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  • Springer  (172,532)
  • American Association for the Advancement of Science  (10,196)
  • 1995-1999  (134,988)
  • 1980-1984  (47,740)
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  • 1983  (47,740)
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  • 1
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    Bulletin of mathematical biology 45 (1983), S. 287-293 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We postulate that the biomass distribution function for an ecological population may be derived from the condition that the biomas diversity functional is maximal subject to an energetic constraint on the total biomass. This leads to a biomass distribution of the form $$p(m) = \bar m^{ - 1} \exp ( - m/\bar m)$$ , where $$\bar m$$ is the mean biomass per individual. The same condition yields a unique value for the biomass diversity functional. These predictions are tested against fishery data and found to be in good agreement. It is argued that the existence of a unique value for biomass diversity may provide a preliminary theoretical foundation for the observed upper limit to species diversity.
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    Bulletin of mathematical biology 45 (1983), S. 311-321 
    ISSN: 1522-9602
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    Notes: Abstract Pigment distribution presages hydranth regeneration in the marine hydroidTubularia. We suggest that such a distribution could result from a reaction-diffusion system. A model system based on a practical reaction scheme is studied and spatial structures found which closely resemble this pigment distribution. Finite-amplitude spatial structures in reaction-diffusion systems are considered. Whereas in one spatial dimension the final structures are normally very similar to the transient patterns which emerge from a linear analysis, it is shown that in more than one dimension this is not necessarily the case. The reasons for this are discussed.
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    Bulletin of mathematical biology 45 (1983), S. 409-424 
    ISSN: 1522-9602
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    Notes: Abstract An analytical model is used to described the behavior of inhaled particulate matter in the human respiratory tract. Three different geometries, symmetric and asymmetric, are utilized to simultate the tracheobronchial (TB) tree. The suitability of each geometry for representing the human is evaluated by comparing calculated aerosol deposition probabilities with experimental data from inhalation exposure tests. A symmetric, dichotomously branching pattern is found to be a reliable description of the TB tree for studies of factors affecting aerosol deposition in the human lung. Calculations with the theoretical model are in excellent agreement with measured aerosol deposition efficiencies. Furthermore, the model accurately predicts experimentally observed features of inhalation exposure data, such as effects of inter-subject lung morphology differences and relative efficiencies of specific deposition mechanisms, on aerosol deposition patterns in the TB tree.
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    Bulletin of mathematical biology 45 (1983), S. 436-436 
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    Bulletin of mathematical biology 45 (1983), S. 437-437 
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    Bulletin of mathematical biology 45 (1983), S. 579-590 
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    Notes: Abstract In this paper we are concerned with problems of the long-term behavior for nonlinear systems in random environment. The general model is assumed to be given by an ordinary differential equation with random parameters or random input. The disturbance process can be taken from a fairly general class of Markov processes having a bounded state space. In terms of the system’s dynamics we give sufficient conditions for the existence and uniqueness of invariant probabilities. Finally, we apply these results to the two-dimensional biochemical model which is known as the Brusselator.
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    Bulletin of mathematical biology 45 (1983), S. 571-577 
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    Notes: Abstract In various applications one faces the problem of estimating a signal from discontinuous observations. For example, in biomedical applications the signal may be the ‘state’ of a given organ and one observes through an external counter the amount of radioactivity sequestered by the organ after injection of a radioactive tracer. Here the problem is studied in the context of nonlinear filtering when the signal can be modelled as either a random variable or a diffusion process, and the observations have a continuous and a purely discontinuous component; both components may be affected by the signal. When the signal is a random variable an explicitly computable solution is obtained; for the diffusion case the solution is given as a sequence of approximating filters that can be computed recursively.
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    Bulletin of mathematical biology 45 (1983), S. 627-634 
    ISSN: 1522-9602
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    Notes: Abstract Eigenvalue problems arise in various biological models. We outline a useful comparison method and a technique using Lyapunov functions that can be applied in many cases. An application to lateral diffusion is discussed.
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    Bulletin of mathematical biology 45 (1983), S. 605-616 
    ISSN: 1522-9602
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    Notes: Abstract This paper reviews, up to their recent developments, two types of models of the cell cycle: those considering the size controls over the cycle events and the transition probability models. The distribution of inter-mitotic time and the sister-sister and motherdaughter correlations implied by the two approaches are discussed in view of some relevant experimental data.
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    Bulletin of mathematical biology 45 (1983), S. 617-626 
    ISSN: 1522-9602
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    Notes: Abstract The development of a blood cell line originating from a pluripotent stem cell pool is modelled by a chain of multidimensional branching processes in which the sojourn times of the cells in certain resting states depend on the size of the following subpopulation. The stability of such a model is discussed qualitatively and some considerations concerning a possible malignant degeneration are presented. The behaviour of models for normal and malignant cell production are illustrated by stochastic stimulations. The model presented here describes the development of a certain line of blood cells (e.g. erythrocytes, monocytes or granulocytes) originating from the pluripotent stem cell up to the functional cell in the blood (for related models see, e.g., Rubinow and Lebowitz,J. math. Biol. 1, 87–225;Biophys. J. 16, 897–910).
