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  (67,029)
  • 1980-1984  (42,164)
  • 1965-1969  (24,865)
  • 1925-1929
  • 1980  (42,164)
  • 1965  (24,865)
  • 1
    Electronic Resource
    Electronic Resource
    Complementary variational principles for diffusion problems with Michaelis-Menten kinetics (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 131-135 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for diffusion problems with Michaelis-Menten kinetics. In an illustrative calculation we obtain an extremely accurate variational solution in good agreement with the numerical solution of McElwain (1978).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462371
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Structural order and partial disorder in biological systems (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 137-141 
    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/BF02462372
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Primitivity of the product of two Leslie matrices (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 181-189 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Necessary and sufficient conditions for primitivity of a product of two Leslie matrices are given. Such a product could be used in modeling the growth of a population governed alternately by two different sets of fertility and survival parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464637
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Frequency analysis of time-varying elastance model of the left ventricle (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 173-180 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Zadeh's transfer function method for linear time-variable systems is used to apply frequency-domain analysis to a periodically time-varying elastance model of the left ventricle. Left ventricular pressure computed from the system function of the time-varying elastance and the phasors of aortic flow shows a typical waveform of the measured ventricular pressure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464636
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    The 9th Annual Northeast Biomedical Engineering Conference (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 901-901 
    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/BF02461068
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Compartmental systems and generating functions (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 49-63 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Compartmental systems can be represented by direct graphs in which each node corresponds to a generating function and each arm to a transfer generating function. A homomorphism is established between a compartmental system and this representation, in analogy with that obtained through the use of the Laplace transformation. From the values obtained experimentally in a given compartment, through the solution of a difference equation, the generating function for the corresponding node can be calculated and the graph of the system can be built up within the degrees of freedom of the model. From the graph it is possible to calculate the transfer generating function between any two connected nodes, the mean permanence time in a given node, the mean transit time between two nodes, and their precursor-successor order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477261
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    On the competitive exclusion principle (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 85-89 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Competitive Exclusion Principle, formulated by V. Volterra (Memorie del R. Comitato Talassografico Italiano,131, 1–142, 1927) for a number of species competing for a common ecological niche, is extended to a number of species competing for many ecological niches.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477264
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Periodic and aperiodic phases of circulatory mixing (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 65-70 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A modification is presented of an earlier theory of the mixing of dye following injection into the circulation. Approximate theoretical relations are given for the concentration of dye in the right heart and in the aorta following right atrial injection. It is shown that when the probability distribution of transit times around the circulation has a prolonged tail, mixing waves are now inscribed about a quasi-exponential relation. Later in time the relation levels off to a uniform asymptotic concentration corresponding to an equilibrium volume of dilution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477262
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Cooperative specific adsorption of ions at charged sites in an electric field (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 91-104 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The adsorption of two cations at the anionic sites of a polymer (e.g., such as a protein) in an electric fields is discussed, taking into account cooperative interaction of the cations mediated through the backbone of the polymer. The calculation of the grand partition function explicitly considers the vacant negative sites of the polymer. As in the case without cooperative interaction, the problem reduces to the determination of the largest eigenvalue of asymmetric matrices. The weights of the different neighbor configurations are determined. Approximate formulae for the grand partition function and for those weights are derived. The formal analogy of these cooperative phenomena and those occurring in quantum (bio)chemistry is pointed out exemplifying an earlier suggestion about the basis of quantum biology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477265
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    A proposed mechanism for the sol-gel transformation (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 105-112 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The transformation from gel to sol in cell cytoplasm is treated as the transition from a lattice of macromolecules linked by Ca++ ions to a random distribution of the macromolecules. The transition is a cooperative process, whose probability is expressed in terms of the theory of runs. The process is related to cell metabolism by the assumption that available Ca++ concentration is regulated by metabolically produced endogenous chelating agents.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477266
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    Kinetic criteria of solid state mechanisms in biology (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 113-118 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Kinetic criteria for solid state physical mechanisms of electron and ion transport in biological systems are summarized, and the mechanisms are discussed. A reaction which is rate-limited by electron or ion transport across a particle or membrane in accord with Ohm's law will show first order kinetics, with an hyperbolic relationship between rate constant and the sum of substrate plus product. Larger initial substrate concentrations produce smaller rate constants, thus giving the appearance of substrate inhibition. Examples are cytochrome oxidase and peroxidase, and pyruvate carboxylase. Ohmic transport mechanisms may be caused by electron conduction or superconduction through protein, by electron conduction through water, or by conduction of ions through membranes. A reaction which is rate-limited by charge transport across an activation energy barrier at an interface in accord with a logarithmic voltage-current law will show reaction kinetics conforming to the Elovich equation, and will have the appearance of a pair of simultaneous first order processes. Examples include decay of photogenerated free radicals in eye melanin particles and in photosynthetic particles of bacteria, and sodium and potassium ion transport across cell surfaces. The logarithmic voltage-current law may be regarded as an empirical relationship describing behavior of interfaces, justified by extensive experimental data on many types of interfaces, or it may be derived theoretically for individual cases from statistical mechanical and/or solid state physical considerations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477267
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    Analysis of some effects of aortic smooth muscle onin vivo aortic pressure curves (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 119-130 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract When aortic pressure curves were predicted previously on the basis of a newly developed model of visco-elastic properties of the aorta, it was necessary to use published viscoelastic constants. These were usually obtained from longitudinal strips of blood vessels long removed from the animal, and therefore probably containing deteriorated smooth muscle. The predicted curves had the same form as actual tracings, substantiating the analysis somewhat, but the pressure levels were low. These low levels, if due to inadequate visco-elastic constants, could be attributed to the use of longitudinal rather than circumferential segments as well as to the use of segments with deteriorated muscle. The present analysis uses data collected by the author testing circumferential viscoelastic properties of fourteen different aortic regions in a way suggested by the author's model of an aortic wall. Moreover, the constants were measured on segments containing muscle relaxed by EDTA solutions and on similar segments containing muscle contracted by neosynephrine. These visco-elastic constants were used in the author's nonlinear differential equation of motion of the aortic wallin vivo to predictin vivo pressure curves. The predicted curves were low in any given aortic region if relaxed constants were used, but at normal levels with contracted constants. In fact, pressure curves predicted using constants obtained from aortic segments containing contracted muscle resembled actual tracings in form and pressure levels. Even the observed variations in the form of the systolic pressure curve down the aorta were predicted by this analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477268
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 13
    Electronic Resource
    Electronic Resource
    Biological similarity relative to allometric quantities (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 131-133 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is an empirical finding that an allometric quantity with dimensional exponents α, β and γ relative to mass, length, and time, respectively, has a value for its allometric exponentb satisfying the relation $$\tfrac{1}{3}(3\alpha + \beta + {\gamma \mathord{\left/ {\vphantom {\gamma 2}} \right. \kern-\nulldelimiterspace} 2}) \leqslant b \leqslant \tfrac{1}{3}(3\alpha + \beta + \gamma ).$$ A theoretical derivation is given of this double inequality using only the fact of constant density and the plausible assumption that metabolic rate is a dominant allometric quantity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477269
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 14
    Electronic Resource
    Electronic Resource
    The entropy of a continuous distribution (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 135-143 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract C. Shannon's definition (Bell System Technical Journal,27, 379–423, 1948) of the entropy of a continuous distribution is dimensionally incorrect and does not have the same significance as the corresponding definition in the discrete case. A new definition is proposed: this modified entropy is more like the entropy of a discrete distribution in one way, in another more like Shannon's “transmission rate.” The ideas are illustrated by reference to Wright's study of the hereditary influence on the coat pattern of the guinea pig.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477270
