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  (388,238)
  • Elsevier  (208,466)
  • 1970-1974  (293,830)
  • 1965-1969  (226,282)
  • 1950-1954  (43,660)
  • 1935-1939
Collection
Keywords
Publisher
Years
Year
  • 1
    facet.materialart.
    Unknown
    Figures of: The Mineral Resources of the Sea (1965)
    Elsevier
    In:  EPIC3Amsterdam, Elsevier
    Details
    Publication Date: 2016-08-25
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Format: image/jpeg
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    PAPER (OA)
  • 2
    Electronic Resource
    Electronic Resource
    Contributions to the theory of organismic sets, II: Aggressiveness and submissiveness (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 49-54 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the theory of organismic sets (Bull. Math. Biophysics,31, 159–198, 1969) we considered organisms as sets endowed with certain “activities,” the latter’s resulting in a set of “products.” Those products may be of a material nature, like a hormone secreted by a cell, or of a non-material nature, like a feeling or an attitude. In the present paper aggressiveness and submissiveness are considered as such non-material products of the activities of the brain cells. A general description of aggressiveness and submissiveness is given in terms of organismic sets. Cycles in “peck order” are thus naturally explained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476664
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Contribution to the theory of organismic sets, III (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 55-66 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In line with previous studies on organismic sets, the division of all organismic sets intogeneral autotrophic and heterotrophic is introduced. The first produce their food themselves from some external source of energy, which in general may be an energy of any kind. The others use other organismic sets as the source of their food and energy. On earth we know only one kind of generalgeneral autotrophic organismic sets, namely, the autotrophic plants which use solar radiation as their source of energy and for production of their own food. It is shown why autotrophic animals do not exist on earth except as microorganisms like, e.g.,Euglena. A rigorous proof of the previously derived theorem that in an organismic set of ordern〉1 no element can be completely specialized is given. It requires the introduction of new postulates. Finally, in considering the organic world as a whole, the notion of organismic sets ofmixed order is introduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476665
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    “A stochastic solution of the 3-body problem in chemical kinetics. The termolecular stochastic process I” (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 67-81 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It appears to be axiomatic that termolecular and higher order reactions occur relatively rarely. The basis for this judgment seems to lie in the supposition that successful 3-Body collisions of 3 interactive species of molecules cannot occur frequently enought to account for chemical or biochemical transformation. In order to provide a more complete mathematical framework than now exists for examining this hypothesis the probability of effective termolecular “δ-collisions” as a function of time is derived. This amounts to adding to the class of reactions for which stochastic models are now available the termolecular reaction. In common with the unimolecular and bimolecular cases this process is seen to satisfy the criterion of consistency-in-the-mean with respect to deterministic formulations. It is planned next to use the termolecular process and the lower order processes in computer-assistedin numero experimental studies aimed at comparing alternative mechanisms of reaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476666
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Maximum likelihood estimation for stochastic first order reactions (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 83-96 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Small sample properties of the maximum likelihood estimator for the rate constant of a stochastic first order reaction are investigated. The approximate bias and variance of the maximum likelihood estimator are derived and tabulated. If observations of the system are made at timesiτ,i=1, 2, ...,N; τ〉0, the observational spacing τ which minimizes the approximate variance of the maximum likelihood estimator is found. The non-applicability of large sample theory to confidence interval derivation is demonstrated by examination of the relative likelihood. Bartlett’s method is employed to derive approximate confidence limits, and is illustrated by using simulated kinetic runs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476667
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Random walk with persistence and external bias (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 311-338 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The partial differential equation of the random walk problem with persistence of direction and external bias is derived. By persistence of direction or internal bias we mean that the probability a particle will travel in a given direction need not be the same for all directions, but depends solely upon the particle's previous direction of motion. The external bias arises from an anisotropy of the medium or an external force on the particle. The problem is treated by considering that the net displacement of a particle arises from two factors, namely, that neither the probability of the particle traveling in any direction after turning nor the distance the particle travels in a given direction need be the same for all directions. A modified Fokker-Planck equation is first obtained using the assumptions that the particles have a distribution of travel times and speeds and that the average time of travel between turns need not be zero. The fional equation incopporating the assumption of a persistence of direction and an external bias is then derived. Applications to the study of diffusion and to long-chain polymers are then made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476407
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Methods of statistical analysis (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 383-383 
    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/BF02476411
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    The transmission of excitation from the membrane to actomyosin (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 385-385 
    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/BF02476412
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    On the spread of information with time and distance (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 367-381 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The transmission of some information or behavior pattern is treated as a flow of “particles” which execute random motions over a population of individuals and which may multiply or disappear. Equations are derived for the number density of these “particles” and from this is calculated the number of individuals through which the “particles” have passed. The results are applied to a number of situations such as 1) uniform spatial distribution with multiplication factor decreasing with time because of loss of interest or confusion of the information, 2) multiplication factor constant but the rate of spreal decreasing with multiple hearings, 3) one-dimensional region with a small starting region with or without an absorbing barrier 4) two-dimensional region with absorbing barrier, 5) continous sources of information within a small region in one dimension, 6) uniform spatial distribution in which individuals do not respond to more than one hearing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476410
