共查询到20条相似文献,搜索用时 15 毫秒
1.
John Z. Hearon 《Bulletin of mathematical biology》1953,15(1):15-21
Some general properties of the solution of the diffusion equation are deduced for the steady-state, spherically symmetric
system. On the basis of these developments some results of N. Rashevsky (Bull. Math. Biophysics,11, 15, 1949) are discussed and the results of a previous investigation (Hearon,Bull. Math. Biophysics,12, 135, 1950b) are extended to more general conditions. In particular these extensions apply to the flow of a soluteagainst its concentration gradient, the nonzero gradient of an inert metabolite, and theaccumulation or exclusion of an inert metabolite in a metabolic system.
A portion of 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》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
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.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
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
11.
Peter B. Bright 《Bulletin of mathematical biology》1967,29(1):123-138
Previous papers by F. M. Snell (Jour. Theor. Biol.,8, 469–479, 1965) and M. A. Fox and H. D. Landahl (Bull. Math. Biophysics,27, Spec. Issue, 183–190, 1965) have found that the formulation by previous authors for the oxygen flow rates through hemoglobin
solution as a function of pressure determined by E. Hemmingsen and P. F. Scholander (Science,132, 1379–1381, 1960) did not give a satisfactory quantitative fit of the curve for constant pressure difference. The suggestion
of Fox and Landahl that the Bohr effect involving the shift in acidity accompanying the oxidation of Hb should give rise to
voltage and pH differences in oxyhemoglobin transport is examined in more detail. In this paper, the previous expressions
for the total oxygen flow rate in terms of the end point concentrations are extended to include the effects of the electrical
field. Estimates of the potential difference shows it to be negligible. A derivation of a voltage-pH relation shows that the
Nernst relation does not apply and a negligible voltage difference does not preclude a pH shift which is the more probable
explanation of the discrepancies observed. Several other predictions suitable for experimental testing are made. 相似文献
12.
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
13.
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
14.
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
15.
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
16.
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
17.
Anatol Rapoport 《Bulletin of mathematical biology》1956,18(4):317-321
A learning curve derived by H. D. Landahl (Bull. Math. Biophysics,3, 71–77, 1941) from postulated neurological structures is shown to be derivable from simplified assumptions by introducing
the information measure of the uncertainty of response. The possible significance of this approach to learning theory is discussed. 相似文献
18.
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
19.
Robert I. Macey 《Bulletin of mathematical biology》1959,21(1):19-32
A generalization of Landahl's approximation method (H. D. Landahl,Bull. Math. Biophysics,15, 49–61, 1953) for non-linear diffusion problems is suggested. The method is applied to sorption, desorption, and free diffusion
problems involving concentration-dependent diffusion coefficients. With some limitations, the results compare favorably with
those obtained by numerical methods. 相似文献
20.
N. Rashevsky 《Bulletin of mathematical biology》1960,22(3):257-262
The discussions of a previous paper (Bull. Math. Biophysics,21, 299–308, 1959) are generalized by considering that the angular direction error made by the driver, as well as the driver's
reaction time are not constant but are randomly distributed. Instead of a critical speed, at which the car will jump off the
road, we now find that for every speed there is a probability of the car to jump off the road but that this probability is
vanishingly small for sufficiently low speeds, yet increases rapidly for high speeds. Thus a more realistic picture of the
process of driving is obtained. When the standard deviation of the distribution functions for the angle and the reaction time
are very small, the expression obtained here reduces to the expression obtained previously. 相似文献