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  • 2005-2009
  • 1980-1984  (53.687)
  • 1975-1979  (43.644)
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  • 1
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    Springer
    In:  EPIC3Naturwissenschaften, Springer, 71(12), pp. 599-608, ISSN: 0028-1042
    Publikationsdatum: 2014-06-04
    Repository-Name: EPIC Alfred Wegener Institut
    Materialart: Article , notRev
    Format: application/pdf
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 967-969 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is observed that a dynamical continuity equation for biomass distribution yields the asymptotic steady-state exponential dependencen=A exp( $$ - m/\bar m$$ ) exhibited by certain fishery data, wherem is the biomass of an individual,n is the number of individuals per unit biomass interval, andA, $$\bar m$$ are positive constants. This dynamical approach to biomass distribution is an alternative to the global maximization principle proposed recently by Lurié and Wagensberg.
    Materialart: Digitale Medien
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 971-972 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 973-974 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 5
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 37-49 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The chromosomal theory of inbreeding based on a gametic interaction system lead us to define a depression coefficientD. Comparison of random, sib and half-sib matings (with inbreeding coefficientF=0, 1/4 and 1/8) shows thatD depends on the structure of the starting population and on values of the model parameters. This result accounts for responses of lines whose depression does not depend directly on the inbreeding coefficient and which theories of inbreeding based on increasing homozygosity fail to explain.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 6
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 59-69 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An idealization of chemical combination is formulated as a model of computability, and it is shown that this model has universal computational power just in case assembly has at least two-dimensional space in which to occur. It is also shown that this model, under reinterpretation, corresponds to a cellular automaton in which growth occurs by differentiation only (i.e., the state into which any cell is born is thereadfter fixed). Hence this latter model of growth is also computationally universal.
    Materialart: Digitale Medien
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  • 7
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Kinetics of biological light emission processes do not mean what they seem to mean, because measured light intensity is not proportional to reactant concentration but to reaction rate. Therefore, the differential equation for light decay is usually different from that of concentration decay, so that mass action interpretations cannot be applied directly to light intensity decay. An observed second order light decay for Chlorella at 6.5°C, implies Elovich solid state reaction kinetics, which agrees with other evidence for solid state processes in photosynthesis. An observed 1.5 order light decay for Cholorella at 28°C implies second order liquid or solid state reaction kinetics. First ordere light decay implies first order reaction kinetics.
    Materialart: Digitale Medien
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  • 8
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 71-78 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Analysis based on the integration of differential inequalities is employed to derive upper and lower bounds on the total populationN(t) = ∫ R θ(x 1,x 2,t) dx 1 dx 2 of a biological species with an area-density distribution function θ=θ(x 1,x 2,t) (≥0) governed by a reaction-diffusion equation of the form ∂θ/∂t =D∇2θ +fθ −gθ n+1 whereD (〉0),n (〉0),f andg are constant parameters, θ=0 at all points on the boundary ∂R of an (arbitrary) two-dimensional regionR, and the initial distribution (θ(x 1,x 2, 0) is such thatN(0) is finite. Forg≥0 withR the entire two-dimensional Euclidean space, a lower bound onN(t) is obtained, showing in particular thatN(∞) is bounded below by a finite positive quantity forf≥0 andn〉1. An upper bound onN(t) is obtained for arbitrary bounded or unbounded)R withn=1,f andg negative, and ∫ R θ(x 1,x 2, 0)2 dx 1 dx 2 sufficiently small in magnitude, implying that the population goes to extinction with increasing values of the time,N(∞)=0. Forg≥0 andR of finite area, the analysis yields upper bounds onN(t), predicting eventual extinction of the population if eitherf≤0 or if the area ofR is less than a certain grouping of the parameters in cases for whichf is positive. These results are directly applicable to biological species with distributions satisfying the Fisher equation in two spatial dimensions and to species governed by certain specialized population models.
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 127-138 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The equilibrium probability distribution of the process level is studied for a general class of reversible stochastic reactions. A calculationally convenient approximation for equilibrium probabilities is derived and its accuracy is investigated over a range of values of the equilibrium constant. A method of approximating the equilibrium means and variance is developed and illustrated forQ th-order processes.
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 565-572 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Beside the concept of material inputs and outputs of components of the representation of biological systems given to us by Rosen, the concept of energy is incorporated. The interaction of material and energy is represented by a cartesian product; and separate material and energetical mappings are considered as the new representation of components. These developments generate aMα category, and it is shown thatMα is isomorphic to theM category of previous developments.
    Materialart: Digitale Medien
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  • 11
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 555-564 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper discusses the solution of a generaln-compartment system with time dependent transition probabilities utilizing the technique described by Cardenas and Matis (1975) (hereafter abbreviated (CM)). In addition, the cumulant generating function is derived for a special class of reversiblen-compartment systems where the time-dependent intensity coefficients corresponding to the migration and death rates are some multiple of each other. The immigration rates can be any integrable function of time. The moments are also obtained and the solution to the two-compartment system is presented explicitly. The solution is illustrated with a linear and a periodic function which forms have been widely reported in the literature.
    Materialart: Digitale Medien
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  • 12
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 573-588 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The relations (inflow) = (dose)/(area under indicator curve), and (volume of distribution) = (throughflow) × (mean transit time) are derived by a matrix method for a system of interconnected subsystems, within which spatial indicator activity gradients may exist, and for compartments, within which the indicator activity is spatially uniform. The inflow theorem, is different from the outflow theorem. Equivalent labeling of multi-input systems reduces them formally to single input systems. Foreign indicator flow-volume kinetics are more general than, and include as a special case, tracer flux-mass (metabolic) kinetics. Volume of distribution in the indicator steady state may be different from the equilibrium volume of distribution.
    Materialart: Digitale Medien
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  • 13
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 219-219 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 14
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 291-299 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Perturbation methods are applied to a differential equation predator-prey model to find the approximate amplitudes and period of limit cycle solutions. In the model the feeding rate per unit predator per unit prey decreases as the prey become scare. The rigorous applicability of the perturbation technique depends on the assumptions that the limit cycle amplitude is relatively small and that near the equilibrium point the growth rate of each species is most sensitive to changes in the density of the other species. The second assumption is usually roughly satisfied in practice and examples are considered which suggest that the first assumption can be greatly relaxed.
    Materialart: Digitale Medien
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  • 15
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 367-387 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Signal Detection Theory can be used to provide a mathematical model describing the choice of a predator trying to distinguish between a model and a Batesian mimic. The mathematical model yields a number of a deductions, in particular that it may or may not assist the mimic population if mimics more closely resemble their models. The assumptions underlying the analysis are discussed in some detail.