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 387-394 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A situation is considered in which a fluid containing a substance flows through a vessel at a constant rate, the substance being permeable to the vessel wall. In the region outside the vessel there is supposed to be rapid mixing in the direction perpendicular to the axis of the vessel but no mixing longitudinally. The solution for the spatial distribution at any time is given for the case of an arbitrary initial distribution along the vessel length in the absence of an input. The solution is also given for the case of a single impulsive input, the concentration being initially zero everywhere.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476432
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    Organismic supercategories and qualitative dynamics of systems (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 339-354 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476778
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    Some realizations of (M, R)-systems and their interpretation (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 303-319 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some years ago (Rosen 1958a, b; 1959) we described a class of metaphorical, relational paradigms for cellular activity which we termed (M, R)-systems. A sizable amount of subsequent work, to be itemized below, has been devoted to an exploration of some of the properties of these systems. The main purpose of the present paper is to put this class of paradigms into a general system-theoretic perspective, with a particular view to appraising the relation between the type of system description embodied in the (M, R)-system and other kinds of physical and mathematical descriptions of cellular systems. Thus, the principal aim is to establish the relationships and connections between the global relational formalism embodied in the (M, R)-systems and the empirical descriptions which still represent the bulk of our biological knowledge.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476776
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 13
    Electronic Resource
    Electronic Resource
    Relational forces and structures produced by them (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 321-338 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476777
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 14
    Electronic Resource
    Electronic Resource
    A mathematical contribution to the study of orientation of organisms (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 431-476 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Organisms orient themselves to a stimulus by two general methods. One method is by directed orientation (taxis); the other is by undirected locomotory reaction (kinesis). An equation, and the methods for finding the necessary parameters of this equation, is derived for the distribution of organisms within a container, with the following limitations: (1) the organisms have no accommodation, (2) they are always active, and (3) the stimulus changes slowly with position. Necessary modifications of the equation are then derived, so that the last two limitations may be eliminated. The equation cannot be solved excatly because of its complexity; hence an approximation method must be used. This method is discussed, an approximate solution is found, and a time constant for equilibrium to be established is derived. Applications tovarious experiments in the literature are then made with fairly satisfactory results. A new interpretation of the theory of klino-kinesis with accommodation is found upon application of the equations developed to experimental work. Further limitations and uses of these equations are then discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476435
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 15
    Electronic Resource
    Electronic Resource
    Structural parameters of communication networks (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 501-507 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Certain parameters are defined which roughly characterize the internal structure of networks. A given network structure uniquely determines the values of the parameters, but the reverse is not true. The parameters therefore define certain classes of networks. One of the parameters, thedispersion D(S) gives an indication of the “compactness” of the internal structure. Addition theorems and inequalities are derived relating the dispersions of sub-systems to the dispersion of the complete structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476438
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 16
    Electronic Resource
    Electronic Resource
    Determination of diffusion and permeability coefficients in nerve trunks (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 489-500 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476437
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 17
    Electronic Resource
    Electronic Resource
    Enzyme localization as a mechanism of apparent active transport (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 509-522 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model based on enzyme localization is developed which gives rise to an apparent active transport of a metabolite into or out of cells. The model is applied to three simple situations, using Fick's equation and the Rashevsky approximation. It is shown that the apparent efficiency can be made as large as desired if, for constant reaction, the outer cell region is made sufficiently small, or, for autocatalytic reaction, if the metabolite concentration in the outer region is sufficiently small. The physical limitations imposed by this mechanism are developed for all three situations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476439
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 18
    Electronic Resource
    Electronic Resource
    Spread of information through a population with socio-structural bias: I. Assumption of transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 523-533 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A previously derived iteration formula for a random net was applied to some data on the spread of information through a population. It was found that if the axon density (the only free parameter in the formula) is determined by the first pair of experimental values, the predicted spread is much more rapid than the observed one. If the successive values of the “apparent axon density” are calculated from the successive experimental values, it is noticed that this quantity at first suffers a sharp drop from an initial high value to its lowest value and then gradually “recovers”. An attempt is made to account for this behavior of the apparent axon density in terms of the “assumption of transitivity”, based on a certain socio-structural bias, namely, that the likely contacts of two individuals who themselves have been in contact are expected to be strongly overlapping. The assumption of transitivity leads to a drop in the apparent axon density from an arbitrary initial value to the vicinity of unity (if the actual axon density is not too small). However, the “recovery” is not accounted for, and thus the predicted spread turns out to beslower than the observed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476440