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 15
    Electronic Resource
    Electronic Resource
    Theorems on random evolution (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 145-150 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the following paper, a possible mode of evolution is described which differs from the traditional modes in not being selective in the Darwinian sense.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477271
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 16
    Electronic Resource
    Electronic Resource
    Information theory and genetics (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 177-181 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A description of the kinds of systems susceptible to information theoretical analysis is given. By means of an example, certain common fallacies in the application of communication theory to biology are illustrated. The entropy-information analogy is discussed. *** DIRECT SUPPORT *** A01E2109 00008
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477274
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 17
    Electronic Resource
    Electronic Resource
    A note on equivalent mathematical models (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 161-175 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model of a process contains parameters supposedly characterizing the system which manifests the process. If the parameters are statistically distributed in a population of such systems, the process manifested by the entire population will in general be described by a different mathematical model. Thus a choice is always at hand between two or more mathematical models, depending on which parameters (if any) are assumed to be distributed and, if so, how. Examples of such alternative interpretations are given for mathematical models of some behavioral processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477273
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 18
    Electronic Resource
    Electronic Resource
    Superimposed random coding of stimulus-response connections (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 191-202 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of economically linking a large number of stimuli with a large number of potential responses is considered to resemble a problem of efficient retrieval of documents (the responses) on the basis of their characterization by descriptors (the stimuli to which the responses are appropriate). In this retrieval problem, a method whereby the codes for descriptors are random positions in a coding field, and whereby codes for all applicable descriptors are superimposed in the same field, seems to be the simplest way of avoiding serious difficulties of retrieval. After a review of this method, the possibility is considered that very simple neural mechanisms could embody the essential features of the method. The aim of the discussion is to learn whether very simple structures and patterns of reinforcement would be adequate to carry out useful information processing in the brain, and to show some conceivable functions of simple neural networks which the experimenter might keep in mind. The discussion also shows how the structure of a simple “perceptron”-like network is suggested by the requirements of a retrieval task.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477276
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 19
    Electronic Resource
    Electronic Resource
    Studies on the electroretinogram. II. Model of an a-wave regenerator mechanism (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 223-233 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model is proposed to relate the regeneration of the ERGa-wave after partial light adaptation to the level of the light adaptation. The model assumes that thea-wave amplitude is a function of some reactive substance associated with ana-wave generator. The maximuma-wave amplitude occurs when the eye is fully dark adapted, and thea-wave generator initiator concentration is at a maximum. Thea-wave generator initiator concentration can be decreased by interacting with a product of the rhodopsin-light energy reaction, and increased by removal of this inhibitor. The removal of the inhibitor depends upon the isomerization of the all-trans-retinene to the 11-cis form. An excess of inhibitory material overa-wave generator initiator would cause a delay in the appearance of thea-wave until the excess inhibitory material is removed. This delay is a linear function of the logarithm of the adapting energy. The agreement of this model with the experimental ERG data is very good.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477279
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 20
    Electronic Resource
    Electronic Resource
    On the quantitative relationship between survival rate of larvae and their food supply (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 215-222 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The survival rate of fishes in their earlier stages of development and the influencing factors present one of the most fundamental problems of fish population dynamics. After I. Hjort's (Cons. L.'explor. Ner.,20, 3–228, 1914) work, there have been many investigators in this field and there is no doubt about the very important role of ova and larvae mortality in the fate of a given fish generation. Less clear are the ideas concerning factors determining the high mortality of fishes in their earlier stages of development; especially the factor of food supply of larvae during the period of transition to exogenic nutrition. The value of this factor has been estimated differently from different points of view. For example, R. J. H. Beverton and S. J. Holt (On the Dynamics of Exploited Fish Population, 1957) have given to the food supply factor its deserved importance. On the other hand, T. V. Dekhnik (Trudy Sevastopolskoi Biologicheskoi Stantsii,13, 216–244, 1960;Ibid.,14, 222–243, 1961) has proved in her investigations that at least for pelagic larvae of Black Sea fishes there is an excessive amount of food, and that therefore food cannot play an important role in larva survival. Not wanting to stop to review the literature of the problem (see Dekhnik,Trudy Sevastopolskoi Biologicheskoi Stantsii,13, 216–244, 1960), we will only remark that the problem as a whole needs further investigation. Not only new data are needed, but also methods for following up analysis have to be worked out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477278
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 21
    Electronic Resource
    Electronic Resource
    Learning fluctuations and hysteresis phenomena (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 253-259 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The investigation described here is anexperimental one which brings to light some new facts and confirms others already reported. They partly concern the hysteresis phenomena handled by N. Rashevsky (Mathematical Biophysics, 1960) and partly provide a point of departure for future biophysical research to be undertaken by biomathematicians.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477281
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 22
    Electronic Resource
    Electronic Resource
    An analysis of aortic pressure curves taking into account visco-elastic properties of the aorta and variations in peripheral resistance (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 27-52 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The aortic pressure curve necessarily reveals the mechanical properties of the aorta and peripheral resistance as well as of the dynamics of blood flow. The present study uses a reasonable model of visco-elastic properties of the aorta, a reasonable form for variations in peripheral resistance and blood flow to predict an aortic pressure tracing. Numerical values of constants measured experimentally were available in the published literature. These were used in the nonlinear differential equations of motion of the system under analysis. The equations yielded to piece-wise solution, giving the aortic circumference and the aortic pressure as functions of time. The form of both curves resembles clinical tracings, but numerical values of circumference were higher and of pressure lower thanin vivo. The discrepancies between predicted and clinical curves may reveal certain inadequacies in published measurements on visco-elastic constants. These measurements have been made on longitudinal rather than circumferential strips often containing dead rather than living muscle. The discrepancies, therefore, indicate specific gaps in our knowledge of aortic behaviorin vitro. The suggested model of the system aided in the design of experiments which could supply data necessary to substantiate or to revise the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476466
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 23
    Electronic Resource
    Electronic Resource
    The venous circulation (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 373-377 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some aspects of the circulation through the veins remain unexplained. The pressure gradient which ordinarily exists across a large vein, for example, is much greater than that necessary to maintain the same flow through a rigid tube of identical diameter (Brecher, 1956; Starling and Evans, 1962). During inspiration, blood flow through the thoracic portion of the inferior vena cava increases markedly, while that through the distal abdominal portion does not change. Furthermore, an active source of pressure drop in the chest is necessary to maintain venous flow. For the open chest the pressure drop occurs mainly during ventricular contraction, while in the closed chest it is produced chiefly by inspiration. The present study indicates that the high distensibility of the veins accounts in significant degree for the behavior characteristic of the venous circulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476842
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 24
    Electronic Resource
    Electronic Resource
    A logical model for growth and differentiation in multi-celled organisms (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 379-387 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper is an attempt to provide a logical model for the process of growth and differentiation in a multi-cellular organism. More specifically it is intended to show how genetic information relating to macroscopic structure and coded in the form of a logical tree could be progressively embodied in the organism as it develops by repeated division from a single cell. The aim is to establish biological analogies rather than mathematical interest, and reproduction, adaption, and the coordinating action of hormones are discussed within the general logical framework.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476843
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 25
    Electronic Resource
    Electronic Resource
    A mathematical model of the urethra (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 407-415 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Models having the form of surfaces of revolution may be used to represent the urethra under pre-voiding pressure. From such models are derived formulas for calculating muscle tension from the shape of a urethragram.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476845
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 26
    Electronic Resource
    Electronic Resource
