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  • 1
    Digitale Medien
    Digitale Medien
    An equation for flow in the renal proximal tubule (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 29-57 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460061
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  • 2
    Digitale Medien
    Digitale Medien
    Seventeenth Annual Meeting of the Classification Society of North America (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 105-105 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460066
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  • 3
    Digitale Medien
    Digitale Medien
    Editorial: Software Survey Section (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. I 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460067
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  • 4
    Digitale Medien
    Digitale Medien
    Dominance of geometric overelastic factors in pulse transmission through arterial branching (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 97-103 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460065
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  • 5
    Digitale Medien
    Digitale Medien
    Galerkin's finite element-Laplace transform technique to transient heat migration in human skin and subcutaneous tissues (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 125-136 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Galerkin's finite element-Laplace transform technique (GAFELTTE) has been used to study transient temperature distribution in human skin and subcutaneous tissues. This study incorporates heat conduction, heat carried by perfusion of blood in the capillary beds and metabolic heat generation in the tissues. Different values of various quantities have been considered in all three parts, namely epidermis, dermis and subcutaneous tissues, depending on physiological considerations. The GAFELTTE provides interface temperatures for a wide range of the values of skin surface temperatures. These values have been used to obtain temperature profiles in the region considered. Steady-state temperature distribution has been deduced from the solution obtained by GAFELTTE and has been compared with the results obtained by using different methods.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460018
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  • 6
    Digitale Medien
    Digitale Medien
    Multiple stable equilibria in a predator-prey system (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 137-148 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Necessary and sufficient conditions are given for three equilibria to occur in a predatorprey model and conditions are given for two of these to be stable. The existence of two stable equilibria requires predator intraspecific competition for either space or food, and the lower the prey growth rate the stronger this predator self-regulation must be. A prey growth rate that is skewed to the right, the ability of a few predators to survive at low prey densities, and predators with high searching effectiveness, long handling times, and large maximum per capita rate of increase all make two stable equilibria more likely.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460019
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  • 7
    Digitale Medien
    Digitale Medien
    Servocontrol of the heart rate in homeothermic animals: On recognizing butterfly catastrophy models in biology (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 107-124 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Drawing evidence from a variety of cardiovascular studies on the heart rate in homeothermic animals, the author establishes the following thesis. The servocontrol (i.e. the autonomic and reflex control) by the medulla oblongata of the heart (rate) is a negative feedback dynamic which is isomorphic (i.e. ‘diffeomorphic’) to the dyamic underlying the heat rate control in those animals (cf. Kuyk,Bull. math. Biol. 46, 81–102, 1984). In fact, unlike in the heat rate case, the qualitative evidence supporting this thesis can not be fully complemented by quantitative data stemming from experiments, because of a lack of pertinent experiments—which, indeed, should measuresimultaneously the heart rate state parameter and thefour control parameters at the input side of the medulla. The results of some of the existing experiments on animal preparations can nevertheless be adduced to recognize that this dynamic can be graphed by the five-dimensional butterfly catastrophe type. The theory leads to new ways of looking at experiments in the field and/or setting up such experiments in the future.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460017
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  • 8
    Digitale Medien
    Digitale Medien
    Simulation of cellular compaction and internalization in mammalian embryo development as driven by minimization of surface energy (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 167-187 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model based upon minimization of surface energy is proposed as an explanation for compaction and internalization of cells during mammalian embryo development. The model is used to simulate and graphically display these phenomena on a computer.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460021
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  • 9
    Digitale Medien
    Digitale Medien
    Topological properties of binary trees grown with order-dependent branching probabilities (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 197-211 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper describes a growth model for binary topological trees. The model defines the branching probability of all segments in the tree. The branching probability of a segment is formulated as a function of two variables, one indicating its type (intermediate or terminal), the other representing its order, i.e. the topological distance to the root segment. The function is determined by two parameters, namely the ratio of branching probabilities of intermediate and terminal segments and the strength of the order dependency, implemented in an exponential form. Expressions are derived for the calculation of symmetry properties of the partitions and it is indicated which part of the parameter domain results in predominantly symmetrical trees.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460023
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  • 10
    Digitale Medien
    Digitale Medien
    Pattern formation and morphogenesis: A reaction-diffusion model (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 213-228 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The problem of cellular differentiation and consequent pattern generation during embryonic development has been mathematically investigated with the help of a reaction-diffusion model. It is by now a well-recognized fact that diffusion of micromolecules (through intercellular gap junctions), which is dependent on the spatial parameter (r), serve the purpose of ‘positional information’ for differentiation. Based on this principle the present model has been constructed by coupling the Goodwin-type equations for RNA and protein synthesis with the diffusion process. The homogeneous Goodwin system can exhibit stable periodic solution if the value of the cooperativity as measured by the Hill coefficient (ρ) is greater than 8, which is not biologically realistic. In the present work it has been observed that inclusion of a negative cross-diffusion can drive the system into local instability for any value of ρ and thus a time-periodic spatial solution is possible around the unstable local equilibrium, eventually leading to a definite pattern formation. Inclusion of a negative cross-diffusion thus makes the system biologically realistic. The cross-diffusion can also give rise to a stationary wave-like dissipative structure.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460024
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  • 11
    Digitale Medien
    Digitale Medien
    Editorial: Software survey section (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. I 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460027
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  • 12
    Digitale Medien
    Digitale Medien
    SCoP: An interactive simulation control program for micro- and minicomputers (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 427-441 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A nes software system is described for building simulation programs on micro- and minicomputers. Model equations are written as C subroutines, compiled and linked to the SCoP package to produce a menu-driven, interactive program. The system maintains a database of names, values, and units for all model parameters and variables. Run-time options include several methods for interactive parameter modification and both graphic and tabular outputs, with output values presented as they are calculated. Simulation output values can be compared with experimental data graphically and a companion program SCoPFit is provided for formal optimization of parameter values.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459691
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  • 13
    Digitale Medien
    Digitale Medien
    Global stability of partially closed food-chains with resources (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 455-468 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We consider the existence and global stability of aq-member equilibrium (1≤q≤n) in partially closed food-chains of lengthn having an abiotic component as resource. We observe that such existence demands bounds of resource supply rate and these bounds are weighted sums of interaction coefficients. Particular results of global sector-stability of partially feasible equilibria of simple food-chains obeying Lotka-Volterra dynamics are shown. Lastly the elasticity of such food-chains when a new species is introduced at the highest trophic level is investigated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462317
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  • 14
    Digitale Medien
    Digitale Medien
    Global stability in time-delayed single-species dynamics (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 485-492 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Criteria are established for three classes of models of single-species dynamics with a single discrete delay to have a globally asymptotically stable positive equilibrium independent of the length of delay.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462319
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  • 15
    Digitale Medien
    Digitale Medien
    Predator-prey systems with group defence: The paradox of enrichment revisited (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 493-508 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The main concern of this paper is with survival or extinction of predators in models of predator-prey systems exhibiting group defence of the prey. It is shown that if there is no mutual interference among predators, enrichment could result in their extinction. However, if there is mutual interference, the predator population survives (at least deterministically).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462320