    Materialart: Digitale Medien
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  • 16
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 419-425 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A new type of physical transition, denotedS→S *, has been detected in irradiated organic molecules (λ=546 nm) through their interaction with specific biological macromolecules. In a specific enzyme-substrate interaction, a clear enhancement of the reaction rate is observed, when the substrate is irradiated with sharply well defined times. These “efficient irradiation times” are always of the 5k sec type (k=1, 2, 3, …). They have been consistently revealed in a great number of specific biological interactions. The present note demonstrates an important property, i.e. that forevery irradiation time aS→S * transition is induced in organic molecules. It is shown that for any irradiation times different from the 5k sec type (k=1, 2, 3, …) states of theS * type may occur, but the biological macromolecules may “detect” only theS * states induced by irradiations of the 5k sec type.
    Materialart: Digitale Medien
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  • 17
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 459-470 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A semi-empirical model applicable to the flow of blood and other particulate suspensions through narrow tubes has been developed. It envisages a central core of blood surrounded by a wall layer of reduced hematocrit. With the help of this model the wall layer thickness and extent of plug flow may be calculated using pressure drop, flow rate and hematocrit reduction data. It has been found from the available data in the literature that for a given sample of blood the extent of plug flow increases with decreasing tube diameter. Also for a flow through a given tube it increases with hematocrit. The wall layer thickness is found to decrease with increase in blood hematocrit. A comparison between the results of rigid particulate suspensions and blood reveals that the thicker wall layer and smaller plug flow radius in the case of blood may be attributed to the deformability of the erythrocytes.
    Materialart: Digitale Medien
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  • 18
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 489-504 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Three dimensional laminar, viscid flow is developed for Newtonian fluids which provides absolute values for axial, radial and tangential velocity fields everywhere if the dimensions of the vessel are known and two simultaneous axial velocities e.g. on and off the central axis in the same plane, and the central axis axial velocity gradient are measured. In addition, normal and shear stresses are determinable. The equation set satisfies geometric and other known flow limiting conditions such as no slip at surfaces etc. and are amenable for inclusion in general, dynamic flow expressions. Alternatively they may be used alone for certain problems involving gradients and secondary flows. A range of illustrations are shown for a distorting vessel with elliptic cross-section and small axial taper (analogous to the pulmonary trunk during ejection).
    Materialart: Digitale Medien
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  • 19
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 521-553 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A regulated left ventricular dynamics model is presented which involves interaction of the dynamics of the left ventricular and circulatory systems and their regulation by the central nervous system. On-line human parametric simulation (parameter estimation) and consequential prognostic implications (based on parametric values) are demonstrated. Model responses to simulated physiologic stresses help delineate tolerances of subjects. In order to have an estimate of the reliability of the model, the sensitivity of the model's responses to changes in the values of its intrinsic parameters is assessed. Also determined is the extent to which errors in measuring the pressure affect the calculated values of the model's simulation parameters and subsequently influence the values of other diagnostically useful variables (such as contractility, oxygen consumption rate, heart rate), when the model is used to determine the limiting physiological stress sustainable by the subject. A comparison of the model's composition with those of other similar cardio-circulatory models is included.
    Materialart: Digitale Medien
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  • 20
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 37 (1975), S. 659-673 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Then-stage harvesting strategy of Elizarov and Svirezhev is examined. As a result, some important new features appear. A discussion is presented on whether or not one should harvest a species at one time stage or wait until a later time. The paper is concerned with contributions which are primarily mathematical formulations and results for continuous, as well as discrete time, logistic growth of a single species being harvested. Age class structure is ignored.
    Materialart: Digitale Medien
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  • 21
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 11-17 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Linear birth and death processes are used to derive simple expressions for sequential extinction times and gene fixation probabilities in asexual populations.
    Materialart: Digitale Medien
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  • 22
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 1-10 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We are here concerned with the functionf which assigns to each pointP of an object the numberf(P) which is the shortest distance fromP to the border. This function appears in various guises in diverse biological studies. The functionf(P) is itself a measure of shape—or more precisely, an infinite set of measures, one for each point (and hence, in view of its geometric definition, usually in a form inconvenient for use). Thus in this paper we sought a reasonable representative of this infinite set of measures, namely themean of the numbersf(P) asP ranges over all points of the entity. Computability studies are developed for various classes of shapes. For example, (1) the mean for a lamina bounded by a polygon circumscribable about a circle of radiusr isr/3; (2) the mean for a domain bounded by a polyhedron circumscribable about a sphere of radiusr isr/4. The transition from pointwise to piecewisef(P), especially in the non-convex case, requires working with inequalities.
    Materialart: Digitale Medien
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  • 23
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 19-40 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model for traveling bands of motile and chemotactic bacteria in the presence of cell growth and death is examined. It is found that asymptotic traveling wave solutions exist in the absence of chemotaxis, due to the balance of growth, death and random motility. Thus random motility confers the ecological advantage of population propagation through migration into nutrient-rich regions. The presence of chemotaxis amplifies this advantage by moving more cells into higher nutrient concentration regions, resulting in larger and faster bands. Therefore there seem to be two types of traveling bands that can be attained by chemotactic bacteria in the presence of growth and death: (1) these growth/death/motility bands; and (2) pure chemotactic ‘Keller-Segel'-type bands. Comparison to experimental observations by Chapman in 1973 indicate that the latter seem to be formed. The relationship between these two types of solution is at present uncertain. The growth/death/motility bands may have relevance on longer time or distance scales characteristic of microbial ecological systems.
    Materialart: Digitale Medien
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  • 24
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 115-125 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Based on the principle of minimum power, a mathematical model of the pathological functional state of the oxygen transport system is presented. The model is used to determine the optimal functional parameters of the oxygen transport system in hyperthyroidism, anemia and hypertension. Theoretical results are compared with clinical data.
    Materialart: Digitale Medien
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  • 25
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 139-153 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A modified SIRS model is developed as a framework for the study of epizootiological dynamics in an insect-pathogen system. Linearized stability analysis reveals that the system with one immune and one susceptible host class can exhibit stable, periodic or unstable behavior depending on model parameters. In general, high pathogenicity, short pathogen propagule lifespan and high host reproductive rate are stabilizing influences. Pathogen transmissibility and propagule production/host do not influence local stability. The effect of seasonal host reproduction is studied because most insect hosts are seasonal in temperate climates. The basic stability dependence on model parameters holds except as modified by the length of the reproduction interval. The results of this study are compared with the recent work of Anderson and May.
    Materialart: Digitale Medien
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  • 26
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 175-184 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The random predator-prey type interactions of the population species in a random varying environment have been investigated. The Fokker-Planck equation for the transition probability, corresponding to the stochastic differential equations established from Lotka-Volterra equations by the introduction of randomness and variability, has been integrated in the form of a path integral. The transition probabilities for extinction or survival of one or several species have been approximately evaluated and investigated.