    Estimation of secretory rates of hormones from the specific activities of metabolites which have multiple secreted precursors (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 389-406 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The calculation of rates of entry of material into an open system of multiple pools in the steady state from the specific activities of end products, which may be derived from several pools, is described. This analysis may be applied to estimate the rates of secretion of steroid hormones from the specific activities of urinary metabolites which may have various hormones as common precursors. In a previous publication (Gurpideet al., 1963) formulae have been presented by which secretory rates could be calculated after a single injection of the tracers assuming that each of the urinary metabolites was uniquely derived from one of the pools in the system. In the present article similar formulae were derived without this assumption. Consequently, it is shown that, under certain circumstances, non-uniquely derived metabolites can be used to estimate secretory rates, and that it may be unnecessary to consider the pathways of conversion of the hormones to the metabolites or the sites where these conversion occur.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476844
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 27
    Electronic Resource
    Electronic Resource
    The use of two radiotracers for transfer-rate determinations in closed two compartment systems (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 431-434 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The sensitivity and “specificity” of measurements for the determination of transferates are enhanced by the use of an additional radiotracer, serving to trace the unlabelled substance. This method presents advantages mostly in systems outside their steady state but only exeptionally in steady state systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476847
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 28
    Electronic Resource
    Electronic Resource
    Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 417-429 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation: $$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB 1(t) is the first order initial entry function for the tracer material,P(t1) the perturbation function.T(t 2) is the tracer input function, andB 1(t−t 2 ,t 1 −t 2 ) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476846
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 29
    Electronic Resource
    Electronic Resource
    Correlation “waves” in brain-like structures (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 435-447 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A correspondence is established between a tangible model of brain structure (and function) and a system of observer-observed interactions. The observed quantities are “stimuli” in the form of signal amplitude distributions in a mass of neuron-like units; the observer is a set of neurons (not circumscribed in a local region) in which a distributed parameter mirrors the stimulus history of the set, i.e., represents a “memory”. Utilizing the theory of the Perceptron, a contemporary brain model, it is demonstrated that large systems composed of many observer-observed interactions exhibit quantum mechanical behavior on a “macroscopic” scale. This behavior entails wave-like phenomena and the need of applying the superposition mechanics to system information content calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476848
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 30
    Electronic Resource
    Electronic Resource
    Mathematical models for cellular systems. The von foerster equation. Part II (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 449-471 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This is the continuation of Part I, which was published in the September, 1965, issue of theBulletin. The birth rate, α(t), is now assumed to be a linear functional of the age density,n. This gives a simple model of self-replenishing stem cell compartments, and leads to a necessary condition for the existence of a steady state. Some examples are presented to illustrate the formalism. They include: (a) An equivivant population with life spanD and no losses from death or migration. The total number of cells is multiplied by 2 in each time intervalD. As a special case, frequently realized in practice, the population may be increasing exponentially with time (“log-phase” of growth). (b) A compartment with “random” emigration of cells and gamma distribution of life spans. (c) An oversimplified version of L. G. Lajtha’s model describing stem cell kinetics. In section IV a simple case in which the loss function depends explicitly onn is discussed very briefly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476849
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 31
    Electronic Resource
    Electronic Resource
    Mathematical models of nonuniform intrapulmonary gas distribution (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 473-476 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary Mathematical models of nonuniform gas distribution in the lungs which assume a two-chambered lung to be ventilated through a third chamber, i.e. a common dead space, have led to diverging results. A breath-by-breath analysis of such a system results in a two-exponential solution whereas a continuous ventilation analysis gives a three-exponential solution. This is caused by the different assumptions made in the two models about the composition of dead space gas. In the breath-by-breath analysis one assumes that theN 2 content of the dead space is zero at the end of inspiration. In the continuous ventilation model one assumes that theN 2 content in the dead space is unknown at all instants during the breathing cycle. No physical significance should be attached to any chamber in this type of analysis. The continuous ventilation model provides a more general solution than the cyclical ventilation model, because the former treats the common dead spaces as an independent unknown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476850
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 32
    Electronic Resource
    Electronic Resource
    On the electrocardiographic field equation (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 493-495 
    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/BF02476852
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 33
    Electronic Resource
    Electronic Resource
    The representation of organisms in terms of predicates (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 477-491 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The different approaches to relational biology developed by N. Rashevsky and R. Rosen consider essentially binary relations between various components of biological functions of the organism. Actually an organism is represented by a set of differentn-ary relations. The present paper is an attempt to outline a possible approach to this more realistic situation. Inasmuch asn-ary relation is ann-place predicate, it is attempted to describe the basic known properties of an organism in terms ofn-place predicates, in which the variables represent the different “components” of the organism. Some possible forms of such predicates are discussed and some general properties of systems of such predicates are studied. It is shown that if the organism is described by predicates of the type discussed here, statements can be derived about the conditions “of reestablishability” of different components. Conclusions similar to those obtained previously by R. Rosen are reached now on a very different basis. A description of the process of cell differentiation in multicellular organisms in terms of predicates studied here is briefly outlined. A comparison of similarities and differences between the approach and Rosen’s description of organisms in terms of the theory of categories is made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476851
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 34
    Electronic Resource
    Electronic Resource
    Temporal organization in cells (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 497-500 
    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/BF02476853
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 35
    Electronic Resource
    Electronic Resource
    29th National Meeting of the Operations Research Society of America (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 503-503 
    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/BF02476855
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 36
    Electronic Resource
    Electronic Resource
    Harold A. White March 4, 1933–July 27, 1965 Obituary notice (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 501-502 
    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/BF02476854
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 37
    Electronic Resource
    Electronic Resource
    Fluctuation analysis in small chemically reacting systems (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 147-160 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theory of noise fluctuations is developed which is applicable to systems of any size in which unimolecular or bimolecular reactions are occurring. The main difference between small and large reacting systems is that in the former the probability of finding a particle in a particular state does not obey a Gaussian distribution, but satisfies a distribution which reflects the mechanism of the chemical reaction. This difference is reflected in the main result of the theory: an autocorrelation function that is expressible as a sum of exponentials, the amplitudes of which are explicit functions of the moments of the distribution. Thus, by using small systems, the autocorrelation function,in principle, allows the elucidation of reaction mechanisms. Numerical simulations indicate that for reacting systems having ten or fewer particles, the deviation of the autocorrelation function from a single exponential should be easily detectable, and that estimates of the first four moments of the distribution should be possible. Accurate inference of the distribution, however, will require further mathematical and experimental advances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464634
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 38
    Electronic Resource
    Electronic Resource
    Concept of energy in biological systems and the effects of irradiations of low energies on enzyme-substrate systems (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 161-172 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The recent mathematical formalization of the concepts of matter and extrinsical energy, which are used for the relational representation of biological systems, is employed in the analysis of the important experimental discoveries of Comorosanet al. related to low energy electromagnetic irradiations on enzyme substrates. By means of the present analysis one of the properties inherent to the experimental phenomena is more precisely exposed, and theoretical developments corresponding to “energetical evolutions” in a biological system (Leguizamón, 1976) may now have an experimental basis. Important limitations are introduced for the validity of the commutativity and associativity of cartesian product of sets, when they represent matter and its linked extrinsical energy. In connection with this last aspect, new important knowledge is obtained for the relational mathematical representation of biological systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464635
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 39
    Electronic Resource
    Electronic Resource
    Traveling waves in a simple population model involving growth and death (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 397-429 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The structure of solutions to a simple spatially dependent population model involving growth and death is investigated. Two forms of motility of the population are considered: (1) random motion only modeled by a Fickian law, and (2) a directed component of motion (chemotaxis), included in addition to the random motion. Under certain growth conditions a traveling wave of constant speed is approached. This speed can be increased by the addition of the chemotaxis with a corresponding increase in the asymptotic population. Development of initial conditions into a wave is illustrated numerically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460793
