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  • Springer  (139,659)
  • 1985-1989  (48,496)
  • 1980-1984  (91,163)
  • 1985  (48,496)
  • 1984  (48,999)
  • 1980  (42,164)
  • 1
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    Bulletin of mathematical biology 46 (1984), S. 967-969 
    ISSN: 1522-9602
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 971-972 
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    Bulletin of mathematical biology 46 (1984), S. 973-974 
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    Bulletin of mathematical biology 47 (1985), S. 1-21 
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    Notes: Abstract A general mechanism underlying bursting is proposed and described. It consists of two coupled nonlinear oscillators with different frequencies, where the slower oscillator alternatively switches the faster one on and off. This mechanism is shown to work in an extended Bonhoefer-van der Pol oscillator as well as in a modified version of the Hodgkin-Huxley equations.
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    Bulletin of mathematical biology 47 (1985), S. 145-153 
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    Notes: Abstract Pointwise upper and lower bounds for the solution of a class of nonlinear diffusion problems with Michaelis-Menten kinetics are presented. Simple analytical bounding curves are obtained and for an illustrative case the calculated values bound the recent numerical solution of P. Hiltmann and P. Lory, 1983.Bull. math. Biol. 45, 661–664.
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    Bulletin of mathematical biology 42 (1980), S. 131-135 
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    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for diffusion problems with Michaelis-Menten kinetics. In an illustrative calculation we obtain an extremely accurate variational solution in good agreement with the numerical solution of McElwain (1978).
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    Bulletin of mathematical biology 42 (1980), S. 137-141 
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    Bulletin of mathematical biology 42 (1980), S. 181-189 
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    Notes: Abstract Necessary and sufficient conditions for primitivity of a product of two Leslie matrices are given. Such a product could be used in modeling the growth of a population governed alternately by two different sets of fertility and survival parameters.
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    Bulletin of mathematical biology 42 (1980), S. 173-180 
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    Notes: Abstract Zadeh's transfer function method for linear time-variable systems is used to apply frequency-domain analysis to a periodically time-varying elastance model of the left ventricle. Left ventricular pressure computed from the system function of the time-varying elastance and the phasors of aortic flow shows a typical waveform of the measured ventricular pressure.
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    Bulletin of mathematical biology 47 (1985), S. 337-342 
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    Notes: Abstract The cellular response in terms of steady-state variance of cell mass concentration to fluctuations in incoming nutrient concentration to a chemostat has been examined. A white noise process is assumed to describe incoming nutrient concentration fluctuations and the variance of cell mass concentration has been found to depend on cell yield (a lumped measure of nutrient concentration fluctuation magnitude and lifetime) and two system time constants.
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    Bulletin of mathematical biology 47 (1985), S. 343-365 
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    Notes: Abstract In a well-known collection of his essays in cognitive psychology Miller (The Psychology of Communication. Penguin, 1974) describes in detail a number of experiments aiming at a determination of the limits (if any) of the human brain in processing information. He concludes that the ‘channel capacity’ of human subjects does not exceed a few bits or that the number of categories of (one-dimensional) stimuli from which unambiguous judgment can be made are of the order of ‘seven plus or minus two’. This ‘magic number’ holds also, Miller found, for the number of random digits a person can correctly recall on a row and also the number of sentences that can be inserted inside a sentence in a natural language and still be read through without confusion. In this paper we propose a dynamical model of information processing by a self-organizing system which is based on the possible use of strange attractors as cognitive devices. It comes as an amusing surprise to find that such a model can, among other things, reproduce the ‘magic number seven plus-minus two’ and also its variance in a number of cases and provide a theoretical justification for them. This justification is based on the optimum length of a code which maximizes the dynamic storing capacity for the strings of digits constituting the set of external stimuli. This provides a mechanism for the fact that the ‘human channel’, which is so narrow and so noisy (of the order of just a few bits per second or a few bits per category) possesses the ability of squeezing or ‘compressing’ practically an unlimited number of bits per symbol—thereby giving rise to a phenomenal memory.
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    Bulletin of mathematical biology 47 (1985), S. 409-424 
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    Notes: Abstract Electrical polarization of an artery or an arteriole may be modeled by the use of equations developed for two-dimensional cable theory. Two special cases have previously been solved: those corresponding to the case in which the radius is either zero (one-dimensional cable theory) or infinite. This paper presents the general solution.