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  • 16
    Digitale Medien
    Digitale Medien
    A class of general stochastic compartmental systems (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 509-523 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper a general class of semi-Markov compartmental systems is studied. Two models for different input processes are analysed. Attention has been paid to the recurrence times associated with each compartment and to the distribution of the number of particles in each compartment. As an example, a three-compartment system is discussed to study the movement between three health states of patients with chronic diseases.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462321
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  • 17
    Digitale Medien
    Digitale Medien
    Optimized homology searches of the gene and protein sequence data banks (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 569-583 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A strategy is presented for searching the gene and protein sequence data banks which combines the use of two previously described algorthms. The implementation of this strategy is thoroughly evaluated with respect to sensitivity, specificity and speed. The establishment of standard benchmarks for comparing programs that rearch the sequence data banks for homology is proposed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462324
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  • 18
    Digitale Medien
    Digitale Medien
    Receptors and functional linkage in membrane permeability: A quantum mechanical model (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 545-567 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract During functional linkage, ligand receptors are coupled to other receptors and to the cell's metabolic-transport apparatus. The linkage guides the cellular processing of matter, energy and information. Previous conceptions of functional linkage have used the ideas of classical physics appropriate to macroscopic objects. This study presents an initial quantum mechanical model of functional linkage in the case of ligands moving through lipid bilayers and hydrophilic transmembrane channels (‘pores’) of molecular dimensions. On the basis of permeability data, energy surfaces consisting of piecewise-constant potential regions are used to model the lipid bilayers and transmembrane channels. The centre-of-mass wavefunction for a ligand on such energy surfaces is analysed and the permeability coefficients calculated from the wavefunction's transmission characteristics. It is found that quasi-bound states in the several ligand-binding regions of a bilayer or pore system can functionally link to facilitate the passage of the molecule across the permeability barrier. Appearance of the linkage is a sensitive function of the ligand's energy. If the centre-of-mass energies are distributed as in a thermalized fluid, the flux via the quantum functional linkage can equal or exceed that of a classical flux for proton transport through rigid pores in which the intrasite barriers are relatively high (0.25–1 eV) and narrow (0.1–1 Å). The functional linkage plays a less important role in bilayer (rather than pore) energy surfaces and at higher molecular weights. If the ligand-receptor interaction is accompanied by energy transfer to or from ligands, the flux via the quantum functional linkage can equal or exceed the classically expected flux at all relevant ligand molecular weights. These findings are discussed in relation to earlier work and the limitations of the model emphasized.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462323
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  • 19
    Digitale Medien
    Digitale Medien
    A nonlinear measure of subalignment similarity and its significance levels (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 617-632 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A new measure of subalignment similarity is introduced. Specifically, similaritys(l,c) is defined as the logarithm to the basep of the probability of findingc or fewer mismatches in a subalignment of lengthl, wherep is the probability of a match. Previous algorithms can not use this measure to find locally optimal subalignments because, unlike Needleman-Wunsch and Sellers similarities, this measure is nonlinear. A new pattern recognition algorithm is described for finding all locally optimal subalignments of two nucleotide sequences. The DD algorithm can uses(l, c) or any other reasonable similarity function to assess the relative interest of subalignments. The DD algorithm searches only the diagonal graph, which lacks insertions and deletions. This search strategy greatly decreases the computation time and does not require an arbitrary choice of gap cost. The paths of the resulting DD graph usually draw attention to likely locations for insertions and deletions. A heuristic formula is derived for estimating significance levels fors(l, c) in the context of the lengths of the two aligned sequences. The DD algorithm has been used to find interesting subalignments between the nucleotide sequences for human and murine interleukin 2.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462327
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  • 20
    Digitale Medien
    Digitale Medien
    Deductive biology—Some cautious steps (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 45-58 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract For certain environments, the Darwinian model allows unique prediction of a function that any surviving system adapted to such an environment has to perform. This is the case for those environments that determine a “survival functional” of position in space-time of known shape. Purely temporal survival functionals can be distinguished from spatial and mixed ones. In each case, there exists an optimum path in combined physical and (reduced) metabolic space. Dependent on the admissible error, approximate solutions of different complexity are sufficient. All solutions possess an afferent, a central, and an efferent part. Within this general frame, specific, “probably simplest”, solutions are proposed for adaptive chemotaxis, insect locomotion, lower vertebrates locomotion, higher vertebrates locomotion, chronobiological systems, and immune systems, respectively—or rather, for the underlying functionals.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463129
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  • 21
    Digitale Medien
    Digitale Medien
    The role of glucagon in the regulation of blood glucose: Model studies (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 59-77 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Mathematical models afford a procedure of unifying concepts and hypotheses by expressing quantitative relationships between observables. The model presented indicates the roles of both insulin and glucagon as regulators of blood glucose, albeit in different ranges of the blood glucose concentrations. Insulin secretion is induced during hyperglycemia, while glucagon secretion results during hypoglycemia. These are demonstrated by simulations of a mathematical model conformed to data from the oral glucose tolerance test and the insulin infusion test in normal control subjects and stable and unstable diabetic patients. The model studies suggest the parameters could prove of value in quantifying the diabetic condition by indicating the degree of instability.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463130
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  • 22
    Digitale Medien
    Digitale Medien
    A note on dynamics of population with history-dependent birth rate (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 123-131 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model for the dynamics of a single-species population whose birth rate depends on densities of previous generations is introduced. A difference equation formulation is proposed and the solutions classified for the various parameter values. Data from an experimental population of mice growing in limited space is cited and compared with the model predictions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463134
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  • 23
    Digitale Medien
    Digitale Medien
    Tension field theories for soft tissues (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 161-182 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract All soft tissues are modeled as either one-dimensionalstrings, two-dimensionalmembranes, or three-dimensionalsolids. Attention is restricted to tissues in which one of the principal stress components is large and positive in comparison with the other negligible components. Results indicate the following: (1) If a deformed string isconstrained to lie on a surface and is free of tangential pressure, the tension is carried by rays which are geodesics of the surface. If a string or membrane isfree to deform in space without normal pressure, the tension rays are straight lines. If a membrane deforms without tangential surface loads, the tension rays are always geodesics on the deformed surface. If a solid deforms without body forces, the tension rays are straight lines. (2) The stress in a string is a constant if the string is free of tangential pressure and has constant cross-sectional area. The stress in flat tension fields free of tangential surface loads decays inversely with distance along a tension ray from the edge of regression. The stress in a spherically symmetric tension field free of body forces decays inversely with the square of the distance from the center of the sphere. (3) Stress singularities can occur in soft tissues, such as at the corners of a closed rectangular hole in a flat membrane strip. (4) The tension rays in the torsion of soft annular membranes are more steeply inclined from the radial direction than the tension rays for hard metals equally displaced.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461433
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  • 24
    Digitale Medien
    Digitale Medien
    Locally optimal subalignments using nonlinear similarity functions (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 633-660 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Nonlinear similarity functions are often better than linear functions at distinguishing interesting subalignments from those due to chance. Nonlinear similarity functions useful for comparing biological sequences are developed. Several new algorithms are presented for finding locally optimal subalignments of two sequences. Unlike previous algorithms, they may use any reasonable similarity function as a selection criterion. Among these algorithms are VV-1, which finds all and only the locally optimal subalignments of two sequences, and CC-1, which finds all and only the weakly locally optimal subalignments of two sequences. The VV-1 algorithm is slow and interesting only for theoretical reasons. In contrast, the CC-1 algorithm has average time complexityO(MN) when used to find only very good subalignments.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462328