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 19
    Electronic Resource
    Electronic Resource
    Spread of information through a population with socio-structural bias: II. Various models with partial transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 535-546 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The assumption of transitivity treated in part I is modified in various ways to describe an information-diffusion process, in which a certain amount of randomness of contact does occur. In one model a parameter is introduced which is indicative of a tendency to go beyond one's immediate vicinity to spread the information as the vicinity becomes saturated with knowers. In another model the randomness appears in the assumption that new knowers are uniformly distributed among the knowers. Two of the equations thus derived, each with two free parameters are in good agreement with experimental results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476441
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 20
    Electronic Resource
    Electronic Resource
    Probabilistic and multiple regression modeling of the biologist’s decision processes and its implications for medical diagnosis (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 439-449 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Current psychological research into the inference (diagnostic) process is briefly reviewed, using as a vehicle an investigation of the prediction of the probability of success of hypothetical applicants to a graduate program in biology. Brunswik’s lens model and multiple regression analysis are used, as is a Bayesian approach. Four judges’ (biologists’) predictions are analyzed. Some general conclusions about inference, drawn from the current data in psychology, are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476785
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 21
    Electronic Resource
    Electronic Resource
    Anin numero study of glucose-insulin interaction (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 451-462 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model has been developed to simulate the glucose-insulin interaction following a glucose load such as occurs in an IVGTT. This model differs from earlier models in that the insulin response to glucose loading is a recurring all or none threshold response. The model has been simulated on a digital computer using the digital analog simulation language CSMP.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476786
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 22
    Electronic Resource
    Electronic Resource
    Wave propagation in bone media (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 463-479 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The composite nature of bone dictates the use of a model for bone which is transversely isotropic. We solve the associated sets of partial differential equations governing the dynamic elastic behavoor of a two-layered cylindrical-shaped bone. The solution is analyzed for long, short, and intermediate length waves. The special case of compact bone is treated for long and short wave lengths and a numerical example is worked out to determine the wave speeds (for short wave lengths) given a set of elastic constants, determined by ultrasonic methods, and the bone density, wave frequency, and radius.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476787
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 23
    Electronic Resource
    Electronic Resource
    Fourth International Biophysics Congress (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 481-481 
    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/BF02476788
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 24
    Electronic Resource
    Electronic Resource
    Obituary of Nicolas Rashevsky (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. i 
    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/BF02477019
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 25
    Electronic Resource
    Electronic Resource
    On the stochastic theory of compartments: I. A single-compartment system (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 53-63 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A stochastic model is developed for a compartment with a single time-dependent input, and generalized to include inputs from several sources. With the number of particles of a given molecular species in the compartment as the random variable, the mean, variance and third central moment of this variable are calculated from its generating function, and compared with previous results. The behavior of the calculated moments is discussed, and the possibility of applying the model to chemical and biological systems is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477024
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 26
    Electronic Resource
    Electronic Resource
    A remark on sensory deprivation from the point of view of organismic sets (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 439-441 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that from the definition of organismic sets (Rashevsky,Organismic Sets. Some Reflections on the Nature of Life and Society, Holland, Michigan, Mathematical Biology, Inc. and Grosse Pointe, Michigan, J. M. Richards Laboratory) a complete sensory deprivation of an organismic set of ordern=2 should result in malfunctioning of the set. A generalization to higher order sets is suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476706
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 27
    Electronic Resource
    Electronic Resource
    Optimal branching structure of the vascular tree (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 431-438 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Optimality in branching structure of the vascular tree was studied. Analysis on its physiological roles as the duct system for blood supply to the capillaries predicted that the vascular tree should be constructed with minimum volume under restriction of determinant pressure, flow and location at the origin and the terminals. Mathematical derivations of this conditional extremum problem yielded some equations expressing the relations between the radii of the branches and their branching angles, which provided numerical solutions for branching points of bi- and poli-terminal minimum volume trees. Comparison of the peritoneal vascular tree in a dog with the minimum volume one computed under the same restrictive conditions showed good agreement in their branching structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476705
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 28
    Electronic Resource
    Electronic Resource