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    Bulletin of mathematical biology 47 (1985), S. 367-407 
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    Notes: Abstract The distance geometry approach for computing the tertiary structure of globular proteins emphasized in this series of papers (Goelet al., J. theor. Biol. 99, 705–757, 1982) is developed further. This development includes incorporation of some secondary structure information—the location of alpha helices in the primary sequence—in the algorithm to compute the tertiary structure of alpha helical globular proteins. An algorithm is developed which estimates the interresidue distances between chain-proximate helices. These distances, in conjunction with the global statistical average distances obtainable from a database of real proteins and determined by the primary sequence of the protein under study, are used to determine the tertiary structure. Five proteins, parvalbumin, hemerythrin, human hemoglobin, lamprey hemoglobin, and sperm whale myoglobin, are investigated. The root mean square (RMS) errors between the calculated structures and those determined by X-ray diffraction range from 4.78 to 7.56 Å. These RMSs are 0.21–2.76 Å lower than those estimated without the secondary structure information. Contact maps and three-dimensional backbone representations also show considerable improvements with the introduction of secondary structure information.
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    Bulletin of mathematical biology 47 (1985), S. I 
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    Bulletin of mathematical biology 47 (1985), S. 425-434 
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    Notes: Abstract If a plane membrane consists of patches, each with a given area and a given diffusion coefficient, then the transient of the total unidirectional flux of a diffusing substance (as defined experimentally by Ussing) is predictable. Here the inverse problem is studied: given only the observed transient of the total unidirectional diffusion flux, the unknown membrane heterogeneity transverse to the flux is to be quantified. The ratio of the arithmetic and of the harmonic means (both area-weighted) of the diffusion coefficients, evaluated over the membrane, is expressed in terms of the observed transient alone and is used to characterize the heterogeneity. A unique exact solution of the inverse problem for two kinds of patches is obtained in closed form. A singular limit of this solution pertains to currently postulated models of endothelial membranes, for which a characteristically shaped transient is predicted.
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    Bulletin of mathematical biology 47 (1985), S. 435-435 
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    Bulletin of mathematical biology 47 (1985), S. 437-474 
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    Notes: Abstract Major types of sequence similarity searching (often, and incorrectly, called ‘homology’ searching) are reviewed and examples of each are presented. The features and limitations of each type of program, and individual implementations of each type are discussed. Two pairs of sequences are used as examples to show how implementations of each type differ in their results and their presentation. Both local and global alignment programs are examined, and the programs reviewed run on many different types of computer architectures, from laboratory computers such as the IBM PC, minicomputers such as the VAX, to large mainframe computers such as DEC-10/20 series.
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    Bulletin of mathematical biology 47 (1985), S. 489-494 
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    Notes: Abstract Criteria for the existence of globally stable equilibria in classical Volterra predator-prey systems represented by loop graphs are provided by comparing the community matrix with a matrix belonging to matrix classS W .
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    Bulletin of mathematical biology 47 (1985), S. 475-487 
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    Notes: Abstract Ordinary reaction-diffusion mechanisms do not account for size invariance properties of morphogenetic fields. We show that such a failure results from ignoring cell individuality. By considering purely topological factors, such as the number of intercellular contacts or the extent of the cell surface in contact with neighbouring cells, size invariance exists in reaction-diffusion systems. Our results are general, model independent and may be applied to any multi-unit ensemble exhibiting coherent behaviour.
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    Bulletin of mathematical biology 47 (1985), S. 495-502 
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    Notes: Abstract The artery is treated as a thick-walled cylindrical shell. Using the large deformation theory, an analytical expression for the pulse wave speed is obtained and the effect of twist on the wave speed is discussed. Numerical results indicate that although phase velocity increases with pressure, it decreases with increasing twist angle.
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    Bulletin of mathematical biology 47 (1985), S. 545-550 
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    Notes: Abstract The effect of the shape of stenosis on the resistance to blood flow through an artery with mild local narrowing has been studied. It is shown that the resistance to flow decreases as the shape of stenosis changes and the maximum resistance is attained in the case of symmetric stenosis.
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    Bulletin of mathematical biology 47 (1985), S. 535-543 
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    Notes: Abstract A set of 2n−2 relations (edges) and a set ofn−1 hypothetical taxonomic units (HTUs) derive from the estimation of a binary phylogeny of a set ofn operational taxonomic units (OTUs). We propose an easy way for numbering thesen−1 hypothetical taxonomic units, as well as for then−2 interior points of an unrooted binary phylogeny. We also present an alternative method to the one proposed by Rohlf (Bull. math. Biol. 45, 33–40, 1983) for numbering the π i=1 n (2i−3) possible rooted binary phylogenies and the π i=1 n−1 (2i−3) possible unrooted binary phylogenies conerning a set ofn operational taxonomic units. An illustrative example of the method is presented. It is hoped that some studies in phylogenetics will become more accessible, from the viewpoint of computational economy, by the use of this method.
