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  • 1981  (14,308)
  • 1964  (5,648)
  • Biology  (19,956)
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  • Articles  (19,956)
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  • 1980-1984  (14,308)
  • 1960-1964  (5,648)
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  • 1
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    Bulletin of mathematical biology 26 (1964), S. 1-7 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract In the arteries, blood flow and blood pressure are pulsatile in nature (Roston, 1962a; Roston 1962b). The patterns of blood movement and mural distension in the arteries are important because they may be associated with life-threatening degenerative changes in the arterial walls. As the vascular channels narrow, the pulsation decreases. At the level of the capillaries, almost no pulsation exists (Best and Taylor, 1961). The tissues are affected by the direct flow in the capillaries and not by the pulsation in the arteries. Thus, such quantities as pulse pressure, systolic pressure, and diastolic pressure which characterize blood movement in the arteries are not important as far as the tissues are concerned. Rather, the average pressure and flow in the capillaries are the quantities significant for tissue blood flow. The present study analyzes the local blood circulation in a typical tissue. Logical extension of this analysis results in insights into the physiological behavior of the circulation which integrate a considerable body of experimental data.
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  • 2
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    Bulletin of mathematical biology 43 (1981), S. 1-19 
    ISSN: 1522-9602
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    Notes: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.
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  • 3
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    Bulletin of mathematical biology 43 (1981), S. 47-58 
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    Notes: Abstract Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.
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  • 4
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    Bulletin of mathematical biology 43 (1981), S. 125-140 
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    Notes: Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Layapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopf's bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.
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  • 5
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    Bulletin of mathematical biology 43 (1981), S. 141-149 
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    Notes: Abstract It was hypothesized in an earlier work that sensory perception can occur only when the perceiving system is uncertain about the nature of the event being perceived. In the absence of any uncertainty, perception will not take place. The response of the sensory afferent neuron (impulse transmission rate) was calculated using Shannon's measure of uncertainty or entropy. It will now be shown that when the event being perceived is the position and momentum of a particle, Shannon's measure of uncertainty leads to the Heisenberg Uncertainty relationship.
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  • 6
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    Bulletin of mathematical biology 43 (1981), S. 239-244 
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    Notes: Abstract It is not unusual for several classifications to be given for the same collection of objects. We present a method, called majority rule, which can be used to define a consensus of these classifications. We also discuss some mathematical properties of this consensus tree.
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  • 7
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    Bulletin of mathematical biology 43 (1981), S. 259-270 
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    Notes: Abstract The dependence of the spatial concentration profiles of morphogens on a characteristic dimension is obtained by continuation techniques for Gierer and Meinhardt's activator-inhibitor model of morphogenesis. The study of the behaviour of the system during growth, where the linear and exponential increase of the characteristic dimension is considered, revealed that more complex patterns of morphogen spatial concentrations appear regularly in a reproducible way.
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  • 8
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    Bulletin of mathematical biology 43 (1981), S. 271-278 
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    Notes: Abstract Computer models have been used by various authors to simulate both the growth of normal cellular tissue and the development of cancerous cells within normal tissue. As these models were the result of considerable idealization, the purpose of the present paper is to propose a model in which the degree of simplification is relaxed: the features of simultaneous growth, and cell growth whose rate depends on the free absorbing periphery of the cell are introduced. Simulation experiments have been conducted using the model, and the results are presented.
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  • 9
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    Bulletin of mathematical biology 43 (1981), S. 341-346 
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    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for a nonlinear model of heat conduction in the human head. Accurate variational solutions are obtained in illustrative calculations. The effect of nonlinearity is seen to be significant from a comparison with the linearized model.
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  • 10
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    Bulletin of mathematical biology 43 (1981), S. 279-325 
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    Notes: Abstract A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.
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  • 11
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    Bulletin of mathematical biology 43 (1981), S. 375-388 
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    Notes: Abstract The irreversible Michaelis-Menten reaction is studied by the use of the method of multiple scales. Three stages of the reaction are identified, one of which is studied in detail. The results are compared with those of two earlier analyses.
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  • 12
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    Bulletin of mathematical biology 43 (1981), S. 389-400 
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    Notes: Abstract A numerical study of the coupled nerve fibre problem is given which verifies and extends the perturbation theory of Luzader. Pulses on adjacent fibres can couple together with two possible stable pulse separations.
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  • 13
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    Bulletin of mathematical biology 43 (1981), S. 401-413 
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    Notes: Abstract A possible mechanism for effects of microwave radiation on the auditory system is the generation of field-induced forces at interfaces that divide materials of dissimilar electrical properties. A general expression for these “Maxwell stresses” is derived and then used to calculate the approximate magnitude of field-induced force within the organ of Corti during microwave exposure. Comparison of the results with data on the force needed to excite cochlear hair cells indicates auditory responses could be evoked by this mechanism at power densities near the threshold of rf hearing sensations.
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  • 14
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    Bulletin of mathematical biology 43 (1981), S. 415-426 
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    Notes: Abstract A definition of homogeneity for neural networks is given which permits their construction as group quotients. The significance of this for neural dynamics is discussed.
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  • 15
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    Bulletin of mathematical biology 43 (1981), S. 447-461 
    ISSN: 1522-9602
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    Notes: Abstract The left ventricle is represented as a cylinder contracting both radially and longitudinally. A simple method is indicated to derive an expression for the rate of change of the kinetic energy of this three-dimensional model, which quantity can be used as an index for the study of the contractile behaviour of the myocardium. An application to the study of muscle mechanics is also indicated.
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  • 16
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    Bulletin of mathematical biology 43 (1981), S. 463-485 
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    Notes: Abstract A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.
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  • 17
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    Bulletin of mathematical biology 43 (1981), S. 513-516 
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  • 18
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    Bulletin of mathematical biology 26 (1964), S. 25-29 
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    Notes: Abstract Error-detecting codes have been known to mathematicians and to electrical engineers for over ten years. In general, such codes utilize an additional orparity bit for purposes of detecting errors by the addition of all positive binary bits or “1’s” occurring in any code word. However, since the process of addition is required for such code detection, it is not surprising that these codes have not been applied to the nucleic acid molecule. In 1962, P. I. Hershberg (Trans. I.R.E., CS-10, 280–4, 1962) outlined a categorical constraint which permitted the realization of a class of error-detecting codes which did not require parity bits. This class of codes is applied to the nucleic acid molecule in the present paper.
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  • 19
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    Bulletin of mathematical biology 26 (1964), S. 31-38 
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    Notes: Abstract Compartment systems are often used as models for tracer and drug kinetics. The structure of a compartment system is here analyzed by means of theory of graphs methods. In particular the precursor-successor relationship between any two compartments is classified according to the structure of the graph of the system and to the values of the elements of the matrix associated with it.
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  • 20
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    Bulletin of mathematical biology 26 (1964), S. 39-43 
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    Notes: Abstract An application of a bifurcation theorem shows the existence of periodic solutions of a system of differential equation used to describe competition between two species. It is then shown that the results are more general than those previously established.
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  • 21
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    Bulletin of mathematical biology 26 (1964), S. 9-24 
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    Notes: Abstract The 2o and 10o field color-matching functions are independent: one specification is not a linear transformation of the other, even after correcting for macular pigment effects. Therefore, the “true” color-matching functions which directly describe the linear responses of the eye must be different for the two field sizes. This means that a given stimulus will, in general, have a different chromaticity depending upon the field size, regardless of the choice of any one colorimetric co-ordinate system for all field sizes. However, in spite of these chromaticity differences, a large uniform field usually appears nearly uniform. Such color uniformity implies that even though chromatic differences occur as a function of retinal position or field size, these differences are small. If this is the case, then the underling “true” color-matching functions determining the observed color-matching functions must be nearly, but not quite, identical. These differences vanish as identity between the sets of color-matching functions is approached. This property suggests a method of calculating the “true” color-matching functions. The “true” color-matching functions must approximate those obtained by minimizing the chromaticity differences between two independent sets of data. This can be done by assuming that the coefficients of transformation should be adjusted so as to produce as nearly identical chromaticities for spectrum stimuli as possible. In this paper, it is also assumed that the “true” color-matching functions have no negative values, as if they were based on actual absorption spectra. This article describes the calculation of the “true” 2o and 10o field color-matching functions satisfying these two conditions. For both field sizes, the maxima of the three functions are near 435, 540, and 585 mμ, after correcting for the filtering effects of the ocular media and macular pigment.
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    Bulletin of mathematical biology 26 (1964), S. 45-47 
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    Notes: Abstract In this note the principal convergence theorem (F. Rosenblatt,Principles of Neurodynamics, Spartan Books, Washington D.C., 1962, 111–116) is proved by a new method.
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    Bulletin of mathematical biology 26 (1964), S. 49-55 
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    Notes: Abstract Considering only nearest neighbor interactions, an expression is obtained for the grand partition function for the adsorption of two kinds of monovalent positive ions at a long chain of one type of monovalent negative fixed sites in an electric field. Expressions are obtained for the fractions of sites which are occupied by each kind of ion as well as of those which are unoccupied as a function of the potential of the electric field.
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    Bulletin of mathematical biology 26 (1964), S. 57-61 
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    Notes: Abstract In connection with a series of previous papers by this author (Bulletin of Mathematical Biophysics,21, 299–308, 375–385;22, 257–262, 263–267;23, 19–29;24, 319–325) results obtained by A. Crawford (Economics 5, 417–428) on the effects of irrelevant lights on reaction times toward a given light stimulus are discussed. The conclusions from a previous paper of this author (Bulletin of Mathematical Biophysics,23, 19–29) are elaborated.
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    Bulletin of mathematical biology 26 (1964), S. 77-81 
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    Notes: Abstract A mathematical model has been constructed to describe experimental data recorded in a study of a simple avoidance situation. The theoretical description makes use of the concept of the effective number of shocks. The model explains the existence of oscillations encountered in previous experiments.
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    Bulletin of mathematical biology 26 (1964), S. 63-75 
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    Notes: Abstract Response probabilities are interpreted from two points of view. One corresponds to fluctuations in physical parameters suggestive of a neurological basis, and the other corresponds to fluctuations in stimulus sample constitution. The two interpretations are shown to be equivalent under rather general conditions, giving the same type of relation between response and training states. This relation is different from that obtained via the response strength concept used in Part I. As a step toward evaluating the difference in predicted behavior for these different response-training relations, a general functional-difference equation is derived that describes the moments of the corresponding stochastic process in experimenter-subject controlled experiments. As an immediate application, it is used to obtain the continuity condition for the solution of the functional equation treated in Part I, and to justify the differentiability conditions assumed in establishing asymptotic properties of the solution as a function of the reinforcement parameter.
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    Bulletin of mathematical biology 26 (1964), S. 83-89 
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    Notes: Abstract A simple avoidance situation is considered in terms of a neural net learning model. Data for the control situation can be represented by an expression having three parameters which determine the initial and the steady state activities together with the transient aspects. The introduction of a learning parameter then allows one to calculate satisfactorily the results obtained in the experimental situation in which shock is applied.
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    Bulletin of mathematical biology 26 (1964), S. 101-101 
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    Bulletin of mathematical biology 26 (1964), S. 91-100 
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    Notes: Abstract An algebraic representation of operations of genetic recombinations is illustrated. It is shown that the recombinations between chromosomes in the two-strand model can be represented by groups, in the sense of the theory of groups. Recombinations between chromosomes with inversions and a translocation are considered as well as cases without them. It is found that the groups derived from such cases are Abelianp-groups (p=2) and that the types of the Abelian groups for the various pairs of chromosomes are different from each other. Differences among those recombination groups are illustrated by showing the sets of generators of the various groups, which generate the corresponding recombination groups by multiplication.