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    Bulletin of mathematical biology 45 (1983), S. 635-641 
    ISSN: 1522-9602
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    Notes: Abstract This paper reviews some recent advances in single population stochastic differential equation growth models. They are a natural way to model population growth in a randomly varying environment. The question of which calculus, Itô or Stratonovich, is preferable is addressed. The two calculi coincide when the noise term is linear, if we take into account the differences in the interpretation of the parameters. This clarifies, among other things, the controversy on the theory of niche limiting similarity proposed by May and MacArthur. The effects of correlations in the environmental fluctuations and statistical methods for estimating parameters and for prediction based on a single population trajectory are mentioned. Applications to fisheries, wildlife management and particularly to environmental impact assessment are now becoming possible and are proposed in this paper.
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    Bulletin of mathematical biology 45 (1983), S. 643-658 
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    Notes: Abstract A survey is given of the application of (functions of) continuous-time Markov chains in the statistical analysis of behavioural time series.
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    Bulletin of mathematical biology 45 (1983), S. 659-659 
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    Bulletin of mathematical biology 45 (1983), S. 661-664 
    ISSN: 1522-9602
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    Notes: Abstract This paper demonstrates that there is one and only one solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a spherical cell. Previous authors have calculated numerical results that differ substantially. Numerical computations using the multiple shooting method support the results of McElwain.
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    Bulletin of mathematical biology 45 (1983), S. 665-720 
    ISSN: 1522-9602
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    Notes: Abstract The mathematics of distance geometry constitutes the basis of a group of algorithms for revealing the structural consequences of diverse forms of information about a macromolecule's conformation. These algorithms are of proven utility in the analysis of experimental conformational data. This paper presents the basic theorems of distance geometry in Euclidean space and gives formal proofs of the correctness and, where possible, of the complexity of these algorithms. The implications of distance geometry for the energy minimization of macromolecules are also discussed.
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    Bulletin of mathematical biology 45 (1983), S. 721-737 
    ISSN: 1522-9602
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    Notes: Abstract A fully developed pulsatile flow in a circular rigid tube is analysed by a microcontinuum approach. Solutions for radial variation of axial velocity and cell rotational velocity across the tube are obtained using the momentum integral method. Simplified forms of the solutions are presented for the relevant physiological data. Marked deviations in the results are observed when compared to a Newtonian fluid model. It is interesting to see that there is sufficient reduction in the mass flow rate, phase lag and friction due to the micropolar character of the fluid.
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    Bulletin of mathematical biology 45 (1983), S. 749-758 
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    Notes: Abstract A mathematical model of the transport of fluorescein across the blood-retina barrier in the transient state and the subsequent diffusion of fluorescein in the vitreous body is presented. The function of the barrier is lumped in a single parameter—the permeability. The sensitivity of this parameter due to changes in the other parameters of the model is given. This establishes the foundation for the quantitative assessment of the barrier function through vitreous fluorophotometry.
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    Bulletin of mathematical biology 45 (1983), S. 739-748 
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    Notes: Abstract The objective of this preliminary study was to develop a new quantitative method of setting the initial insulin infusion patterns in treatment of diabetic patients. The method is based upon the mathematical estimation of the insulin profile required to maintain the glucose level within the normal range after glucose loading in diabetic patients. Using our previously developed equivalent circuit model of glucose kinetics and the reported data of an intravenous glucose tolerance test (IVGTT) in two groups of normal and diabetic patients, two important physiological parameters of the model (the peripheral tissue's insulin resistivity and the hepatic sensitivity to glucose level) were computed for two clinical groups. Then the insulin profile was obtained by computing the plasma insulin concentrations required to keep the total glucose utilization rate of the tissue and the liver in the diabetic group equal to that of the normal group. The simulation result indicated that the computed insulin profile produced a plasma glucose profile which was more closely matched to the normal group's glucose profile than with the case of emulating the normal group's insulin profile in the diabetic group.
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    Bulletin of mathematical biology 45 (1983), S. 759-780 
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    Notes: Abstract This paper shows that the Na conductance changes can be explained quantitatively, based on the following assumptions: (1) there exist in nerve membranes the electron transfer (ET) complexes and traps, (2) there is energy migration among them. The gating mechanism is explained in physical terms. Its mathematical expression differs from the Hodgkin-Huxley equations, but resembles the Hoyt formulation. In the present model, the physical parameters for the squid axon can be estimated from currently available experimental data. The density of the ET complexes is on the order of 105/μm2, and the density of the traps is 103/μm2. The magnitude of the energy transfer rate between ET complexes is about 106/sec at large depolarization and decreases with decreasing depolarizations, as does the Na inactivation rate. The energy gap between the two stable states of the transfer electron in the ET complex is estimated to be around 0.1 eV, which is approximately the same as that for the photosynthetic systems.
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    Bulletin of mathematical biology 45 (1983), S. 781-792 
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    Notes: Abstract The role of symmetry in simplifying the theory of complex neural systems is argued. When the structural symmetries of a network are expressed as an ismorphism group, implications emerge for the dynamics. Various qualitative possibilities concerning stability of uniform motion in homogeneous nets are discussed and an approach to neural hierarchies is outlined.
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    Bulletin of mathematical biology 45 (1983), S. 793-805 
    ISSN: 1522-9602
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    Notes: Abstract By constructing appropriate Liapunov functionals, asymptotic behaviour of the solutions of various delay differential systems describing prey-predator, competition and symbiosis models has been studied. It has been shown that equilibrium states of these models are globally stable, provided certain conditions in terms of instantaneous and delay interaction coefficients are satisfied.