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  • 25
    Digitale Medien
    Digitale Medien
    Adaptability: The significance of variability from molecule to ecosystem (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 701-703 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462331
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  • 26
    Digitale Medien
    Digitale Medien
    Convergence in a resource-based competition system (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 681-699 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A resource-based competition model of two consumer species and one resource species is formulated in the form of a Lotka-Volterra system. The competition involves both exploitation and interference. By a method of asymptotic estimates, sufficient conditions are derived for the three species system to converge ast→∞ to an equilibrium point with all three species present; a generalization of the result forn≥2 and single resource species is indicated. The strong form of equilibrium perisistence of the three species consumer-resource system is achieved by the ability of each of the consumer species to exploit the resource and interfere with others in such a way which will avoid exclusion by the other.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462330
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  • 27
    Digitale Medien
    Digitale Medien
    A survey of linear singular systems (1986)
    Springer
    Circuits, systems and signal processing 5 (1986), S. 3-36 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract This paper is a brief historical review of linear singular systems, followed by a survey of results on their solution and properties. The frequency domain and time domain approaches are discussed together to sketch an overall picture of the current status of the theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600184
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  • 28
    Digitale Medien
    Digitale Medien
    Analysis of the transient behavior of kidney models (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 211-221 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Non-steady-state equations for kidney models are stated. General conservation relations for these equations are derived. Transient equations for the central core model of the renal medulla are developed. Solution of the equations by Laplace transform methods for time invariant volume flows is discussed. The general theory of solving models with time dependent flows by finite difference methods is developed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461436
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  • 29
    Digitale Medien
    Digitale Medien
    Ecosystem-like behavior of a random-interaction model I (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 513-524 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The behavior of large systems of randomly-interacting variables is examined using an intentionally simplified model. The stable positive solutions are found to exhibit to a significant degree some well-known properties of ecological systems. This resemblance (including for example the predominance of “predator-prey” interactions) is all the more striking in view of the lack of biological “data” at the input end. The findings suggest it advisable to distinguish two kinds of properties in ecosystems. One kind would depend on specifically biological mechanisms; the other would characterize a wide class of persistent systems, and arise from the need for a dynamic balance between positive and negative feedback.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460775
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  • 30
    Digitale Medien
    Digitale Medien
    Mathematical analysis of cancer chemotherapy: The effects of chemotherapeutic agents on the cell cycle traverse (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 499-512 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract For the tumor model of Skipper and Zubrod, which has been analyzed previously for the theoretical FLM function and the effect of chemotherapy against tumors of known or assumed kinetic characteristics, the theoretical continuous labeling (CL) function is derived by considering an equivalent tumor (in terms of unlabeled cell populations) in which the density function of phase duration of cells inS-phasef 2(a 2)=δ(a 2−∞) and the loss functionL 2(t)=0. This mathematical concept of blocking is applied to the analysis of synchronization in tumor growth and blocking effects in cancer chemotherapy. These effects of chemical agents on the cell cycle progression are being incorporated into a previously written computer simulation program for cancer chemotherapy. Whereas, a program is written and used to simulate the CL functions for L1210 leukemia, and primary and metastatic Lewis lung carcinoma.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460774
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  • 31
    Digitale Medien
    Digitale Medien
    Global stability in a class of prey-predator models (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 525-533 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Global stability is established in a class of prey-predator models. This includes a prey-predator model in which the predator has Type 2 functional response and no intraspecific interactions. Two simple examples demonstrate that Kolmogoroff’s theorem does not apply to some members of this class of models.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460776
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  • 32
    Digitale Medien
    Digitale Medien
    A theoretical study of the temperature distribution in skeletal muscle undergoing rhythmic contractions (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 535-540 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The skeletal muscle is regarded as a periodically deformed plate. An equation of energy for the biological tissue in the system is used in the Lagrange variables. With the heat exchange through the above tissues to the exterior media and also with account of some relations between the physiological factors the approximate analytical solution for this equation is obtained and compared with the physiological data.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460777
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  • 33
    Digitale Medien
    Digitale Medien
    A comment on Bobisud's paper on evolution of cannibalism (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 541-545 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract One of Bobisud's (1976) models for the evolution, of cannibalism is discussed. His analysis is criticised for not being based on the principle of individual selection. Assuming the operation of that principle, we show by simulating his model that cannibals may establish themselves in a noncannibal population. This will happen both in cases where Bobisud concluded cannibalism to be optimal and in cases where he concluded cannibalism not to be optimal.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460778
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  • 34
    Digitale Medien
    Digitale Medien
    Prediction of light-induced transient thermal response of the retina (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 547-547 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460779
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  • 35
    Digitale Medien
    Digitale Medien
    Dynamical similarity and the theory of biological transformations (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 549-579 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The D'Arcy Thompson concept of biological transformations is developed in a form analogous to such physical concepts as the Law of Corresponding States in thermodynamics, and the Principles of Similitude found in engineering. We find that such concepts depend on a distinction between fundamental and derived quantities, in which the values assigned to the fundamental quantities set the natural scales for the derived ones. Among other things, we see that critical phenomena, such as phase transitions, arise as an immediate consequence of this distinction. In a biological context, we explore the implications of Thompson's hypothesis that closely related organisms are phenotypically similar, assuming that the organisms we see are the result of selection processes operating on phenotypes.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460731
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  • 36
    Digitale Medien
    Digitale Medien
    Distributed sensory coding applied to simulations of iconic storage and metacontrast (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 605-623 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract If information is coded in the combination of activities of many neurons operating in parallel, then information present in a network can be defined by the correlation of present network activity with the activity which had been elicited by a stimulus in the past; a high correlation indicates the presence of the previously encoded stimulus. Information is distributed in the network because coding is dependent upon the activities of all cells. A model based on Hartline-Ratliff lateral inhibition with a time delay shows that lateral inhibition can distribute information across a parallel network, reduce output noise, and also briefly store information. With no changes in model parameters, and the use of a correlation measure for recognition, the model can stimulate psychophysical results in eleven variations of the metacontrast masking paradigm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460733
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  • 37
    Digitale Medien
    Digitale Medien
    Theoretical study of nasal deposition (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 581-604 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A theory is derived to calculate the regional and total deposition of aerosol particles in the nasal passages during inhalation. The particle size studied range from 0.2 to 10.0 μm diameter. The deposition is calculated in five regions; (I) the region filled with nasal hair, (II) the nasal valve, (III) the expansion region, (IV) the turbinate region and (V) the posterior bend. Equations are derived to determine the deposition caused by direct impaction on the nasal hairs and bends of the passages. The calculations show the deposition due to direct impaction does not account for the amount or location of deposited particles measured in experiments. Secondary flows have been speculated to exist in the expansion region after the nasal valve and an equation is derived to estimate the deposition caused by the secondary flows. The calculated deposition, due to direct impaction and secondary flows, shows general agreement with the experiment as to the predicted amount and location of deposited particles.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460732