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    Bulletin of mathematical biology 26 (1964), S. 103-111 
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    Notes: Abstract It is shown that a rather close relationship exists between the (ℳ,ℛ)-systems, defined previously as prototypes of abstract biological systems, and the sequential machines which have been studied by various authors. The theory of sequential machines is reformulated in a way suitable for its application to the study of the intertransformability of (ℳ,ℛ)-systems as a result of environmental alteration. The important concept of strong connectedness is most useful in this direction, and is used to derive a number of results on intertransformability. Some suggestions are made for further studies along these lines.
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    Bulletin of mathematical biology 26 (1964), S. 113-120 
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    Notes: Abstract Blood flows into the aorta and its branches during left ventricular systole. Most of the arterial walls in the body stretch during systole in accordance with their elastic properties (Roston, 1962a, b). During diastole, the rebound of the distended walls supplies an additional propulsive force pushing the blood forward. Since the metabolic exchange between most of the tissues in the body and their blood vessels is ordinarily the same throughout the cardiac cycle, it makes little difference whether or not the blood flow occurs during systole or diastole. The circulation in the coronary arteries behaves in a quite different way. Because the muscle fibers of the heart contract during systole and relax during diastole, different conditions for blood flow and metabolic exchange exist during the phases of the cardiac cycle. As a result, specification of whether blood flows in the coronary arteries during systole or diastole may be important. Such specification complicates the study of the coronary artery circulation. For example, because of the arterial elasticity, some of the blood which enters the coronary arteries during diastole comes in contact with the muscle fibers during systole. The present work contains a theoretical study of the coronary artery circulation.
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    Bulletin of mathematical biology 26 (1964), S. 139-146 
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    Notes: Abstract A study is made of the adsorption of one kind of monovalent positive ion at a long chain of alternating monovalent negative fixed charged (“lattice”) and uncharged (“interstitial”) sites both of one type in an electric field. Considering only nearest neighbor interactions an expression is obtained for the grand partition function. The fractions of sites of both types which are occupied and unoccupied are determined. It is shown that an equilibrium constant can be defined for the adsorption of ions at oppositely charged sites.
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    Bulletin of mathematical biology 26 (1964), S. 121-138 
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    Notes: Abstract This paper proposes a model for color perception which accounts for variations in the dimension of the space of perceived colors. The model assumes that there is only one type of cone with only one shape of response curve, but that different cone's response curves differ by translation. It also assumes that the final discrimination system, learned from originally random connections, maximizes discrimination in the normal visual environment. Learning mechanisms are discussed, and the form which the final discrimination system ought to take is plausibly derived. An algorithm for the tristimulus curves is obtained from this model, and it is shown that a good fit of the empirical data can be obtained.
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    Bulletin of mathematical biology 26 (1964), S. 187-191 
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    Notes: Abstract It has been suggested by Robert Rosen (Bull. Math. Biophysics,22, 227–255, 1960) that multiple alleles or pseudoalleles correspond to multiple cites of degenerate states of some quantum mechanical observable which acts as a source of primary genetic information. It is pointed out here that if the quantum mechanical states are determined by the different sequences of the purine and pyrimidine bases in the DNA molecule, the expected number of pseudoalleles would be much too large. The expected number is considerably reduced if we assume that a quantum mechanical state determines the coupling between a molecule of transfer RNA and the corresponding amino acid.
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    Bulletin of mathematical biology 26 (1964), S. 147-166 
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    Notes: Abstract This paper describes a mathematical model developed to simulate the physical characteristics of the human thermal system in the transient state. Physiological parameters, such as local metabolic heat generation rates, local blood flow rates, and rates of sweating, must be specified as input data. Automatic computation of these parameters will be built into the model at a later date when it is used to study thermal regulation in the human. Finite-difference techniques have been used to solve the heat conduction equation on a Control Data Corporation 1604 computer. Since numerical techniques were used, it was possible to include many more factors in this model than in previous ones. The body was divided into 15 geometric regions, which were the head, the thorax, the abdomen, and the proximal, medial, and distal segments of the arms and legs. Axial gradients in a given segment were neglected. In each segment, the large arteries and veins were approximated by an arterial pool and a venous pool which were distributed radially throughout the segment. Accumulation of heat in the blood of the large arteries and veins, and heat transfer from the large arteries and veins to the surrounding tissue were taken into account. The venous streams were collected together at the heart before flowing into the capillaries of the lungs. Each of the segments was subdivided into 15 radial sections, thereby allowing considerable freedom in the assignment of physical properties such as thermal conductivity and rate of blood flow to the capillaries. The program has been carefully checked for errors, and it is now being used to analyze some problems of current interest.
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    Bulletin of mathematical biology 26 (1964), S. 193-198 
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    Notes: Abstract A model is introduced in which the reabsorption of sodium is governed by an enzymatic process. This process is in turn assumed to be influenced by the extracellular volume which depends on the amount of sodium in the body at a given time. The model allows for damped oscillations when the sodium intake lies within range of values and thus can account for observed oscillations.
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    Bulletin of mathematical biology 26 (1964), S. 167-185 
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    Notes: Abstract A neurobiophysical model is proposed for the explanation of some characteristics of schizophrenic behavior. The normal reactions to exogenous stimuli are mediated through a set of centers, while some endogenous stimuli result in abnormal reactions removed from reality, such as dreamlike states, paranoias, hallucinations, etc. The two sets of centers are cross-inhibited and the usual equations for such cross-inhibited systems are applied. In normal life exogenous stimuli as a rule result preponderantly in pleasant reactions, and the corresponding pathways are therefore reinforced. This results in an inhibition of the abnormal reactions. If the life history of an individual is such that a sufficiently large number of ordinarily experienced stimuli leads to unpleasant reactions and, therefore, the corresponding pathways are inhibited, the endogenously stimulated centers for abnormal reactions prevail and various schizophrenic symptoms occur. The same result may be achieved with a normal life history but through organic changes in the system, which differentially affect various thresholds and excitation parameters. The model thus leads to the conclusion that what appears now to be a large array of contradictory findings in the “organic” versus the “psychological” controversy is actually not a contradiction, but is a result of the dependence of normal and abnormal behaviors on a large number of neurobiophysical parameters. Some general comparisons between the conclusions drawn from the model and some known facts are made. The model also provides a first step toward a neurobiophysical interpretation of the mechanism of psychotherapy.
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    Bulletin of mathematical biology 43 (1981), S. 59-67 
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    Notes: Abstract The theory of computational complexity and certain explicitly-stated hypotheses imply limitations on the information processing power of biological systems. Parallelism, special purpose organization, and analog mechanisms may provide speedup critical for life processes, but have little power in the face of exponential growth. We show that “polynomially simulatable” biological systems cannot exhibit dynamic behavior which produces the solution of an intractable problem. The argument implies that parallelism does not allow biological systems to defeat the exponential explosion, but rather is important because it allows polynomial time algorithms to be used more efficiently.
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    Bulletin of mathematical biology 43 (1981), S. 81-88 
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    Notes: Abstract A correlation matrix analysis is applied to the base sequence of MS2 and ϕX174 in comparison with sets of simulated sequences with different degrees of constaint Significant differences between a codified sequence, and a statistical one in terms of the “correlation matrix” for sets of different length cannot be found. This result is analysed in terms of nucleotide sequences with different levels of informational content.
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    Bulletin of mathematical biology 43 (1981), S. 101-109 
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    Notes: Abstract A method of calculating the volume of a tree distal to a cut at the origin of a branch, using branching, diameter and length ratios, has been developed. The method was applied to bronchial tree casts from human, dog, sheep, hamster, and rat lungs. It was found that the exponenta in the equation weight=k×diameter a is approximately equal to 3.0 in sheep lung casts, as found by Hooper (1977), but it is greater than 3.0 in casts from the other four species.
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    Bulletin of mathematical biology 43 (1981), S. 111-116 
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    Notes: Abstract In this note we examine a continuous time version of a compartmental model introduced in a discrete time setting by S. R. Bernard. The model allows for more than one particle to leave the system at any time. This introduces additional randomness into the system, over the pure death system and this is reflected in the variance function.
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    Bulletin of mathematical biology 43 (1981), S. 89-99 
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    Notes: Abstract The mean first passage time for free diffusion can be derived directly by solving a simple analogue steady state problem. In this problem the diffusion starting region is considered as a time independent source of diffusing particles and the diffusion target assumes the behaviour of a perfectly absorbing sink. It is shown here that the transit time between the source and the sink, which in this particular problem is equal to the ratio between the holdup of the system and the total flux, is identical to the Brownian movement concept of the mean first passage time for free diffusion. This established identity considerably facilitates the derivation and investigation of the timing of diffusion in complicated structures such as those commonly found in living organisms.
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    Bulletin of mathematical biology 43 (1981), S. 121-123 
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    Bulletin of mathematical biology 43 (1981), S. 117-120 
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    Bulletin of mathematical biology 43 (1981), S. 201-211 
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    Notes: Abstract In this paper three stochastic models are developed for a class of two-compartment systems to analyse the randomness of the leaving process of the particles in the system. Results in closed form for the distribution of the leaving process of the particles in the system are given both for general and exponential sojourn time distributions and also in association with forward recurrence time distributions with and without Poisson input.
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    Bulletin of mathematical biology 43 (1981), S. 213-232 
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    Notes: Abstract Two simple models are proposed and analysed, in which it is shown that the formation of a new polymer, resulting from an “error” in the template action mechanism of production of an old polymer, may compromise the stability of the initial system under specific conditions, in the context of prebiotic evolution. Autocatalysis is shown to be a “selective advantage”, enabling the “mutant” to dominate in concentration and even replace the initial polymer. The addition of a third molecule playing the role of a catalyst causes hysteresis effects.
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    Bulletin of mathematical biology 43 (1981), S. 165-181 
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    Notes: Abstract The problem of extinction of the prey population in a microbial predator-prey interaction in a chemostat has been examined. Usual deterministic lumped parameter models were used for the dynamics of the chemostat for large numbers of the two populations; the generalized birth and death stochastic process was employed for the description of the random variations at small prey numbers. Extinction probabilities of the prey population were calculated for different holding times and chemostat volumes, and their dependence upon the growth parameters of the two populations was studied. It was found that extinction was possible when the Monod model was used for the specific growth rate of the predators as a function of the prey number density. On the other hand, the decrease of the feeding activity of the predators at low prey densities predicted by the multiple saturation model acts as a regulatory factor that prevents extinction of the prey. In view of the fact that extinction of the prey has never been observed in the laboratory, the latter model seems more appropriate to describe the dynamics of microbial predation.
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    Bulletin of mathematical biology 43 (1981), S. 233-238 
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    Notes: Abstract During exposures of the eye to light, the choroidal circulation may have a regulatory influence on the retinal temperature. This is investigated using a mathematical model and a finite-difference technique. It is predicted that the choroidal blood flow a small effect on retinal temperature, which may be important.
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    Bulletin of mathematical biology 43 (1981), S. 427-446 
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    Notes: Abstract A probabilistic model of a spatially localized, mutually exitatory (inhibitory) population of neurons is formulated to help explain average evoked potential and post-stimulus time histogram measurements. The model is based on the stochastic activity of single neurons within interactive masses of neurons which exhibit co-operative behavior. Macrostate variables corresponding to the above measurements are related through the model to features of neural operation at the individual and ensemble level. Steady-state solution are obtained and their physiological implications are discussed.