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 40
    Electronic Resource
    Electronic Resource
    Intracellular mechanisms of adaptation and self-regulation in self-organizing networks: The role of chemical transducers (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 365-396 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper describes mechanisms of intracellular and intercellular adaptation that are due to spatial or temporal factors. The spatial mechanisms support self-regulating pattern formation that is capable of directing self-organization in a large class of systems, including examples of directed intercellular growth, transmitter production, and intracellular conductance changes. A balance between intracellular flows and counterflows causes adaptation. This balance can be shifted by environmental inputs. The decrease in Ca2+-modulated outward K+ conductance in certain molluscan nerve cells is a likely example. Examples wherein Ca2+ acts as a second messenger that shunts receptor sensitivity can also be discussed from this perspective. The systems differ in basic ways from recent diffusion models. Chemical transducers driven by membrane-bound intracellular signals can establish long-range intercellular interactions that compensate for variable intercellular distances and are invariant under developmental size changes; diffusional signals do not. The intracellular adaptational mechanisms are formally analogous to intercellular mechanisms that include cellular properties which are omitted in recent reaction-diffusion models of pattern formation. The cellular models use these properties to compute size-invariant properties despite wide variations in their intercellular signals. Mechanisms of temporal adaptation can be derived from the simplest laws of chemical transduction by using a correspondence principle. These mechanisms lead to such properties of intercellular signals as transient overshoot, antagonistic rebound, and an inverted U in sensitivity as intracellular signals or adaptation levels shift. Such effects are implicated in studies of behavioral, reinforcement, motor control, and cognitive coding.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460792
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 41
    Electronic Resource
    Electronic Resource
    A model for early death caused by radiation pneumonitis and pulmonary fibrosis after inhaling insoluble radioactive particles (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 447-459 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Large radiation doses to the lung can cause early death from cardiopulmonary insufficiency resulting from radiation pneumonitis and pulmonary fibrosis. A model for early death following inhalation of insoluble radioactive particles is propose. The model is based on three assumptions: (1) early death results from damage to a cluster of cells from a large number of cell clusters at risk, (2) the dose that causes early death depends on how the radiation is delivered in time and (3) the cell clusters at risk to damage are equally sensitive ro radiation. Results from asymptotic theory of extreme values, along with biophysical considerations, suggest that the cumultive distribution function for the absorbed radiation dose to the production of pulmonary injury sufficient to cause early death is best estimated by the third asymptotic distribution without a threshold. This distribution function is identical to the Weibull cumulative distribution function. Data for Beagle dogs after inhaling relatively insoluble forms of alpha- or beta-gamma-emitting particles are shown to support the Weibull model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460795
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 42
    Electronic Resource
    Electronic Resource
    Models of human lung airways and their application to inhaled particle deposition (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 461-480 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Models of the human respiratory tract were developed based on detailed morphometric measurements of a silicone rubber cast of the human tracheobronchial airways. Emphasis was placed on the “Typical Path Lung Model” which used one typical pathway to represent a portion of the lung, such as a lobe, or to represent the whole lung. The models contain geometrical parameters, including airway segment diameters, lengths, branching angles and angles of inclination to gravity, which are needed for estimating inhaled particle deposition. Aerosol depositions for various breathing patterns and particle sizes were calculated using these lung models and the modified Findeisen-Landahl computational scheme. The results agree reasonably well with recent experimental data. Regional deposition, including lobar deposition fractions, are also calculated and compared with results based on the ICRP lung deposition model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460796
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 43
    Electronic Resource
    Electronic Resource
    On the completely symmetric compartmental system (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 481-488 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The completely symmetrical system is defined as having identical transfer coefficients between pairs of compartments and the same loss coefficient for each compartment. The eigenvalues and eigenvector are explicitly found along with the inverses of the system matrix and the matrix of eigenvectors. Many properties, special instances of more general theorems, can be seen at once from the explicit analytic solution of the initial value, washout and washin problems. The system serves as a known case for testing estimation procedures, algorithms for solutions of linear systems, eigenvalue-eigenvector and inversion routines and is of considerable tutorial value.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460797
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 44
    Electronic Resource
    Electronic Resource
    Natural transformations of organismic structures (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 431-446 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The mathematical structures underlying the theories of organismic sets, (M, R)-systems and molecular sets are shown to be transformed naturally within the theory of categories and functors. Their natural transformations allow the comparison of distinct entities, as well as the modelling of dynamics in “organismic” structures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460794
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 45
    Electronic Resource
    Electronic Resource
    The dipole flip-flop theory for the excitation and conduction of excitable tissues—I. Dipole's behavior and gating currents (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 489-505 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract To explain the sodium conductance change using Wei's dipole model (Wei, 1969), we may expect that during depolarization the dipole's population difference, ΔN, is first reduced and then returns more slowly to its resting value. This paper shows that the experimental results of gating currents support this idea. Such time course of ΔN, however, is not a usual relaxation process. To account for the unusual behavior of ΔN, we propose two additional assumptions: (1) there exists a special coupling system (probably the intramolecular vibrations) whose coupling strength with the dipoles is much stronger than with the thermal bath (intermolecular vibrations), and (2) there also exist “traps” for the dipole's excitation energy so that this energy is transformed into other energy forms at a rate increasing with the increase of depolarization. Experiments suggest that the traps are proteins located at the inner membrane surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460966
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 46
    Electronic Resource
    Electronic Resource
    Some generalized conjugacy theorems and the concepts of fitness and survival in logistic growth models (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 507-528 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Current research into the dynamics of iterative ecological and biological models has lead to a number of theorems concerning the existence of various types of iterative dynamical behavior. In particular, much study has been done on the dynamical behavior of the “simplest dynamical system”f b(x)=bx(1−x), which is just the canonical discrete form of logistic growth equations found in ecology, sociobiology, and population biology. In this paper, we make use of some of the techniques and concepts of topological dynamics to construct a number of generalized conjugacy theorems. These theorems are then used to demonstrate that the mappingf b has a number of conjugacy classes in which the dynamics of the iterates is equivalent to within a change of variables. The concepts of fitness and survival in logistic equations are then shown to be independent, if we follow certain intuitive definitions for these concepts. This conclusion follows from a comparison of the conjugacy classes of the functionf b and the extinction sets off b.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460967
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 47
    Electronic Resource
    Electronic Resource
    Use of transient and steady-state measurements of the unidirectional flux ratio for the determination of the free energy change of chemical reactions and active transport systems (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 529-537 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract For chemical reactions not at equilibrium but proceeding in the forward direction in the steady state, a result found by a method first introduced by H. G. Britton (1963, 1965) is generalized to prove that if $${{\vec J} \mathord{\left/ {\vphantom {{\vec J} {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftarrow}$}}{J} }}} \right. \kern-\nulldelimiterspace} {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftarrow}$}}{J} }}$$ is the unidirectional flux ratio, $${{\vec J} \mathord{\left/ {\vphantom {{\vec J} {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftarrow}$}}{J} }}} \right. \kern-\nulldelimiterspace} {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftarrow}$}}{J} }}$$ exp (−ΔG/RT). The conditions under which the equality or inequality applies are discussed. If the unidirectional fluxes are not in the steady state, the unidirectional flux ratio is time invariant in certain specific situations. One such important case is for chemical reaction systems with an ordered sequence of reactions. For systems with more than one pathway, $${{\vec J} \mathord{\left/ {\vphantom {{\vec J} {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftarrow}$}}{J} }}} \right. \kern-\nulldelimiterspace} {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftarrow}$}}{J} }}$$ is not constant except for special cases. These results also apply to diffusional and active transport systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460968
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 48
    Electronic Resource
    Electronic Resource
    On Varma's prey-predator problem (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 599-600 
    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/BF02460971
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 49
    Electronic Resource
    Electronic Resource