    Materialart: Digitale Medien
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  • 27
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 155-174 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract If two microbial populations compete for a single resource in a homogeneous environment with time invariant inputs they cannot coexist indefinitely if the resource competed for is not renewed by biological activity within the system. Mathematical studies have shown that in a predator-prey system, where the resource (prey) is self-renewing, the two competitors (predators) can coexist in a limit cycle. This suggests that if the resource competed for is renewed by biological activity within the system coexistence can occur in any microbial system provided that it exhibits the same features as, but without being, a predator-prey one. A food chain involving commensalism, competition and amensalism is presented here. Two subcases are considered. It is only when maintenance effects are taken into account that coexistence, in limit cycles, can occur for this system. Limit cycle solutions for the system are demonstrated with the help of computer simulations. Some necessary conditions for coexistence are presented, as are some speculations regarding the possible physical explanations of the results.
    Materialart: Digitale Medien
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  • 28
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 127-137 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The branching structure of the mammalian arterial tree has been known to be close to that of an optimal conduit system of the minimum work model characterized as the branch system of constant wall shear rate. The physiological mechanism producing such construction was considered to be based on the local response of arterial caliber induced by the wall shear stress (shear rate × blood viscosity) and thereby maintaining this stress constant, which was previously observed at the canine common carotid artery shunted to the external jugular vein. The stress levels at various parts of the arterial system estimated from available data fell within ±50% of the mean (15 dyn/cm2), which was consistent with the value predicted from the model. Theoretical analyses on the cost function of the model indicated that the suspected variation of shear rate levels in the arterial tree due to the anomalous changes in blood viscosity which might bring about 3- to 4-fold differences between the minimum and maximum shear rates would cause less than 10% increase in the total energy cost. It was concluded that a local adaptive response to wall shear stress is the mechanism which effectively optimizes the design of the arterial tree.
    Materialart: Digitale Medien
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  • 29
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 185-185 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 30
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 187-203 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The structure of the genetic code is related to a Gray code, which is a plausible theoretical model for an amino acid code. The proposed model implies that the most important factor in shaping the code was the effects of mistakes in translation, not effects of mutations. Another possible implication is that the preservation of stiffness and flexibility at appropriate places in a protein chain is as important in protein structure as the appropriate placement of hydrophilic (external) and hydrophobic (internal) residues. Other results are a simple conceptualization of the relationships among the 20 amino acids and their relations to their codons. The detailed relationships are summarized in the following ‘similarity alphabet’: ala, thr, gly, pro, ser; asp, asn, glu, gln, lys; his, arg, trp, tyr, phe; leu, met, ile, val, cys; (ATGPS DNEQK HRWYF LMIVC in the one-letter code). This alphabet falls into four groups of amino acids: small, external, large, internal. The approximate relation of the groups to their codons is expressed as: the first base of a codon controls size—a purine means a small amino acid, a pyrimidine means large; the middle base controls cloisterednes—purine means external, pyrimidine means internal. These relationships express the minimum change principle upon which the code appears to be founded.
    Materialart: Digitale Medien
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  • 31
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 269-282 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A theoretical study of the Brusselator model with non-uniform distribution of component A and a concentration-dependent diffusion coefficient has been performed. Numerical simulation reveals that a variable diffusion coefficient alters the bifurcation pattern and the stability properties of the steady-state as well as periodic solutions. A simple approximate method, based on one-point collocation, has been proposed to analyze the bifurcation phenomena for the case of fixed boundary conditions and low system size.
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  • 32
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 283-294 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper the effects of the occurrence of cut trees in the topological analysis of branching patterns have been studied. It is assumed that branches are removed at random from the trees. We prove that, for both the segmental and terminal growth models, the probability distributions of the cut trees are identical to those of complete trees.
    Materialart: Digitale Medien
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  • 33
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 247-268 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The goal of this work is an examination of capillary exchange models as mathematical operators. The concentration function relations for the Krogh cylinder of a single capillary, basic to many organ models, are studied via the theory of operators on the Lebesgue normed spacesL p[0,∞], (1〈-p〈-∞). A discussion is included of theL p -normsvis-à-vis the coefficient of variation currently used in finding capillary parameters and evaluating parameter searches. The capillary model determines two operators on the space of locally integrable functions: O K (relating extravascular concentration to intravascular) and K a, k (relating intravascular concentration to input), wherek is the ratio of permeabilitysurface area (PS) to extravascular volume, and α is the ratio of PS to flow. These operators are shown to induce contractive (‖O K ‖ p 〈-1, ‖K a, k ‖ p 〈-1), isotone, linear operators onL p . The uniform convergence relation $$K_{a,k} = \mathop {\lim _{(p)} }\limits_{N \to \infty } \left( {\sum\limits_{n = 0}^N {P_n (a)O_k^n } } \right)$$ (as operators onL p) is derived, whereP n (a) is the Poisson probabilitye −a a n /n!. For the important special cases ofp=∞, 1, 2 the norms are found (‖Ok‖=‖Ka,k‖p=1). Consideration is also given to the norms and operators when the functions involved are limited to a finite interval of time.
    Materialart: Digitale Medien
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  • 34
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 295-326 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract One particular kind of structure offers possible explanations, for long-term memory, efficient consolidation of stored information from the environment, clustering of data strings and multimodal functioning. It is a possible model for pieces of neural structure and its use offers a uniform method for both studying and constructing an extensive class of mechanisms.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 35
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 327-332 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Levenshtein dissimilarity measures are used to compare sequences in application areas including coding theory, computer science and macromolecular biology. In general, they measure sequence dissimilarity by the length of a shortest weighted sequence of insertions, deletions and substitutions required, to transform one sequence into another. Those Levenshtein dissimilarity measures based on insertions and deletions are analyzed by a model involving valuations on a partially ordered set. The model reveals structural relationships among poset, valuation and dissimilarity measure. As a consequence, certain Levenshtein dissimilarity measures are shown to be metrics characterized by betweenness properties and computable in terms of well-known measures of sequence similarity.