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    Bulletin of mathematical biology 45 (1983), S. 807-826 
    ISSN: 1522-9602
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    Notes: Abstract Sensitivity analyses have been used to examine the flow structure of two hypothetical ecosystem models. These analyses have results which relate to important aspects of ecosystem theory. Cycles are shown to increase the sensitivity of the network, while increased throughflow is shown to decrease the sensitivity. Such results indicate that several factors can be modified to decrease the sensitivity of ecosystems to environmental stress.
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    Bulletin of mathematical biology 45 (1983), S. 827-836 
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    Notes: Abstract A continous, deterministic mathematical model is used to predict population distributions by age at any time, given the initial distribution and the variation of birth and death rates with age and time. Solutions are obtained on a computer using a semi-discretization algorithm in which time derivatives in the partial differential equations are replaced by finite-difference expressions. The resulting sets of ordinary differential equations are solved by a predictor-corrector method. Graphical results are shown for some examples.
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    Bulletin of mathematical biology 45 (1983), S. 849-855 
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    Notes: Abstract A new formula for the complexity of graphs is proposed and applied to the points lines and ‘connections’ of some chemically relevant graphs.
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    Bulletin of mathematical biology 45 (1983), S. 837-847 
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    Notes: Abstract This paper reports general and specialized results on analytical solutions to the governing phenomenological equations for chemotactic redistribution and population growth of motile bacteria. It is shown that the number of bacteria cells per unit volume,b, is proportional to a certain prescribed function ofs, the concentration of the critical substrate chemotactic agent, for steady-state solutions through an arbitrary spatial region with a boundary that is impermeable to bacteria cell transport. Moreover, it is demonstrated that the steady-state solution forb ands is unique for a prescribed total number of bacteria cells in the spatial region and a generic Robin boundary condition ons. The latter solution can be approximated to desired accuracy in terms of the Poisson-Green's function associated with the spatial region. Also, as shown by example, closed-form exact steady-state solutions are obtainable for certain consumption rate functions and geometrically symmetric spatial regions. A solutional procedure is formulated for the initialvalue problem in cases for which significant population growth is present and bacteria cell redistribution due to motility and chemotactic flow proceeds slowly relative to the diffusion of the chemoattractant substrate. Finally, a remarkably simple exact analytical solution is reported for a stradily propagating plane-wave which features motility, chemotactic motion and bacteria population growth regulated by substrate diffusion.
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    Bulletin of mathematical biology 45 (1983), S. 857-867 
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    Notes: Abstract This paper discusses the flow of blood in large artries under the influence of linear periodic acceleration. The governing equations and boundary conditions are established and analytical solutions for the velocity, fluid acceleration, bulk flow and shear stress are obtained. The results for these physical quantitites are computed for the case of an artery the size of a normal human aorta. It is found that the flow field variables are directly proportional to the external accelerating force. The behaviour of the velocity profile along the radial distance at different stages of times at fixed applied acceleration is also shown.
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    Bulletin of mathematical biology 45 (1983), S. 931-968 
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    Notes: Abstract The evolutionary selection circuits model of learning has been specified algorithmically. The basic structural components of the selection circuits model are enzymatic neurons, that is, neurons whose firing behavior is controlled by membrane-bound macromolecules called excitases. Learning involves changes in the excitase contents of neurons through a process of variation and selection. In this paper we report on the behavior of a basic version of the learning algorithm which has been developed through extensive interactive experiments with the model. This algorithm is effective in that it enables single neurons or networks of neurons to learn simple pattern classification tasks in a number of time steps which appears experimentally to be a linear function of problem size, as measured by the number of patterns of presynaptic input. The experimental behavior of the algorithm establishes that evolutionary mechanisms of learning are competent to serve as major mechanisms of neuronal adaptation. As an example, we show how the evolutionary learning algorithm can contribute to adaptive motor control processes in which the learning system develops the ability to reach a target in the presence of randomly imposed disturbances.
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    Bulletin of mathematical biology 45 (1983), S. 981-990 
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    Notes: Abstract In the present paper we discuss the behaviour of solutions of a dynamical system describing the growth of cells in a well-mixed continuous culture where the supply of the growth-limiting nutrient depends on the activity of an enzyme outside the cell membrane. It turns out that for positive dilution rates there exists an exponentially attractive two-dimensional simplex. Furthermore, the reversed system restricted to this simplex is quasimonotone. In every case all trajectories tend to an equilibrium state.
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    Bulletin of mathematical biology 45 (1983), S. 991-1004 
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    Notes: Abstract We present a Gause predator-prey model incorporating mutual interference among predators, a density-dependent predator death rate and a time lag due to gestation. It is well known that mutual interference is stabilizing, whereas time delays are destabilizing. We show that in combining the two, a long time-lag usually, but not always, destabilizes the system. We also show that increasing delays can cause a bifurcation into periodic solutions.