    On the evolution of prebiotic enzyme coupled macromolecular systems (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 539-549 
    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/BF02460969
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 50
    Electronic Resource
    Electronic Resource
    The geometry of chaos: Dynamics of a nonlinear second-order difference equation (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 551-597 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The nonlinear second-order difference equationx n+1=axn(1-xn−1), where 0≦x nX≦1 anda ≧1, is examined from varying points of view, analytical, numerical and geometrical. An analytic expression is obtained for an invariant attracting curveC ∞ (a) in phase space, which becomes the central object of study. This basic curve, which replaces the simple parabolic shape typical of many analogous first-order models, may have a complicated geometrical structure. As the parametera increases,C ∞(a) undergoes transformations characterized by the dynamical descriptions: stable node→stable focus→stable limit cycle →chaotic attractor. Although the limited characterization ofchaos by the appearance of nonperiodic solutions and solutions of arbitrarily large period is relied upon, this appears to be only a simplified approximation of the real behavior of solutions. Trajectories (x n, xn+1),n=0,1,…, are calculated using the related nonlinear planar mapT a(x,y)=(y,ay(1−x)), and regions of persistence and escape are described for characteristic values ofa. The study of persistence, of even more fundamental interest than the associated problems of periodicity and stability, receives special attention. We introduce a geometrical model, similar in many respects to that for the well-known analoguex n+1=axn(1−x n), but having several new and important features. It appears that as the parametera increases in the chaotic regime there are infinitely many intermittent bursts of increase in the probability that any initial point (x 0, x1) will persist in the unit square under successive iterations of the mappingT a, an unexpected property that should be of interest for applications. A discussion of the applicability of these results to population dynamics theory is given, and it is suggested that such equations might find useful application to problems in developmental biology as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460970
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 51
    Electronic Resource
    Electronic Resource
    A mathematical model of the functional state of the oxygen transport system (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 627-645 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Based on the principle of minimum power, a mathematical model of the functional state of the oxygen transport system is presented. The optimization model minimizes the power expenditure of the heart, bone marrow, lung and other tissues. The model is used to determine the functional parameters of the oxygen transport system in man under both normal and varying barometric pressures. Theoretical results are compared with experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460984
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 52
    Electronic Resource
    Electronic Resource
    Theory of cation-phospholipid-induced shape changes in a lipid bilayer couple (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 601-625 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A quantitative model of ion binding and molecular interactions in the lipid bilayer membrane is proposed and found to be useful in examining the factors underlying such membrane characteristics as shape, sidedness, stability and vesicle size at various cation concentrations. The lipid membrane behaves as a bilayer couple whose preferential radius of curvature depends on the expansion or contraction of one monolayer relative to the other. It is proposed that molecular packing may be altered by electrostatic repulsion of adjacent like-charged phospholipid headgroups, or by bringing two headgroups closer together by divalent cation crossbridging. The surface concentrations of each type of cation-phospholipid complex can be described by simple binding equilibria and the Gouy-Chapman-Stern formulation for the surface potential in a diffuse double layer. The asymmetric distribution of acidic phospholipids in most biological membranes can account for the differential effects of identical ionic environments on either side of the bilayer. The fraction of vesicle material which tends to have a right-side-out orientation may be approximated by a normal distribution about the mean curvature. The theory generates vesicle sidedness distributions that, when fitted to experimental results from human erythrocyte membranes, provide an alternative method of estimating intrinsic cationphospholipid dissociation constants and other molecular parameters of the bilayer. The results also corroborate earlier suggestions that the Gouy-Chapman theory tends to overestimate free counter-ion concentrations at the surface under large surface potentials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460983
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 53
    Electronic Resource
    Electronic Resource
    Photoelectric properties of the “yellow strips” inVespa orientalis; a mathematical model (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 681-689 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The “yellow strips” on the cuticle of the Oriental Hornet (Vespa orientalis, Hymenoptera, Vespinae), present photoelectric properties. A mathematical model for the relative changes in resistance as a photoconductive process conforms to the general model for a semiconductor with traps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460986
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 54
    Electronic Resource
    Electronic Resource
    Damped oscillating processes in biological and biochemical systems (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 701-718 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Damped nonlinear oscillations in biological and biochemical systems are investigated by the extended Krylov-Bogoliubov-Mitropolskii (KBM) method. A review on the extension made by Popov to the KBM method is given and also further improvements are presented. Applications are made to models of oscillating chemical reactions (Lefever and Nicolis, 1971), FitzHugh (1961) equations, and population dynamics (Gatto and Rinaldi, 1977). Comparison to damped oscillating physical and engineering systems is made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460988
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 55
    Electronic Resource
    Electronic Resource
    The problem of time unit in Leslie’s population model (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 719-728 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The conditions that will allow the lumping together of several age classes in the Leslie model are investigated. We show that if the lumping is to be valid for all population distributions, then the parameters of the model must be periodic. Lumping is valid when the population is in equilibrium, but equilibrium should be tested before the model is lumped.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460989
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 56
    Electronic Resource
    Electronic Resource
    Applied catastrophe theory in the social and biological sciences (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 647-679 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Catastrophe theory is a mathematical theory which, allied with a new and controversial methodology, has claimed wide application, particularly in the biological and the social sciences. These claims have recently been heatedly opposed. This article describes the debate and assesses the merits of the different arguments advanced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460985
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 57
    Electronic Resource
    Electronic Resource
    Effects of red cell permeability on transcapillary tracer transport: The case of negligible back diffusion (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 765-795 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Estimates of capillary tracer permeability calculated using multiple indicator data depend upon the particular model adopted to describe blood tissue exchange. The model proposed by Crone (1963) is appropriate when some of the injected tracer diffuses into the tissue but does not return appreciably to the bloodstream before data collection is terminated. Under these conditions extraction of tracer by the tissue depends on a single dimensionless parameter, αcap, defined as the ratio of capillary permeability surface area to water flow. The effects of finite red cell tracer permeability on the Crone model estimate of capillary permeability are examined in the present study. The results indicate that even when back diffusion from the extravascular space is negligible, significant errors in the Crone model estimate can be expected when capillary permeability is relatively high and the ratio of red cell to capillary permeability is less than unity. However, when an aliquot of blood is equilibrated with tracer prior to injection and the dimensionless capillary permeability is relatively low (i.e. αcap ≦ 0.25 for a haematocrit≦50%), the whole blood Crone model estimate of αcap will be within 10% of the actual value, irrespective of red cell permeability. Red cell-plasma exchange for commonly used tracer-organ combinations should not significantly affect Crone estimates of capillary permeability under normal physiological conditions, but may be important in low flow situations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461058
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 58
    Electronic Resource
    Electronic Resource
    A geometric model for the myocardium: Biventricular wall stresses in normal and hypertrophied states (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 807-828 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Assuming truncated ellipsoidal geometry for the right and left ventricles, a model is developed for the myocardium enabling biventricular mechanical behavior to be studied. Employing pressure-volume data taken from normal dog hearts and from hearts in which the pulmonary artery has been banded over periods of 2–40 weeks, it is shown that: (a) right ventricular wall stresses are higher than left ventricular stresses; (b) right ventricular wall stress increases initially to a maximum after 3–4 weeks followed by a decline to normal and even subnormal levels, attaining a minimum value at 32–33 weeks; (c) left ventricular stresses behave in a similar manner, attaining their maximum and minimum levels after 7–8 weeks and 32–33 weeks respectively. These results suggest that surgical or medical therapy in patients with hypertrophied ventricles might be more appropriate during the period of wall stress reduction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461060
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 59
    Electronic Resource
    Electronic Resource
    A mathematical model of the oscillations in the aphakic eye (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 837-845 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper we describe a mathematical model of the oscillations of the diaphragm which limits the vitreous body from the anterior segment of the human eye after the lens has been removed in a cataract operation. We study the motion of this diaphragm driven by movements of the eye. Firstly, a mathematical statement of the problem is given and then we solve the problem exactly for a given class of eye movements. From the analysis we deduce that significant oscillations of the membrane are driven by saccades and that it is the angular acceleration of the eye which causes these types of oscillations. A numerical example is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461062