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  • 38
    Digitale Medien
    Digitale Medien
    What do mathematical models tell us about circadian clocks? (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 625-635 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The paper reviews a series of models for circadian clocks and discusses their conclusions and predictions. Attention is focused on Pittendrigh's empirical model, two mathematical models by the author and Winfree's work.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460734
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  • 39
    Digitale Medien
    Digitale Medien
    Electric field distribution, ionic selectivity and permeability in nerve (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 637-649 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract From a model of facilitated ionic transport across axonal membranes proposed by McIlroy (1975), the equipotentials and electric field distributions in the vicinity of a potassium conducting pore and of a sodium conducting pore are computed and presented as two-dimensional mappings. The model is then extended to include the effect of impurity ions in the conducting pores viz. of potassium ions in a sodium pore and of sodium ions in a potassium pore. The ionic selectivities and permeabilities of the transported species are discussed in relation to the extended model. Bounds are deduced for the ionic selectivity coefficients for both the sodium and potassium current-carrying systems in squid giant axons and the electric-field distributions in the vicinities of the pores are computed for the extended model and compared with the impurity-free fields first calculated. Finally the permeability coefficients defined in terms of the extended model are shown to reconcile the results of attempts to measure permeability by means of radioactive tracer techniques, with the classical description of the resting nerve.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460735
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  • 40
    Digitale Medien
    Digitale Medien
    Self-similar solution of a distributed model for transcapillary exchange and solute removal by the liver (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 661-669 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The partial differential equations describing transcapillary exchange and subsequent removal of solutis from an idealized liver sinusoid are amenable to solution by similarity analysis. The power and utility of this technique, which is not widely appreciated as a method for solving biological models, is illustrated here for a system whose Laplace transforms is difficult to invert.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460737
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  • 41
    Digitale Medien
    Digitale Medien
    Steady-state distribution of bacteria chemotactic toward oxygen (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 671-674 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The phenomenological theory for the chemotaxis and consumption of oxygen by motile aerobic bacteria is shown to yield a remarkably simple one-dimensional steady-state solution for a congregation of bacteria close to the surface of an oxygen-depleted aqueous medium.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460738
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  • 42
    Digitale Medien
    Digitale Medien
    On the identification by filtering techniques of a biologicaln-compartment model in which the transport rate parameters are assumed to be stochastic processes (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 651-660 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper biological compartmental models are considered which take into account the intrinsic randomness of the transport rate parameters and their possible variability in time. An identification procedure is presented for the estimation of the stochastic processes representing the transport rate parameters of a compartmental model from a noisy input-output experiment. The problem is formulated in terms of nonlinear filtering. A simple model is discussed for the case in which the transport rate parameters are independent of each other. The possibility of testing possible important features of the behavior of the transport rate parameters is also evidenced.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460736
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  • 43
    Digitale Medien
    Digitale Medien
    Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 853-863 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂ci/∂t=Di∇2ci+Qi(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c 1(x,t),...,c n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460611
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  • 44
    Digitale Medien
    Digitale Medien
    Mathematical models in biological discovery. Lecture notes in biomathematics (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 873-875 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460613
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  • 45
    Digitale Medien
    Digitale Medien
    An isoclinal approach to the comparative statics of biological communities (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 59-75 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An understanding of the comparative statics of biological communities is important both as a means of explaining the long-term effects of changes in environmental conditions, and as a framework for viewing community time trajectories. A general formulation of community dynamics is presented here which, given full information about a particular community's dynamic behavior, describes the impact of a change in environmental conditions on the community steady state. However, since such full information is often lacking in studies of biological communities, various approaches to partial information analysis of comparative statics are presented and compared, including a generalized protocol for isocline analysis. The suggested isocline protocol is shown to be a useful tool for both full and partial information analyses, as well as for both general and partial equilibrium studies.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460062
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  • 46
    Digitale Medien
    Digitale Medien
    An interpretation of Fujita's frequency diagrams in phyllotaxis (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 77-86 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Fujita's diagrams in phyllotaxis, showing the frequencies of divergence angles as a function of these angles for low phyllotactic patterns such as (2, 1) and (3, 2), which are approximately normal curves centered at the limitdivergence angle of 137.51°, are shown to be puzzling when compared to results and observations in the field. An analysis of these diagrams is proposed, in the context of Fujita's methodology, of data from other sources, of a mathematical theorem on lattices, and of the contact pressure theory of phyllotaxis.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460063
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  • 47
    Digitale Medien
    Digitale Medien
    Existence of steady-state probability distributions in multilocus models for genotype evolution (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 87-95 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is shown that a representative Fisher-Wright model withn(≥3) diallelic loci admits a necessary condition for existence of a time-independent steady-state probability distribution. This necessary condition states that a global integral depending on the phenotype fitness functions of natural selection must be larger than a certain quantity depending on the parameters associated with genetic drift.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460064
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  • 48
    Digitale Medien
    Digitale Medien
    Transient phase kinetics of activation of human plasminogen (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 149-166 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Equations for the time-dependent concentrations of all species involved in the general mechanism of human plasminogen activation proposed by Wohlet al. (J. biol. Chem. 255, 2005–2013, 1980) have been derived. These equations are valid for the whole course of the reaction: for both the transient phase and the steady state. In addition, we compare our results with the ones obtained by the above-mentioned authors for the steady state assuming rapid equilibrium conditions. Finally, we propose a method for the determination of all velocity constants.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460020
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  • 49
    Digitale Medien
    Digitale Medien
    Interval graphs and maps of DNA (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 189-195 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A special class of interval graphs is defined and characterized, and an algorithm is given for their construction. These graphs are motivated by an important representation of DNA called restriction maps by molecular biologists. Circular restriction maps are easily included.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460022
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  • 50
    Digitale Medien
    Digitale Medien
    On mathematical modeling of critical variables in cancer treatment (goals: Better understanding of the past and better planning in the future) (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 253-278 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Over the past 25 years stepwise improvement in the cure of disseminated cancers has been good, fair or very poor depending on the particular cancer one is discussing. “Cancer chemotherapy provides variably effective treatment for the majority of forms of human cancer and curative treatment for some 12 categories.” We have been slow to gain and learn how to apply quantitative information on the biologic phenomena that underlie the responsiveness, or lack of responsiveness, of many different cancers to single drugs and combinations of drugs delivered in different ways. I am of the opinion that continuing development and integration of rational biomathematical models based on principles already identified, and testing them for compatibility with much already available experimental and clinical data, will lead to models that will help in planning more effective treatment regimens for cancers now classified as moderately refractory or very refractory to chemotherapy. Some of the critical variables are considered briefly. My advice, for what it is worth, is “try to be sure that the biologic concepts that you use in modeling are almost as good as the arithmetic.”