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    Bulletin of mathematical biology 47 (1985), S. 503-512 
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    Notes: Abstract The heterogeneity of rat brain opiate receptors was examined by analyzing competition data. The binding of three prototypical tritiated opioid agonists, [3H]-dihydromorphine ([3H]-DHM), [3H]-D-ala2-D-leu5-enkephalin ([3H]-DADLE), and [3H]-ethylketocyclazocine ([3H]-EKC) was determined in the presence of varying concentrations of each of these unlabeled ligands, generating nine displacement curves. A computer program was then used to find the best fit of a model system to these data, assuming two, three or four independent binding sites. The best fit was a four-site model. One of these sites is specific for DHM; two are relatively selective for DHM and DADLE respectively, but also bind EKC. The remaining site binds only EKC with high affinity. These results, together with displacement data using naloxone, FK33824, and D-ala2-met5-enkephalinamide, are discussed in terms of current opiate receptor models.
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    Bulletin of mathematical biology 47 (1985), S. 651-668 
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    Notes: Abstract This work continues with an examination of capillary exchange models as operators, namely the operatorsO k andK αk relating extravascular and intravascular concentration to input for the Krogh cylinder model of a single capillary, a model basic to many organ models. Fundamental algebraic and analytic properties are presented: the operators belong to a commutative Banach algebra; an addition theorem holdsK αk +K βk =K α+β,k ; the operatorK αk has an inverse;K αk -1 , (as an operator on LebesgueL p space or on the locally integrable functions); partial derivatives are given forK αk [f](t) andO k [f](t) (sensitivity functions); and inequalities are established for the derivatives. Dominance relations between model curves are inferred. Error bound formulas are presented forK andO as bounds on ‖K αk f-K βl f‖ p and ‖O k f-O l f‖ p for allL p . Consequent limitations on relative errors are shown. The implications for operators on a finite time interval are deduced.
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    Bulletin of mathematical biology 47 (1985), S. 669-683 
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    Notes: Abstract The nonlinear nature of the hydraulic permeability, as well as the corresponding pressure and displacement fields, in a soft tissue are studied for steady-state permeation. From a two-phase continuum model analytical expressions are derived that can be used with the results from a permeation experiment to determine the dependence of the permeability on the strain. In the process it is found that, because of the compaction of the tissue arising from fluid flow, it is necessary to distinguish between the apparent and intrinsic permeability. The former, which is an averaged quantity, is the permeability usually obtained in permeation studies. However, as shown from the analysis, it can differ substantially from the latter, which is the local permeability in the tissue.
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    Bulletin of mathematical biology 47 (1985), S. I 
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    Bulletin of mathematical biology 47 (1985), S. 695-695 
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    Bulletin of mathematical biology 47 (1985), S. 697-738 
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    Notes: Abstract The analytic, eccentric spheres model of the torso was used to examine the validity of approximating the ‘infinite medium’ potential by integrating ‘finite medium potentials’ over the torso surface. Although idealized, the analytic model is sophisticated enough for all important torso conductivity and geometry parameters to be preserved in the formulation. The model generates both ‘finite medium’ potentials (for which the torso is surrounded by air) and also ‘infinite medium’ potentials (for which the outermost layer of the torso extends outward to infinity). The finite medium torso potentials were integrated over the torso surface in accordance with the approximation used by many investigators in an effort to make the surface distribution more representative of the primary cardiac sources. The resulting potential distribution was compared with the true infinite medium potential, in which the effects of internal inhomogeneities (secondary sources) were taken into account. The difference between the two representations was found to be significant, and caution should be used when interpreting such data.
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    Bulletin of mathematical biology 47 (1985), S. 739-748 
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    Notes: Abstract Environ analysis, an input-output analysis for models of ecological systems, has been previously formulated for linear systems. This note has a twofold purpose: first, we indicate that a variation of parameters technique can be applied, at least in principle, to computeboth input and output environs; and second, we show that this technique may be used for computation of environs in nonautonomous, nonlinear compartment models. This nonlinear theory, obtained as a direct extension of dynamical system developments, allows the traditional environ partitioning of compartmental storages and flows. An example of a nonlinear nutrient-producer-consumer system whose output environs can be computed asymptotically is presented to illustrate these concepts.
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    Bulletin of mathematical biology 47 (1985), S. 749-755 
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    Notes: Abstract Prolonged exposure to cyanide leads to a delayed but reversible disappearance of tetanic hyperpolarization in theXenopus node (G. M. Schoepfle,Am. J. Physiol. 231, 1033–1038, 1976). This effect is attributed to a pronounced decline in the absolute values of the ATP and ADP concentrations, such that the ATP-driven ion translocation is no longer possible, regardless of the existing values for (Na)i, (K)i and the (ATP)/(ADP) ratio. Mathematically, this would imply a vanishing of a constant pump conductance gp in the exression for electrogenic pump current densitityJ p, whereJ p=g p (V m −E p) in whichV m is membrane potential andE p is an ATP-and sodium-dependent e.m.f.