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 60
    Electronic Resource
    Electronic Resource
    Pursuit-evasion wave trains in prey-predator systems with diffusionally coupled delays (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 871-887 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Lotka-Volterra system of prey-predator equations is considered with a special type of continuous time delay. In the case of equal diffusion coefficients Hopf’s bifurcation technique is used to show the existence of travelling wave train solutions for the prey-predator system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461065
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 61
    Electronic Resource
    Electronic Resource
    Mathematical model of the activation of prothrombin by factor X a and factor V t (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 861-870 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model of prothrombin activation is being proposed which includes the feedback mechanism of thrombin and the alteration of factor V by thrombin. This model is in good agreement with experimental data for the dependence of the rate of thrombin formation on the concentrations of factors V and X a . In particular, it correctly predicts the existence and location of a maximum in both of these cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461064
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 62
    Electronic Resource
    Electronic Resource
    A three-dimensional model of the upper tracheobronchial tree (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 847-859 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new model of the upper tracheobronchial tree is proposed to account for the three-dimensional nature of the airway system. In addition to the tube length, the tube diameter, and the branching angle, the model includes information on the orientation angle of each tube relative to its parent tube. The orientation angle, defined as the angle between two successive bifurcations, is useful for calculating the gravitational inclination of each tube. The information on orientation angle is further used to construct a binary coding system for identifying individual tubes in the airway tree. The proposed model is asymmetrical, but the same principles can be readily used to construct a symmetrical one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461063
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 63
    Electronic Resource
    Electronic Resource
    On control and optimal control in biodynamic systems (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 889-897 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In any control system for which the number of independent controls is smaller than the number of degrees of freedom to be controlled, our choice of control in any state is restricted to a submanifold of smaller dimension than the tangent space. This simple fact has a number of important consequences for questions of biological import; we consider its implications for adaptation, for senescent phenomena and for the determination of tertiary structures of polypeptides through control of certain average properties. We also formulate the Pontryagin Maximum Principle of Optimal control theory in such a way as to inquire whether specific biodynamic systems can be regarded as optimal with respect to rate of accumulation of particular quantities of the system. We find that if this is possible, the quantity in question must play the role of a clock.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461066
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 64
    Electronic Resource
    Electronic Resource
    Mathematical models in the health sciences: A computer-aided approach (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 899-900 
    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/BF02461067
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 65
    Electronic Resource
    Electronic Resource
    Steady-state diffusion through a finite pore into an infinite reservoir: An exact solution (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 57-65 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An outline is given of an analysis that leads to an exact solution for the problem of steady-state diffusion through a finite thick pore into an infinite region surrounding the mouth of the pore. From this exact formula a simple expression for the flux is derived. This expression approximates the flux with a relative error of less than 3.42 per cent independently of the ratiol/a wherel is the length of the pore anda its radius. If desired, more accurate expressions for the flux can be obtained from the exact solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476468
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 66
    Electronic Resource
    Electronic Resource
    The single file model for the diffusion of ions through a membrane (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 79-86 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The model proposed by A. L. Hodgkin and R. D. Keynes (Jour. of Physiol.,128, 61–88, 1955) for the diffusion of potassium through the nerve membrane is extended to cover an arbitrary number of species of ions with charges not necessarily the same. One type of interference is also investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476470
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 67
    Electronic Resource
    Electronic Resource
    On the theory of the cardiovascular system (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 71-83 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Most theoretical studies of the circulation have focussed on the transmission line properties of arteries. Only a small number of papers have dealt with the circulation as a closed (lumped) system with two pumps connected by the lesser and greater circulation (Beneken, inCirculatory Analog Computers, No. Holland Publ. Co., Amsterdam, 1963; Defares,et al., inCirculatory Analog Computers, No. Holland Publ. Co., Amsterdam, 1963; Grodins,Quart. Rev. of Biology,34, 93, 1959; Guyton,Cardiac Output and its Regulation, Saunders Publ. Co., New York, 1963). F. W. Cope's recent studies in this journal (Bull. Math. Biophysics,22, 19, 1960;23, 337, 1961;24, 137, 1962) deal with essentially the same questions, although here the circuit is not “closed”. We have attempted to extend the analysis of the areflex (closed) circulation. The complete study is reported elsewhere (Defares,et al., Acta Physiol, et Parmac. Neerl., 1963).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477263
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 68
    Electronic Resource
    Electronic Resource
    Equations of heat distribution within the body (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 67-78 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A vector integral equation describing heat distribution within the body has been derived. The factors considered are heat conduction, forced convection via the circulatory system, environmental exchange, metabolic heat production, and change in heat content. The vector partial differential equation and alternative forms incorporating boundary conditions were also developed. A difference equation based on a first-order approximation to the fundamental equations was derived to form the basis of a model for heat distribution within the body. It has been shown that factors involving conduction and convection must be considered independently unless the temperature of the blood flowing from a region of the body is equal to the average temperature of the tissue in that region. If this relation between tissue and blood temperature does exist, only a single temperature from each eleeent is needed to describe the heat distribution. In this latter case, models which ascribe all heat transfer to “equivalent” conduction or to convection can give valid predictions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476469
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 69
    Electronic Resource
    Electronic Resource
    Determination of equilibrium constants and maximum binding capacities in complexIn vitro systems: I. The mammillary system (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 87-98 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that in a system containingn types of mutually noninteracting binding sites, the association constants are then roots of annth order polynomial while the maximum binding capacities can be evaluated by solving a set ofn simultaneous linear equations. Thenth order polynomial and the system ofn linear equations are defined in terms of 2n intermediate coefficients, the coefficients being themselves evaluated by substituting 2n sets of appropriate experimental data into an auxiliary system of 2n linear equations. The existence and uniqueness of the solutions are established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476471
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 70
    Electronic Resource
    Electronic Resource
    Southern Regional Graduate Summer Session in Statistics at Oklahoma State University (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 111-111 
    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/BF02476473
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 71
    Electronic Resource
    Electronic Resource
    Important announcement to our contributors and readers (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 113-113 
    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/BF02476474
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 72
    Electronic Resource
    Electronic Resource
    A theory of ion transport across cell surfaces by a process analogous to electron transport across liquid-solid interfaces (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 99-109 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A kinetic theory of ion transport across cell surfaces has been developed in a form analogous to the kinetic theory of electron transport across solid-liquid interfaces of biological particles. The ionic theory is based on the observation that, at least in one instance, the voltage-current behavior for ion conduction across a cell surface is describable by the Tafel equation, in analogy to the conduction of electrons across solid-liquid interfaces. The theory predicts that the kinetics of ion transport across cell surfaces should conform to the Elovich rate equation, which is shown to be true for various experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476472
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 73
    Electronic Resource
    Electronic Resource
    Letter to the editor (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 114-114 
    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/BF02476475
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 74
    Electronic Resource
    Electronic Resource
    Mathematical development of a physical model of some visco-elastic properties of the aorta (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 115-115 
    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/BF02476476
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 75
    Electronic Resource
    Electronic Resource
    A biographical sketch of Nicolas Rashevsky (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 3-4 
    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/BF02477255
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 76
    Electronic Resource
    Electronic Resource
    A letter read to professor Rashevsky at a dinner in his honor December 11, 1964 (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 5-10 
    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/BF02477256
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 77
    Electronic Resource
    Electronic Resource