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459681
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  • 51
    Digitale Medien
    Digitale Medien
    Physiological pharmacokinetics (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 309-322 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A discussion of the bases of physiological pharmacokinetics is followed by a brief review of the fundamental mass balance equations of the models. Some examples are outlined, together with a listing of published reviews which give many more references and detailed examples. Finally, some thoughts on future research directions are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459684
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  • 52
    Digitale Medien
    Digitale Medien
    Cell kinetics simulation languages (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 323-336 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The use of stochastic simulation languages in cell kinetics research is discussed. Two special purpose simulation languages; CELLSIM and CELLGROW are described and example problems are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459685
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  • 53
    Digitale Medien
    Digitale Medien
    Chemical carcinogenesis and toxicity models: Matching complexity to objectives (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 293-307 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Mathematical models predicting tissue doses of chemical toxicants can be either highly complex or simple, depending upon the end results needed. As an example of a highly complex mathematical model, the Miller Model of the distribution of reactive gases in human and animal lungs is described. The Miller Model accounts for the convection, the radial and axial diffusion, and the chemical reactions of gases as an inhaled breath passes down the airways. The geometry and physiology of human and animal lungs are used to calculate the convection and diffusion likely in each generation or bifurcating series of airways commencing with the trachea and extending 24 generations in humans. The chemical reactivity of ozone, an air pollutant, is accounted for by simulating second-order chemical reactions with the fluid lining materials of the lung and tissue biological molecules. The flux of ozone into three compartments (pulmonary tissue, overlying liquid layer and capillary blood) in each generation of the lung is calculated to provide molecular doses of ozone reaching each region of the lung. These results of calculated molecular dose are then used to construct dose-response curves for a variety of biological endpoints. A much simpler model is also described which recognizes the saturable or Michaelis-Menten type of kinetics controlling the removal of nickelous ion (nickel) from the lung. This model is used to calculate the chronic lung burden of the human lung for occupational, environmental and cigarette smoking exposure scenarios. In both the complex Miller Model and the simpler nickel lung burden model, the results can be used to calculate molecular doses at the potential site of action of these environmental chemicals and to unify a wide variety of studies. The predictions made are more likely to be valid since multiple investigators using a variety of animal species have participated in generation of the primary data. As a methodology, mathematical modeling based on physiological, physicochemical and anatomical principles provides a means of eliminating non-scientific considerations from the important process of regulating and recognizing toxic or cancer causing chemicals in the human environment.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459683
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  • 54
    Digitale Medien
    Digitale Medien
    Kinetic simulation of anticancer drug effects on metabolic pathway fluxes: Two case studies (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 337-351 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper presents a brief review of applications of kinetic simulation of multi-enzyme networks to the study of antimetabolite drugs used as anticancer agents. Kinetic models consist of systems of nonlinear differential equations that describe changes in concentrations of cellular metabolites with respect to time. Such models have been used to predict the effect of changes in activity of enzymes, or changes in enzyme kinetic parameters, on sensitivity to inhibition. Kinetic simulation has provided insight into several aspects of the biochemical pharmacology of antimetabolites, including drug sensitivity and resistance, and drug-drug interactions. Two specific studies are described in detail. The first concerns the importance of the ratio of competing enzymes in determining the selectivity of inhibitors of one of the competing enzymes, studied by a simple model. The second case study examines the effect of alternative biosynthetic pathways, thede novo and salvage pathways of pyrimidine nucleotide biosynthesis, on the selectivity of antipyrimidine drugs, as studied by a detailed model of 27 reactions of pyrimidine metabolism.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459686
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  • 55
    Digitale Medien
    Digitale Medien
    Cancer chemotherapy: Optimal control using the Verhulst-Pearl equation (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 381-404 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract General (deterministic) ordinary differential equations for the representation of cancer growth are presented when the growth is perturbed due to the action of a chemotherapeutic agent. The Verhulst-Pearl equation is introduced as a particular example of a growth equation applicable to human tumors. An optimal control problem with general performance criterion and state equation is formulated and shown to possess a novel feedback control relationship. This relationship is used in two continuous drug delivery problems involving the Verhulst-Pearl equation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459688
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  • 56
    Digitale Medien
    Digitale Medien
    Use of the circuit simulation program SPICE2 for analysis of the metabolism of anticancer drugs (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 353-380 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Complex networks of biological processes are analogous to electrical circuits. For each step in a biological or electrical network, flow is dependent on the driving force and the conductivity of the step. The relationship between biological flows and their driving forces can therefore be expressed as relationships between analogous currents and voltages. The time dependence of approach to equilibrium or a steady state is determined by the rates of depletion of material in various compartments. Electrical capacitance is therefore analogous to compartment volume. Once these generalized concepts of flow, force and capacitance are recognized, it becomes clear that computer programs designed for analysis of electrical circuits may be used for simulation of biological networks. A set of simple mathematical descriptions of the individual steps and a diagram showing how the steps are arranged with respect to each other are all that is necessary to perform a simulation; there is no need for computer programming skills or differential equations. The use of SPICE2 for simulation of the cellular and plasma pharmacokinetics of cytosine arabinoside (araC) is described as an example. A network model is developed which considers cellular pharmacokinetics (membrane transport, intracellular phosphorylation and dephosphorylation), and plasma pharmacokinetics following infusions of araC.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459687
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  • 57
    Digitale Medien
    Digitale Medien
    Future directions in computer simulation (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 405-415 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Developments in computer hardware and software are making significant improvements in the availability of simulation for biomedical researchers. This paper reviews past and present techniques for digital computer simulation and looks at improvements likely in the near future. In the area of hardware, personal computers are making computing and simulation more widely available and at the same time, supercomputers and special-purpose numerical processors are making it possible to solve larger problems. Software developments for simulation are reducing the time, effort and special skills required to produce a simulation program. A new hierarchical linker is proposed to make it easy to synthesize a global model by combining existing submodels. In the more distant future, computer models may be constructed graphically and with the assistance of intelligent programs capable of analysis and information retrieval.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459689
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  • 58
    Digitale Medien
    Digitale Medien
    Strategies for computer modeling (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 417-426 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Modeling is a ubiquitous and often misunderstood enterprise in which data from diverse disciplines are analyzed by techniques from other diverse disciplines in an attempt to confirm or falsify a set of hypotheses about the real world. Guidelines are offered for designing models to match the goals of modeling biological systems. Techniques for the construction and interpretation of models are discussed. The requirements for credibility of models are detailed, and tests are suggested for their validation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459690
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  • 59
    Digitale Medien
    Digitale Medien
    First Conference of the International Federation of Classification Societies (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 453-453 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459693
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  • 60
    Digitale Medien
    Digitale Medien
    Conference retrospective: An appropriate modeling infrastructure for cancer research (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 443-452 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Presentations and discussions at the symposium illustrate some general issues in biomedical modeling for cancer research. Given the motivations for modeling and assumptions concerning who should be involved in the modeling process, one can identify some basic needs to be met in supports to modelers. These concern both the models themselves and ways of presenting them to users. In conclusion, some thoughts are offered on economic and educational issues that may affect the infusion of modeling into biomedical research.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459692
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  • 61
    Digitale Medien
    Digitale Medien
    Editorial: Software survey section (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. I 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459694
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  • 62
    Digitale Medien
    Digitale Medien