    First order kinetics in a distributed model (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 443-456 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In order to determine the kinetics of passage of a substance through an organ containing a tangle of vessels, we study the response of a tube to various inflows (perfusion, brief injection, ...). The introduction of the catabolic terms and of the spatial dependence between bulk concentration and surface concentration allows one to account for the difference of arteriovenous concentrations observed experimentally for many metabolites. The relationships between the physico-chemical parameters of the organ and the operational parameters of the model demonstrate the importance of the transit time through the considered vessels. If one considers the different pathways as independent, the introduction of the transit time distribution for an inert substance enables one to compute the response of the organ analytically or by recurrence, using convolution. The parameters of the model can be obtained by the moments method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476707
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 29
    Electronic Resource
    Electronic Resource
    Stochastic simulation of the gas diffusion in the air phase of the human lung (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 457-466 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The solution of the diffusion equation in the gas phase of the human lung is very difficult because of the structure of the bronchial tree. It is shown by means of physical arguments, how one can reduce the diffusion equation to a simple one-dimensional form. The solution is then obtained by a stochastic simulation, which is easily realized on a digital computer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476708
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 30
    Electronic Resource
    Electronic Resource
    A new mathematical model of the respiratory center (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 467-481 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new mathematical model of the oscillatory behavior of the respiratory center has been developed based upon published records of neuronal activity during respiration in the pons and medulla. In contrast with a previous model, four, rather than two, networks are assumed to interact in the respiratory center so as to produce the respiratory oscillation. A mathematical description of this interaction, in the form of a set of four first-order, nonlinear, coupled differential equations, is derived; the behavior of the solutions of this system is studied qualitatively, and expressions for the durations of the inspiratory and expiratory phases are obtained in terms of some parameters. It is found that central and chemical influences drive the medullar neurons to a position somewhere between saturation and full cutoff, and the pontine neurons deeply into cutoff. The control of the duration of the different phases by these chemical and central means is discussed. In order to effect a decrease in the magnitude of the various times, the neurons have to be driven towards operating points of higher central facilitation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476709
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 31
    Electronic Resource
    Electronic Resource
    A mathematical model for calcium homeostasis (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 483-502 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In vivo control of calcium is analysed under the assumption that hormonal influences via plasma levels of parathormone and calcitonin are of prime (but not absolutely dominating) importance. A brief review concerning the physiological significance of body calcium and the mode of action of these two hormones is presented as an introduction to the basic philosophy of the study. A theoretical quasi-linear lumped-parameter model is developed to describe variations in ionic calcium, parathormone and calcitonin plasma concentrations to specific input stimuli. Formal evaluation of the system response requires the determination of ten constants, together with quantitation of ingested calcium entry into the plasma compartment which isindependent of hormonal influences. Values for various parameters are deduced from published data and experimental procedures are outlined to facilitate determination of the remaining unknowns. It is suggested that the proposed model should prove useful for investigations concerning general hormonal actions on calcium homeostatic mechanisms in both normal and diseased states, with particular reference to calcitonin.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476710
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 32
    Electronic Resource
    Electronic Resource
    The struggle for life: III. A predator-prey chain (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 521-532 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Ann species predator-prey chain is analyzed to determine what oscillations occur in population sizes. It is found that only the populations of the first and second species in the chain must necessarily oscillate around the point of equilibrium if they do not come to equilibrium. The other species may or may not oscillate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476712
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 33
    Electronic Resource
    Electronic Resource
    Mathematical models for exchange of substances in regional vascular beds— Measurement of the rates within vivo counters (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 503-520 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Sangren and Sheppard developed a mathematical model for first-order processes taking place in the regional circulation, applicable—for example—to tracer studies of potassium transport. It permits calculation of specific activity at any point along a “tube of flow” or in the cuff of tissue surrounding it as a function of time following a spike injection of tracer. In efforts to relate to the exchange a rate curves obtained within vivo counters pointed at the region of interest, we developed a compartment-system model of the process. In investigating the properties of the Sangren and Sheppard model integrated over an entire circulatory bed, as thein vivo counter would see it, we found that when the distribution of transit times of the “tubes of flow” can be approximated by an exponential sum, the solution reduces to that of the compartment system model. This results in an important simplification in the calculation, and insight into the assumptions underlying the two different models. A curve-fitting computer program for the compartment model has been written and applied to double-isotope studies of potassium transport in the hind leg of the dog.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476711
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 34
    Electronic Resource
    Electronic Resource
    A numerical experiment on the determination of kinetic rate constants in the presence of diffusion (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 547-558 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two chemicals,A andB, are allowed to diffuse together and a reaction described by $$A + B\mathop \rightleftharpoons \limits_{K_{ - 1} }^{K_1 } C$$ is allowed to proceed. This system is described mathematically by a system of partial differential equations. A numerical procedure is presented to find the rate constants ofK 1 andK −1. A systematic analysis of the effects of errors is also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476714
