似文献
7.
The purpose of this work is to express current concepts on the relationship between the rates of secretion of thyroxin and
of thyroid stimulating hormone (TSH) by a set of linear differential equations (two attempts have been made previously in
this direction; cf. Roston,Bull. Math. Biophysics,21, 271–282, 1959; Danziger and Elmergreen,Bull. Math. Biophysics,16, 15–21, 1954), and to show that the solutions to these equations fulfill two criteria: that they correctly express the previously
observed behavior of thyroxin and TSH, and that they allow certain predictions to be made which are amenable to experimental
verification or disproval by currently existing techniques. This mathematical model is necessarily only an approximation of
reality. 相似文献
8.
N. Rashevsky 《Bulletin of mathematical biology》1969,31(3):605-617
A previous study (Bull. Math. Biophysics,31, 417–427, 1969) on the definitions of stability of equilibria in organismic sets determined byQ relations is continued. An attempt is made to bring this definition into a form as similar as possible to that used in physical
systems determined byF-relations. With examples taken from physics, biology and sociology, it is shown that a definition of equilibria forQ-relational systems similar to the definitions used in physics can be obtained, provided the concept of stable or unstable
structures of a system determined byQ-relations is considered in a probabilistic manner. This offers an illustration of “fuzzy categories,” a notion introduced
by I. Bąianu and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968), in their paper on organismic supercategories, which is designed to provide a mathematical formalism for
Rashevsky's theory of Organismic Sets (Bull. Math. Biophysics,29, 389–393, 1967;30, 163–174, 1968;31, 159–198, 1969). A suggestion is made for a method of mapping the abstract discrete space ofQ-relations on a continuum of variables ofF-relations. Problems of polymorphism and metamorphosis, both in biological and social organisms, are discussed in the light
of the theory. 相似文献
9.
Robert Plonsey 《Bulletin of mathematical biology》1966,28(2):161-166
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. 相似文献
10.
D. A. Sprott 《Bulletin of mathematical biology》1957,19(3):163-170
Some probability distributions connected with distinct hits on targets, using two different firing schemes, are developed.
It is assumed that any shot has a probabilityp, not necessarily unity, of hitting the target at which it was aimed. The development uses a well-known expression for the
probability that exactlyt ofN possible events occur simultaneously. Some of the formulae developed here include as special cases the probabilities derived
separately and by more complicated arguments in papers by N. Rashevsky. (Bull. Math. Biophysics,17, 45–50, 1955) and A. Rapoport (Bull. Math. Biophysics,13, 133–38, 1951). 相似文献
11.
Charles J. Mode 《Bulletin of mathematical biology》1967,29(2):343-348
Some theoretical results obtained in a previous publication (Bull. Math. Biophysics,28: 25–50, 1966) are studied from the numerical point of view. Possible medical interpretations are suggested. 相似文献
12.
John Z. Hearon 《Bulletin of mathematical biology》1955,17(1):7-13
A differential equation has been derived by A. Rapoport,Bull. Math. Biophysics,14, 159 (1952), giving the time course of the fraction of the population who have performed a given act. The general solution
of this equation is obtained, some properties of the solution are deduced, and a special case presented in detail. 相似文献
13.
Anatol Rapoport 《Bulletin of mathematical biology》1960,22(1):85-97
The derivation of H. D. Landahl’s learning curve (1941,Bull. Math. Biophysics,3, 71–77) from a single information-theoretical assumption obtained previously (Rapoport, 1956,Bull. Math. Biophysics,18, 317–21) is extended to obtain the entire family of such curves with the number of stimuliM (to each of which one ofN responses is to be associated) as a parameter. No additional assumptions are required. The entire family thus appears as
a function of a single free parameter,k, all other parameters being experimentally determined. The theory is compared with a set of experiments involving the learning
of artificial languages. An alternative quasi-neurological model leading to the same equation is offered. 相似文献
14.