    On the geometry of space-and time-equivalent catastrophes (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 1-25 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The geometrical nature of the Elementary catastrophes (Thom, 1969) is reviewed. Histories of the movement of catastrophe manifolds and bifurcation sets are presented for some of the space-equivalent unfoldings described by Wassermann (1975). These unfoldings provide descriptions of the variation with time of the stability of stationary states of associated potential energy functions. Identification of these stationary energy states with stationary states of a system therefore provides a description of its behavior with time. Qualitative descriptions of this type are particularly useful when the complexity of a system prevents a detailed quantitative description. Histories of bifurcation set movements suggest different types of system behavior at different space-like coordinates. This type of theory may be a useful model for the processes leading to differentiation of cells and to emergence of adult forms of a biological organism.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463127
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  • 63
    Digitale Medien
    Digitale Medien
    Prediction of limit cycles in mathematical models of biological oscillations (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 27-44 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Three conjectures are given which predict the existence of unique stable limit cycle oscillations in a class of piecewise linear (PL) differential equations. The equations are appropriate to model biological or other complex systems in which there are switchlike interactions between the elements of the network. Methods are presented which can be used to develop mathematical models which are conjectured to display stable limit cycle oscillations, from qualitative experimental information about relative phases of activity in the dynamical systems. Several illustrative numerical examples are given, and one experimental example from neurobiology is discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463128
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  • 64
    Digitale Medien
    Digitale Medien
    Least energy regulation of the arterial system (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 79-93 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The formulation and results of the Kalman State Regulator Problem are applied to a mathematical model of the arterial system of a dog to obtain an optimal control for blood pressure. The criterion for optimality is minimum energy per cycle.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463131
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  • 65
    Digitale Medien
    Digitale Medien
    Pressure-flow relationships in a model for the arterial system (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 95-105 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model is developed in state variable form suitable for the study of the control of blood pressure and flow in the mammalian cardiovascular system. The applicability of the model to steady state, both mean and pulsatile, and transient phenomena is demonstrated by the agreement of the results with experimental data. This model was developed to study the neural and renal-endocrine-electrolyte control of cardiovascular functions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463132
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  • 66
    Digitale Medien
    Digitale Medien
    Conditions for periodic solutions of volterra differential systems (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 133-160 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract As a contribution to the discussion of oscillatory models for interacting species it is shown that two-species Volterra models can never have limit cycles, and a complete enumeration is given of conditions which the parameters of these models must satisfy in order that a part of the phase space be filled with a family of closed curves; sketches of phase portraits are also given. These results complement and correct older results by Bautin and by Coppel on quadratic differential systems. The paper opens with a brief discussion of some more practical aspects of the ecological application of oscillatory models.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461432
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  • 67
    Digitale Medien
    Digitale Medien
    The kinetics of diffused substances in some biological systems (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 107-121 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The purpose of this paper is to present a method for the determination of a solution for a coupled system of first order initial boundary-value problems arising from some biological systems. The physical problem is to determine the suspended and the superficial molecular concentrations of a traced substance passing through an organ containing a tangle of vessels, such as the kidney-ureter system. The approach to the problem is by successive approximation which leads to a recursion formula for the determination of the solution as well as error estimates for the approximations. The recursion formula involves only direct integration which indicates a promising possibility in obtaining numerical results by using a computer. In addition to the determination of a solution, some qualitative analysis of the solution is given. This includes the existence of a unique solution, the continuous dependency of the solution on the data, and the stability problem of a steady-state solution.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463133
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  • 68
    Digitale Medien
    Digitale Medien
    Some properties of solutions of the semi-state model for nonlinear nonstationary systems (1986)
    Springer
    Circuits, systems and signal processing 5 (1986), S. 109-123 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract Certain properties of solutions similar to set invariance, set attractivity, boundedness, BIBO stability, etc. are investigated for the semistate model $$P(t)\dot x = M(t,x)x + D(t,x)u,y = q(t,x,u).$$ For systems considered, it is assumed that the reduction to a normal form of lower order is not possible. Using the direct method of Liapunov, the properties of solutions are investigated without actual knowledge of solutions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600190
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  • 69
    Digitale Medien
    Digitale Medien
    Multiple time scales for nonlinear systems (1986)
    Springer
    Circuits, systems and signal processing 5 (1986), S. 153-169 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract In this paper we extend the results on the multiple time-scale structure for linear autonomous systems of the form $$\dot x = A( \in )x$$ (cf. Coderchet al. [1]) to nonlinear autonomous systems. Our main result is in obtaining conditions under which the linearized system and the nonlinear system around an equilibrium point have the same time-scale structure.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600193
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  • 70
    Digitale Medien
    Digitale Medien
    Heat transfer in perfused biological tissue—II. The “macroscopic” temperature distribution in tissue (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 183-199 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In Part I, the general solution of the heat transport equation was given for a medium of constant thermal properties, containing a general convection fieldv(r,t). Starting from this general solution, an average or “macroscopic” temperature distribution is calculated in this paper, since in most physiological problems only an average or “macroscopic” temperature is accessible to the measurement. It is shown that the averaged temperature distribution is influenced alone by the order of the local symmetries of the convection field. These local symmetries can be deduced from anatomical data on the vascular architecture. In order to perform the averaging process, a detailed discussion, and an estimate of the correlation between the microscopic temperature variation and the convection field is carried out. Hereby, great emphasis is put on the experimental consequences of these results. As an illustrative example, the calculation of the macroscopic temperature distribution in a medium traversed by parallel capillaries is outlined.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461434
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  • 71
    Digitale Medien
    Digitale Medien
    A note on dipole sources in conducting biological tissues (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 201-209 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The study of current flow fields in biologicaltissue requires finding the potential field from dipole sources such that the normal gradient vanishes at the exterior surface. A convenient way to determine the dipole field is by taking the gradient of the potential field set up by a point source. However, the point source problem is ill-posed when the normal gradient is required to vanish at the outer surface. In the paper the nature of this problem is discussed and several methods for overcoming the difficulty are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461435
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  • 72
    Digitale Medien
    Digitale Medien
    A hydrodynamic model of aqueous flow in the posterior chamber of the eye (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 223-235 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An analysis of the hydrodynamics of aqueous flow in the posterior chamber of the anterior segment of the eye is presented. The viscid, incompressible description of fluid dynamics in a spherical geometry is utilized to reduce the problem to a biharmonic-type equation using a “Stokes Stream Function”. Analogous to Poiseuille flow in a cylindrical pipe, velocity profiles are deduced and an Ohms Law relationship between pressure and flow is derived in terms of the geometry of the assumed model. This result is then incorporated into a synthesized electric circuit analog of flow between ciliary artery and episcleral vein. Applications to open angle and pupilary block glaucoma are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461437
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  • 73
    Digitale Medien
    Digitale Medien
    On the nerve impulse equation: The dynamic responses of nerve impulse (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 247-255 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract With the assumption of dipole interaction with the membrane matrix, the dipole barrier under an applied field shows a minimum in its time transient. Kinetic equations governing the migration of ions are presented. Na+ activation, Na+ inactivation and K+ delay are all part of the same mechanism in this model with no other separate assumptions needed. Voltage Clamp equation and action potential equation are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461439
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  • 74
    Digitale Medien
    Digitale Medien
    Metabolic model and dosimetric data for copper (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 265-269 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A metabolic model for copper is derived and presented in the context of the International Commission on Radiological Protection (ICRP) dosimetry models for the lungs and gastrointestinal tract.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461441