    Materialart: Digitale Medien
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  • 36
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 337-337 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 37
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 333-336 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is pointed out that the methane flux measured experimentally for certain ponds and swamps is quantitatively consistent with a commensal dependence of Methanobacteria on O2-chemotactic motile aerobic bacteria. The Methano species is thereby shielded from oxygen and provided with carbon dioxide for the anaerobic production of methane.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 38
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 357-370 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A sufficient condition is given for stochastic boundedness persistence of a top predator in generalized Lotka-Volterra-type stochastic food web models in arbitrary bounded regions of state space. The main result indicates that persistence in the corresponding deterministic system is preserved in the stochastic system if the intensities of the random fluctuations are not too large.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 39
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 371-377 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract One of Bobisud's models for the evolution of cannibalism is reanalyzed by applying the method of finding evolutionarily stable strategies (or ESS's). It is demonstrated that ‘no cannibalism’ never will be an ESS if the initial rate of cannibalism is too large. It is further demonstrated that individual selection may even result in the evolution of cannibalism during food abundance. Some empirical case studies are briefly discussed in relation to this model.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 40
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 379-387 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A computer algorithm is presented which equiprobably generates any member of the set of all directed trees withk labeled terminal nodes and unlabeled interior nodes. The algorithm requires roughlyk 2 /2 storage locations. The one-time initialization requiresO(k 2 ) time, while generating each tree requiresO(k) time.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 41
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 515-527 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The comparison of several sequences is central to many problems of molecular biology. Finding consensus patterns that define genetic control regions or that determine structural or functional themes are examples of these problems. Previously proposed methods, such as dynamic programming, are not adequate for solving problems of realistic size. This paper gives a new and practical solution for finding unknown patterns that occur imperfectly above a preset frequency. Algorithms for finding the patterns are given as well as estimates of statistical significance.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 42
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 501-514 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A new development is introduced here in the use of dynamic programming in finding pattern similarities in genetic sequences, as was first done by Needleman and Wunsch (1969). A condition of pattern similarity is defined and an algorithm is given which scans any set of similarities and screens out those which fail to meet the condition. When the set to be scanned contains every pair of segments, one from each of two given sequences of lengthsm andn (i.e. every possible location for a pattern similarity), then it completes the scan in a number of computational steps proportional tom·n, leaving those pairs of segments which satisfy the similarity condition. The algorithm is based on the concept of match density, as suggested by Goad and Kanehisa (1982).
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 43
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 529-543 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper concerns sequences of letters in which certain “distinguished” words are of interest. Such sequences arise as data in numerous fields including genetics and neuroscience. A probability distribution is given for the number of occurrences of a chosen word in a randomized sequence of letters. Such words are considered “favored” if they occur more than expected at random. Favored words have been discovered in nerve impulse trains and may reflect a neural coding scheme.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 44
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 545-552 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract As the volume of protein sequence data grows, rapid methods for searching the protein sequence database become of primary importance. Rigorous comparison of sequences is obtained with the well-known dynamic programming algorithms. However, these algorithms are not rapid enough to use for routinely searching the entire database. In this paper we discuss some methods that can be used for rapid searches.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 45
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 553-566 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We give algorithms for computing the extent of similarity between two or three sequences of letters. The similarity measures we consider include a penalty for inserting gaps within the sequence in order to enhance similarity. The magnitude of the penalty for gaps is assumed to be independent of their size in order to accommodate certain biological applications. Our algorithm for three sequence comparisons, which is based on solving a system of recursive equations, improves upon the efficiency of existing methods. Although the system of recursive equations utilized by the algorithm is quite complicated as it stands, it has none the less been simplified by appeal to combinatorial considerations.
    Materialart: Digitale Medien
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  • 46
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 567-577 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Well-known dynamic programming algorithms exist for comparing two finite sequences inO(N 2) time and storage, whereN is the common sequence length. Extensions to the comparison ofM finite sequences requireO((2N) M) time and storage, making such algorithms difficult even forM=3. A simple generalization of the sequences makes it possible to obtain some results about the geometry of sequence alignments. These ideas suggest heuristic approaches to problems of comparing several sequences. IfM sequences are known to be related by a binary tree, they can be aligned inO(MN 2) time andO(N 2+NM) storage.
    Materialart: Digitale Medien
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  • 47
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 661-672 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Protein sequences of the Dayhoff databank of 1984 have been analyzed to evaluate the occurrences of the 400 dipeptides and 8000 tripeptides. Expected values and standard deviations for the di- and tripeptides were determined by Monte Carlo and binomial approximation. A condensed format containing this information, labeled a uniqueness diagram, is presented and made available in the form of a microfiche.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 48
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 827-844 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In two-state sliding filament models of muscle contraction a partial differential equation must be solved to find the cross-bridge distribution functionn(x, t). In this paper the analytical form of this function is obtained by integration along the characteristic line and special cases are presented in which the explicit expression forn(x, t) can be completely determined. These analytical solutions provide a direct mathematical connection between the microscopic contraction parameters contained in the kinetic theories and macroscopic muscle dynamics and are thus used to investigate what parameters influence the transient contractile tension in typical experimental conditions. The results of this investigation are consistent with relevant aspects of muscle physiology.
    Materialart: Digitale Medien
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  • 49
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    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 845-857 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Experiments on random binary, ternary, etc. (P=2, 3,…, 10) switching nets are reported. Behavioral cycle lengths are examined as functions of output variety,P, input connectance,K, and net size,N. Overall, output variety appears an influential, well-behaved net property. Strong, but well-behaved interactions appear among net variables. In high connectance nets, median cycle length grows approx. asP N/2. Other factors constant, one-connected nets show the shortest cycles, and connectance effects appear to converge asymptotically aroundN. Data for cycle length as a function of net size suggest a concavity not compatible with the Kauffman “square root law” (Kauffman, 1969). Evidence of a positive relationship between cycle length and run-in length is found in two-input nets; weaker evidence is obtained that in higher connectance nets this relationship becomes negative in sign. The “modular complexity” ofP〉2 nets is examined briefly.
    Materialart: Digitale Medien
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  • 50
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    Digitale Medien
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    Bulletin of mathematical biology 46 (1984), S. 869-877 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The influence of topographical situation on the spread of infection is studied. The investigation is based on a multigroup model. The population under consideration is thought to be divided into subpopulations living in regions that are separated from each other by natural barriers (mountains). Infection is carried from one region to another by migrating infectives. Migration is possible only along the river system so that the structure of the epidemiological network is that of a symmetric tree. The results allow comparison of the velocity of propagation of the epidemic for different geographical situations and allow quantification of the “channel-effect”, according to which mountainous regions are channels rather than barriers to the spread of an epidemic.
    Materialart: Digitale Medien
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  • 51
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    Bulletin of mathematical biology 37 (1975), S. 97-100 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 52
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    Bulletin of mathematical biology 37 (1975), S. 1-9 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The study of systems exhibiting a band-pass function is completed for systems whose parameters are time-dependent. In the case of periodic parametric excitations, it is demonstrated that some systems can get into “resonance” for a particular frequency. By studying this problem, a new and probably fruitful approach of some rhythmic behaviours can be made.