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    Bulletin of mathematical biology 43 (1981), S. 503-512 
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    Notes: Abstract We consider a one-compartment system with stochastic transfer rate characterized either by Gaussian or by two-level jump process and study the time evolution of the (statistical) moments of the (random) amount of the substance present in the system. The effect of the coloured as well as of the white noise is investigated and it is found that the presence of stochasticity in the transfer rate parameter increases the relaxation time of the system. Finally, we obtain the conditions for the stability of the system in the moment sense.
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    Bulletin of mathematical biology 43 (1981), S. 487-501 
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    Notes: Abstract A model is described in which damage to a single intracellular locus can lead to a tumorigenic transformation. Assuming a large number of independent intracellular loci to be at risk and assuming that damage to a locus sufficient to cause a tumorigenic transformation occurs with probability greater than zero for all doses greater than zero, leads to the use of the Weibull distribution to characterize the probability of a nonspontaneous tumorigenic cellular transformation occurring after exposure to a given dose of carcinogen. The excess lifetime tumor incidence (i.e., the proportion of tumor bearers) above the spontaneous incidence is used as an estimate of the non-spontaneous incidence and is characterized by a tumor incidence function that represents the probability of occurrence of one or more non-spontaneous tumorigenic cellular transformations amongN(D) independent surviving cells per individual, after exposure to a doseD of carcinogen. The tumor incidence function is fitted to published data for the excess tumor incidence after exposure of animals or humans to ionizing radiation and after exposure of animals to chemical carcinogens.
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    Bulletin of mathematical biology 43 (1981), S. 549-561 
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    Notes: Abstract This paper deals with a stochasticn-compartment irreversible system with a non-homogeneous Poisson input and arbitrary residence time for each of the compartments. Results relating to the number of particles present in each of the compartments as well as the total number of particles present in the system at any time are derived. Further, explicit expressions for the auto covariance function for each compartment and the cross-covariance function between any two compartments with a given time lag are obtained. As a particular case, then-compartment irreversible system is analyzed with homogeneous Poisson input and exponential residence time distribution for each of the compartments. The possible applications of the model are discussed.
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    Bulletin of mathematical biology 43 (1981), S. 563-577 
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    Notes: Abstract This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.
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    Bulletin of mathematical biology 43 (1981), S. 579-591 
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    Notes: Abstract The relationships that define the structure of a given ecosystem, social system, or even a physiological function can only exist if certain parameters are confined to a certain range of values. As the values change and exceed this given range the relationships are forced to change, and so produce a new pattern of relationships. The concept of a dynamic structure captures this potential for structural change in relation to a set of parameters. The precise definition of structure and allowable transformation constitutes the definition of a category. The total range of parameters associated with all the relevant structures provides a parameter space which is assumed to be a manifold. Maps with extra structure from the manifold to the category define dynamic structures. The domain of differential dynamic systems is the manifold, and a flow or movement across the manifold is associated with a series of structural transformations in the category. In some cases a structure outruns its parameter range, to be faced with an obstruction—an absence of possible transformations. Ways of studying such “obstructions” are considered along with the related problem of extending a dynamic structure beyond a previously given set of parameters. The cost or resistance of transformations is also studied. The concepts of dynamic structures are illustrated by the structural change of food webs and they are used in a necessarily qualitative fashion to study dominance structures of social orders and finally to speculate on the qualitative nature of evolutionary change of functional aspects of organisms.
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    Bulletin of mathematical biology 43 (1981), S. 705-715 
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    Notes: Abstract The preceding paper (Thorn, 1981) has shown that in a linear pharmacokinetic system with a multimodal impulse response the peak drug level may sometimes be smaller with slower rates of injection. This paper presents two theorems on this paradoxical injection rate effect where the injection is a constant infusion of finite duration. The first theorem establishes a graphical method for determining whether a given impulse response will give a paradoxical injection rate effect; and the second establishes that the maximum paradoxical increase in peak drug level is by a factor of two. It is further shown that in order to approach this maximum paradoxical increase the impulse response must contain two isolated, sharp, narrow pulses of approximately equal area. Some examples of bimodal arterial dye-dilution curves from the literature are discussed as impulse responses; and there is also a discussion of the behavior of drug level maxima and minima at different injection rates.
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    Bulletin of mathematical biology 43 (1981), S. 693-703 
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    Notes: Abstract This paper presents three theorems on the peak drug levels that result from injection into a linear pharmacokinetic system. As a preliminary, the “rate of injection” is defined in terms of time expansion or time contraction of the injection function (input). The first theorem then states that the peak drug level will not be greater when the rate of injection is slow than when it is fast, if the impulse response is unimodal. The second theorem sets limits for the time of the maximum drug level, in relation to the time of the maximum of the (unimodal) impulse response and the duration of the input. The third theorem defines conditions which assure a definitely lower peak drug level if the rate of injection is slower. A graphical method is suggested for determining the times and magnitudes of the peak drug levels that result from constant infusions of a fixed dose at different rates. An example is provided to show that if the impulse response is multimodal then the peak drug level may sometimes increase with a decrease in the injection rate.
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    Bulletin of mathematical biology 26 (1964), S. 199-199 
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    Bulletin of mathematical biology 26 (1964), S. 201-201 
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    Bulletin of mathematical biology 26 (1964), S. 203-203 
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    Bulletin of mathematical biology 43 (1981), S. 33-45 
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    Notes: Abstract A two urn Polya-type scheme is considered in whichr black balls (corresponding to the stable form of an element) are added to urn one at every stage and the same number of balls are removed at random at every stage from the same urn. In between these two operations, which form a stage or iteration, a fixed number of balls is exchanged at random between urns one and two. Urn one has a given initial number of white balls (corresponding to a radioactive form of the same element). The problem of interest is to study the stochastic aspect of the number of white balls remaining in urn one (and/or urn two) aftern iterations.
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    Bulletin of mathematical biology 43 (1981), S. 21-32 
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    Notes: Abstract We obtain within the action-angle variable approach new expressions, involving the Dirac delta function, for time periods and time averages of dynamical variables which are useful for nonlinear biological oscillator problems. We combine these with Laplace transformation techniques for evaluating the required perturbation expansions. The radii of convergence of these series are determined through a complex variable approach. The method is powerful enough to yield explicit results for such systems as the two species Volterra model, Goodwin's model of protein synthesis etc. and as an illustration, is applied here to Cowan's model of neuroelectric activity. We also point out the usefulness of the action integral in the case where parameters occurring in dynamics have slow time variations.
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    Bulletin of mathematical biology 43 (1981), S. 69-79 
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    Notes: Abstract Zwanzig and Mori's projection-operator method is used in order to derive a generalized nonlinear Fokker-Planck equation for one “relevant” species in the many species conservative Volterra model. The deterministic, autonomous, Markovian equations of motion, when averaged over a suitable ensemble of initial conditions in general give rise to a non-autonomous, non-Markovian stochastic process for the evolution of this relevant species. Moreover, this relevant species may show irreversible damping, although self-interaction terms are absent in the many species model.
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    Bulletin of mathematical biology 43 (1981), S. 151-163 
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    Notes: Abstract The hydrodynamical problem of flow in proximal renal tubule is investigated by considering axisymmetric flow of a viscous, incompressible fluid through a long narrow tube of varying cross-section with reabsorption at the wall. Two cases for reabsorption have been studied (i) when the bulk flow,Q, decays exponentially with the axial distancex, and (ii) whenQ is an arbitrary function ofx such thatQ-Q 0 can be expressed as a Fourier integral (whereQ 0 is the flux atx=0). The analytic expressions for flow variables have been obtained by applying perturbation method in terms of wall parameter ε. The effects of ε on pressure drop across the tube, radial velocity and wall shear have been studied in the case of exponentially decaying bulk flow and it has been found that the results are in agreement with the existing ones for the renal tubules.
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    Bulletin of mathematical biology 43 (1981), S. 183-199 
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    Notes: Abstract Voltage clamp experiments, which determine the kinetic parameters of calcium conductance of cardiac muscle, (d ∞,f ∞, τ d and τ f ) are analyzed with a generally accepted expression for slow inward currentI s=g sdf (E-E R). Activation (d) and inactivation (f) reach the final valuesd ∞ andf ∞ with time constants τ d and τ f respectively. The analysis indicates that the measuredf ∞ agrees with the theoreticalf ∞, but the measuredd ∞ differs from the theoreticald ∞ by a factor which depends on τ d . The peak tension can be made to correlate closely with the theoreticald ∞ after a correction factor is applied to the raw measurements of activation. It can be shown that experiments designed to measure τ f can also be used to determine τ d with greater accuracy.
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    Bulletin of mathematical biology 43 (1981), S. 245-247 
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    Bulletin of mathematical biology 43 (1981), S. 249-257 
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    Notes: Abstract A deterministic model for an SIR epidemic with silent infections is investigated. It is shown for the model studied that the extent to which silent infections are present may be determined from data concerning only those individuals with symptomatic infection.
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    Bulletin of mathematical biology 43 (1981), S. 327-340 
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    Notes: Abstract An urn contains balls of different colors. Specified numbers of each color are added and form a reinforcement. The total reinforcement is randomly removed, forming a depletion. The process, not necessarily with the same reinforcements, is performed a number of times. The factorial moment generating function of the urn configurations at any stage is given in terms of multivariate difference operators. Cases when the reinforcement vector is defined as a stochastic variable are considered. The problem is a generalization of an urn model associated with radioactive atoms and stable atoms proposed by S. R. Bernard. The solutions given here have a definite application to the problem of modelling tracers in compartmental systems.
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    Bulletin of mathematical biology 43 (1981), S. 347-360 
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    Notes: Abstract A multi-compartmental model with particles producing offspring according to the Markov branching process has been studied. Explicit results are given for the two-compartmental system and for irreversible general multicompartmental systems. The known models in stochastic compartmental analysis are shown to be particular cases of this model and applications are cited.
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    Bulletin of mathematical biology 43 (1981), S. 371-372 
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    Bulletin of mathematical biology 43 (1981), S. 361-370 
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    Notes: Abstract The irreversible Michaelis-Menten scheme may be reduced to a pair of autonomous first-order differential equations. The phase-plane behaviour of these is investigated.
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    Bulletin of mathematical biology 43 (1981), S. 372-373 
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    Bulletin of mathematical biology 43 (1981), S. 517-548 
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    Notes: Abstract A discrete one-dimensional model of convection-diffusion in branching alveolar ducts is described and it is shown that, for a suitable choice of effective axial dispersion, the solution closely approximates that for an axially symmetric representation, at least for Peclet numbers Pe〈1. Following earlier work a composite model of a uniform lung is formed by matching such a respiratory pathway (now having the more convenient one-dimensional form) onto a trumpet representation of the conducting airways. Enhanced mixing due to heart action, and isotropic volume changes of trumpet (in addition to the pathway) during breathing are additional factors included. Calculations are made of O2 concentrations during steady-state breathing and of the concentration of inert gas during single breath wash-out of a gas mixture containing it. Predicted alveolar levels in each case agree extremely well with published data, although no alveolar slope is obtained for the inert gas.
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    Bulletin of mathematical biology 43 (1981), S. 593-610 
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    Notes: Abstract The evolution and local stability of a system of two interacting species in a finite two-dimensional habitat is investigated by taking into account the effects of self- and cross-dispersion and convection of the species. In absence of cross-dispersion, an equilibrium state which is stable without dispersion is always stable with dispersion provided that the dispersion coefficients of the two species are equal. However, when the dispersion coefficients of the two species are different, the possibility of self-dispersive instability arises. It is also pointed out that the cross-dispersion of species may lead to stability or instability depending upon the nature and the magnitude of the cross-dispersive interactions in comparison to the self-dispersive interactions. The self-convective movement of species increases the stability of the equilibrium state and can stabilize an otherwise unstable equilibrium state. The effect of cross-convection (in absence of self-dispersion and self-convection) is to stabilize the equilibrium state in a prey-predator model with positive cross-dispersion coefficients for the prey species. Finally, it is shown that if the system is stable under homogeneous boundary conditions it remains so under non-homogeneous boundary conditions.