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  • 75
    Digitale Medien
    Digitale Medien
    Analytical conditions for the conservative form of the ecological equations (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 257-264 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The analytical conditions by which a Volterra's general system describingn interacting species can be put in the “conservative” form have been examined. The cases forn=2, 3, 4 have been analyzed in detail and a general condition for any value ofn is deduced. The analytical and biological constraints following by this approach are compared to the conclusions drawn by Leigh on the ground of purely biological considerations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461440
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  • 76
    Digitale Medien
    Digitale Medien
    On the stochastic theory of compartments: III. General time-dependent reversible systems (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 237-246 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract General formulation of stochastic single- and multi-compartment reversible systems with time-dependent transitions is made. The correspondence between the stochastic mean and the deterministic value is established in case of time-dependence and it is shown how the consequence of this can be utilized to compute the distribution and the moments of each individual compartment of the system. A two-compartment reversible system previously proposed by Cardenas and Matis (1975a) is analyzed on the basis of the theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461438
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  • 77
    Digitale Medien
    Digitale Medien
    Mathematical models of metabolic regulation, symposia biologica hungarica (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 271-272 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461442
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  • 78
    Digitale Medien
    Digitale Medien
    Optimal control of pests in the presence of predators (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 319-333 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Optimal control theory is applied to the problem of controlling pests by biological and chemical means simultaneously. The net birth rate of the pests is controlled chemically while at the same time predators are allowed to operate. Several numerical examples are included.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461604
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  • 79
    Digitale Medien
    Digitale Medien
    Transient behaviour of the single loop solute cycling model of the renal medulla (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 273-300 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Transient solutions are developed for the buildup of a concentration gradient in the single loop solute cycling model of the renal medulla. The “pump” from ascending limb to descending limb is considered in both unsaturated and completely saturated modes of operation. Both analytic solutions and semianalytic solutions obtained from inverting Laplace transforms are considered. The classic representation of concentration buildup by the multiplication process is compared with calculated profiles. The “single effect” is found to vary both in time and space.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461602
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  • 80
    Digitale Medien
    Digitale Medien
    The Krylov-Bogoliubov-Mitropolskii method applied to models of population dynamics (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 335-345 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this study the possibility of applying the asymptotic method of Krylov-Bogoliubov-Mitropolskii to problems of population dynamics is shown. Especially a general Volterra-Gause-Witt type model for prey-predator interaction is investigated. A discussion on the results obtained is given for the general model and for a particular case as well.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461605
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  • 81
    Digitale Medien
    Digitale Medien
    A dynamical field theory for dissipative systems: The hierarchical structure of field thermodynamics (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 301-318 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The analytical exploration of hierarchical structures is a central problem in modern biology. In many ways, the most basic tenet of any theory of any biological system is that its behavior lies within the laws of thermodynamics. Thus an investigation into the hierarchical structure of field thermodynamics is in effect an investigation into the underlying structures common to all biological systems. In field thermodynamics, the dynamics is prescribed at the hierarchical level of description concerned with the motions of classes of the various molecular species flowing in the system. Of crucial importance are scale factors which convert potentials into potential energies per mole of the various molecular species. On the other hand, the overall behavior of the system is presented at a higher hierarchical level of description in terms of systemic properties such as charge density or entropy density. Three questions are investigated: (1) how is the transition from the specific to the systemic level of description effected, (2) given the scale factors at the specific level how does one find those at the systemic level, and (3) what relationship can one, find between the scale factors at the two levels of description? Answering these questions necessitates an examination of the nature of the forces at the two levels of the hierarchy of descriptions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461603
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  • 82
    Digitale Medien
    Digitale Medien
    Reconstitution of the transition matrix from experimental data (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 369-376 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The identification of a linear compartment model, which may describe a chemical or biological process, is a difficult task, since the available data is generally limited. In this paper we propose a method for determining the state transition matrix by minimizing a given quadratic criterion. To solve the resulting matrix equation, an assumption has to be made which constitutes a necessary condition for the identifiability of the model. Moreover when this assumption is satisfied, it is shown that the knowledge of one line or one column of the transition matrix is sufficient to define it completely.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461608
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  • 83
    Digitale Medien
    Digitale Medien
    Analytical solution to isometric mechanogram of hill’s model of striated muscle (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 359-368 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The two-element muscle model considered consists of a contractile element defined by a hyperbolic force-velocity relation connected in series with an “exponential spring”. Differential equations for the isometrically developed force during a tetanic contraction and the corresponding contractile element shortening velocity are derived and their stability is investigated. Analytical solutions to both equations are obtained. Two numerical examples are given, the second chosen to illustrate pressure-induced hypertrophy of a cardiac muscle.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461607
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  • 84
    Digitale Medien
    Digitale Medien
    Lag time in microbe growth as an age-dependent branching process with two phase types (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 347-358 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We study a two-type, age-dependent branching process in which the branching probabilities of one of the types may vary with time. Specifically this modification of the Bellman-Harris process starts with a Type I particle which may either die or change to a Type II particle depending upon a time varying probability. A Type II particle may either die or reproduce with fixed probabilities but may not return to a particle of Type I. In this way the process models the lag phenomenon observed in microbe growth subsequent to transfer to a new culture medium while the organism is adapting to its new environment. We show that if the mean reproduction rate of Type II particles exceeds 1, then the population size grows exponentially. Further the extinction probability for this process is related to that of the Bellman-Harris process. Finally the governing equations are solved for several choices of the growth parameters and the solutions are graphically displayed showing that a wide variety of behavior can be modeled by this process.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461606
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  • 85
    Digitale Medien
    Digitale Medien
    Linear age-dependent population growth with harvesting (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 377-385 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper studies the effect of harvesting a fraction of a population where the population growth is modelled by a linear age-dependent model, the Von Foerster equation. Two harvesting strategies are considered: the first is where a fraction of the population greater than agec is removed, and the second is where a fraction of the population of age greater thanc but less thanc+n is removed. In the case where the death rate and fertility rate are time independent, the effect of harvesting on the stable age distribution is examined.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461609
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  • 86
    Digitale Medien
    Digitale Medien
    A comment on the Richardson-Miekisz field theory of thermodynamics (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 425-426 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461612
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  • 87
    Digitale Medien
    Digitale Medien
    Multiple speciation, competitive exclusion, evolutionary pattern, and the grand ensemble in volterra eco-dynamics (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 387-410 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The general means are set forth by which, in a highly speciated Volterra eco-system, the bifurcation of a species into two in a competitive-exclusion configuration, provides a description of odd as well as even systems. The the Gibbs ensemble theory earlier developed is extended to grand ensembles in which the number of ecotypical species in genera-like clusters is allowed to be variable. The probability law for the sizes of clusters is deduced, and shown very closely to imply independent Poisson statistics for the cluster sizes, in answer to a fundamental issue of bioevolution. The role of the eco-analogs of Gibbs’ chemical potentials is brought forth, with a suggestion of how to describe cluster-to-cluster eco-genetic flows, and therewith a definite relationship between the degrees of speciation of genetically linked clusters on the one hand, and amplitudes of population fluctuations of member species within the clusters on the other hand.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461610
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  • 88
    Digitale Medien
    Digitale Medien