    Some comments on re-estalishability (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 11-14 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The present note consists of two separate but related parts. In the first, a new graphtheoretic proof is presented that an (ℳ,R)-system must always contain a nonreestablishable component. The second considers some questions concerning the relation between re-establishability and the time-lag structure in (ℳ,R)-systems. It is supposed that the reader is familiar with the terminology of the author's previous work on (ℳ,R)-systems, particularly R. Rosen,Bull. Math. Biophysics,20, 245–260, 1958.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477257
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 78
    Electronic Resource
    Electronic Resource
    Model studies of blood-glucose regulation (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 21-37 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A simplified, linearized model of the system regulating blood-glucose concentrations is reviewed. This model, which predicts a damped sine wave response to an oral glucose load, lumps the large number of kinetic parameters into a much smaller number which can, at least in part, characterize the human glucose regulatory system. The predictions based on the model are compared with measurements of blood-glucose and blood-insulin concentrations during the oral glucose-tolerance test. Various other conditions are simulated and their implications are discussed in terms of the mathematical model used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477259
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 79
    Electronic Resource
    Electronic Resource
    On compartmentalization (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 15-19 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The notion of a compartment is discussed in terms of the Markovian process. From the stochastic matrix (the elements of which are state transition probabilities between different states of a particle of a chemical element), one may find a (generally) nonstochastic matrix; the elements of this second matrix are probabilities that, starting from some initial state, the particle will reach another seleced state (W. Feller, 1962,An Introduction to Probability Theory). Forming equivalence classes of states it can be shown that the equivalence classes based on an equivalence relation, which holds for the elements of the above-mentioned nonstochastic matrix, are essential for the notion of a compartment. From this procedure it is also obvious that a rigorous definition of a physically realizable compartment is impossible. Some conclusions on the practical use of compartmental analysis are drawn.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477258
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 80
    Electronic Resource
    Electronic Resource
    On the use of the Von Foerster equation for the solution and generalization of a problem studied by S. A. Tyler and R. Baserga (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 39-48 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a population of cells labeled with a single injection of tritiated thymidine at timet=0, it is assumed that a constant fraction, 1−z, of the cells which are potentially able to divide fail to do so, and that the cells which do divide all have identical generation time,D. Death and emigration of cells are neglected. In mitosis, the partitioning of label among the two daughter cells is supposed to follow the binomial probability law. Using the formalism developed by H. Von Foerster the fraction of labeled cells in the total population is computed as a function oft, the time after injection of label. Ift is an integral multiple ofD the results coincide with those of S. A. Tyler and R. Baserga.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477260
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 81
    Electronic Resource
    Electronic Resource
    Development of structure in a society with a dominance relation when new members are added successively (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 151-160 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A society with a dominance relation is considered to be built up by starting with a small society and adding new members in succession. As each member is added he engages in contests with each of the older members to determine the dominance relation between them. The probability that the older member dominates is considered to depend on the size of the society and linearly on the older members score. A recurrence relation for the hierarchy index is derived. The approach of the society to a hierarchical structure is considered for various special cases of this probability. Reasonable assumptions concerning this dominance probability are shown to lead to structures close to the hierarchy. If the new member dominates all the older ones below a certain rank, and is dominated by all those above this rank, then the hierarchy will persist if it is the initial structure, or the structure will tend to hierarchy as the size increases, if it is not the initial structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477272
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 82
    Electronic Resource
    Electronic Resource
    Theory of hemoglobin facilitated oxygen transport (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 183-190 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The transport of oxygen in a hemoglobin-saturated medium is theoretically investigated using classical transport theory. It is found that all the chemical complexes can be expressed as a single function of oxygen pressure. A potential difference together with apH shift is predicted to occur across the medium.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477275
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 83
    Electronic Resource
    Electronic Resource
    Notes on magnetic actions upon the nervous system (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 203-214 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Several physical effects (magnetomotive force on ions, magnetic induction of electrical field, magnetic changes of inductance) are quantitatively analyzed in an attempt to attain an insight on how externally applied static magnetic fields influence the activity of the neuron and the Nervous System as a whole or in part. The possible magnetic action on shifting excited zones of the axon appears as most promising for prediction and interpretation of measurable effects. Magnetic fields may modify nervous functions by multiplication and addition of very small biophysical effects.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477277
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 84
    Electronic Resource
    Electronic Resource
    Molecular set theory: II. An aspect of the biomathematical theory of sets (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 235-251 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In an earlier paper (Molecular Set Theory: I.Bull. Math. Biophysics,22, 285–307, 1960) the author proposed a “Molecular Set Theory” as a formal mathematical meta-theoretic system for representing complex reactions not only of biological interest, but also of general chemical interest. The present paper is a refinement and extension of the earlier work along more formal algebraic lines. For example the beginnings of an algebra of molecular transformations is presented. It also emphasizes that this development, together with the genetical set theory of Woodger's and Rashevsky's set-theoretic contributions to Relational Biology, points to the existence of a biomathematical theory of sets which is not deducible from the general mathematical, abstract theory of sets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477280
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 85
    Electronic Resource
    Electronic Resource
    Man/machine interaction in adaptively controlled experimental conditions (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 261-273 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Systems in which a human subject interacts with an adaptive control mechanism through display and response facilities are examined. A cybernetic model is discussed, together with supporting experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477282
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 86
    Electronic Resource
    Electronic Resource
    Computer simulation of stem-cell kinetics (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 275-290 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Computer simulation of the stem-cell system has been motivated by a desire to provide a device which may assist the experimenter in his development of complex research strategies in the rapidly developing investigative fields that relate to erythropoiesis and granulopoiesis. A simulation program, written in FORTRAN II for the IBM-7094, is being developed with the requirements of flexibility and broad applicability in mind. The biological model for which it originally was developed differs from those previously advanced by visualizing differentiation into the erythrocytic and granulocytic series as occurring during the post-mitotic phase of a stem cell's growth, the cell's susceptibility to erythropoietic and granulopoietic stimuli varying as its biochemical development unfolds. One might test this model by attempting to demonstrate an asymmetrical interference between erythropoietic and granulopoietic challenges to the stem-cell system. A method for establishing an initial stable configuration of the model is presented. The simulation of the introduction of exogenous erythropoietic stimuli is described. And there is a brief description of the feedback mechanism employed to stabilize the size of the stem-cell population.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477283
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 87
    Electronic Resource
    Electronic Resource
    A note on visual integrative mechanisms (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 305-310 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a system as complex and as effective as the eye, the cooperative interaction of different mechanisms may be taken as axiomatic. With this as a starting point, various visual phenomena are considered, such as short term memory, eye movements, and flicker fusion. Simple data on mean values lend support to the proposition that the spatial and temporal characteristics of these phenomena are matched with one another. The significance of this for a mechanism of vision is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477285
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 88
    Electronic Resource
    Electronic Resource
    Matrix algebra of a generalized linear stochastic model. Nonconfluent and general confluent cases (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 311-315 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Matrix algebra is the natural tool for the study of linear stochastic models with many parameters. Complete solutions are given for the nonconfluent and the general confluent cases. It is shown that the axiomatics of a generalized linear stochastic model are naturally described within the framework of the linear algebra in an Euclidean space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477286
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 89
    Electronic Resource
    Electronic Resource