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    Bulletin of mathematical biology 45 (1983), S. 969-980 
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    Notes: Abstract The cycle structure of enzymatic neural networks may be characterized in terms of number of cycles exhibited, size of cycle state sets and cycle lengths. Simulation experiments show that the stability properties of these networks have some unusual features which are not exhibited by networks of two-state switching elements or by randomly constructed ecosystem models. The behavioral and structural stability of these systems decreases with their structural complexity, as measured by the number of components. The behavioral and structural stability of enzymatic neural networks also decreases with structural complexity, as measured by the number of excitase types, but only up to the middle level of excitases per neuron. This is the point of highest potential responsiveness of the system to environmental stimuli. Beyond this point the behavioral and structural stability increase. This is due to the fact that the number of possible states increases up to this point and decreases beyond it. The number of possible states, not the number of components, serves as the useful measure of complexity in these types of systems. The selection circuits learning algorithm has been used to evolve networks whose cycle structures have desired features.
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    Bulletin of mathematical biology 45 (1983), S. 1005-1011 
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    Notes: Abstract Similarity criteria of the functional design of the mammalian cardiovascular system are scant. For the analysis of mammalian cardiac energetics physiological parameters such as mean arterial blood pressure, stroke volume, heart rate, metabolic rate and heart and body weights are considered pertinent. Based on these parameters, a new similarity principle is established via allometric equations, dimensional analysis and Buckingham's pi-theorem. The principle states that the ratio of left ventricular external work to metabolic rate is inversely proportional to resting heart rates of mammals. The proportionality constant is dimensionless and is invariant of mammalian body weights.
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    Bulletin of mathematical biology 45 (1983), S. 1029-1045 
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    Notes: Abstract The mathematical theory of categories is used as a tool in the description of the structure and function of natural systems. The connections between the category of natural systems, with observables and dynamics, and the phenomenological calculus of response tensors, duality- and adjoint-invariance diagrams are established. The unified theory is applied to the analysis of hierarchies, pattern generation and the structure and dynamics of proteins.
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    Bulletin of mathematical biology 45 (1983), S. 1047-1072 
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    Notes: Abstract This is an investigation of natural systems from the standpoint of the mathematical theory of categories. It examines the relationships which exist between different descriptions through measurement of observables and dynamical interactions. We begin with a category theory of formal systems with observables, and then proceed to a category theory of dynamical systems. The two categories are then combined to represent natural systems. Topological considerations enter in the study of stability and bifurcation phenomena. Special emphasis is placed on natural systems which model biological processes. The categorical system theory developed is applied to the analysis of several biological problems and biological system theories.
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    Notes: Abstract Tetanic hyperpolarization for theXenopus node is simulated by means of iterative solutions of the Frankenhaeuser-Huxley excitation equations together with an active transport current density term which is dependent on sodium and potassium levels as well as the ADP/ATP ratio. All time-dependent variables at the end of one interspike interval are introduced as initial conditions for the next response, whereupon all time-dependent changes in voltage and permeability factors appear identical for the third and fourth responses of a sequence. Net change in internal sodium concentration is zero throughout the third and fourth intervals if sodium loading of the system is initially adjusted to a critical level. Extent of tetanic hyperpolarization is a function of the pump conductance.
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    Bulletin of mathematical biology 45 (1983), S. 1097-1097 
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    Bulletin of mathematical biology 45 (1983), S. 1073-1096 
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    Notes: Abstract The properties of nonlinear equations describing the solute and solvent transport across a simplified Patlak-Goldstein-Hoffman model (two membranes in series without unstirred layers) are investigated both analytically and numerically. The analysis shows that the principal coefficients measured in transport experiments in the presence of active transport are dependent on the experimental conditions. These ‘apparent’ system parameters are extensions of the corresponding parameters determined both in passive systems and in the linear Kedem-Katchalsky theory. Moreover, they are related to the local phenomenological coefficients of the single membranes of the array. Several relationships between measurable quantities and the local system parameters are indicated, allowing the planning of experiments aimed at the measurement of the latter. Data in the literature have been used to check the proposed volume flow equation.
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    Bulletin of mathematical biology 59 (1997), S. 23-41 
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    Notes: Abstract We consider a host-solitary parasitoid system with three categories of individuals: parasitoids, healthy hosts and parasitized hosts. Parasitoids are assumed to discriminate perfectly between the two kinds of hosts and they can reject those which are already parasitized. If parasitoids systematically accept or reject superparasitism or behave randomly, the system is always unstable. Using an optimal foraging model, we determine the behavior of parasitoids which leads to maximization of the instantaneous reproductive rate. When following this adaptive decision rule, parasitoids accept or refuse superparasitism according to the densities of both healthy and parasitized hosts. We study the dynamics of the system when parasitoids follow the optimal rule and show that under certain conditions it possesses a locally stable equilibrium point. In addition, our model predicts that at equilibrium parasitoids show partial preferences for superparasitism.
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    Bulletin of mathematical biology 59 (1997), S. 205-232 
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    Notes: Abstract A system of differential equations for the control of tumor growth cells in a cycle nonspecific chemotherapy is analyzed. Spontaneously acquired drug resistance is taken into account, and a criterion for the selection of chemotherapeutic treatment is used. This criterion purports to describe the possibility of improvement of the patient's health when treatment is discontinued. Contrary to our early results which also take drug resistance into account, in this context strategies of continuous chemotherapy in which rest periods take part may be better than maximum drug concentration throughout the treatment (which appears to be in accordance with clinical practice). This bears out our previous conjecture that when drug resistance is accounted for, the imperfections in the usual modelling of treatment criteria, which in general do not allow for patient recuperation, ruled out the possibility of rest periods in optimal continuous chemotherapy.