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    Bulletin of mathematical biology 43 (1981), S. 611-618 
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    Notes: Abstract Various observations suggest that sympathetic ganglia act as local integrative centers redistributing preganglionic excitation (i.e. the information issued by the central nervous system) to the postganglionic fibers (and effector organs). In order to support this concept a simple mathematical model of the elementary integration process, treating the case of a single preganglionic compound action potential, has been developed. This quantitative description, based on a few elementary assumptions, shows a possible way of processing preganglionic excitation in the ganglion. It is shown that on a particular ganglion cell the probability distribution of the number of activated synapses obeys hypergeometric distribution and hence, the postganglionic compound action potential is built up of several compound action potentials occurring at different times. The former correspond to different groups of firing cells. The model discloses modes of structural and temporal pattern generation performed by the sympathetic ganglion.
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    Bulletin of mathematical biology 43 (1981), S. 619-639 
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    Notes: Abstract Amino acid sequences have already been examined in some detail in order to relate them to structural aspects, homology and gene duplication. This report introduces the concept of internal uniqueness of tripeptides within protein sequences and uses the Monte Carlo method to study this property. Some idea of internal uniqueness may be obtained from such an analysis using only a single sequence if the probability of the random occurrence is about 0.001 or less. This method of analysis is similar to that used in quantitative evaluations of homology. When the probability of the random occurrence is larger than 0.001 a homologous group of sequences is required and the random probabilities may be compared with the real occurrences within the group. From such an examination insulin and cytochrome c are identified as protein sequences with high internal uniqueness. A comparison of data from internal uniqueness and gene duplication analyses shows that these two properties need not be related. Results of the analysis point to internal uniqueness as an additional parameter for inclusion in speculations on why twenty amino acids are coded in protein structure.
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    Bulletin of mathematical biology 43 (1981), S. 641-650 
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    Notes: Abstract The concept of a tolerance net formalises simultaneously spatial closeness and nearness of neuronal activity. A method of constructing tolerance group nets is presented, leading to a means of construction of all very homogenous tolerance nets as group quotients. The dihedral group of order eight is taken as an illustrative example.
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    Bulletin of mathematical biology 43 (1981), S. 681-691 
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    Notes: Abstract Two methods are described for calculating the value of the exponentx in the equation flow =k×diameter x , as pertaining to a branch of the bronchial tree. In the lungs from three humans, two dogs, one hamster, and one rat mean values ofx between 2.419 and 2.903 were found. They lie within the range of 2.333 to 3.0 predicted by the analysis of Uylings (Bull. Math. Biol. 39, 501–519, 1977).
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    Bulletin of mathematical biology 43 (1981), S. 665-680 
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    Notes: Abstract A stochastic analysis of a nonlinear selection model is presented. The model, based on Eigen and Schuster's theory of selection and evolution of biological macromolecules, considers the effects of fluctuations on the individual concentrations of macromolecules as well as the total population numbers in constrained systems. Our analysis shows that one of the models most often treated deterministically (referred to as constant organization in the literature) becomes unstable when fluctuations in the total population number are considered. An alternative model which apparently has built in self-regulating properties is analyzed and proves to be stable except for some special cases of degeneracy.
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    Bulletin of mathematical biology 43 (1981), S. 651-664 
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    Notes: Abstract Previous compartmental models have introduced variability either at the particle or at the replicate level. This paper integrates both types of variability through the concept of clustering. The paper develops two different, general clustered models, each with time-dependent hazard rates for the clusters and for the particles within the clusters, and each with random initial number and sizes of clusters. The coefficient of variation of the total number of particles,CV[X(t)], for either model is shown to be bounded below, under very broad conditions, by the coefficient of variation of the initial number of clusters,CV[c(0)]. This high relative variability of the clustered models makes them potentially very useful in kinetic modeling. In many applications, binding and clustering are common phenomena, and two applications of the models to such phenomena are breifly outlined.
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    Bulletin of mathematical biology 43 (1981), S. 717-717 
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    Bulletin of mathematical biology 43 (1981), S. 719-719 
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    Helgoland marine research 10 (1964), S. 1-6 
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    Helgoland marine research 10 (1964), S. 64-72 
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    Description / Table of Contents: Zusammenfassung 1. Vergleichende Untersuchungen an Diatomeen von verschiedenen Standorten der Gezeitenzone ergaben in allen Fällen eine beträchtliche osmotische Resistenz. Diese kann für die einzelnen Arten sehr unterschiedlich sein. Die festgestellten Resistenzspannen erreichen zum Teil diejenigen, die aus der Literatur für vielzellige Algen des Litorals bekannt sind, zum Teil liegt die Resistenz aber in engeren Grenzen. 2. Unter den Eigenschaften, mit denen sich die Diatomeen auch gegenüber starken Konzentrationsschwankungen behaupten können, tritt ihre Fähigkeit zur Erhöhung und Verminderung der Zellsaftkonzentration besonders hervor. Sie ist spezifisch verschieden stark ausgeprägt und wird durch Plasmolyse- und Turgorresistenz ergänzt. Möglicherweise werden die Zellen ferner durch ihre große Populationsdichte, Gallertausscheidungen und aktive Bewegungen vor der kritischen osmotischen Beanspruchung geschützt. 3. Für die Diatomeen des gleichen Standorts ist nicht ein bestimmter Resistenztyp charakteristisch; es können vielmehr Formen mit verschiedenem Verhalten am gleichen Ort vorkommen.
    Notes: Abstract Diatoms of littoral regions are often exposed to considerable salinity fluctuations. This fact suggests that these unicellular organisms exhibit osmotic resistances similar to those found in larger multicellular algae. The responses of typical representatives of the littoral diatom flora were studied after transfer into diluted or concentrated sea water. The technique applied made it possible to compare the results with corresponding data from literature obtained on green, brown and red algae of the tidal zone. The total amount of resistance of the diatoms studied may reach the values obtained on these multicellular algae or may be lower. The results imply the presence of mechanisms capable of flexible osmotic adjustments to salinity changes. In addition to their osmotic resistance sensu strictu, protection from the ill effects of extreme salinities may be of importance, for example, through the formation of jelly, variations in population density and perhaps the ability to migrate into more suitable conditions. All species tested have shown an ability for osmoregulation or for passively tolerating changes in internal osmoconcentration. Some may tolerate plasmolysis even for prolonged periods. Diatoms exhibiting quantitative and qualitative differences in osmotic resistance may occur in the same microhabitat.
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    Helgoland marine research 10 (1964), S. 7-18 
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    Description / Table of Contents: Summary 1. Oxygen consumption by a group of 25 lobsters was essentially constant over a range of ambient oxygen concentrations from 1.0 to 8.5 mg/l. Consumption by groups of 35 and 50 lobsters at 15° C decreased as the concentration decreased. 2. Oxygen consumption by individuals at 10° and 15° C increased as the oxygen concentration increased. 3. Oxygen consumption increased as activity increased with crowding. 4. Oxygen consumption almost doubled after feeding. 5. Oxygen consumption per unit weight decreased with increasing size. 6. The average rate of oxygen consumption by individuals doubled over the temperature range 12° to 25° C. 7. Oxygen consumption in air at 6° to 25° C was much less than in water.
    Notes: Kurzfassung Bei einer Gruppe von 25 Hummern wurde der Sauerstoffverbrauch in Dauerfluß-Respirometern gemessen. Bei 10° C erwies er sich als im wesentlichen konstant über einen Bereich der Sauerstoffkonzentration im umgebenden Wasser von 1,0 bis 8,5 mg/l. Bei Gruppen von 35 und 50 Hummern, welche bei 15° C getestet wurden, nahm der Sauerstoffverbrauch jedoch mit fallender Sauerstoffkonzentration etwas ab. Anstieg der Individuenzahl pro Raumeinheit (“crowding”) führte zu steigender Bewegungsaktivität und zu erhöhtem Sauerstoffverbrauch. Nahrungsaufnahme verursachte fast eine Verdoppelung des Sauerstoffverbrauchs. Kleine Individuen verbrauchen pro Gewichtseinheit mehr Sauerstoff als große. In manometrischen Respirometern stieg der Sauerstoffverbrauch bei hohen Sauerstoffkonzentrationen im umgebenden Wasser mit der Temperatur. Bei 6° bis 25° C war der Sauerstoffverbrauch in der Luft wesentlich geringer als im Wasser.
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    Description / Table of Contents: Summary 1. The effect of exposure to air on the oxygen uptake, lactic acid production, and quantities of certain phosphoryleated intermediates ofC. depressus has been determined. 2. On transference to air, aerobic conditions with a reduced metabolic rate are first maintained; access of oxygen and water loss are controlled by the opercular micropyle. 3. Dehydration stresses then lead to occlusion of the mantle cavity and subsequent anaerobiosis. 4. Starvation results in a lower metabolic rate, aerobic or anaerobic, and a reduced demand for substrates now mobilized from reserves. 5. The reduced demand is also related to the amount of dehydration and the latter is so adjusted to allow viability over a long period. 6. Eventually toxic products kill the animal.
    Notes: Kurzfassung C. depressus vermag lange außerhalb des Wassers zu leben und stellt somit ein ideales Versuchstier dar für Studien über die Wirkungen von Trockenfallperioden. Es wird ein kurzer Abriß der bisherigen Ergebnisse über biochemische Veränderungen während der Luftexponierung gegeben. In Luft erfolgt eine Verringerung der Sauerstoffaufnahme, wobei der Unterschied zwischenC. depressus vom unteren und oberen Gezeitenbereich sehr ausgeprägt ist. In den ersten 7 Tagen steigt der Milchsäuregehalt geringfügig. Dieser Umstand deutet auf eine geringe anaerobe Stoffwechselintensität hin. Die quantitativen Veränderungen einiger phosphorilierter Intermediärprodukte werden untersucht. Die auffälligste Veränderung betrifft den ATP-Gehalt, welcher in den ersten 3 Tagen auf die Hälfte absinkt. Es tritt ferner eine deutliche Anreicherung von Glukose-6-Phosphat ein. Die Beziehungen zwischen dem Verhalten der Tiere, dem Wasserverlust und den biochemischen Veränderungen werden diskutiert.
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    Helgoland marine research 10 (1964), S. 29-37 
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    Description / Table of Contents: Summary 1. The rate of photosynthesis at varying amounts of natural sunlight has been measured for large pennate littoral diatoms which inhabit the sand flats of Barnstable Harbor, Massachusetts, and which exhibit vertical migration to the surface at low tide. 2. The algae require only 12 gm. cal./cm.2/hr. to reach their maximum photosynthetic capacity. 3. Full mid-day summer sunlight (75 gm. cal./cm.2/hr.) results in only a 10% inhibition of maximum photosynthesis. 4. Measurements of light penetration through the sand in which the diatoms are found indicated 10% of solar radiation reaches 1.5 mm. 5. At noon on a cloudless mid-summer day these species existing as deep as 3.0 mm. are probably above their compensation level, while those from 2.0 mm. to the surface are able to photosynthesize at 90% or better of their maximum rate. 6. The photosynthetic efficiency at low light levels enables these diatoms to fix considerable carbon even when the flats are exposed when the sun angle is low. 7. The migration pattern of these diatoms does not result in significant inhibition of photosynthesis but rather their photosynthetic apparatus is well adapted to such migratory activity.