    Properties of solution of the diffusion-reaction equation (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 291-303 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An arbitrary set of chemical reactions is considered to occur among chemical speciesX i . In a closed uniform reaction system certain linear combinations of the concentrations of theX i are constants. The general construction of all such linear combinations with non-negative coefficients is given in terms of the molecular formulae for theX i . It is shown that to each such linear combination there corresponds another which is a harmonic function when the reactions take place in an open spatially distributed stationary reaction system of arbitrary shape. Under the usual boundary conditions these harmonic functions are constants. With some restrictions upon the diffusion and permeability coefficients these constants are evaluated. This evaluation is the basis for relations between the total concentration of a given chemical group (e.g., the sum of the concentrations of a free molecule, or ion, and its various bound forms) in the reaction system, and in the surrounding medium. The bearing of these relations on apparent active transport is noted and illustrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477284
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 90
    Electronic Resource
    Electronic Resource
    Analysis of tracer experiments: VI. Determination of partitioned initial entry functions (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 329-332 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that the partitioned initial entry functions previously introduced in multicompartment analysis can be directly and uniquely determined from the experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477288
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 91
    Electronic Resource
    Electronic Resource
    A neural net model for escape learning (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 317-328 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An escape learning situation is discussed in terms of a neural model in which a stimulus can result in a conditioned excitement and a specific conditioned response. By using the simplest relations between the strengths of conditioning and the number of reinforcements and by introducing a distribution of fluctuations occurring regularly in time, one can calculate the probabilities of various responses, as well as the various latencies, in successive trials. The results are in moderately satisfactory agreement with the data of R. L. Solomon and L. C. Wynne (Psychol. Monogr.,67, No. 4, 1953). Consequences of the model for various experimental situations are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477287
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 92
    Electronic Resource
    Electronic Resource
    Effects of the collateral circulation of the heart (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 1-8 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Collateral circulation minimizes the myocardial injury which results from narrowing of a coronary artery. A large collateral circulation has disadvantages, however. It may divert so much of the limited blood flow through the adjacent nonarteriosclerotic coronary artery that the blood supply of the normal muscle supplied by that artery may be inadequate during heavy exercise. In the presence of a large collateral circulation, both the normal and ischemic regions of the heart may be extremely vulnerable to small arteriosclerotic changes narrowing the patent artery near the aorta. The effective increase in flow which results from arteriolar vasodilatation produced by drugs may be much greater in the presence of a small collateral circulation than a large one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476463
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 93
    Electronic Resource
    Electronic Resource
    Simple theory of transfusions (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 9-20 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A transfusion can be hypothesized to be required when a determination factor (D=probability of adverse effects if transfusion not given/adverse effects if transfusion is given) exceeds some predetermined value.D varies between the limits 0 and ∞, and in most clinical situations will be a small number on the order of 20. Since the probabilities contributing to the denominator ofD are essentially independent of each other, they can be summed to obtain the probability of ill effects. A method of handling an exception to this, the incompatibility reactions following multiple transfusions within a short time interval, is pointed out. The probability of adverse effects if a transfusion is not given is more difficult to evaluate; values gathered from the literature are presented, as well as methods for obtaining further data. Two techniques for estimating future transfusion requirements are discussed. One is a correlative procedure, which functions by analyzing similar cases admitted to the hospital. The second procedure is an estimate of stability (homeostasis), based on a parameter introduced by B. C. Patten (Scince,134, 1010–1011, 1961). The dilution of endogenous cells and plasma by transfusions is considered and the consequences of many small transfusions compared with those of few (and larger) transfusions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476464
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 94
    Electronic Resource
    Electronic Resource
    Some possible quantitative aspects of a neurophysiological model of schizophrenias (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 21-26 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In continuation of a previous paper (Bull. Math. Biophysics,26, 167–185, 1964) simple equations are derived for the rate of development of schizophrenia as a function of some psychobiological parameters of the individual and of an index which characterizes the frequency of traumatic experiences of the individual. A clue to the understanding of why schizophrenia is more likely to develop at an early adult age is thus provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476465
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 95
    Electronic Resource
    Electronic Resource
    longitudinal diffusion along the nephron during stop flow (1965)
    Springer
    Bulletin of mathematical biology 27 (1965), S. 53-56 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical analysis is presented which shows that during stop flow experiments longitudinal diffusion of solute along the nephron is of too small a magnitude to interfere with the interpretation of data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476467
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 96
    Electronic Resource
    Electronic Resource
    Theoretical evaluation of aerosol deposition in anatomical models of mammalian lung airways (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 1-15 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A computational model to predict deposition of a wide variety of particulate pollutants in several species of mammals is presented. The model incorporates breathing pattern and detailed anatomical models of the respiratory tract based on extensive morphometric measurements of individual airways. The predicted deposition from this general model is in close agreement with observed deposition of monodisperse aerosols in rats. Particle size and density and respiratory breathing patterns are the critical parameters affecting regional deposition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462363
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 97
    Electronic Resource
    Electronic Resource
    Theory of antigen-antibody induced particulate aggreagation—I. General assumptions and basic theory (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 17-36 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theory of antigen-antibody induced particulate aggregation is developed by investigating the stability of model systems of particles. Conditions for the formation of large aggregates are derived by imposing the requirement that at equilibrium a statistically significant number of redundant bonds would occur in a reduced monomer-dimer model system. A relationship is obtained which predicts the fractional agglutination in the reduced dimer system as a function of the antigen, antibody and particulate concentrations: $$\frac{g}{{2f c_0 (1 - g)^{2^ - } }} = \frac{{s_1 }}{r} + \frac{{s_1 s_2 }}{{2!r^2 }} + ... + \frac{{s_1 s_2 ...s_j }}{{j!r^j }},$$ wherec 0 is the initial concentration of monomer,f is a proximity factor,g is the fractional agglutination,s i is the average rate of formation of theith bond from an (i−1)th bound dimer, andr is the average rate of dissociation of a single antibody-antigen bond.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462364
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 98
    Electronic Resource
    Electronic Resource
    Theory of antigen-antibody induced particulate aggregation—II theoretical analysis and comparison with experimental results (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 37-56 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The roles of the concentrations of the three interacting constituents in the aggregation process (antibodies, antigens and particulates) are analyzed in detail. It is shown that the basic equation derived in Part I is consistent over a broad range of conditions with experimental findings previously reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462365
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 99
    Electronic Resource
    Electronic Resource
    Hypothalamic regulation of pituitary secretion of luteinizing hormone—II feedback control of gonadotropin secretion (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 57-78 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A general mathematical model describing the biochemical interactions of the hormones luteinizing hormone releasing hormone (LHRH), luteinizing hormone (LH) and testosterone (T) in the male is presented. The model structure consists of a negative feedback system of three ordinary differential equations, in which the qualitative behavior is either a stable constant equilibrium solution or oscillatory solutions. A specific realization of the model is used to describe the experimental observations of pulsatile hormone release, its experimental suppression, the onset of puberty, the effects of castration, and several other qualitative and quantitative results. This model is presented as a first step in understanding the physicochemical interactions of the hypothalamic-pituitary-gonadal axis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462366
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 100
    Electronic Resource
    Electronic Resource
    Dipole theory of interactions of nerve signals (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 79-94 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Based upon the transition rate equation of dipoles in the membrane, we deal with two important aspects of interaction of nerve signals: (1) conditions for nerve excitation and (2) frequency spectrum analysis of nerve impulse. Interrelations between signal amplitudes and frequencies are formulated in detail. There are several important conclusions which can be drawn from our calculations. First, toexcite the nerve, low frequencies are generally more effective than high frequencies. Second, tosedate the nerve (i.e. to suppress undesired activities), high frequencies would suit better. Third, harmonics produced through interactions of nerve signals are not necessarily weaker than the fundamental frequencies. The great significance of our theory is that it indicates in principle the feasibility to alter or rewrite the information contents of a nerve message in our body by applying stimulations of appropriate strengths and frequencies. Thus, the theory provides a physical basis and hence some understanding for a new branch of medicine—neuro therapy such as Nogier's auriculotherapy, Lamy's phonophoresis, Voll's electroacupuncture and the fast rising TENS (transcutaneous electro-neuro stimulation).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462367
    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...