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    Bulletin of mathematical biology 59 (1997), S. 255-262 
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    Notes: Abstract A logistic density-dependent matrix model is developed in which the matrices contain only parameters and recruitment is a function of adult population density. The model was applied to simulate introductions of white-tailed deer into an area; the fitted model predicted a carrying capacity of 215 deer, which was close to the observed carrying capacity of 220 deer. The rate of population increase depends on the dominant eigenvalue of the Leslie matrix, and the age structure of the simulated population approaches a stable age distribution at the carrying capacity, which was similar to that generated by the Leslie matrix. The logistic equation has been applied to study many phenomena, and the matrix model can be applied to these same processes. For example, random variation can be added to life history parameters, and population abundances generated with random effects on fecundity show both the affect of annual variation in fecundity and a longer-term pattern resulting from the age structure.
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    Bulletin of mathematical biology 59 (1997), S. 399-406 
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    Bulletin of mathematical biology 59 (1997), S. 707-724 
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    Notes: Abstract A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Spontaneously acquired drug resistance is accounted for, as well as the evolution in time of normal cells. In addition, optimization of conflicting objectives forms the aim of the chemotherapeutic treatment. For general cell growth, some results are given, whereas for the special case of Malthusian (exponential) growth of tumor cells and rather general growth rate for normal cells, the optimal strategy is worked out. The latter, from the clinical standpoint, corresponds to maximum drug concentration throughout the treatment.
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    Bulletin of mathematical biology 59 (1997), S. 787-807 
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    Bulletin of mathematical biology 59 (1997), S. 809-831 
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    Notes: Abstract This study examines the influence of various host-feeding patterns on host-parasitoid population dynamics. The following types of host-feeding patterns are considered: concurrent and non-destructive, non-concurrent and non-destructive, and non-concurrent and destructive. The host-parasitoid population dynamics is described by the Lotka-Volterra continuous-time model. This study shows that when parasitoids behave optimally, i.e. they maximize their fitness measured by the instantaneous per capita growth rate, the non-destructive type of host feeding stabilizes host-parasitoid dynamics. Other types of host feeding, i.e. destructive, concurrent, or non-concurrent, do not qualitatively change the neutral stability of the Lotka-Volterra model. Moreover, it is shown that the pattern of host feeding which maximizes parasitoid fitness is either non-concurrent and destructive, or concurrent and non-destructive host feeding, depending on the host abundance and parameters of the model. The effects of the adaptive choice of host-feeding patterns on host-parasitoid population dynamics are discussed.
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    Bulletin of mathematical biology 59 (1997), S. 931-952 
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    Notes: Abstract Game theory has had remarkable success as a framework for the discussion of animal behaviour and evolution. It suggested new interpretations and prompted new observational studies. Most of this work has been done with 2-player games. That is the individuals of a population compete in pairwise interactions. While this is often the case in nature, it is not exclusively so. Here we introduce a class of models for situations in which more than two (possibly very many) individuals compete simultaneously. It is shown that the solutions (i.e. the behaviour which may be expected to be observable for long periods) are more complex than for 2-player games. The concluding section lists some of the new phenomena which can occur.
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    Notes: Abstract A method allowing to measure the inhomogeneous distribution of purines/pyrimidines in nucleotide sequences is developed. We show that this measure relates to the coding or non-coding character of the considered sequence. Coding sequences present a near to the random Pu or Py distribution. This property is shared by both protein-coding DNA and functional RNA-coding DNA. Non-coding sequences present a highly clustered inhomogeneity. We propose the hypothesis, corroborated with appropriate computer simulations, that this is due to the action of various transposition events accumulated for long time periods.
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    Bulletin of mathematical biology 59 (1997), S. 1047-1075 
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    Notes: Abstract The potential generated in the smooth muscle of the vas deferens on release of a quantum of transmitter from a varicosity was analyzed using a three-dimensional bidomain continuum model. Current was injected at the origin of the bidomain; this current had the temporal characteristics of the junctional current. The membrane potential, intracellular potential, and extracellular potential, as well as the extracellular current, were then calculated throughout the bidomain at different times. Calculations were performed to show the effect of changing the anisotropy ratios of the intracellular and extracellular conductivities on the spread of current and potential in each of the three dimensions. These results provide a theoretical framework for ascertaining the time course of transmitter interaction at a varicosity following the secretion of a quantum of transmitter.
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    Bulletin of mathematical biology 59 (1997), S. 1145-1154 
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    Notes: Abstract Parabolic growth invariably results in the survival of all competing types. Under the constraint of constant total concentration, there is a unique equilibrium in the simplex interior, which is asymptotically stable inside the whole simplex. The appropriate Lyapunov function is obtained in terms of the excess productivity which is shown to be maximized for the competitive system with fractional order kinetics. Claims to the contrary are refuted.