N. Rashevsky 《Bulletin of mathematical biology》1968,30(1):153-162
In a previous paper (Bull. Math. Biophysics,22, 257–262, 1960), an expression for the probability that a car jumps off a road as a function of the speed and the size of
the car was derived mostly from geometric and kinematic considerations, introducing only the reaction time as a biological
parameter. In subsequent papers (Bull. Math. Biophysics,29, 181–186, 187–188, 1967) a more detailed study was made of the exact shape of the tracking curve of the car which involved
several biological parameters of the driver. In the present paper the results of the previous studies are combined, and a
more general equation for the probability of jumping off the road is obtained. This probability, as in the earlier study,
increases with the speedv, widths
o and lengthl
o of the car, and decreases with widths of the lane. However, this probability also depends on several parameters which characterize the psychobiological constitution
of the driver. Unpublished experiments by Ehrlich, which corroborate the general conclusions, are briefly described. 相似文献
15.
N. Rashevsky 《Bulletin of mathematical biology》1968,30(4):751-760
Previous studies of L. Danziger and G. Elmergreen (Bull. Math. Biophysics,16, 15–21, 1954;18, 1–13, 1956) of possible biochemical periodicities in organisms assumed non-linear biochemical interaction between different
metabolites, because linear systems do not lead to undamped ocsillations. They treated homogeneous systems. Later N. Rashevsky
generalized their results to a more realistic case where the non-homogeneity due to the histological structure is considered.
(Some Medical Aspects of Mathematical Biology, Springfield, Illinois: Charles C. Thomas, Publisher, 1964;Bull. Math. Biophysics,29, 389–393, 1967.) As long as the histological structure remains constant, the existence of sustained periodicities requires
the assumption of non-linearity of biochemical interactions. If, however, the secretions of an endocrine gland affect the
histological structure of the target organ, notably as in the menstrual cycle, and if there is a feed-back, the equations
become non-linear and may admit sustained periodic solutions even if the purely biochemical interactions are linear. 相似文献
16.
J. S. Griffith 《Bulletin of mathematical biology》1965,27(2):187-195
The field equation derived in Part I (Griffith,Bull. Math. Biophysics,25, 111–120, 1963a) is examined further. The stability of critical solutions is investigated and it is shown that, at least
in certain cases, general solutions tend toward critical solutions. The relationship between the present field theory and
a conventional matrix formulation is derived. 相似文献
17.
N. Rashevsky 《Bulletin of mathematical biology》1966,28(1):117-124
The notion of relations between sets, defined in a previous publication (Bull. Math. Biophysics,23, 233–235, 1961) is generalized and some biological examples are given. A generalization ton-ary relation is suggested. 相似文献
18.
Kevin D. Reilly 《Bulletin of mathematical biology》1968,30(4):565-579
A mathematical model for learning of a conditioned avoidance behavior is presented. An identification of the net excitation
of a neural model (Rashevsky, N., 1960.Mathematical Biophysics. Vol. II. New York: Dover Publications, Inc.) with the instantaneous probability of response is introduced and its usefulness
in discussing block-trial learning performances in the conditioned avoidance situation is outlined for normal and brain-operated
animals, using experimental data collected by the author. Later, the model is applied to consecutive trial learning and connection
is made with the approach of H. D. Landahl (1964. “An Avoidance Learning Situation. A Neural Net Model.”Bull. Math. Biophysics,26, 83–89; and 1965, “A Neural Net Model for Escape Learning.”Bull. Math. Biophysics,27, Special Edition, 317–328) wherein lie further data with which the model can be compared. 相似文献
19.
N. Rashevsky 《Bulletin of mathematical biology》1972,34(1):65-69
By generalizing a previous paper on periodicities in the endocrine system (Bull. Math. Biophysics,30, 735–749, 1968), it is shown that nonperiodic, sporadic oscillations in the system are also possible. A procedure of describing
the feedback mechanism between the endocrine system and the central nervous system is suggested. It is shown that the combined
system: endocrine—CNS, also may show sporadic fluctuations. 相似文献
20.
Michael A. B. Deakin 《Bulletin of mathematical biology》1967,29(3):565-574
In a previous paper (Bull. Math. Biophysics,29, 549–563, 1967) the author derived equations to represent the flow of blood in an artery. It was pointed out that these did
not completely characterize the system and that an additional hypothesis was required. The hypothesis of minimal energy dissipation
had been thought to imply a central tendency on the part of suspended particles (erythrocytes). It is here shown that if the
fluid is non-Newtonian this may not be so. 相似文献