    Materialart: Digitale Medien
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  • 53
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 37 (1975), S. 19-35 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Analytical techniques are developed which permit objective control of asiist device driving systems. In addition to being objective, the techniques described in this paper are optimal in the sense of minimizing a performance index which consists of a term involving left ventricular power and a term involving deviations of aorta hemodynamic parameters from normal values. Comparisons are included of off-line computations and measurements on dogs with experimentally induced myocardial infarctions undergoing intraaortic balloon pumping.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 54
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 37 (1975), S. 427-458 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model simulating a cell growing in a culture medium is obtained. Using this model, various behavioral patterns of the cell are obtained under different types of disturbances, in particular when (i) a Mg2+ deficiency experiment and, (ii) a split-dose ionizing radiation experiment are carried out, (iii) when disturbances on the rate constants of the biochemical reactions taking place in the nucleus of the cell are applied, and (iv) when the cell's interior components are perturbed. The cell model results obtained agree well with experimental results for the Mg2+ and split dose experiments, and explain the mechanism of the split dose radiation experiment without the need to introduce additional axioms (e.g. healing processes) into the dynamics of the cell. Conditions are obtained which cause the cell to behave in a rapidly growing ‘tumor-like’ mode; it is shown that once the cell moves into this ‘tumor-like’ mode, its behavior is irreversible, i.e. if a disturbance of opposite type is then applied to the ‘tumor’ cell, the cell will not revert back to its original normal behavior.
    Materialart: Digitale Medien
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  • 55
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    Digitale Medien
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    Bulletin of mathematical biology 37 (1975), S. 85-90 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Solution of the equation that describes simulatenous liquid flow and diffusion in a spherical model of the vitreous body of the eye shows that a small dissolved specie can move both anteriorly and posteriorly from a source behind the lens even though there is a slow liquid movement almost entirely in the posterior direction. This results explains why tracer studies using large particles (dyes or colloids) show only a posterior flow, whereas studies using sodium ion show anterior movement as well.
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  • 56
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    Digitale Medien
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    Bulletin of mathematical biology 37 (1975), S. 101-107 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 57
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    Digitale Medien
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    Bulletin of mathematical biology 37 (1975), S. 111-111 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 58
    Digitale Medien
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    Bulletin of mathematical biology 37 (1975), S. 221-221 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 59
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 37 (1975), S. 255-268 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The equations relating hybridized RNA to free RNA, in the case of simple hybridization, or to ratio of labelled and unlabelled RNA in competitive hybridization, are derived. Analysis of the equations shows how hybridization data may be used to infer properties of the distribution of components in an RNA mixture, or the relation between two distributions in competitive hybridization. A critical examination of the assumptions underlying the equations indicates that some of then may be violated in certain cases, or have no current support, evidential or theoretical. The consequences of such qualifications for the interpretation of hybridization data are indicated.
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  • 60
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    Bulletin of mathematical biology 37 (1975), S. 589-636 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The steady state spatial patterns arising in nonlinear reaction-diffusion systems beyond an instability point of the thermodynamic branch are studied on a simple model network. A detailed comparison between the analytical solutions of the kinetic equations, obtained by bifurcation theory, and the results of computer simulations is presented for different boundary conditions. The characteristics of the dissipative structures are discussed and it is shown that the observed behavior depends strongly on both the boundary and initial conditions. The theoretical expressions are limited to the neighborhood of the marginal stability point. Computer simulations allow not only the verification of their predictions but also the investigation of the behavior of the system for larger deviations from the instability point. It is shown that new features such as multiplicity of solutions and secondary bifurcations can appear in this region.
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  • 61
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    Circuits, systems and signal processing 3 (1984), S. 267-294 
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract Pipeline techniques have been successfully applied to speeding up processing in both general- and special-purpose digital computers. Application of these techniques to nonrecursive (FIR) filters has been suggested and is quite straightforward. Application to recursive (IIR) filters has not previously been shown. In this paper, the technique for applying pipeline techniques to recursive filters is shown and the advantages and disadvantages of the technique are discussed. Using these techniques, recursive digital filters operating at hitherto impossibly high rates can be designed.
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  • 62
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    Circuits, systems and signal processing 3 (1984), S. 295-314 
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract The long-standing problem of reconstructing a function from its samples is considered again. Assuming a sequence of oversampled values, a set of appropriate idealized reconstruction filters can be defined, which do not suffer from instability or slow convergence. The realization — a cascade of a nonrecursive digital filter, D/A-converter, and a fixed/analog smoothing filter — demands the design of the digital filter for the increase of the sampling rate. The design of this nonrecursive filter is the purpose of this paper. Approximations in the frequency as well as in the time domain are presented.
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  • 63
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    Circuits, systems and signal processing 3 (1984), S. 105-122 
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract In this paper we formulate power systems as nonlinear nearly Hamiltonian systems. Using the invariance principle for ordinary differential equations, necessary and sufficient conditions for asymptotic stability are established and a new method of estimating the domain of attraction of the stable equilibrium point is developed. The present results constitute a novel approach to stability analysis and involve the following three steps: a. Given a system with dissipation, the stability of its equilibrium is ascertained by determining the stability of the associated conservative system. b. Attractivity of the stable equilibrium of the entire system (with dissipation) is determined from the system topology. c. An estimate of the domain of attraction of the asymptotically stable equilibrium is obtained by making use of results obtained in (a) and (b). The stability criterion developed in this paper sheds new light on the mechanism of instability in power systems and it provides analytical verification to the concept of the potential-energy boundary surface (PEBS). The PEBS is a hypersurface which makes up a part of the boundary of the domain of attraction of the stable equilibrium in a power system. The existence and properties of the PEBS have thus far been deduced primarily via simulations and heuristic methods.
    Materialart: Digitale Medien
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  • 64
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    Circuits, systems and signal processing 3 (1984), S. 161-176 
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract In conventional television systems, picture scanning in vertical and temporal directions is usually very defective with regard to the sampling theorem. In this paper some deficiencies such as aliasing, line-structure distortion, line flickering, and large-area flickering are investigated with regard to their dependence on the inter-lacedpicture-scanning process. The three-dimensional reconstruction filtering of the sampled picture is especially analyzed with respect of the viewer's perception. Furthermore, it will be shown that in connection with a new concept of picture scanning published earlier [1], [2], a flat-field reproduction without any 25/30-Hz flicker can be achieved by vertical filtering only. This is true even though the final reproduction by the monitor is performed with interlace. The vertical filtering can then be optimized in the sense of maximum picture sharpness and resolution with negligible ringing as well. Practical results are given in this paper.
    Materialart: Digitale Medien
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  • 65
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    Circuits, systems and signal processing 3 (1984), S. 177-191 
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract In this paper a new type of “velocity-selecting/rejecting filter” which passes or stops a particular event in a seismic signal is proposed. The velocity-selecting filter is based on a time-space band-pass filter with sharp passband for a particular direction, and similarly, the velocity-rejecting filter is based on a time-space band-stop filter. A technique for designing such filters, in terms of an infinite-impulse-response (IIR) filter, is presented, in which a rotated version of separable filter is used. Finally, numerical examples are included to illustrate the design theory.
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  • 66
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    Circuits, systems and signal processing 3 (1984), S. 347-359 
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 67
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    Circuits, systems and signal processing 3 (1984), S. 315-325 
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract A special type of factorization for operators defined on partially ordered Hilbert resolution spaces is considered. The main result includes, as a particular case, the classical Schur-Coleski triangular factorization. Connections with stochastic optimization and image-processing problems are established.