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    Bulletin of mathematical biology 47 (1985), S. 757-764 
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    Notes: Abstract For the two-parameter (A, α) exponentially-stiffening constituitive relation, typical of many biological materials, it is shown that the uniaxial stress-strain behavior of an initially curved strip is significantly changed by the residual bending stresses. Closedform theoretical results depend on the thickness to radius ratio (h/R) and the relative strain level ε(h/R). The bending stresses tend to obscure accurate measurement ofA and α unless care is taken. However, it is shown that by changing co-ordinates to (dℝ/d∈, ℝ)-space, bothA and α can be recovered from the high stress data, and α alone can be recovered from the low stress data. This has practical application to the mechanics of cornea, sclera, and heart muscle.
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    Bulletin of mathematical biology 47 (1985), S. 765-769 
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    Notes: Abstract An axisymmetric flow of a power law fluid through circular tubes under constant pressure gradient with the flow parameters varying radially is analyzed theoretically. The main finding is that for the Fahraeus-Lindqvist (F-L) effect to occur, it is necessary to have at least one of the parametersK (consistency) andn (index) as a discontinuous function ofr in the absence of wall slip; and with slip condition the parameters could be continuous functions ofr under specific conditions. In both the cases the existence of more than one discontinuity cannot be ruled out. The results obtained are consistent with experimental findings of blood flow through narrow tubes.
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    Bulletin of mathematical biology 47 (1985), S. 771-782 
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    Notes: Abstract This is a study of the properties of a zygotic algebra of two linked autosomal loci with different recombination rates in males and females, without selection or mutation and with random mating. The above-mentioned zygotic algebra contains a genetic subalgebra. A canonical basis of this subalgebra is constructed and the train roots are calculated.
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    Bulletin of mathematical biology 47 (1985), S. 799-799 
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    Bulletin of mathematical biology 47 (1985), S. 783-789 
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    Notes: Abstract Among the conformations which the DNA molecule can adopt, the transition beween the A and B families, controlled by water content (relative humidity), seems to be implicated in the transcription process. Focusing on the main structural difference involved (tilting of base normals with respect to the helix axis), a model is constructed, solitary wave solutions of the resulting equation of motion are demonstrated and possible experimental implications indicated.
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    Bulletin of mathematical biology 47 (1985), S. 791-797 
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    Notes: Abstract Balls are removed one-at-a-time at equal time intervals from an urn initially containingw 0 white balls and a large number b of black balls and each black or white ball is immediately replaced by a black ball. The distribution of the number of white balls remaining aftert iterations (under certain limiting operations) is taken from the literature. The problem is to use this result to find the time required to remove a fixed number of white ballsw 1 from the urn. We then find the mean and variance of this distribution and also look at the special case whenw 1 =w 0.
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    Bulletin of mathematical biology 47 (1985), S. I 
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    Bulletin of mathematical biology 42 (1980), S. 901-901 
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    Bulletin of mathematical biology 46 (1984), S. 11-17 
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    Notes: Abstract Linear birth and death processes are used to derive simple expressions for sequential extinction times and gene fixation probabilities in asexual populations.
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    Bulletin of mathematical biology 46 (1984), S. 1-10 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 19-40 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 115-125 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 139-153 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 175-184 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 155-174 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 127-137 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 185-185 
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    Bulletin of mathematical biology 46 (1984), S. 187-203 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 269-282 
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    Notes: 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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    Bulletin of mathematical biology 46 (1984), S. 283-294 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 247-268 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 295-326 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 327-332 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 337-337 
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    Bulletin of mathematical biology 46 (1984), S. 333-336 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 357-370 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 371-377 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 379-387 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 515-527 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 501-514 
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    Notes: 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).
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    Bulletin of mathematical biology 46 (1984), S. 529-543 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 545-552 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 553-566 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 567-577 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 661-672 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 827-844 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 845-857 
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    Notes: 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.
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    Bulletin of mathematical biology 46 (1984), S. 869-877 
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    Notes: 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.
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    Circuits, systems and signal processing 4 (1985), S. 285-300 
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    Notes: Abstract Magnetostatic surface wave (MSSW) devices made with pure and gallium-substituted yttrium-iron garnet (Ga:La-YIG) films are described. These devices include nondispersive and dispersive delay lines, band-pass filters, oscillators, and resonators. By controlling the magnitude of the bias magnetic field and the temperature of operation, it is possible to tune these devices over a wide frequency range extending from 0.3 to 4 GHz and from 3 to 18 GHz using Ga:La-YIG and pure YIG films, respectively. These devices could be used in pulse compression radar, microscan receivers, complicated Fourier transform processors, and fundamental oscillator circuits. In this paper, we briefly show results for pure YIG devices tunable in C and X bands and discuss, in detail, the performance of the Ga:La-YIG devices for UHF applications.