    Notes: Kurzfassung Diatomeen der Sandflächen des Barnstable Harbor (Massachusetts, USA) wurden eingesammelt und ihre Photosyntheserate bei verschiedenen Quantitäten natürlichen Sonnenlichts mit Hilfe der C−14-Methode ermittelt. Es zeigte sich, da7sB die Diatomeen dem Lichtfaktor gegenüber eine sehr große Toleranz besitzen. Die Intensität der Photosynthese erreichte Maximalwerte bei etwa 14% des mittäglichen Mitte-Sommer-Sonnenlichts; aber selbst volles Sonnenlicht verursachte nur einen geringfügigen Leistungsabfall. Es wurden Messungen über das Durchdringungsvermögen der Sonnenstrahlung bis in die Sandschichten, in welchen die Diatomeen bei Niedrigwasser leben, durchgeführt. Diese Messungen zeigen, daß bei trockengefallenem Sand und an einem wolkenlosen Sonnentag gegen Nachmittag die Photosyntheserate die Atmungsintensität übertreffen kann, selbst wenn die Diatomeen 3,0 mm unter der Sandoberfläche leben. In 2,0 mm Sandtiefe bis zur Oberfläche kommt die Photosyntheserate unter den genannten Bedingungen bis auf 90% oder näher an die Maximalleistung heran. Der hohe photosynthetische Nutzeffekt bei geringen Lichtintensitäten ermöglicht den Diatomeen, beachtliche Kohlenstoffmengen zu fixieren, selbst bei niedrigem Sonnenstand. Der Photosynthese-Mechanismus ist gut an die Wanderbewegungen der Diatomeen angepaßt.
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    Helgoland marine research 10 (1964), S. 73-90 
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    Description / Table of Contents: Zusammenfassung 1. Die negative Turgorregulation vonChaetomorpha linum nach Herabsetzung des Salzgehaltes im Außenmedium beruht in der Hauptsache auf einer Erniedrigung des osmotischen Potentials des Zellsaftes durch Abgabe von K. und Cl′. 2. Während der positiven Turgorregulation nach Erhöhung des Salzgehaltes im Außenmedium konnte umgekehrt eine starke Speicherung von K. und Cl′ beobachtet werden. 3. Das Natrium als wichtigstes Kation des Seewassers ist für beide Prozesse osmotisch kaum von Bedeutung. Die Änderung des Natriumgehaltes im Versuchsmaterial betrug in beiden Fällen nur etwa 10% der Änderung seines Chloridwertes und nur etwa 5% der Änderung seines osmotischen Gesamtpotentials. 4. Kalziummangel im Außenmedium führte zu einer starken Abgabe von KCl durch die Versuchspflanzen, welche dabei einen beträchtlichen Turgorverlust erlitten. 5. Die ebenfalls durch Kalziummangel bewirkte starke Verquellung der Zellwände wird im Zusammenhang mit der sprughaften Abnahme des Kalziumgehaltes der Versuchspflanzen auf einen Ionenaustauschvorgang zurückgeführt, bei dem das Zellwand-Kalzium durch Natrium ersetzt werden dürfte.
    Notes: Abstract Some algae of the intertidal zone are capable of regulating their turgor pressure. In 1896Drevs had already shown that this process is affected primarily by accumulation (positive turgor-regulation) or extrusion (negative turgor-regulation) of mineral salts and that transformation of stock material (e. g. starch) into osmotic active substances (e. g. sucrose) and vice versa plays no important role. His results are being confirmed by the present paper. InChaetomorpha linum (Müller)Kützing, lowering of salinity resulted in a significant release of potassium and chlorine (negative turgor-regulation). Changes in sodium content were only small. In algae exposed to a salinity of 30‰, the total sodium concentration was only about 10% that of the external medium. Salinity increase led to a marked accumulation (positive turgor-regulation) of potassium and chlorine. Even in this process sodium was engaged only to a small degree — despite its high concentration in the surrounding medium. In both cases internal changes in sodium content amounted only to about 5% of the total osmotic changes in the external medium. After transfer from 30‰ salinity into isosmotic artificial sea water without Ca··, a rapid loss of potassium and chlorine was observed. The abrupt decrease of the calcium content accompanied by a marked swelling of cell walls, leading to a significant reduction of cell space, is interpreted as ion exchange process changing the cell wall Ca.. against Na..
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    Helgoland marine research 10 (1964), S. 38-63 
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    Description / Table of Contents: Zusammenfassung 1. Es wird die Größenabhängigkeit des Sauerstoffverbrauchs vonArenicola bei Temperaturen zwischen 2° C und 30° C in Versuchsserien im Frühjahr und Herbst gemessen. 2. Da der Sauerstoffverbrauch je Gewichtseinheit bei den Würmern keine konstante Größe darstellt, werden die Parametera und b der allometrischen Gleichung: y=b·w a zur Auswertung der Versuchsergebnisse herangezogen. 3. Der Exponentα hat keine konstante Größe, sondern ändert sich mit der Temperatur. Sein Wert liegt fürArenicola im allgemeinen zwischen 0,7 und 0,8, was einer Zwischenstellung zwischen oberflächen- und gewichtsproportionaler Atmung entspricht. 4. Der Faktor b stellt die aus der Gesamtheit der Meßwerte — unter Berücksichtigung der Größenfunktion — berechnete Atmungsgröße eines Tieres von der Gewichtseinheit dar. b hat daher in der quantitativen Versuchsauswertung an die Stelle der einfachen Angabe O2-Verbrauch : Gewicht zu treten. 5. Die Temperaturabhängigkeit des Sauerstoffverbrauchs vonArenicola ist durch Unstetigkeiten charakterisiert, worunter Temperaturbereiche verstanden werden sollen, in denen der Sauerstoffverbrauch erheblich über oder unter den nach der RGT-Regel zu erwartenden Werten liegt. 6. Aus diesen Unstetigkeiten erklärt sich die geringe Temperaturabhängigkeit des Stoffwechsels vonArenicola in dem Bereich zwischen 10° C und 20° C. Eine zweite Unstetigkeit verhindert bei den Würmern im Frühjahr ein zu starkes Absinken des Stoffwechsels unterhalb von 5° C. In vielen Versuchen findet man hier bei abnehmender Temperatur einen erhöhten Sauerstoffverbrauch. 7. Die Lage und Ausdehnung der Unstetigkeiten verschiebt sich im Verlauf des Jahres im Sinn der Milieu-Temperaturen.
    Notes: Abstract A knowledge of the rate of oxygen consumption is very important for the evaluation of many physiological and ecological problems. Among the many factors affecting respiratory rate, water temperature and body size are particularly considered here. The modifying effects of body size may be expressed mathematically by the allometric formula: y=b · w a , where b represents the rate of O2 consumption of an individual whose weight is expressed in a chosen metrical weight unity (i. e. in grams, ounces, etc.), anda represents the decrease of metabolic rate during growth. InArenicola the exponent is not the same at all temperatures tested. In most cases it lies between 0.7 and 0.8, i. e., between a weight proportional respiratory rate and a surface proportional one. Minimum values fora were found in experiments conducted in summer at 20° C and in spring at 15° C. They characterize an optimum efficiency of metabolism at these temperatures. Determinations of b demonstrated that metabolic rate ofArenicola is significantly less affected in spring (10° to 20° C) and autumn (10° to 25° C) than is usually known from biological processes. However, the temperature coefficients above and below these temperature ranges are very high. Another break in the temperature-rate curve could be demonstrated below 5° C in spring.
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    Helgoland marine research 10 (1964), S. 91-103 
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    Description / Table of Contents: Zusammenfassung 1. Junge Strandkrabben von 4–16 mm Carapaxbreite wurden bis zur Geschlechtsreife unter konstanten Umweltbedingungen aufgezogen. 2. Die Dauer ihrer Häutungsintervalle nimmt bei konstanter Temperatur mit der Körpergröße stetig zu. 3. Die Dauer der Häutungsintervalle hängt von der Temperatur und der Ernährung ab. Von der Tageslänge scheint sie weitgehend unabhängig zu sein. 4. Der relative Grösßenzuwachs bei jeder Häutung ist im gesamten untersuchten Größenbereich und bei den verschiedenen Temperaturen bei allen Häutungen gleich: Bei den Häutungen verdoppelt sich jeweils das Körpervolumen. 5. Augenstielamputationen und Verlust von Extremitäten wirken auf den Häutungsrhythmus in gleicher Weise: Die Schwankungsbreite in der Dauer der Häutungsintervalle ist vermindert. Die Häutungsintervalle sind in 20° C deutlich, in 10° C nur geringfügig verkürzt. 6. Durch die Anwesenheit größerer Artgenossen werden die Häutungen verzögert. Die optische Wahrnehmung spielt dabei keine Rolle. 7. Aus diesen Ergebnissen wird folgendes geschlossen: Der ausschlaggebende Faktor für die Auslösung von Häutungen ist ein bestimmter Größenzuwachs. Temperatur und Ernährung beeinflussen den Häutungsrhythmus dadurch, daß sie das Tempo des Wachstums bestimmen. Die winterliche Häutungsruhe in Freilandpopulationen wird nicht durch den Kurztag bedingt, sondern durch die Kälte. Diese hemmt lediglich das Wachstum, sie verhindert nicht die Häutungen über das häutungshemmende Hormon. Dieses vermindert vielmehr die Temperaturabhängigkeit des Häutungsrhythmus, indem es die Häutungen im Warmen stärker verzögert als im Kalten. Es gestattet die Anpassung des Häutungstermins an die individuelle Lage der Tiere. Es hemmt in Anwesenheit größerer Artgenossen die Häutung. Beim Verlust mehrerer Gliedmaßen wird seine Sekretion eingestellt, so daß die nächste Häutung vorzeitig erfolgt. Das häutungshemmende Hormon bedingt dementsprechend die große individuelle Variation in der Dauer der Häutungsintervalle.
    Notes: Abstract Young crabs (carapace width 4 to 16 mm) were raised under controlled conditions in the laboratory. The time intervals between subsequent moults increase at all test temperatures with increasing body size. The length of intermoult periods varies with temperature and feeding. It is not affected by day length. Moulting takes place as soon as a certain increase in size is attained. In comparable size groups, the amount of this increase is identical in all test temperatures. Moreover, the relation of increase to initial size is constant over the whole size range investigated. The body volume doubles at each moult. Eyestalk amputations and loss of extremities have similar effects: They shorten the intermoult periods at 20° C considerably, but at 10° C they do so only slightly; furthermore, the amplitude of fluctuations is narrowed. The presence of large specimens tends to retard moulting in smaller ones; this response is independent of visual stimuli. The following assumptions are made: Low temperatures retard the moulting rhythm directly by slowing down growth. They are not acting via the moult inhibiting hormone. Loss of several extremities causes a stop of hormone delivery resulting in shortened intermoult periods. Recognition by touch of a larger specimen causes increased hormone delivery and thus retardation of the subsequent moulting process.