    Materialart: Digitale Medien
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  • 68
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    Circuits, systems and signal processing 3 (1984), S. 409-417 
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract In a recent paper on nonlocal expansions necessary and sufficient conditions are given under whichf −1 has a generalized power series expansion, whenf is an invertible locally Lipschitz map between certain general subsets of a complex Banach space. Here we establish the validity of a conceptually interesting algorithm for obtaining the expansion. Basically, we show that a certain contraction mapping iteration generates iteratesℐ 1,ℐ 2,... such that eachℐ k yields all of the terms of the generalized power series expansion off −1 up to order (k + 1), assuming merely that the expansion off −1 exists. An earlier different result along related lines is mentioned.
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  • 69
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    Circuits, systems and signal processing 3 (1984), S. 447-475 
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract The representation of functions in a basis function expansionz(t)= ∑k=1/∞=,a k〉 x k (t) is straightforward when the basis functionsx k (t) are orthogonal. There has been very little work up to this time in determining how to use nonorthogonal bases in signal representation. On the other hand, applications in data compression and signal synthesis often require using specific tailor-made bases. Presented here is a method for constructing very general nonorthogonal bases. Orthogonality has often been used to show that a basis spans the set of functions of interest and to calculate the coefficients of the representation. In this paper, both of these fundamental aspects are addressed for nonorthogonal bases. A new basis {y k (t)} is obtained by performing a linear transformation on a known existing basis {x k (t)}. This transformation is constructed such that the coefficients of signal representation on the new basis are readily found. Then, a useful and sufficient condition is placed upon the new basis such that representations converge. The fundamental methods are applied to the standard examples of signal representation. The complex sinusoids, the Rademacher functions, the orthogonal polynomials, and the decaying exponentials are used as the original basis {x k (t)} from which a new basis {y k (t)} is generated. Two examples are given to illustrate general applications: one in signal synthesis and one in signal analysis.
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  • 70
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    Bulletin of mathematical biology 37 (1975), S. 109-109 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
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  • 71
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    Bulletin of mathematical biology 37 (1975), S. i 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
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  • 72
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    Bulletin of mathematical biology 37 (1975), S. 139-146 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Krylov-Bogoliubov-Mitropolsky perturbation method was used to study the effect of nonlinearity in the Volterra-gause-Witt (VGW) model for a two species prey-predator system. The first order corrections to both the frequency of oscillation and the amplitude of the linearized system were computed. It was found that the basic qualitative features of the nonlinearity are exhibited by the first order result. We have also discussed the Lotka-Volterra problem which is a special case of VGW model.
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  • 73
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    Bulletin of mathematical biology 37 (1975), S. 147-160 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper presents a mathematical analysis of a tumor model first proposed by Skipper and Zubrod. The tumor model is comprised of three compartments, a proliferative compartment, a nonproliferative but viable compartment, and a dead compartment. By the suitable selection of functions describing loss of cells from the proliferative and nonproliferative compartments, the model is capable of describing tumor behavior during periods of growth and drug treatment. The loss functions during treatment are related to pharmacokinetic functions and may be chosen according to known drug properties. Tumor properties may be simulated by the appropriate choice of cell cycle parameters. It therefore seems feasible to simulate tumor behavior for scheduled treatment with chemotherapeutic agents. Another important result of this analysis is the derivation of a fraction labelled mitosis function which incorporates the nonproliferative compartments.
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  • 74
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    Bulletin of mathematical biology 37 (1975), S. 161-180 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Techniques of modelling and simulation are discussed as they relate to bioengineering systems. The advantages and disadvantages of different analytical engineering methods utilized to gather information concerning the behavior of complex physiological and neuromuscular control mechanisms are explained. An Inners Criterion is developed to determine if the roots of a model lie within a certain “biologically realistic region” ΓB, in the complex plane which contains the roots of linearized models for a large variety of neuromuscular systems. Several algorithmic methods based on the Jury Inners Test are described which specify whether the model roots lie within the desired region, thereby providing an indication as to the validity of the proposed model. This technique can help to eliminate tedious simulation on an unrealistic model with roots lying far outside this region. An exemplary model for control of vergence eye movements is presented and shown to satisfy the ΓB criterion; several counter-examples are also discussed. The Inners approach can be adapted to other classes of bioengineering systems by specifying the region based on models that are contained in the class of interest.
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  • 75
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    Bulletin of mathematical biology 37 (1975), S. 215-218 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
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  • 76
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    Bulletin of mathematical biology 37 (1975), S. 220-220 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
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  • 77
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    Bulletin of mathematical biology 37 (1975), S. 223-254 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper I consider how information is required to specify various systems. It is shown that the transitive information of any physical system, is distributed among three distinct components. One of these, the selective component, is required to specify the elemental parts of the system. Another, the connective component, is required to specify the macrostructure of the system; that is the way the parts are put together. And a third, the conformative component, is required to specify the intrinsic complexion or microstructure of the system. An interesting method for analyzing branched systems which takes account of connective ambiguity is described in some detail. The relationship between information and entropy, known as the Clausius-Shannon Identity, is then discussed with reference to selected thermodynamic models: and that aspect of information which is often overlooked, namely the distinction, between transitive and intransitive information is highlighted. The applications (or perhaps more correctly, the limitations of applying this treatment) to problems of biological interest are also indicated.
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  • 78
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    Bulletin of mathematical biology 37 (1975), S. 269-275 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper discusses two compartment models with interaction allowed between the compartments. The total number of particles in the system at any time is discussed along with the number to the found in each separate compartment. An interesting result is that the number of particles in each of the two compartments areindependent random variables. Some asymptotic results are also given. The paper is a continuation of some earlier work by the author.
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  • 79
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    Bulletin of mathematical biology 37 (1975), S. 277-289 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract General criteria which either preclude time-periodic dissipative structure solutions or imply asymptotically steady solutions are derived for generic systems of reaction-diffusion equations ∂c i /∂t =D i ∇2 c i +Q i (c) subject to boundary conditions of practical interest, where the enumerator indexi runsl ton, c i =c i (x,t) denotes the concentration or density of theith participating molecular or biological species,D i is the diffusivity constant for theith species, andQ i (c), an algebraic function of then-tuplec=(c 1,...,c n ), expresses the local rate of production of theith species due to chemical reactions or biological interactions. It is demonstrated that certain functionals ofc which decrease monotonically with time can often be found, as exemplified here for Volterra and Verhulst-Volterran-species model systems, and thus time-periodic dissipative structure solutions are precluded for such systems of reaction-diffusion equations. It is shown that all solutions to a generic system of reaction-diffusion equations evolve dynamically to a unique steady state, $$\mathop {\lim }\limits_{t \to \infty } c_i (x, t) = \hat c_i (x)$$ , if the diffusivity constants are all sufficiently large in magnitude. A necessary condition for the existence of a periodic solution (either spatially uniform or non-uniform) is formulated in terms of the curl ofQ(c) inc-space. Finally, necessary and sufficient conditions are derived for the existence of time-periodic dissipative structure solutions in cases of “weak diffusion” with the reaction rate terms dominant in the governing equations.