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    Circuits, systems and signal processing 4 (1985), S. 301-316 
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    Notes: Conclusion Significant improvements are required in the performance of MSW dispersive delay lines and filter banks before they are ready for systems application. Typically delay lines with bandwidths of 1 GHz or greater, differential delays in the range 200 ns to 1μs, and minimum phase errors (〈±1 °) are required for large (∿40 dB) dynamic range compressive receivers. However, techniques are evolving (see rest of this issue) in this relatively new area of technology which will allow systems performance requirements on phase errors to be met. Possible approaches to low phase error dispersive delay lines include reflective arrays, stepped ground planes, and multiple YIG films. The stepped ground plane technique is the most advanced and uses an optimization approach to the delay-line design, which results in a minimum phase error [20]. Ultimately the minimum achievable phase error will be limited by reflections from transducers and multiple mode effects in the delay lines. The MSW compressive receiver requires parallel advances in high-speed digital processing techniques to achieve its full potential. The MSW filter bank provides a simple channelization technique applicable up to approximately 20 GHz. Narrowband channels with 10 dB insertion loss, 3 dB bandwidths of 10 to 40 MHz, and 50 dB bandwidths of 30 to 120 MHz are possible with the already demonstrated techniques. Broader bandwidth channels in the range 50 to 200 MHz with flat passband response require improved transducer design techniques. The channelized receiver does not require extremely high-speed operations but, since a large number of channels are involved, size and cost become very significant.
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    Circuits, systems and signal processing 4 (1985), S. 413-434 
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    Notes: Abstract In recent studies, it has been verifiedheuristically andexperimentally (via simulations) that instability in power systems due to a fault occurs when one machine or a group of machines, called thecritical group, loses synchronism with the remaining machines. Using energy functions associated with a critical group (rather than system-wide functions), transient stability results which are less conservative than other existing results, have been obtained. The existence and identity of a critical group is ascertained in these studies byoff-line simulations. In this paper, we present results, for power systems with uniform damping, which establishanalytically theexistence and theidentity of the critical group of machines due to a given fault. We also present a result to determine estimates of the domain of attraction of asymptotically stable equilibrium points in power systems. The results presented herein can potentially be usedon-line to determine which machines belong to a critical group, and to use this information for corrective action (e.g.,shedding of the critical generators orfast valving for these generators). The applicability of the present results is demonstrated by means of a specific example (a 162-bus, 17-generator model of the power network of the State of Iowa).
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    Circuits, systems and signal processing 4 (1985), S. 367-383 
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    Notes: Abstract In a previous paper [1], a new algorithm for ARMA spectral estimation of stationary time series has been presented. The algorithm is based on nonlinear least squares fit of the sample partial autocorrelations to the partial autocorrelations generated by the assumed ARMA model. This paper explores the statistical properties of the above algorithm, including some numerical examples of the asymptotic variance of the estimated parameters, as compared to the Cramer-Rao bound. The results confirm the good performance of the algorithm and suggest an improvement in its implementation.
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    Circuits, systems and signal processing 4 (1985), S. 335-350 
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    Notes: Abstract A potential application of MSW technology lies in the area of time delay for future low-sidelobe wide-bandwidth phased array antennas. High-precision MSW electronically tunable analog time-delay units in transmit/receive modules in phased arrays have the potential of greatly enhancing antenna system capabilities, by increasing instantaneous operating bandwidth and decreasing sidelobe levels, over phased array systems using only phase shifters or switched lines for beam steering and control. This paper provides a status report of MSW time delays for such arrays.
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    Bulletin of mathematical biology 47 (1985), S. 35-52 
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    Notes: Abstract The present study deals with the effect of externally-imposed body accelerations on blood flow in arteries. Body accelerations may be caused deliberately, for example making the subjecs lie down on vibrating tables: or unintentionally during travel in road vehicles, aircraft or spacecraft. A mathematical model of flow in single arteries subject to a pulsating pressure gradient as well as body acceleration is presented. The resulting equations are solved by using the technique of Laplace transforms. Computational results are presented for the effects of body accelerations on flow variables namely flow rate, velocity of flow, acceleration and shear stress corresponding to typical arteries of human subjects.
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    Bulletin of mathematical biology 47 (1985), S. 53-70 
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    Notes: Abstract The left ventricle is modelled as a prolate spheroid of viscoelastic material with an aim to demonstrate the qualitative effects of anistropy and nonhomogeneity in the calculation of intact ventricular wall stresses. The pericardial pressure is accounted for in the analysis and an attempt is made to examine to what extent this influences the ventricular stresses. Numerical results are also obtained by computing the analytical expressions derived through the analysis.
