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1.
N. Rashevsky 《Bulletin of mathematical biology》1964,26(1):57-61
In connection with a series of previous papers by this author (Bulletin of Mathematical Biophysics,21, 299–308, 375–385;22, 257–262, 263–267;23, 19–29;24, 319–325) results obtained by A. Crawford (Economics
5, 417–428) on the effects of irrelevant lights on reaction times toward a given light stimulus are discussed. The conclusions
from a previous paper of this author (Bulletin of Mathematical Biophysics,23, 19–29) are elaborated. 相似文献
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
N. Rashevsky 《Bulletin of mathematical biology》1968,30(2):355-357
It is suggested that the development of organismic sets is governed not by the maximalization of the integral survival value,
as suggested previously (Bull. Math. Biophysics,28, 283–308, 1966;29, 139–152, 1967;30, 163–174, 1968), but by maximizing the number of new relations which appear as an organismic set develops. 相似文献
10.
N. Rashevsky 《Bulletin of mathematical biology》1972,34(2):213-222
This paper compares two previously published neural models for epilepsies (Bull. Math. Biophysics,33, 539–553, 1971;34, 71–78, 1972). The second model is developed in more detail and an attempt is made to bring it more in line with established
neurological findings. The question of classification of some epilepsies is briefly discussed. 相似文献
11.
The theory of relations between sets, proposed and outlined in previous publications (Bull. Math. Biophysics,23, 233–235, 1961;28, 117–124, 1966;28, 309–313, 1966), is tentatively expanded and generalized with a view to biological applications. 相似文献
12.
George Karreman 《Bulletin of mathematical biology》1961,23(2):135-140
By the same method as in the previous paper by the author (Bull. Math. Biophysics,23, 55–68, 1961), the mobile electron system is studied in tryptophan which has donated an electron to another molecule. The
obtained net charge distribution of tryptophan+ is compared with those of the semiquinones of riboflavin (FMN−, FMNH and FMNH
2
+
). From this comparison, a suggestion is obtained for the structure of each of two charge transfer complexes between riboflavin
and tryptophan in neutral and acid solution. 相似文献
13.
H. E. Hart 《Bulletin of mathematical biology》1960,22(1):41-52
The methods of C. W. Sheppard and A. S. Householder (Jour. App. Physcis,22, 510–20, 1951), H. D. Landahl (Bull. Math. Biophysics,16, 151–54, 1954) and H. E. Hart (Bull. Math. Biophysics,17, 87–94, 1955;ibid.,19, 61–72, 1957;ibid.,20, 281–87, 1958) are employed in studying the kinetics of generalN compartment systems. It is shown that the nature of the transfer processes occurring in fluid flow systems and the chemical
processes occurring in quadratic systems and in catalyzed quadratic systems can in principle be completely determined for
all polynomial dependencies. Systems involving three-body and higher-order interactions can be completely solved, however,
only if supplementary information is available.
Research supported by the Atomic Energy Commission, Contract AT (30-1)-1551. 相似文献
14.
Ernesto Trucco 《Bulletin of mathematical biology》1957,19(1):19-21
In the bio-topological transformation between graphs denoted by (T
(1)
X) N. Rashevsky (Bull. Math. Biophysics,18, 173–88, 1956) considers the number of fundamental sets which (a) have only one specialized point as source (and no other
sources), (b) have no points in common (are “disjoined”); he proves that this number is an invariant of the transformation.
In this note we show that Rashevsky's Theorem can be extended as follows:The number of fundamental sets of the first category is an invariant of the transformation. We must, however, count the subsidiary points of the transformed graph as specialized points. We recall that fundamental
sets of the first category are those whose sources consist of specialized points only (Trucco,Bull. Math. Biophysics,18, 65–85, 1956). But in this modified version of the Theorem the fundamental sets may have more than one source and need not
be disjoined. 相似文献
15.
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
16.
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
17.
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
18.
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
19.
I. Băianu 《Bulletin of mathematical biology》1971,33(3):339-354
The representation of biological systems by means of organismic supercategories, developed in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–71;32, 539–561), is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Băianu
and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis
of this comparison some concrete result concerning dynamics of genetic system, development, fertilization, regeneration, analogies,
and oncogenesis are derived. 相似文献
20.
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