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    Bulletin of mathematical biology 59 (1997), S. 1191-1201 
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    Bulletin of mathematical biology 60 (1998), S. 195-196 
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    Bulletin of mathematical biology 60 (1998), S. 101-129 
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    Notes: Abstract Due to the increasing importance of the extracellular matrix in many biological problems, in this paper we develop a model for fibroblast and collagen orientation with the ultimate objective of understanding how fibroblasts form and remodel the extracellular matrix, in particular its collagen component. The model uses integrodifferential equations to describe the interaction between the cells and fibers at a point in space with various orientations. The equations are studied both analytically and numerically to discover different types of solutions and their behavior. In particular we examine solutions where all the fibroblasts and collagen have discrete orientations, a localized continuum of orientations and a continuous distribution of orientations with several maxima. The effect of altering the parameters in the system is explored, including the angular diffusion coefficient for the fibroblasts, as well as the strength and range of the interaction between fibroblasts and collagen. We find the initial conditions and the range of influence between the collagen and the fibroblasts are the two factors which determine the behavior of the solutions. The implications of this for wound healing and cancer are discussed including the conclusion that the major factor in determining the degree of scarring is the initial deposition of collagen.
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    Bulletin of mathematical biology 60 (1998), S. 215-230 
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    Notes: Abstract This paper considers the time to extinction for a stochastic epidemic model of SEIR form without replacement of susceptibles. It first shows how previous rigorous results can be heuristically explained in terms of the more transparent dynamics of an approximating deterministic system. The model is then extended to include a host population structured into patches, with weak nearest-neighbour mixing of infection. It is shown, by considering the approximating deterministic system, that the expected time to extinction in a population of n + 1 patches each of size N is of the form a log N + bn, provided that N 〉 N c where N c is a critical patch size below which transits are unlikely to occur. This corresponds to the simple decomposition of the time of an epidemic into the time it takes to spread through one patch plus the time it takes to transit to each of n successive patches. Expressions for this threshold and the coefficients of the time to extinction are given in terms of the transmission parameters of infection and the coupling strength between patches. These expressions are compared with numerical results using parameters relevant to a study of phocine distemper virus in North Sea seals, and the agreement is found to be good for large and small N. In the region when N ≈ N c , where transits may or may not occur, interesting transitional behaviour is seen, leading to a non-monotonicity of the extinction time as a function of N.
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    Bulletin of mathematical biology 60 (1998), S. 409-415 
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    Bulletin of mathematical biology 60 (1998), S. 355-372 
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    Notes: Abstract When directly transmitted infectious diseases are modeled assuming an everlasting induced immunity (and constant contact rate), there are well-established formulas to deal with, which is not true if we include the loss of induced immunity. In general, the immunity induced by the disease is everlasting. We propose a model considering the loss of immunity and present methods for the estimation of two epidemiological parameters: the force of infection and the basic reproduction ratio. We also analyze the effects of the loss of immunity on these parameters. Based on these results, we conclude that reinfection can play an important role in highly vaccinated populations.
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    Bulletin of mathematical biology 60 (1998), S. 449-475 
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    Notes: Abstract We studied mathematical models for the length distributions of actin filaments under the effects of polymerization/depolymerization, and fragmentation. In this paper, we emphasize the effects of these two processes acting alone. In this case, simple discrete and continuous models can be derived and solved explicitly (in several special cases), making the problem interesting from a modeling and pedagogical point of view. In a companion paper (Ermentrout and Edelstein-Keshet, 1998, Bull. Math. Biol. 60, 477–503) we investigate what happens when the processes act together, with particular attention to fragmentation by gelsolin, and with a greater level of biological detail.
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    Bulletin of mathematical biology 60 (1998), S. 197-213 
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    Notes: Abstract A possible experimental design for combination experiments is to compare the doseresponse curve of a single agent with the corresponding curve of the same agent using either a fixed amount of a second one or a fixed dose ratio. No interaction is then often defined by a parallel shift of these curves. We have performed a systematic study for various types of doseresponse relations both for the dose-additivity (Loewe additivity) and for the independence (Bliss independence) criteria for defining zero interaction. Parallelism between doseresponse curves of a single agent and those of the same agent in the presence of a fixed amount of another one is found for the Loewe-additivity criterion for linear doseresponse relations. For nonlinear relations, one has to differentiate between effect parallelism (parallel shift on the effect scale) and dose parallelism (parallel shift on the dose scale). In the case of Loewe additivity, zero-interaction dose parallelism is found for power, Weibull, median-effect and logistic doseresponse relations, given that special parameter relationships are fulfilled. The mechanistic model of competitive interaction exhibits dose parallelism but not effect parallelism for Loewe additivity. Bliss independence and Loewe additivity lead to identical results for exponential doseresponse curves. This is the only case for which dose parallelism was found for Bliss independence. Parallelism between single-agent doseresponse relations and Loewe additivity mixture relations is found for examples with a fixed doseratio design. However, this is again not a general property of the design adopted but holds only if special conditions are fulfilled. The comparison of combination doseresponse curves with single-agent relations has to be performed taking into account both potency and shape parameters. The results of this analysis lead to the conclusion that parallelism between zero interaction combination and single-agent doseresponse relations is found only for special cases and cannot be used as a general criterion for defining zero-interaction in combined-action assessment even if the correct potency shift is taken into account.