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    Bulletin of mathematical biology 47 (1985), S. 111-122 
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    Notes: Abstract A Montes Carlo computer simulation is designed in order to described the evolution of an ecosystem under imposed environmental conditions of energy. Some preliminary results of a simple situation show a suggestive matching between the detailed random behaviors of individuals and a global deterministic model. This fact may provide a new insight into the understanding and control of biomass production processes and represents a new tool for the evaluation of the reliability of the classical treatments.
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    Bulletin of mathematical biology 47 (1985), S. 71-110 
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    Notes: Abstract A commonly accepted mathematical model for the slow-wave electrical activity of the gastro-intestinal tract of humans and animals comprises a set of interconnected nonlinear oscillators. Using a van der Pol oscillator with third-power conductance characteristics as the unit oscillator a number of structures have been analysed using a matrix Krylov-Bogolioubov method linearisation. The mode analysis of one-dimensional chains and two-dimensional arrays has been reported. In this paper the method has been extended to consider a tubular structure which is relevant to modelling small-intestinal rhythms. It is shown that this structure is capable of producing stable single models, non-resonant double modes and degenerated modes. General expressions are obtained for anm×n structure and examples given of two special conditions of 3×4 (i.e. odd numbers of oscillators in a ring) and 4×3 cases. The analytical results obtained for these two cases have been vertified experimentally using an electronic implementation of coupled van der Pol oscillators. Results obtained using fifth-power non-linear oscillators are summarised.
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    Bulletin of mathematical biology 42 (1980), S. 147-160 
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    Notes: Abstract A theory of noise fluctuations is developed which is applicable to systems of any size in which unimolecular or bimolecular reactions are occurring. The main difference between small and large reacting systems is that in the former the probability of finding a particle in a particular state does not obey a Gaussian distribution, but satisfies a distribution which reflects the mechanism of the chemical reaction. This difference is reflected in the main result of the theory: an autocorrelation function that is expressible as a sum of exponentials, the amplitudes of which are explicit functions of the moments of the distribution. Thus, by using small systems, the autocorrelation function,in principle, allows the elucidation of reaction mechanisms. Numerical simulations indicate that for reacting systems having ten or fewer particles, the deviation of the autocorrelation function from a single exponential should be easily detectable, and that estimates of the first four moments of the distribution should be possible. Accurate inference of the distribution, however, will require further mathematical and experimental advances.
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    Bulletin of mathematical biology 42 (1980), S. 161-172 
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    Notes: Abstract The recent mathematical formalization of the concepts of matter and extrinsical energy, which are used for the relational representation of biological systems, is employed in the analysis of the important experimental discoveries of Comorosanet al. related to low energy electromagnetic irradiations on enzyme substrates. By means of the present analysis one of the properties inherent to the experimental phenomena is more precisely exposed, and theoretical developments corresponding to “energetical evolutions” in a biological system (Leguizamón, 1976) may now have an experimental basis. Important limitations are introduced for the validity of the commutativity and associativity of cartesian product of sets, when they represent matter and its linked extrinsical energy. In connection with this last aspect, new important knowledge is obtained for the relational mathematical representation of biological systems.
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    Bulletin of mathematical biology 47 (1985), S. 157-157 
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    Bulletin of mathematical biology 47 (1985), S. 161-192 
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    Bulletin of mathematical biology 47 (1985), S. 159-159 
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    Bulletin of mathematical biology 47 (1985), S. 205-213 
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    Notes: Abstract An urn contains balls ofs different colors. The problem of the reinforcement of a specified color and random depletion of balls has been considered by Shenton (1981, 1983). In this paper, the theory is applied to the biological age dependent half-life of radioactive iodine in man; the data of Cook and Snyder (1965) is used. The intake of radioactive iodine and its retention subsequently is studied.
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    Bulletin of mathematical biology 47 (1985), S. 193-204 
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    Notes: Abstract One of the limitations of stochastic, linear compartmental systems is the small degree of variability in the contents of compartments. S. R. Bernard's (1981) urn model (S. R. Bernardet al., Bull. math. Biol. 43, 33–45.) which allows for bulk arrivals and departures from a one-compartment system, was suggested as a way of increasing content variability. In this paper, we show how the probability distribution of the contents of an urn model may be simply derived by studying an appropriate set of exchangeable random variables. In addition, we show how further increases in variability may be modeled by allowing the size of arrivals and departures to be random.
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    Bulletin of mathematical biology 47 (1985), S. 231-238 
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    Notes: Abstract A stochastic model based on Eigen and Schuster's theory of biomolecular self-replication is studied by treating the master equation with the system-size expansion technique. The steady-state results are found to be in good agreement with the previous results and with those derived from the principle of detailed balancing. Multispecies competition and coexistence are studied carefully with the conclusions that a stable steady state is predicted for the former and a metastable state for the latter. The stochastic selection processes are also analyzed and discussed.