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 35
    Electronic Resource
    Electronic Resource
    Observations on cardiac energetics: I. Theoretical introduction (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 533-546 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Equations are developed to describe the energy expenditure of the human heart. As well as the external potential and kinetic energy terms, general consideration is given to other possible avenues of energy consumption. Emphasis is placed upon using mathematical variables which are readily available for experimental verification. The errors involved in assuming that mean values for the physiological parameters give reasonable estimations for the external mechanical performance are examined, and a theoretical estimation for the discrepancy in the kinetic component is presented. Logical extension of the mathematical derivation leads to a determination of cardiac external mechanical efficiency and clearly demonstrates the significance of the ventricular pressure-volume loop in this context. Finally, experimental procedures are suggested to clarify further some of the conclusions reached through the theoretical analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476713
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 36
    Electronic Resource
    Electronic Resource
    Organismic sets. Sex in animal and human societies (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 559-563 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The question is discussed as to the reason why some animal societies, such as bees or ants, are sexually differentiated, that is, onlysome of its members are exhibiting reproducing activities. It is indicated that human society may be on its way to such a sexual differentiation which may eventually come.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476715
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 37
    Electronic Resource
    Electronic Resource
    Some biochemical threshold mechanisms (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 565-565 
    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/BF02476716
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 38
    Electronic Resource
    Electronic Resource
    Announcement (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 567-567 
    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/BF02476717
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 39
    Electronic Resource
    Electronic Resource
    The structure of DNA as deduced from fiber X-ray crystallography (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 301-311 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract X-ray diffraction patterns obtained experimentally for fibers, together with their chemical structures, can be analyzed theoretically in terms of an integral equation. The partially unknown electron density function can be solved by iteration. This mathematical technique has been applied with success to study the secondary structures of DNA fibers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458338
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 40
    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
  • 41
    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
  • 42
    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
  • 43
    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
  • 44
    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
  • 45
    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
  • 46
    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
  • 47
    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
  • 48
    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
  • 49
    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
  • 50
    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
  • 51
    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
  • 52
    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
  • 53
    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
  • 54
    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
  • 55
    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
  • 56
    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
  • 57
    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
  • 58
    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
  • 59
    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
  • 60
    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
  • 61
    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
  • 62
    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
  • 63
    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
  • 64
    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
  • 65
    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
  • 66
    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
  • 67
    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
  • 68
    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
  • 69
    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
  • 70
    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
  • 71
    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
  • 72
    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
  • 73
    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
  • 74
    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
  • 75
    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
  • 76
    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
  • 77
    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
  • 78
    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
  • 79
    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
  • 80
    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
  • 81
    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
  • 82
    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
  • 83
    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
  • 84
    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
  • 85
    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
  • 86
    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
  • 87
    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
  • 88
    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
  • 89
    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
  • 90
    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
  • 91
    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
  • 92
    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
  • 93
    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
  • 94
    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
  • 95
    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
  • 96
    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
  • 97
    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
  • 98
    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
  • 99
    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
  • 100
    Electronic Resource
    Electronic Resource
    Information Processing in the Visual Systems of Arthropods (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 339-340 
    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/BF02461333
    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...