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    Bulletin of mathematical biology 59 (1997), S. 763-785 
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    Notes: Abstract The purpose of this study was to investigate strategies in the monotherapy treatment of HIV infection in the presence of drug-resistant (mutant) strains. A mathematical system is developed to model resistance in HIV chemotherapy. It includes the key players in the immune response to HIV infection: virus and both uninfected CD4+ and infected CD4+ T-cell populations. We model the latent and progressive stages of the disease, and then introduce monotherapy treatment. The model is a system of differential equations describing the interaction of two distinct classes of HIV—drug-sensitive (wild type) and drug-resistant (mutant)—with lymphocytes in the peripheral blood. We then introduce chemotherapy effects. In the absence of treatment, the model produces the three types of qualitative clinical behavior—anuninfected steady state, andinfected steady state (latency), andprogression to AIDS. Simulation of treatment is provided for monotherapy, during theprogression to AIDS state, in the consideration of resistance effects. Treatment benefit is based on an increase or retention in CD4+ T-cell counts together with a low viral titer. We explore the following treatment approaches: an antiviral drug which reduces viral infectivity that is administered early—when the CD4+ T-cell count is ≥300/mm3, and late—when the CD4+ T-cell count is less than 300/mm3. We compare all results with data. When treatment is initiated during the progression to AIDS state, treatment prevents T-cell collapse, but gradually loses effectiveness due to drug resistance. We hypothesize that it is the careful balance of mutant and wild-type HIV strains which provides the greatest prolonged benefit from treatment. This is best achieved when treatment is initiated when the CD4+ T-cell counts are greater than 250/mm3, but less than 400/mm3 in this model (i.e. not too early, not too late). These results are supported by clinical data. The work is novel in that it is the first model to accurately simultate data before, during and after monotherapy treatment. Our model also provides insight into recent clinical results, as well as suggests plausible guidelines for clinical testing in the monotherapy of HIV infection.
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    Bulletin of mathematical biology 59 (1997), S. 833-856 
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    Notes: Abstract A mathematical model which describes adhesion of bacteria to host cell lines is presented. The model is flexible enough to account for the following situations: extracellular bacteria are either in exponential or in stationary phase. Adhesion is described as a reversible binding process in which the bacteria attach to or detach from specific receptors uniformly distributed on the cell surface. In turn, attached bacteria can either replicate or, conversely, they are restrained to remain in stationary phase. In the first case, however, we must consider the problem of whether the decrease of unoccupied receptors as adhesion progresses imposes a limit to the replicating capacity of the attached bacteria. The effect exerted by the multiplicity of infection (MOI), i.e. the ratio of the number of bacteria to the number of host cells, on the process of adhesion is also contemplated by the model. This has revealed that experiments performed at the same values of MOI can show completely different levels of adhered bacteria, depending on the number of host cells in the assays. This finding demonstrates that the report of the MOI values is insufficient to characterize comparative studies of bacterial adhesion since it could lead to a misunderstanding of the corresponding data. Simplified models based on the steady-state approximation and in equilibrium analysis by means of a Lagmuir adsorption isotherm for the attached bacteria are also discussed. This allows us to define the adhesion coefficient (β) in a given bacterium-cell system so that, with the exception of those systems where these coefficients cannot be defined, larger values of β are related to a greater adhesion capacity. An overview of the procedures to perform quantitative adhesion data analysis is outlined. Finally, theoretical predictions are compared with experimental results from the literature.
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    Bulletin of mathematical biology 59 (1997), S. 897-910 
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    Notes: Abstract A new measure of toxicity based on stochastic modelling of single photon-counting processes, representing time-resolved phagocyte luminescence of xenobiotic-perturbed human neutrophils, has been constructed. The stochastic measure of toxicity has been verified by the QSAR method, and then compared and contrasted with the traditional toxicity measure used in bio- and chemiluminescent research. Phenol and benzene homologues were chosen as perturbers due to their importance from the viewpoint of ecotoxicology and occupational medicine.
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    Bulletin of mathematical biology 59 (1997), S. 953-973 
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    Notes: Abstract We describe a mathematical model of the flow and deformation in a human teat. Our aim is to compare the theoretical milk yield during infant breast feeding with that obtained through the use of a breast pump. Infants use a peristaltic motion of the tongue, along with some suction, to extract milk, whereas breast pumps use a cyclic pattern of suction only. Our model is based on quasi-linear poroelasticity whereby the teat is modelled as a cylindrical porous elastic material saturated with fluid. We impose a cyclic axial suction pressure difference across the teat and impose a radial compressive force moving along the teat which mimics infant suckling. This is compared to the case of cyclic and steady pumping only which models the action of breast pumps. The results illustrate that there is an optimal time to apply the compressive force during the suction cycle that will increase the flow rate in our theoretical teat. The model and results may be of use in the future design of effective breast pumps.
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    Bulletin of mathematical biology 59 (1997), S. 993-1012 
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    Notes: Abstract In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materals are depicted in graphical forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissues.