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    Bulletin of mathematical biology 47 (1985), S. 215-229 
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    Notes: Abstract A consensus in dex method comprises a consensus method and a consensus index that are defined on a common set of objects (e.g. classifications). For each profile of objects, the consensus method returns a consensus object representing information or structure shared among profile objects, while the consensus index returns a quantitative measure of agreement among profile objects. Since the relationship between consensus method and consensus index is poorly understood, we propose simple axioms prescribing it in the most general terms. Many taxonomic consensus index methods violate these axioms because their consensus indices measure consensus object invariants rather than profile agreement. We propose paradigms to obtain consensus index methods that measure agreement and satisfy the axioms. These paradigms salvage concepts underlying consensus index methods violating the axioms.
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    Bulletin of mathematical biology 47 (1985), S. 239-262 
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    Notes: Abstract The theory of multitype branching processes is applied to the kinetics of polynucleotide replication. The results obtained are compared with the solutions of the deterministic differential equations of conventional chemical kinetics.
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    Bulletin of mathematical biology 47 (1985), S. 263-272 
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    Notes: Abstract We investigate the circumstances under which the moments of the order statistics of the extinction times of a set of independent branching processes exist. This extends a result of Schuster and Sigmund,Bull. math. Biol. 46, 11–17, 1984, which was found in a special random selection model. Furthermore we discussed existence of the expectation of extinction times of multitype branching processes and extend well known results for irreducible processes to the reducible case.
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    Bulletin of mathematical biology 47 (1985), S. 287-293 
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    Notes: Abstract This note presents a general time-dependent study of linear stochastic compartmental models in discrete time. The transient distribution of the state of the system is obtained by adapting methods used in the continuous time analysis. Covariance functions with and without a time lag are then deduced by a simple probabilistic argument. Results are derived in the Markov case and are partly extended to the semi-Markov case.
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    Bulletin of mathematical biology 47 (1985), S. 273-286 
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    Notes: Abstract A simple practical method exists for classifying and comparing planar curves composed of connected line segments. This method assigns, a single numberD, the fractal dimension, to each curve.D=log(n)/[log(n)+log(d/L)], where:n is the number of line segments,L is the total length of the line segments, andd is the planar diameter of the curve (the greatest distance between any two endpoints). At one end of the spectrum, for straight line curves,D=1; at the other end of the spectrum, for random walk curves,D→2. Standard statistics are done on the logarithms of the fractal dimension [log(D)]. With this measure, trails of biological movement, such as the growth paths of the cells and the paths of wandering organisms, can be analyzed to determine the likelihood that these trails are random walks and also to compare the straightness of the trails before and after experimental interventions.
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    Bulletin of mathematical biology 47 (1985), S. 295-304 
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    Notes: Abstract A model is proposed of an ecological community where some (or all) of the subpopulations exhibit mutual interference. Mutual interference introduces sublinearities which makes the persistence analysis of the community more complex since the model is no longer a dynamical system. A transformation is introduced which yields a dynamical system, thereby making a persistence analysis more tractable. The results are applied to determining top-predator persistence of a simple food chain and to the question of invasibility of a stable community by a new subpopulation.
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    Bulletin of mathematical biology 42 (1980), S. 397-429 
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    Notes: Abstract The structure of solutions to a simple spatially dependent population model involving growth and death is investigated. Two forms of motility of the population are considered: (1) random motion only modeled by a Fickian law, and (2) a directed component of motion (chemotaxis), included in addition to the random motion. Under certain growth conditions a traveling wave of constant speed is approached. This speed can be increased by the addition of the chemotaxis with a corresponding increase in the asymptotic population. Development of initial conditions into a wave is illustrated numerically.
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    Bulletin of mathematical biology 42 (1980), S. 365-396 
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    Notes: Abstract This paper describes mechanisms of intracellular and intercellular adaptation that are due to spatial or temporal factors. The spatial mechanisms support self-regulating pattern formation that is capable of directing self-organization in a large class of systems, including examples of directed intercellular growth, transmitter production, and intracellular conductance changes. A balance between intracellular flows and counterflows causes adaptation. This balance can be shifted by environmental inputs. The decrease in Ca2+-modulated outward K+ conductance in certain molluscan nerve cells is a likely example. Examples wherein Ca2+ acts as a second messenger that shunts receptor sensitivity can also be discussed from this perspective. The systems differ in basic ways from recent diffusion models. Chemical transducers driven by membrane-bound intracellular signals can establish long-range intercellular interactions that compensate for variable intercellular distances and are invariant under developmental size changes; diffusional signals do not. The intracellular adaptational mechanisms are formally analogous to intercellular mechanisms that include cellular properties which are omitted in recent reaction-diffusion models of pattern formation. The cellular models use these properties to compute size-invariant properties despite wide variations in their intercellular signals. Mechanisms of temporal adaptation can be derived from the simplest laws of chemical transduction by using a correspondence principle. These mechanisms lead to such properties of intercellular signals as transient overshoot, antagonistic rebound, and an inverted U in sensitivity as intracellular signals or adaptation levels shift. Such effects are implicated in studies of behavioral, reinforcement, motor control, and cognitive coding.