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    Helgoland marine research 10 (1964), S. 104-117 
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    Topics: Biology
    Description / Table of Contents: Zusammenfassung 1. Durch Untersuchungen an den natürlichen Standorten wurde versucht, den Nahrungserwerb und seine Beziehungen zu ökologischen Faktoren bei dem SchlangensternOphiocoma scolopendrina und dem FedersternHeterometra savignyi zu analysieren. 2. Die Aktivitätsphasen der ortsfesten, in der Gezeitenzone lebendenO. scolopendrina werden von den Tiden, den Wasserbewegungen und der Bodenstruktur am Wohnplatz bestimmt. Die wellenempfindlichen Tiere sind bei Hochwasser meist inaktiv. Der Nahrungserwerb findet in Gezeitentümpeln bei Niedrigwasser, an trocken fallenden Stellen nur solange das auf- oder ablaufende Wasser zu niedrig steht, als daß sich Wellen bilden können, statt. 3. Die Tiere sind zwar Allesfresser, doch überwiegt pflanzliche Nahrung. 4. Drei verschiedene Formen des Nahrungserwerbs sind zu unterscheiden: Absammeln oder -rupfen vom Boden (in unbewegtem Wasser), Filtrieren (in strömendem Wasser) und Abweiden des Staubfilms von der Wasseroberfläche (nur am Tage in auflaufendem Wasser). 5. Nahrungsaufnahme und -transport in den Magen erfolgen ausschließlich durch die Ambulacralfüßchen. Zum Filtrieren werden sie steif ausgestreckt und bilden unter jedem Arm zwei Filterkammreihen. Dieser Filterapparat ist sehr grob und nur in stärkeren Strömungen, die reichliches Geschwebe heranführen, wirkungsvoll. 6. BeiO. scolopendrina ist die Filtration nur für die auf trocken fallenden Habitaten wohnenden Individuen von größerer Bedeutung, bei den anderen überwiegt die Futteraufnahme vom Boden. 7. Aus den Untersuchungsergebnissen anO. scolopendrina muß geschlossen werden, daß die in größerer Tiefe am Meeresboden stellenweise massenhaft vorkommendenOphiothrix fragilis undOphiothrix quinquemaculata, die dort z. T. auf dem Rücken liegen und in der Regel ihre Arme erhoben halten, nicht, wie vielfach angenommen, herabsinkende Nahrung auffangen, sondern diese ausschließlich aus stärkeren und an organischem Material reichen Strömungen abfiltrieren. 8. Der Nahrungserwerb der 20armigen, nachtaktiven und in lagunenartigen Flachwassergebieten mit schwachen Strömungen lebendenH. savignyi geschieht ausschließlich durch Filtration feinen, vorwiegend lebenden Geschwebes. 9. Die Arme stellen sich, die aboralen Seiten gegen die Strömung gerichtet, nebeneinander und bilden zusammen einen einheitlichen flachen Filtrationsfächer, den bei einer Strömung von 2 cm/sec etwa 60 l/min passieren. Das feinmaschige Filternetz wird von den zwischen den Pinnulae steif ausgestreckten Tentakelreihen dargestellt. 10. Diese Befunde machen wahrscheinlich, daß auch die anderen Crinoiden, im Gegensatz zur bisherigen Anschauung, ihre Nahrung ausschließlich oder vorwiegend durch Filtration aus einer Strömung gewinnen, der nicht ein aus den oralen Armseiten gebildeter Fangtrichter, sondern die aboralen Armseiten als Filtrationsfächer entgegengestellt werden.
    Notes: Abstract At different seasons, long-term field observations, experiments and measurements were conducted onOphiocoma scolopendrina andHeterometra savignyi in order to investigate their food uptake mechanism and its relation to environmental factors.O. scolopendrina lives in the tidal zone. It obtains food in three different ways: in quiet waters it collects or plucks food from the substratum; in running waters it filters, and while the tide is coming in, it removes (during the day time) dry particles from the water surface. In the filtration process, the ambulacral feet line up and form filtrating combs. This filtering mechanism works effectively, however, only in currents having a significant speed and containing larger suspended particles. It is suggested thatOphiothrix quinquemaculata andO. fragilis also obtain their floating food exclusively by filtration from relatively fast currents rich in organic particles, rather than by collecting sinking particles as has often been assumed. Both species live in greater depths at the sea bottom, where they occassionally occur in great numbers. They lie on the floor, sometimes on their backs, and usually with their arms up.H. savignyi lives in shallow water areas having weak currents and feeds exclusively by filtration of fine, mostly living, suspended material. The animals arrange their 20 arms to form a shallow filtration fan and turn their aboral regions towards the current. The tentacles, stiffly stretched and between the pinnulae, form a fine filter net. Contrary to previously held opinions, these results suggest that the other crinoid species also obtain their food exclusively or predominantly by filtration from weak currents; it is not the catching funnel formed by the oral sides, but a shallow filter fan formed by the aboral arm surfaces that points toward the current.
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    Helgoland marine research 10 (1964), S. 118-139 
    ISSN: 1438-3888
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract This review concerns itself with two aspects of reproductive biology: commencement of gametogenesis and spawning. The activation of gametogenesis followed by gonadal growth, with a subsequent release of gametes. The gamete formation-spawning cycle varies in duration from weekly to yearly periods depending upon the species and geographical origin. The importance of exogenous factors is discussed. Among those exogenous factors which can be demonstrated to affect the gamete formation-spawning cycle are food, salinity, light and temperature. Gonad growth constitutes a more significant fraction of the entire reproductive cycle than does spawning and gametogenesis. The time during which gametes are released occupies a small fraction of the entire reproductive cycle. Since spawning is such a dramatic act, it has been described in detail for many species. Numerous investigators have shown interest in the factors and relationships which work to insure synchronization of spawning. These studies are fully discussed. Some considerations of larval ecology in relation to parental reproductive patterns are given. Finally, the possible mechanism involved in coordination of reproduction is presented.
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    Helgoland marine research 10 (1964), S. 153-154 
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    Topics: Biology
    Notes: Abstract Anmerkung der Schriftleitung:Drebes Beitrag zumVierten Meeresbiologischen Symposion, Hamburg-Altona, 28.–31. Oktober 1963, wird hier nur als Kurzfassung wiedergegeben. Eine ausführliche Darstellung erfolgt zu einem späteren Zeitpunkt.
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    Helgoland marine research 10 (1964), S. 140-152 
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    Topics: Biology
    Description / Table of Contents: Schlussfolgerung und Zusammenfassung Wir können also mit einiger Sicherheit sagen, daß diejenigen marinen Ceratien, die Mikroschwärmer (Nebenformen) bilden, diese als männliche Gameten verwenden, welche vom weiblichen Gameten, einer der vegetativen ähnlichen Zelle (nahezu?) vollständig resorbiert werden. Die Zygote dürfte beweglich und in der Form im ganzen ungeändert bleiben und in diesem Zustand die Meiosis durchführen. Ob Cytokinesen im diploiden Zustand eingeschaltet werden, bleibt zu erfahren. Im Gegensatz dazu ist bei Süßwasserarten die Zygote, oder ein ihr folgendes diploides Stadium, eine Cyste, deren einziger Keimlingsschwärmer die Meiosis durchführt; über die Gamie ist hier nichts bekannt. Die Annahme über den Zyklus der marinen Ceratien wird durch Beobachtungen an dem in Kultur reichlich Kopulations- und Meiosezustände liefernden phagotrophen marinen DinophytenOxyrrhis gestützt, welche wir kürzlich näher untersuchten (unpubl.). Bei dieser wird aus einer Isogamie recht kleiner, irreversibler Isogameten eine monadoide Zygote erhalten, die nach einer ausgiebigen Wachstumsphase im beweglichen Zustand in 2 Schritten die Meiosis durchführt und dabei 4 haploide Schwärmer hervorbringt. Auch hier lieferte übrigens eine cytologische Beobachtung den Schlüssel. Ein von anderer Seite (Dodge 1963) publiziertes und wiederum fälschlich der Mitose zugeordnetes Postzygotän der Meiosis, das dem „Knäuelstadium“ der Ceratien recht ähnelt, zeigte uns, daß auch beiOxyrrhis Sexualität vorkommt und veranlaßte die Nachuntersuchung. Die Schwierigkeit, die Zyklen solcher mariner Flagellaten zu erkennen, liegt also darin, daß der Kernphasenwechsel nicht wie bei limnischen Formen durch einen ihm parallelen Gestaltwechsel der Zelle akzentuiert und deutlich gemacht wird. Nochmals sei anerkannt, daß die vorgelegte Deutung nur durch die sorgfältige Arbeit der älteren Beobachter möglich war; nahezu alle für sie wichtigen Zustände wurden bereits in der Literatur bis 1930 geschildert.
    Notes: Abstract On the basis of older literature and our new observations, a hypothesis is presented to illustrate our present view on the sexual cycle of the Ceratia. In the fresh-waterC. cornutum it has been possible to demonstrate that the “Knäuelstadium” ofBorgert (1910) represents in fact the postzygotene of meiosis. Formerly the “Knäuelstadium” was considered to be a stage of mitosis but, contrary to this view, occurs only in the Praeceratia, i. e. the swarmers emerging in spring from the germinating cysts (Scoczylas 1958). The “Knäuelstadium” has also been observed in marine Ceratia, but in cells of normal shape (Borgert 1910,Schneider 1924), which therefore function as meiocytes. The microswarmers (truncata-, lineata- andlata-forms;Lohmann 1908,Apstein 1910, 1911, and others) are the male gametes which copulate with females similar to vegetative cells, and which in this process are completely (flagellums?) resorbed by the latter. Stages of copulation have been observed in preserved material byApstein (1911),Borgert (1910),Tschirn (1920) and by us, and in the living state inC. horridum also by us. The latter species is monoecious. The marine Ceratia therefore seem to be haplonts in which the zygotes cannot be distinguished from vegetative cells, neither by a resting stage nor by obvious differences in shape. The possibility of diplophasic mitosis, however, has not been excluded.
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    Helgoland marine research 10 (1964), S. 187-201 
    ISSN: 1438-3888
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Description / Table of Contents: Summary 1. Methods are described for the sensitive determination of pristane and similar hydrocarbons in individual planktonic organisms and for the isolation of pristane from copepod oil. 2. Pristane (2, 6, 10, 14-tetramethylpentadecane) occurs in unusually high concentrations (1–3% of the body lipid) inCalanus finmarchicus, C. glacialis, andC. hyperboreus, and at lower concentrations in a wide range of planktonic animals from the Gulf of Maine and continental slope waters. 3. A predator,Paraeuchaeta norvegica, contains pristane at an intermediate level between that ofCalanus and the other herbivores, probably as a result of feeding onCalanus. 4. On the basis of relative abundance and structural similarity, phytol is suggested as the precursor of pristane in herbivorous zooplankton. 5. Pristane content is unaltered or increased during the metabolism of the major deposit lipids ofCalanus hyperboreus during starvation in the laboratory or in nature. Because of its low density, pristane may contribute to the bouyancy ofCalanus, especially when the other lipids are metabolized. 6. Pristane may prove useful as a biochemical integrator for the total assimilation of phytoplankton byCalanus. 7. Some planktonic organisms may be characterized by the presence of specific compounds, e. g. pristane inCalanus and several unknown compounds inRhincalanus. 8. Specific products of organisms of limited geographical occurence may prove useful as biochemical tags of water masses.
    Notes: Kurzfassung Pristan (2, 6, 10, 14-Tetramethylpentadecan) kommt in niedriger Konzentration in manchen planktonischen Tieren des Golfs von Maine, USA, und der Gewässer des kontinentalen Schelfes vor. Dieser Kohlenwasserstoff leitet sich vermutlich vom Phytol in der Nahrung der planktonischen Herbivoren ab. Seine Konzentration ist ungewöhnlich hoch inCalanus finmarchius, C. glacialis undC. hyperboreus, wo er möglicherweise als auftriebsregulierende Substanz in Hungerzeiten wichtig ist. Arten, wieParaeuchaeta norvegica, welcheCalanus verzehren, stellen sekundäre Pristanquellen innerhalb der marinen Nahrungskette dar. Die proCalanus-Individuum angetroffene Pristanmenge könnte als Indikator für die gesamte Nahrungsassimilation dienen. Pristan und andere artspezifische Stoffe können in das die Individuen umgebende Wasser gelangen und dann als biochemische Markierungs-Substanzen dienen.