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  • 80
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    Bulletin of mathematical biology 37 (1975), S. 323-365 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model nonlinear network involving chemical reactions and diffusion is studied. The time evolution and bounds on the steady state solutions are analyzed. Spatially ordered solutions of the equations of the dissipative structure type are found by bifurcation theory. These solutions are calculated analytically and their qualitative properties are discussed.
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  • 81
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    Bulletin of mathematical biology 37 (1975), S. 637-657 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Models based on molecular mechanisms are presented for pattern formation in developing organisms. It is assumed that there exists a diffusion governed gradient in the morphogenetic field. It is shown that cellular differentiation and the subsequent pattern formation result from the interaction of the diffusing morphogen with the genetic regulatory mechanism of cells. In a second stage it is shown that starting from a homogeneous distribution of morphogen, polarity can be generated spontaneously in the morphogenetic field giving rise to the establishment of a gradient. The stability of these gradients is demonstrated. The onset of a morphogenetic gradient and pattern formation are combined in a single coherent model. Size invariance and its biological implications are discussed.
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  • 82
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    Bulletin of mathematical biology 46 (1984), S. 81-102 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The temperature regulation in homothermic animals is an example of a negative feedback system. It shows sudden changes of parameter values, and therefore suggests the use of catastrophe theory for its description. This paper reports on work done on the human temperature regulation mechanism to shows that the five-dimensional dual butterfly catastrophe model is sufficient for its description. Nearly all experiments reported in the literature overlook the dynamic multiparametric nature of the process. Use of catastrophe theory, on the other hand, shows that one cannot find a model with fewer than five parameters for such a system. From work by Benzinger and Kitzinger, the exact shape of part of the corresponding bifurcation set is determined.
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  • 83
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    Bulletin of mathematical biology 46 (1984), S. 103-114 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper is an analytical study on the pulse wave velocities in the aorta. In conformity to a physiologic state of loading, the distensibility of the vessel wall has been accounted for. The wall material is treated by using the theory of large elastic deformations. The orthotropicity of wall tissues and the effect of the surrounding tissues have been incorporated in the analysis which is based on the use of the strain energy function suggested by Vaishnavet al. Numerical values of the wave velocities of the canine middle descending thoracic aorta are computed by using the derived analytical expressions.
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  • 84
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    Bulletin of mathematical biology 46 (1984), S. 41-80 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The theory of a symmetrical 3-barrier, 4-site, single-filing ionic channel is developed. The model goes beyond earlier models by including additional sites, as well as barriers which need not be symmetrical in the applied field, and contains the earlier models as special cases. It is itself a special case of the most general 4-site model, which has 5 barriers. By considering the barriers at the mouth and middle of the channel to be sufficiently larger than the barriers separating the sites in each channel half, these barriers can be neglected; thus this case reduces to a 3-barrier model where the sites in each channel half can then be assumed to be in equilibrium with each other. The alternative 3-barrier, 4-site case, where the barrier between the sites is considered to be larger than that at the mouth of the channel, is considered elsewhere. Pure cation permeation is considered and only single-salt properties of the system are analyzed, namely occupancy, conductance, flux ratio exponent and current-voltage relation. The concentration dependences of these properties are computed and interrelated and, where possible, also given in analytical form. The mathematical relations are obtained for a channel which is symmetrical around its middle, which is the appropriate assumption for the gramicidin channel. However, the barriers themselves are allowed to be asymmetric with respect to the potential dependence, which has been found to be essential for gramicidin. Mathematically, a straight-forward matrix formulation is used; but a general theoretical method is presented for reducing a complex model (with more than 2 sites) to a simpler cases when equilibrium exists across one or several barriers, as is often the cases. This method is a prototype which makes analytical solutions of complex barrier models possible in many cases.
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  • 85
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    Bulletin of mathematical biology 46 (1984), S. 219-227 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A chain-like arrangement of four urns (a catenary system) into which different color balls (white, corresponding to radio atoms, and black, corresponding to stable atoms) are being transferred is used to simulate the transport of atoms down the GI tract of man and animals. Into the first urn (stomach) are placedw o white balls andr black balls while in the 2nd (small intestines) and 3rd (large intestines) urn, onlyr blacks are put in, with no whites. A sample of sizer is transferred from the 1st, 2nd and 3rd urns to the 2nd, 3rd and 4th (infinite universe) urns. From the random variable difference equations the first and second moments for the distribution of the number of radio atoms present in each urn are obtained. The variance of the contents of radioatoms in the excretion urn is
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  • 86
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    Bulletin of mathematical biology 46 (1984), S. 229-234 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A power series solution is presented which describes the steady-state concentration profiles for substrate and product molecules in immobilized enzyme systems. Diffusional effects and product inhibition are incorporated into this model. The kinetic consequences of diffusion limitation and product inhibition for immobilized enzymes are discussed and are compared to kinetic behavior characteristic of other types of effects, such as substrate inhibition and substrate activation.
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  • 87
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    Bulletin of mathematical biology 46 (1984), S. 205-217 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The use of spheroids as a tumor model has become commonplace since it was discovered that many cell lines can form spheroids when grown on a surface to which the cells cannot attach. This culture system complicates experiments which depend on oxygen supply because the oxygen concentration in the vicinity of a stationary spheroid has not been well defined. We present in this paper solutions to the oxygen diffusion equation for simple geometries: a spheroid in an infinite stationary medium and in a finite spherical stationary medium. Comparison of these solutions provides an estimate of the oxygen supply to a spheroid in a Petri dish. We show that typical spheroids can be expected to cause a substantial depletion of the oxygen in the nearby medium. Any disturbance of the medium or the spheroids will temporarily increase the oxygen supply. We provide a method for estimating the rate of return to equilibrium in the finite cases. These results indicate that the oxygen supply to stationary spheroids can be altered temporarily by small movements or changes in temperature which cause convection currents, or permanently by changes in the depth of the medium.
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  • 88
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    Bulletin of mathematical biology 46 (1984), S. 235-246 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Alternative sufficient conditions are derived that guarantee the stability of spatially heterogenous steady-state distributions of motile aerobic bacterial populations attracted chemotactically by oxygen, motile anaerobic populations repelled by oxygen, and the oxygen concentration itself through a stationary aqueous medium. In particular, it follows from the latter criteria that the heterogeneous steady-state distributions for cylindrical regions with arbitrary cross-sections, uniform depth and mixed Dirichlet-Neumann boundary conditions on the oxygen concentration (appropriate to certain still-water bodies in nature) are stable with respect to arbitrary perturbations in the bacteria cell and the oxygen distributions.