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    Bulletin of mathematical biology 42 (1980), S. 447-459 
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    Notes: Abstract Large radiation doses to the lung can cause early death from cardiopulmonary insufficiency resulting from radiation pneumonitis and pulmonary fibrosis. A model for early death following inhalation of insoluble radioactive particles is propose. The model is based on three assumptions: (1) early death results from damage to a cluster of cells from a large number of cell clusters at risk, (2) the dose that causes early death depends on how the radiation is delivered in time and (3) the cell clusters at risk to damage are equally sensitive ro radiation. Results from asymptotic theory of extreme values, along with biophysical considerations, suggest that the cumultive distribution function for the absorbed radiation dose to the production of pulmonary injury sufficient to cause early death is best estimated by the third asymptotic distribution without a threshold. This distribution function is identical to the Weibull cumulative distribution function. Data for Beagle dogs after inhaling relatively insoluble forms of alpha- or beta-gamma-emitting particles are shown to support the Weibull model.
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    Bulletin of mathematical biology 42 (1980), S. 461-480 
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    Notes: Abstract Models of the human respiratory tract were developed based on detailed morphometric measurements of a silicone rubber cast of the human tracheobronchial airways. Emphasis was placed on the “Typical Path Lung Model” which used one typical pathway to represent a portion of the lung, such as a lobe, or to represent the whole lung. The models contain geometrical parameters, including airway segment diameters, lengths, branching angles and angles of inclination to gravity, which are needed for estimating inhaled particle deposition. Aerosol depositions for various breathing patterns and particle sizes were calculated using these lung models and the modified Findeisen-Landahl computational scheme. The results agree reasonably well with recent experimental data. Regional deposition, including lobar deposition fractions, are also calculated and compared with results based on the ICRP lung deposition model.
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    Bulletin of mathematical biology 42 (1980), S. 481-488 
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    Notes: Abstract The completely symmetrical system is defined as having identical transfer coefficients between pairs of compartments and the same loss coefficient for each compartment. The eigenvalues and eigenvector are explicitly found along with the inverses of the system matrix and the matrix of eigenvectors. Many properties, special instances of more general theorems, can be seen at once from the explicit analytic solution of the initial value, washout and washin problems. The system serves as a known case for testing estimation procedures, algorithms for solutions of linear systems, eigenvalue-eigenvector and inversion routines and is of considerable tutorial value.
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    Bulletin of mathematical biology 42 (1980), S. 431-446 
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    Notes: Abstract The mathematical structures underlying the theories of organismic sets, (M, R)-systems and molecular sets are shown to be transformed naturally within the theory of categories and functors. Their natural transformations allow the comparison of distinct entities, as well as the modelling of dynamics in “organismic” structures.
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    Bulletin of mathematical biology 42 (1980), S. 489-505 
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    Notes: Abstract To explain the sodium conductance change using Wei's dipole model (Wei, 1969), we may expect that during depolarization the dipole's population difference, ΔN, is first reduced and then returns more slowly to its resting value. This paper shows that the experimental results of gating currents support this idea. Such time course of ΔN, however, is not a usual relaxation process. To account for the unusual behavior of ΔN, we propose two additional assumptions: (1) there exists a special coupling system (probably the intramolecular vibrations) whose coupling strength with the dipoles is much stronger than with the thermal bath (intermolecular vibrations), and (2) there also exist “traps” for the dipole's excitation energy so that this energy is transformed into other energy forms at a rate increasing with the increase of depolarization. Experiments suggest that the traps are proteins located at the inner membrane surface.
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    Bulletin of mathematical biology 42 (1980), S. 507-528 
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    Notes: Abstract Current research into the dynamics of iterative ecological and biological models has lead to a number of theorems concerning the existence of various types of iterative dynamical behavior. In particular, much study has been done on the dynamical behavior of the “simplest dynamical system”f b(x)=bx(1−x), which is just the canonical discrete form of logistic growth equations found in ecology, sociobiology, and population biology. In this paper, we make use of some of the techniques and concepts of topological dynamics to construct a number of generalized conjugacy theorems. These theorems are then used to demonstrate that the mappingf b has a number of conjugacy classes in which the dynamics of the iterates is equivalent to within a change of variables. The concepts of fitness and survival in logistic equations are then shown to be independent, if we follow certain intuitive definitions for these concepts. This conclusion follows from a comparison of the conjugacy classes of the functionf b and the extinction sets off b.
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