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    Helgoland marine research 10 (1964), S. 202-216 
    ISSN: 1438-3888
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Description / Table of Contents: Zusammenfassung 1. Die Veränderungen der abiotischen Faktoren, die schon den frühen Untersuchern bekannt waren, werden besprochen. 2. Langfristige Änderungen des Salzgehaltes werden durch die Abflußmenge der Elbe bedingt. 3. Kurzfristige Änderungen der abiotischen Faktoren bringen die Gezeiten; ihr Ausmaß wird weitgehend von den Wetterbedingungen beeinflußt. Im Watt sind während der Ebbe je nach den Außenbedingungen starke Veränderungen im Chemismus festzustellen, deren Ursache z. T. auf die Photosynthese der Diatomeen zurückzuführen ist. Messungen selbst an nahe beieinander gelegenen Punkten bringen schon große Unterschiede der abiotischen Faktoren. 4. In einem durch Molen abgegrenzten Gebiet an der „Alten Liebe“ ist der Salzgehalt immer etwas höher als Folge seiner topographischen Besonderheit. 5. Die Wirkungen der Veränderungen abiotischer Faktoren auf das biologische Geschehen werden an einigen Beispielen erläutert, z. B. das Erscheinen und Verschwinden bestimmter Arten in einzelnen Jahren in Abhängigkeit von der Abflußmenge der Elbe und im Zusammenhang damit von der Höhe des Salzgehaltes.
    Notes: Abstract The changes of abiotic factors, especially salinity, water temperature, O2-content, pH and alcalinity in the Elbe river near Cuxhaven are documented. Long-term salinity fluctuations depend on the water outflow of the Elbe. Short-term salinity changes are caused by the tides. During the period from 1949 to 1953 and again in 1959, salinity was high (above 20% in summer). From 1954 to 1958, as well as in 1961, salinity was low, at times considerably below 15‰ At high tide with its increasing salinity, plankton samples contain more copepods and larvae of balanids and spionids since the maximum population density of these forms occurs in the polyhalinicum at the light-ship “Elbe 3”. If the conditions are favorable, the larvae can settle and start a new population. In a small locality near the “Alte Liebe” pier, marked off by two jetties, the salinity is always somewhat higher than it is in the river Elbe. In this higher salinity, populations ofCoryne sarsi as well as youngAsterias rubens were found in all years characterized by increased salinities (monthly average about 15 to 20%). In years with higher salinitiesTeredo navalis caused increased deterioration of timber work. Small water pools in the mud flat area showed profound changes in water temperature, salinity and pH. Their O2 content is very high due to the photosynthesis of diatoms, reaching saturation values of 320%. These extremes disappear quickly as the water returns at high tide.
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    Helgoland marine research 10 (1964), S. 155-186 
    ISSN: 1438-3888
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Description / Table of Contents: Zusammenfassung 1. Die Wasserbewegung erweist sich als ein Umweltfaktor von erstrangiger Bedeutung. Sie bestimmt weitgehend die Verteilung der Substrate, Anordnung und Gestalt der Organismen, besonders der Sedentarier im Felslitoral. Dennoch ist sie in letzterem noch nicht vermessen worden, denn auf Grund der Vielfalt ihrer Erscheinungen und mutmaßlichen Wirkungsweisen muß vorerst untersucht werden, welche Ursachen und Wirkungen überhaupt verknüpft erscheinen. 2. Die Vereinigung zweier Erfahrungsbereiche macht nun eine erste Zuordnung der hydrodynamischen Erscheinungen noch vor deren Vermessung im Biotop möglich: Ozeanographie, Geologie, Geomorphologie und Wasserbau bieten zusammen ein so großes, einschlägiges Material, daß schon eine Vielzahl von Bewegungserscheinungen im Litoral vergleichend erkannt werden kann. Die wissenschaftliche Taucherei im Litoral ließ durch die gewonnene Anschauung eine Fülle von Ursachen und Wirkungen verknüpfen. 3. Die bislang erkannten etwa 27 unterschiedlichen Verknüpfungsweisen werden nach 5 Gesichtspunkten analysiert und mit je einem Beispiel belegt. Der künftigen metrischen Bearbeitung sollen damit die Ansatzpunkte geliefert werden. 4. Grunderscheinungen: Die Staudruckwirkung läßt sich an Substrat- und Organismenfestigkeit, die der Durchflußmenge an Ernährung und Belüftung ablesen, jene der Wasserversetzung, z. B. an der Medusenverdriftung. Die Teilchengeschwindigkeit bildet die allgemeinste Meßeinheit. 5. Bewegungsweisen: Der streichende Wasserkörper trennt in seinen zwei Formen flächige und radiäre Wuchstypen, der schwingende verändert die Orientierung der flächigen Formen, der zerreißende führt zur Auslese von z. B. gepanzerten Schildformen. 6. Expositionsgefälle: Die Küstenexposition ist etwa nach den Halophyten-, Lithophyten-und Hydroidenzonen zu bemessen, das Gefälle bei zunehmender Tiefe nach der Orientierung der Hydroiden und Anthozoen in den kritischen Tiefen. Die Wirkung der Substratgestalt läßt sich der Hydroiden-Anordnung, die der Substratgliederung jener der Mikrofauna entnehmen. 7. Einfache Wirkungsweisen: Jeweils nach den Aspekten und den Ausschnitten (welche die Wirkungen bestimmen) getrennt dargestellt: a) Die Aspekte: Die Bedeutung der Substratfestigkeit wird durch die Aufwuchsverhältnisse in Blockfeldern, die der Störung durch die Hydroiden-Auswahl in Tangbeständen, die der Resistenz am Beispiel der Brandungs-Selektion erörtert; jene der Verschüttung, der Säuberung und des Scheuerns mit Vorgängen am Felslitoral-Rand, in Höhlen und Geschiebeböden belegt. Der Aspekt Ernährung wird an Hand des Wasserdurchzuges der höhlenbewohnenden Filtrierer, der der Lüftung am Beispiel der Abgabe von Fortpflanzungsprodukten geschildert. Befruchtung und Verbreitung hängen wiederum mit der Wasserversetzung zusammen. b) Die wirkenden Ausschnitte: Die Kennzeichen der Maxima werden aus dem Verhältnis Lithophyten- zu Halophytenzone, die der Mittelwerte aus dem der Hydroiden- und Sedimentzonen an den Felslitoralgrenzen abgeleitet, jene der Minima aus Mortalitätsverhältnissen unter künstlichen Bedingungen. 8. Komplexe Wirkungen: Expositionsbedingte Wuchsformen-Auswahl wird durch Reihen von Arten und Standortmodifikationen belegt, die Abwandlung der Filterformen an Hand der flächigen Hydroiden geschildert. Wuchsform und Bestandsdichte in ihrer korrelierten Abhängigkeit lassen die Hydroidenzonen der Höhlen erkennen. Die unterschiedliche Expositionsabhängigkeit der Ernährungstypen zeigt die Gegenüberstellung der aktiven und passiven Filtrierer.
    Notes: Abstract Water movement is shown to be a very important environmental factor. It largely determines the distribution of substrates and the position and shape of organisms, especially in sedentary inhabitants of rocky littoral areas. In spite of its great ecological significance, water movement has not yet been measured in these areas. However, earlier information obtained in the fields of oceanography, geology and geomorphology, as well as in connection with marine construction, offer sufficient background data to assess the major hydrodynamic phenomena in littoral habitats. Thus scientific diving made it possible in numerous cases to relate cause and effect. The relations observed are documented by one example in each case and analysed on the basis of 5 different aspects.
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    Helgoland marine research 10 (1964), S. 231-245 
    ISSN: 1438-3888
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Description / Table of Contents: Zusammenfassung 1. Sehr kalte und sehr eisreiche Winter sind selten von deutschen Hydrographen untersucht worden. Das Studium der Temperatur- und Salzgehaltsverhältnisse während des Eiswinters 1962/63 in der südlichen Nordsee ist daher von besonderem Interesse. Die Beobachtungsdaten stammen von 5 deutschen Nordseefeuerschiffen, den Helgoländer und den Hamburg-Hull-Route Terminstationen sowie von den „Uthörn“-Fahrten der Biologischen Anstalt Helgoland. 2. Bei den Feuerschiffen und bei Helgoland-Reede sind negative monatliche Temperatur-Abweichungen von 3° bis 4° C beobachtet worden. Die zugehörigen mittleren monatlichen Salzgehaltsabweichungen liegen dagegen weit über den Normalwerten. 3. Das Ende des Eiswinters wurde mit dem 5. März 1963 bestimmt. Eine Temperatur-und Salzgehaltsschichtung blieb auch während der kältesten Wintermonate erhalten. 4. Die vertikale Temperaturverteilung zwischen Helgoland und der Elbmündung zeigt, daß die Abkühlung des Meerwassers nicht nur von Ost nach West fortschreitet, sondern auch von der Oberfläche zum Boden. Sogar zur Zeit des Temperatur-minimums blieb eine bemerkenswerte Temperaturdifferenz zwischen der Oberfläche und dem Boden bestehen. 5. Die Anzeichen starker Vermischungsvorgänge entlang der Konvergenz der Deutschen Bucht werden dargestellt. 6. An Hand von Tabellen werden die wichtigsten Temperatur- und Salzgehaltsdaten zusammengestellt.
    Notes: Abstract Very cold winters with severe ice conditions have hardly been investigated by hydrographers of German institutions. In order to assess the hydrographical situation during the cold winter 1962/63, temperature and salinity information was used, provided by (a) five light vessels in the German Bight, (b) measurements obtained at several routine positions near Helgoland and along the route Hamburg-Hull, (c) data from the “Uthörn” cruises of the Biologische Anstalt Helgoland. Near the light vessels and at the Helgoland road, negative deviations of 3° to 4°C were observed (monthly means). The corresponding salinity values are far above the normal. The severe ice winter ended approximately on the fifth of March, 1963. Temperature and salinity stratifications could even be observed during the coldest winter months. Vertical T°C-distributions between Helgoland and the mouth of river Elbe demonstrate that the cooling of the sea water is not only advancing from east to west but also from the surface down to the bottom. Even at the time of the T°C-minimum, there is a remarkable T°C-difference between surface and bottom water. There are indications of strong mixing processes along the convergence of the German Bight.
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    Helgoland marine research 10 (1964), S. 257-262 
    ISSN: 1438-3888
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    Topics: Biology
    Description / Table of Contents: Zusammenfassung 1. In der unteren Elbe zwischen Schnackenburg und der Störmündung wurden während des kalten Winters 1962/63 ungewöhnlich hohe Gesamtkeimzahlen gefunden, die besonders im Februar die bisher in über 7jähriger Untersuchungszeit gewonnenen Maximalwerte um ein Mehrfaches übertrafen. 2. Unter der Eisdecke fand im Fluß eine lebhafte bakterielle Nitratreduktion (Denitrifikation) statt, die einen sehr starken Rückgang des NO3- und eine kräftige Zunahme des NO2-Gehaltes im Elbwasser zur Folge hatte. 3. Die Ursache der extrem hohen Gesamtkeimzahlen dürfte vor allem in dem Zusammentreffen von geringer Wasserführung der Elbe und anhaltend niedriger Temperatur liegen. Die starke Denitrifikation ist in erster Linie auf den durch die Eisdecke bedingten Sauerstoffmangel im Flußwasser zurückzuführen.