    The stochastic theory of compartments—a mammillary system (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 427-427 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461613
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  • 89
    Digitale Medien
    Digitale Medien
    Ionic concentration profiles and charge distribution for the domain of a polarized spherical cell (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 411-424 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Solutions of the Poisson-Boltzmann equation yield potential profiles and equilibrium distributions of ions on either side of a spherical shell membrane across which there exists a separation of ionic charges. For the special case in which the membrane is permeable to only one ion the total charge separation is analyzed in terms of the potential difference given by the Nernst equation. Potential profiles and ionic charge distributions are also given for situations involving a uniform distribution of fixed charges within the membrane.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02461611
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  • 90
    Digitale Medien
    Digitale Medien
    An elementary approach to catastrophe theory (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 429-450 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The recently proved classification theorem of René Thom has led to the development of the new science of Catastrophe Theory. This theory has been widely held to be particularly relevant in biological applications. The present paper presents a simplified proof of Thom’s Theorem and assesses its importance in biology.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460770
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  • 91
    Digitale Medien
    Digitale Medien
    Mechanical behaviour of ventricular aneurysms (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 451-464 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model describes the mechanical behaviour of ventricular aneurysms assuming a spherical geometry for the left ventricle. Employing pressure-volume data obtained from normal dog hearts 1–2 hours after infarction, conditions are obtained on infarct thickness and angle of damage for ventricular rupture to occur. The results indicate that rupture is more likely to occur in the early period following infarction and that the dominant factor is the per cent thickness of the infarct.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460771
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  • 92
    Digitale Medien
    Digitale Medien
    A stochastic approach to predator-prey models (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 483-498 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A deterministic investigation of a linear differential equation system which describes predator vs prey behavior as a function of equilibrium densities and reproductive rates is given. A more realistic structure of this model in a stochastic framework is presented. The reproductive rates and initial population sizes are considered to be random variables and their probabilistic behavior characterized by various joint probability distributions. The deterministic behaviors of the prey and predator species as functions of time are compared with the mean behaviors in the stochastic model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460773
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  • 93
    Digitale Medien
    Digitale Medien
    Effects of external pressures on the pressure-volume relation of the left ventricle (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 465-482 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The effects of ventricular geometry, muscle mass, muscle elasticity and external pressures on the pressure-volume and muscle stiffness-stress relations have been quantitated on the basis of a theoretical model. Data taken from patients before and after interventions with nitroprusside and angiotensin were applied to the model in order to explain the possible causes for the marked shifts in the pressure-volume relations. The results indicate that (a) ventricular geometry does not markedly alter the pressure-volume and stiffness-stress relations unless there is a drastic change from a spherical shape to an ellipsoidal shape orvice versa, (b) increases in muscle mass and muscle elasticity of the order of 30% result in significant alterations in the P-V relations but are not the cause for the parallel shifts unless accompanied by substantial external pressures, (c) the parallel shifts in the pressure-volume relations can be accounted for entirely by the presence of external pressures without changes in muscle mass or muscle elasticity. Thus manipulation of right ventricular pressures or pericardial pressures by drug interventions may be useful in the treatment of left heart disease and the presence of such pressures must be considered in the analysis of ventricular function curves.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460772
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  • 94
    Digitale Medien
    Digitale Medien
    Qualitative similarities between the behavior of coupled oscillators and circadian rhythms (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 675-692 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper summarizes in a nonmathematical way the major properties of coupled oscillators which relate to circadian rhythms. For certain values of the coupling strength it is far easier to maintain synchrony than to achieve it among the various interacting units. This property not only simulates the free run period lability but also the effects of critical pulses.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460599
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  • 95
    Digitale Medien
    Digitale Medien
    The effects of asymptomatic attacks on the spread of infectious disease: A deterministic model (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 707-718 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A deterministic model for a multi-agent disease epidemic with asymptomatic attacks is proposed and investigated. The limitations inherent in the assumptions of the model are discussed in connection with specific agents of disease. The mathematical treatment of the model is separated into analyses of the equilibrium situation and the transient behavior of the disease outbreak. Explicit formulas are derived for the number of susceptibles in the population as well as for the numbers of each type of infective—those with and without symptoms. These theoretical results are followed by a discussion of the practical considerations which must be taken into account to obtain useful information from the model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460601
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  • 96
    Digitale Medien
    Digitale Medien
    On a model and the kinetics of photo-enhanced enzyme reactions (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 719-726 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The recently observed enhancement, by laser irradiation, of the specific activity of the enzyme chymotrypsin (which hydrolyses Benzoyl-L-tyrosine-ethyl ester) at low enzyme concentration is considered. The enhancement of the reaction rate is attributed to a coherently excited state of the enzyme molecule (activated through Raman scattering of the laser light) following a prediction due to Fröhlich. The model is described, the kinetics of the process is framed and the observed enzyme-concentration dependence of the specific activity is reproduced. Predictions of the model are delineated to urge verification of the main contentions through further experimentation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460602
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  • 97
    Digitale Medien
    Digitale Medien
    A two-component theory of aerosol deposition in lung airways (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 693-706 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The deposition of aerosol particles in the human lung airways is due to two distinct mechanisms. One is by direct deposition resulting from diffusion, sedimentation and impaction as the aerosol moves in and out of the lung. The other is an indirect mechanism by which particles are transported mechanically from the tidal air to the residential air and eventually captured by the airways due to intrinsic particle motion. This last mechanism is not well understood at present. Using a trumpet airway model constructed from Weibel's data, a two-component theory is developed. In this theory, the particle concentrations in the airways and the alveoli at a given airway depth are considered to be quantitatively different. This difference in concentrations will cause a net mixing between the tidal and residential aerosol as the aerosol is breathed in and out. A distribution parameter is then introduced to account for the distribution of ventilation. The effect of intrinsic particle motion on the aerosol mixing is also included. From this theory, total and regional deposition in the lung at the steady mouth breathing without pause is calculated for several different respiratory cycles. The results agree reasonably well with the experimental data.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460600
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  • 98
    Digitale Medien
    Digitale Medien
    On the kinetics of enzyme reactions (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 727-734 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The Abel type differential equation governing the kinetics of the enzyme reactions is derived. Approximate solutions of this equation corresponding to the transient phase of the reaction, before a steady state is reached, are considered. It is shown that in several cases it is possible to obtain explicit, approximate solutions to the transient phase.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460603
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  • 99
    Digitale Medien
    Digitale Medien
    Complementary variational principles for the steady-state finite cable model of nerve membranes (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 735-742 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Maximum and minimum principles for the steady-state finite cable model of nerve membranes are derived from the canonical theory of complementary variational principles. An accurate variational solution is obtained in an illustrative calculation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460604
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  • 100
    Digitale Medien
    Digitale Medien
    Dynamical systems under constant organization I. Topological analysis of a family of non-linear differential equations —A model for catalytic hypercycles (1978)
    Springer
    Bulletin of mathematical biology 40 (1978), S. 743-769 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The paper presents a qualitative analysis of the following systems ofn differential equations: $$\dot x_i = x_i x_j - x_i \sum\nolimits_r^n { = 1} x_r x_s {\mathbf{ }}(j = i - 1 + n\delta _{i1} {\mathbf{ }}and{\mathbf{ }}s = r - 1 + n\delta _{r1} )$$ , which show cyclic symmetry. These dynamical systems are of particular interest in the theory of selforganization and biological evolution as well as for application to other fields.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460605
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