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  • 89
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    Bulletin of mathematical biology 46 (1984), S. 339-355 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Closed positive feedback loops of catalytic reactions between macromolecules, or hypercycles, provide a kinetic mechanism whereby each Species serves to catalyze selfreproduction of its successor in the loop. Hypercycles of five members or more evolve into limit cycles characteristic of a biochemical clock. Computer study of the coupled non-linear differential equations which describe these systems shows that the periodT n of then-species limit cycle is given byT n=nτn, where τn is an elemental repeat period reflecting translational time invariance. Analytic solutions of the equations are developed so that the time evolution of elementaryn-hypercycles can be traced in dynamical detail. It is shown that the magnitude of τn is, to good approximation, a linear function ofn. For a givenn, τn is a very sensitive function of the relative concentration a given member of the loop has at the time its predecessor dominates the state of the hypercycle. These concentrations decrease with increasingn. Aroundn=15 they become so small that elementary hypercycles become unstable against disruptive concentration fluctuations. Species concentrations for more realistic hypercycles tend not to be as small, so that the present estimate of a maximum number of components is a lower bound.
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  • 90
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    Bulletin of mathematical biology 46 (1984), S. 399-406 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The technique of the probability generating function is used to derive the stochastic differential equations for a nonlinear model based on Eigen and Schuster's theory of biomolecular selection and evolution. The stabilities of various steady states are analyzed by using the linear stability approximation. The instability of a small starting population is investigated numerically. The minimum starting populations required for steady-state survival are then estimated for a wide range of parameters.
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  • 91
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    Bulletin of mathematical biology 46 (1984), S. 389-398 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Some morphological features of the human bronchial tree were simulated by computergenerated trees. The trees were ordered by the methods of Horsfield and Strahler. Delta, the difference between the Horsfield orders of the two branches at a bifurcation, was determined by pseudorandom numbers generated according to a distribution of probabilities defined on input. By trial and error a distribution was found which resulted in trees being generated with average Strahler order branching ratios of 2.82, similar to a real bronchial tree. Branching angles and length ratio could also be defined on input. By varying these input parameters it was found that the form of the tree was quite sensitive to them, and that by a suitable choice the intrasegmental part of the bronchial tree could be simulated. It is concluded that branching ratio, length ratio, mean branching angles and distribution of delta are controlled within tight limits in the bronchial tree, and this may support the concept of optimal design.
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  • 92
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    Bulletin of mathematical biology 46 (1984), S. 407-422 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper perturbation methods are used for the mathematical analysis of coupled relaxation oscillators. This study covers entrainment by an external periodic stimulus as well as mutual entrainment of coupled oscillators with different limit cycles. The oscillators are of a type one meets in the modeling of biological oscillators by chemical reactions and electronic circuits. Special attention is given to entrainment different from 1∶1. The results relate to phenomena occurring in physiological experiments, such as the periodic stimulation of neural and cardiac cells, and in the non-regular functioning of organs and organisms, such as the AV-block in the heart.
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  • 93
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    Bulletin of mathematical biology 46 (1984), S. 423-446 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A new, more realistic model of the action of ionizing radiation on mammalian cells growingin vitro is presented. Although this model requires a large number of parameters, these are linked to biologically observable quantities rather than being abstract sensitivities, as had previously been the case. Three different stochastic processes are required: {X(t);t ∈ [0, τ]}, representing damage alterations during irradiation; {(X(t), S(t));t ∈ [τ, τ+T D]}, representing changes in both damageX(t) and cell cycle positionS(t) during the post-irradiation cell cycle; and {N x(t);t ∈ [0,T G]}, representing the subsequent colony growth process conditioned on the value ofX(τ+T D). The assumptions used to define these processes extend a previous model of short term DNA damage formation and repair (Nelson S. J. 1982,Radiat. Res. 92, 120–145) to include the influence of cell cycle progression on damage in the irradiated cell and the effect of permanent inherited damage on the daughter cells' colony growth pattern. Expressions corresponding to commonly measured radiation effects are derived from the model and compared with predictions from previous models. It is found that these previous models oversimplified the mechanism of radiation action because they did not adequately represent repair during irradiation, the influence of radiation-induced cycle delays and damage inheritance by any daughter cells. Suggestions are then made for ways in which the new model can be used to test the importance of these effects.
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  • 94
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    Bulletin of mathematical biology 46 (1984), S. 461-465 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
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  • 95
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    Bulletin of mathematical biology 46 (1984), S. 467-472 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
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  • 96
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    Bulletin of mathematical biology 46 (1984), S. 447-460 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A stochastic approach is utilized to develop a model equation capable of describing the time course of germination in a sample of bacterial spores. The time required by a spore to complete the change characteristic of germination consists of an initial interval of no change followed immediately by the duration of the change itself. The experimental basis of the proposed model is the observation that each of these time intervals is distributed over a range of values in a spore sample. Mixed continuous and discrete probabilities are employed in arriving at an average single-spore germination curve which, to a different scale, describes the sample in time.
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  • 97
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    Bulletin of mathematical biology 46 (1984), S. 473-500 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Mathematical methods for comparison of nucleic acid sequences are reviewed. There are two major methods of sequence comparison: dynamic programming and a method referred to here as the regions method. The problem types discussed are comparison of two sequences, location of long matching segments, efficient database searches and comparison of several sequences.
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  • 98
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    Bulletin of mathematical biology 46 (1984), S. 579-590 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An algorithm for nucleic acid and protein sequence alignment is presented. It is a non-metric local similarity minimal-difference algorithm and in the current implementation, assembles the matching regions found into a pseudo-global format. Its strengths are its speed of execution and the especially convenient presentation of its output. The algorithm is intended for use in sequence melding and local (small-region) similarity searching. It is not designed to replace a metric Needleman-Wunsch-Sellers-type similarity algorithm. The program is written in FORTRAN and is designed to be easily transportable to a variety of computer systems.
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  • 99
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    Bulletin of mathematical biology 46 (1984), S. 591-621 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This is a review of past and present attempts to predict the secondary structure of ribonucleic acids (RNAs) through mathematical and computer methods. Related areas covering classification, enumeration and graphical representations of structures are also covered. Various general prediction techniques are discussed, especially the use of thermodynamic criteria to construct an optimal structure. The emphasis in this approach is on the use of dynamic programming algorithms to minimize free energy. One such algorithm is introduced which comprises existing ones as special cases.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 100
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 46 (1984), S. 641-659 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is shown that the concepts of grammar complexity and syntactic structure provide a useful mathematical framework for the investigation of some current problems in protein structure. Grammar complexity gives a measure of the degree of aperiodicity of a sequence and also an optimization criterion for evaluating amino acid categorizations. Three systems of amino acid categorization are compared in relation to their value for describing molecular architecture.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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