    Notes: Abstract Counts of total bacteria showed an unusually high increase in the river Elbe during the cold winter of 1962/63. Especially in February the number of bacteria was repeatedly higher than the maximum values measured during the whole 7-year period of investigation. A significant reduction of nitrate (denitrification) occurred beneath the ice-cover of the river. This caused a high increase of the NO2-concentration of the water, as well as a great decrease of the NO3-concentration. The extremely high bacteria counts were caused by the coincidence of an unusually small water transport and low temperature. The intensive denitrification results from oxygen deficiency in the water beneath the river's ice cover.
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    Helgoland marine research 10 (1964), S. 246-256 
    ISSN: 1438-3888
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Description / Table of Contents: Zusammenfassung 1. Es wurde die Bakterienverteilung auf zwei Schnitten (Feuerschiff Elbe I — Helgoland und Feuerschiff P 8 — Helgoland) am 12. und 13. Februar untersucht. Die See war zu dieser Zeit mit Eisfeldern bedeckt. Es besteht eine eindeutige Beziehung zwischen Temperatur und Salzgehalt zur Bakterienzahl, d. h. bakterienreicheres Küstenwasser vermischte sich mit keimärmerem Seewasser. 2. Durch die Einschlüsse von Sedimenten in den Eisschollen findet eine beträchtliche Keimverfrachtung statt. 3. In der Erwärmungsphase 1963 findet eine starke Bakterienzunahme statt, die vermutlich vorwiegend auf Süßwassereinflüsse zurückzuführen ist. 4. Die vor Helgoland 1963 gefundenen sehr hohen Bakterienzahlen fallen mit zeitlich einige Wochen früher festgestellten sehr hohen Bakterienzahlen in der Elbe zusammen, während die Bakterienzahlen des entsprechenden Vorjahreszeitraumes in der Elbe und vor Helgoland bedeutend niedriger lagen.
    Notes: Abstract In order to count the total number of bacteria, the pour-plate method and a modified 2216 E medium (Zobell 1946) were used; temperature and salinity were recorded. Two cruises were conducted: one in the direction of the estuary of the river Elbe, the other in the direction of the open North Sea (light-ship P 8, located 25 nautical miles westwardly from Helgoland). The highest bacterial numbers were found at the stations closest to the mainland, and a close correlation between temperature, salinity and bacterial numbers was discovered. In other words, coastal water high in bacterial numbers and rich in organic substances was mixed with water of the open sea with a low bacterial content. To some extent transportation of bacteria via ice floes is responsible for the high bacterial numbers in the colder water. During the warm-up periods in early spring of 1963, a sharp increase in bacterial numbers was found in the samples taken in the waters at the permanent station between Helgoland and the nearby Dune. These numbers correspond with a decrease in salinity. The bacterial curves are to some extent in agreement with those found in the river Elbe in the winter and spring of 1963 byRheinheimer (1964). From all these facts it becomes apparent that the bacterial numbers recorded near Helgoland are strongly influenced by the water of the river Elbe, and therefore the effects of the cold winter 1962/63 upon bacteria of the coast of Helgoland are to an important part indirect ones.
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    Helgoland marine research 10 (1964), S. 217-230 
    ISSN: 1438-3888
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Description / Table of Contents: Zusammenfassung 1. Im Anschluß an frühere systematische Untersuchungen über die Wassermischvorgänge vor den Weser- und Elbästuaren wurden im Sommerhalbjahr 1963 im gleichen Raume sedimentologische Arbeiten durchgeführt, die zur Lösung von Fragen der offensichtlichen Beeinflussung der oberflächennahen Sedimente aus den beiden markanten Ästuarwasserkörpern beitragen können. Hierbei wurde gleichzeitig im Bereich des Eisenchemismus der Bodenoberfläche eine Beeinflussung aus Pleistozänhorizonten in den über 20 m tiefen Außenrinnen der Vorästuare evident. 2. Die Verteilung des anorganischen Phosphats (PO4-P in µg/kg Trockensediment) im Sediment nordwestlich des Feuerschiffes Elbe 1 und südöstlich des Feuerschiffes P 12 läßt in beiden Gebieten jeweils den Einfluß aus dem Elbe- und aus dem Weserästuar offenbar werden. Nach einem besonderen Verfahren wird hierbei das adsorbierte und vor allem das am Eisen in FePO4 z. T. irreversibel gebundene PO4 erfaßt. Der Phosphatgehalt beträgt im Zentrum der beiden Ästuarsedimentzungen (bei Elbe 1 und bei P 12) etwa 50 mg PO4-P/kg, während die entsprechenden Werte in den nicht aus den Ästuaren beeinflußten Zwischengebieten auf etwa die Hälfte herabsinken. Der Gehalt an PO4-P im Sediment liegt übrigens um etwa drei Zehnerpotenzen höher als in den überlagerten Wasserschichten. Es wird noch auf die besondere „Eutrophierung“ des Sedimentes westlich von Elbe 1 eingegangen, die ihre Ursache vor allem in der dortigen Verklappung von Abwasserschlamm der Großstadt Hamburg hat. 3. Die Korngrößenverteilung im Seegebiet vor den Nordergründen, also in den Vorästuaren von Elbe und Weser, spiegelt ebenfalls in etwa die Beeinflussung der oberflächennahen Sedimentschichten aus den übergelagerten beiden Wasserzungen wieder, aus denen feinkörnige Sinkstoffe von ca. ±50 µm Teilchendurchmesser zu Boden rieseln und zwischen denen (auf den nordwestlichen Nordergründen selbst und im Bereiche der Nordergründe-Tonne) die Sedimentkörnung zwei- bis viermal größer ist. Die durchschnittliche Körnung in den Ästuarsedimentzungen beträgt ca. ≦50 µm, in den Zwischenzonen etwa 100–200 µm. Die Sandkörner in diesen Zwischenzonen weisen oft einen hohen Grad an Rundheit (Rundschliff) auf, d. h. sie haben eine längere marine Vorgeschichte als die Körner in den Ästuarrinnen selbst. 4. Es folgt die Verteilung der gesamten organischen Substanz in den oberflächennahen, durchoxydierten (etwa 1–5 cm mächtige Oxydation) Schichten, wie sie auf dem Wege der „nassen Verbrennung“ mit K2Cr2O7 ermittelt wurde. Im Zentrum der Ästuarsedimentzungen und hier besonders im Kerngebiet der Elbezunge nordwestlich Elbe 1 steigen die Werte auf etwa 10% organische Substanz i. Tr. an, ein Maximum, das sich ohne weiteres aus dem Hamburger Abwasserschlamm erklärt. In den Zwischengebieten sinken die entsprechenden Werte dann oft auf Spuren herab. 5. Das sogenannte mobile Eisen, das ist das an die Sedimentpartikel adsorbierte oder zum geringen Teil auch im FePO4 gebundene Eisen (nicht etwa auch noch das in den Mineralen fest gebundene Eisen), das nach einem besonderen Verfahren mittels Ammonzitrat aus dem Sediment geholt wird, ist in den feinkörnigen Ästuarsedimenten wesentlich mehr angereichert als etwa in den sandigen Zwischenpartien. So belaufen sich z. B. die entsprechenden Werte in den Ästuarzungen auf 10–20‰ Fe/kg i. Tr. und in den Zwischenzonen nur auf ca. 1‰ und weniger. Die Feinstsedimente adsorbieren wesentlich größere Mengen dieses Eisens. Die sandigeren Sedimente auf den Nordergründen werden in ihrem geringen Eisengehalt weitgehend gesteuert von absolut betrachtet nur geringen pleistozänen Eisenvorkommen, die aber repräsentativ sind für eine ganz typische Verteilung eisenoolithisch umhüllter Sandkörner, welche in ihrer Existenz nicht nur hinweisen auf erodierte Pleistozänhorizonte, sondern darüber hinaus auch noch als Indikator für die Sedimentwanderung in der Nähe (10–20 km Umkreis) solcher Erosionsrinnen gelten. Die quantitative Erfassung dieser „rostigen“ Indikator-Sandkörner erfolgt durch Auszählung auf einer cm2-Zählplatte im Binokular bei 40facher Vergrößerung nach besonderer Vorbehandlung des betreffenden Sandes. Im Verlaufe der bisherigen Untersuchungen wurde bereits festgestellt, daß die sogenannten „Braunkornzahlen/cm2 Sandoberfläche“ im Bereich von 0 bis etwa 40 Einheiten darauf hinweisen, daß der ortsteinhaltige Erosionshorizont etwa 20 km und mehr vom Beobachtungspunkt entfernt ist. Bei Werten von über 50 und bis über 100 Einheiten befindet man sich in der Nähe solcher Eisenoolithe liefernden Horizonte. 6. In mehreren Darstellungen folgt abschließend die Verteilung der Sedimentkörnungen, des Gehaltes an mobilem Eisen und der aufschlußreichen Braunkornzahlen aus dem Gebiet der tiefen Alten Weser-Rinne nördlich des Roten-Sand-Leuchtturmes sowie ihres Vorfeldes am Westende der Nordergründe. Aus den Isolinienbildern geht eindeutig hervor, wie nicht nur die Korngröße selbst, sondern auch der Gehalt an mobilem Eisen aus der Pleistozänrinne heraus beeinflußt wird. Die Körnung steigt im Bereich der Rinne auf 600 und u. U. gar 1000 µm und mehr an, wobei gleichzeitig im Bodengreifer häufig „rostige“ Flintsteine und anderes Pleistozängeröll zutage tritt. In der Erosionsrinne beläuft sich ferner der Gehalt an mobilem Eisen auf ±1‰ Fe i. Tr., während die feinkörnigeren (aber nicht schlickigen) Sedimente in den Seitenräumen der Alten Weser nur noch Spuren an Eisen aufweisen. Und schließlich deutet der Verlauf der Braunkornisolinien mit über 100 Einheiten/cm2 in und vor der Rinne und in einem weiten Ausholen dieser Isolinie nach Nordwesten bis an die 20-m-Linie vor den Nordergründen auf die Beeinflussung der Sedimentoberfläche aus der Erosionsrinne hin.
    Notes: Abstract In the preestuaries of the rivers Weser and Elbe (i. e. in the area west of “Elbe 1” and southeast of “P 12” as well as in the northwestern part of the “Nordergründe” and in the “Alte Weser”), the effects of estuary river water on the underlying sediment surfaces have been studied. Another aspect investigated was the effect of eroded Pleistocene horizons on the iron chemistry of these sediments. These horizons are located in the area of the pre-estuaries of both rivers at a depth of more than 20 m below SKN. The oolitic iron-containing sand grains were quantitatively measured using a special counting method. They are spread out according to the hydrodynamics and bottom dynamics in the pre-estuary of the “Alte Weser” and in additional troughs formed by erosion in the Pleistocene of the estuaries. Thus they represent convenient and reliable indicators for the sediment migration in these troughs; moreover, they suggest the existence of such troughs, which are found only in the southeastern part of the North Sea. In general, it was possible to establish that the sediment areas located beneath the typical bodies of estuary water are especially eutrophic, containing 50 mg and more of PO4 phosphorus per kg dry sediment, 10 to 20% total organic substance and 10 to 20% colloidal iron. These data represent values equivalent to the third power of the respective concentrations in the sea water. — The variations in the chemistry of the interlaying sand zones in the “Nordergründe” concern primarily the iron factor and are mainly affected by the Pleistocene horizons.
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