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1.
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
2.
Robert Rosen 《Bulletin of mathematical biology》1965,27(1):11-14
The present note consists of two separate but related parts. In the first, a new graphtheoretic proof is presented that an
(ℳ,R)-system must always contain a nonreestablishable component. The second considers some questions concerning the relation between
re-establishability and the time-lag structure in (ℳ,R)-systems. It is supposed that the reader is familiar with the terminology of the author's previous work on (ℳ,R)-systems, particularly R. Rosen,Bull. Math. Biophysics,20, 245–260, 1958. 相似文献
3.
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
4.
Lloyd A. Demetrius 《Bulletin of mathematical biology》1966,28(2):153-160
Rosen’s identification of abstract biological systems, called (M,R)-systems, with sequential machines is formally characterized. It is then shown that the determination of environmental alterations
of (M,R)-systems from a knowledge of the response sequence and the structure of the system, which we call behavioral reversibility,
can be interpreted as information-losslessness of sequential machines. Applying this relationship, necessary conditions for
behavioral reversibility are derived. It is further shown that, similar to Rosen’s work on structural reversibility, (M,R)-systems are behaviorally reversible only if the number of physically realizable mappings are restricted. 相似文献
5.
I. Băianu 《Bulletin of mathematical biology》1973,35(1-2):213-217
On the basis of Rosen's representation of (M, R)-systems as sequential machines (Rosen,Bull. Math. Biophys.,26, 103–111, 1964), the existence of projective limits in categories of general (M, R)-systems is proved. 相似文献
6.
Robert Rosen 《Bulletin of mathematical biology》1959,21(4):387-394
The notion of automaton as used by J. von Neumann is formalized according to methods previously described (Rosen, 1958,Bull. Math. Biophysics
20, 245–60; 317–41). It is observed that a logical paradox arises when one attempts to describe the notion of self-reproducing
automaton in this formalism. This paradox is discussed, together with some of the recent attempts to construct automata which
exhibit self-reproduction. The relation of these results to biological problems is then investigated. 相似文献
7.
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
8.
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
9.
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
10.
N. Rashevsky 《Bulletin of mathematical biology》1968,30(2):351-353
It is suggested how nonoriented graphs may be used to representn-ary relations in organisms and to study the changes in variousn-ary relations under the transformation proposed in a previous paper (Bull. Math. Biophysics,16, 317–348, 1954). 相似文献
11.
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
12.
Robert Rosen 《Bulletin of mathematical biology》1963,25(1):41-50
The environmentally induced alterations in structure of (M, ℜ) which were described previously (R. Rosen,Bull. Math. Biophysics,23, 165–171, 1961) are examined from the standpoint of determining under what circumstances they can be reversed by further
environmental interactions. For simplicity we consider only the case of (M, ℜ)-systems possessing one “metabolic” and one “genetic” component. In the case of environmentally induced alteration of
the “metabolic” component alone, a necessary and sufficient condition is given for the reversibility of the alteration. In
the case of alteration of the “genetic” component, the situation becomes more complex; several partial results are given,
but a full analysis is not available at this time. Some possible biological implications of this analysis are discussed.
This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air
Research and Development Command, under Contract no. AF-49(638)-917 and Grant no. AF-AFOSR-9-63. 相似文献
13.
N. Rashevsky 《Bulletin of mathematical biology》1957,19(3):205-208
The possibility of several homotopic classes of mappings of the graph of an organism onto the primordial graph (Bull. Math. Biophysics,16, 317–48, 1954) is considered. An application of this possibility is suggested for the theoretical determination as to what
type of new biological functions may be acquired by certain cells which originally perform a different biological function. 相似文献
14.
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
15.
N. Rashevsky 《Bulletin of mathematical biology》1959,21(1):97-100
In line with a recent suggestion by the author (Bull. Math. Biophysics,20, 267–73, September, 1958) that not only does the organism as a whole map on the primordial, but that each organ can also
be thus mapped, it is shown that the previously introduced abstract spaces, which represent an organism, contain subspaces
which map continuously on the space of the primordial. Several theorems about those subspaces are proven. 相似文献
16.
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
17.
N. Rashevsky 《Bulletin of mathematical biology》1963,25(1):59-74
The principle of adequate design (N. Rashevsky,Mathematical Biophysics, 3rd Ed., Vol. II, Dover Publications, Inc., New York, 1960) is applied to some parts of the cardiovascular system, extending
the work of David Cohn (Bull. Math. Biophysics,16, 59–74, 1954;ibid.,17, 219–227, 1955). In addition to the diameterr
a
of the aorta and the peripheral resistanceR, calculated by Cohn, other quantities are estimated as to their order of magnitude. It is shown that the specifications of
the average metabolic rate lead, from considerations of design, to the possibility of evaluating the orders of magnitude of
the average blood pressure, the systolic and diastolic pressures, stroke volume of the heart, duration of the cardiac period
and the volume elasticity of the aorta. The calculated values are of the correct orders of magnitude. The purpose of the paper
is to illustrate how the application of the principle of adequate design can lead to the evaluation of the above parameters
from purely theoretical considerations, rather than from indirect measurements. 相似文献
18.
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
19.
N. Rashevsky 《Bulletin of mathematical biology》1959,21(1):101-106
In a preceding paper (Bull. Math. Biophysics
20, 71–93, 1958) the principle of biotopological mapping was formulated in terms of a continuous mapping of an abstract space,
made from the set of biological properties which characterize the organism, by an appropriate definition of neighborhoods.
In this paper it is shown that we may consider directly the mappings of the different sets of properties which characterize
different organisms without taking recourse to abstract spaces. All the verificable conclusions made in the preceding paper
remain valid. A serious difficulty mentioned previously is, however, avoided and the possibility of more general predictions
is established. 相似文献
20.
Robert Rosen 《Bulletin of mathematical biology》1960,22(2):199-205
An error appearing in the proof of Theorem 4 of a previous paper of the author’s (1959,Bull. Math. Biophysics,21, 289–97) is pointed out, and a new proof of the theorem is supplied. We also obtain a corollary from Theorem 3 ofloc. cit. which reveals the existence of a hitherto unrecognized class of codes. 相似文献