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    Bulletin of mathematical biology 59 (1997), S. 1077-1100 
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    Notes: Abstract Adult dermal wounds, in contrast to fetal wounds, heal with the formation of scar tissue. A crucial factor in determining the degree of scarring is the ratio of types I and III collagen, which regulates the diameter of the combined fibers. We developed a reaction-diffusion model which focuses on the control of collagen synthesis by different isoforms of the polypeptide transforming growth factor-β (TGFβ). We used the model to investigate the current controversy as to whether the fibroblasts migrate into the wound from the surrounding unwounded dermis or from the underlying subcutaneous tissue. Numerical simulations of a spatially independent, temporal model led to a value of the collagen ratio consistent with that of healthy tissue for the fetus, but corresponding to scarring in the adult. We investigated the effect of topical application of TGFβ and show that addition of isoform 3 reduces scar tissue formation, in agreement with the experiment. However, numerical solutions of the reaction-diffusion system do not exhibit this sensitivity to growth factor application. Mathematically, this corresponds to the observation that behind healing wavefront solutions, a particular healed state is always selected independent of transients, even though there is a continuum of possible positive steady states. We explain this phenomenon using a caricature system of equations, which reflects the key qualitative features of the full model but has a much simpler mathematical form. Biologically, our results suggest that the migration into a wound of fibroblasts and TGFβ from the surrounding dermis alone cannot account for the essential features of the healing process, and that fibroblasts entering from the underlying subcutaneous tissue are crucial to the healing process.
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    Bulletin of mathematical biology 59 (1997), S. 1125-1144 
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    Notes: Abstract Oscillations in cytosolic Ca2+ concentrations in living cells are often a manifestation of propagating waves of Ca2+. Numerical simulations with a realistic model of inositol 1, 4, 5-trisphosphate (IP3)-induced Ca2+ wave trains lead to wave speeds that increase linearly at long times when (a) IP3 levels are in the range for Ca2+ oscillations, (b) a gradient of phase is established by either an initial ramp or pulse of IP3, and (c) IP3 concentrations asymptotically become uniform. We explore this phenomenon with analytical and numerical methods using a simple two-variable reduction of the De Young-Keizer model of the IP3 receptor that includes the influence of Ca2+ buffers. For concentrations of IP3 in the oscillatory regime, numerical solution of the resulting reaction diffusion equations produces nonlinear wave trains that shows the same asymptotic growth of wave speed. Due to buffering, diffusion of Ca2+ is quite slow and, as previously noted, these waves occur without appreciable bulk movement of Ca2+. Thus, following Neu and Murray, we explore the behavior of these waves using an asymptotic expansion based on the small size of the buffered diffusion constant for Ca2+. We find that the gradient in phase of the wave obeys Burgers' equation asymptotically in time. This result is used to explain the linear increase of the wave speed observed in the simulations.
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    Bulletin of mathematical biology 59 (1997), S. 1183-1189 
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    Notes: Abstract The robustness of patterning events in development is a key feature that must be accounted for in proposed models of these events. When considering explicitly cellular systems, robustness can be exhibited at different levels of organization. Consideration of two widespread patterning mechanisms suggests that robustness at the level of cell communities can result from variable development at the level of individual cells; models of these mechanisms show how interactions between participating cells guarantee community-level robustness. Cooperative interactions enhance homogeneity within communities of like cells and the sharpness of boundaries between communities of distinct cells, while competitive interactions amplify small inhomogeneities within communities of initially equivalent cells, resulting in fine-grained patterns of cell specialization.
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    Bulletin of mathematical biology 60 (1998), S. 1-26 
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    Notes: Abstract Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate, numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development.
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    Bulletin of mathematical biology 60 (1998), S. 79-100 
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    Notes: Abstract A model, based on the principles of continuum mechanics, is presented for the analysis of cell-velocity fields within wool follicles. The model requires specification of three follicle characteristics in the form of spatially varying fields: viscosity, cell density and cell production rate. The viscosity is introduced as an attempt to model both complex intercellular interactions and individual cell deformation as the cells move. It is demonstrated that the distribution of cell production is more important than axial variation in viscosity in determining the overall flow pattern.
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    Bulletin of mathematical biology 60 (1998), S. 131-150 
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    Notes: Abstract A microbial trichome extracts nutrients from its immediate surroundings. It may also oxidize electron donors, reduce electron acceptors, and exude the ‘waste’ products of endogenous redox metabolism. Finally, it may effect light harvesting. These exchange fluxes are summed up in a generic model, which covers photoautotrophs as well as chemoheterotrophs. The focus is on endogenous metabolism and the cellular homeostasis of both reducing and phosphorylating equivalents. A novel result is the formulation of four ‘rules’, akin to the Pasteur effect, which govern the compatibility of endogenous metabolism with various assimilatory processes.
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    Bulletin of mathematical biology 60 (1998), S. 49-65 
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    Notes: Abstract In this paper we present a deterministic, discrete-time model for a two-patch predator-prey metapopulation. We study optimal harvesting for the metapopulation using dynamic programming. Some rules are established as generalizations of rules for a single-species metapopulation harvesting theory. We also establish rules to harvest relatively more (or less) vulnerable prey subpopulations and more (or less) efficient predator subpopulations.
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    Bulletin of mathematical biology 60 (1998), S. 919-935 
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    Notes: Abstract To analyze signals measured from human blood flow in the time-frequency domain, we used the wavelet transform which gives good time resolution for high-frequency components and good frequency resolution for low-frequency components. Five characteristic frequency peaks, corresponding to five almost periodic rhythmic activities, were found on the time scale of minutes. These oscillations were characterized by time and spatial invariant measures. The potential of this approach in studying the blood-flow dynamics was illustrated by revealing differences between the groups of control subjects and athletes.
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    Bulletin of mathematical biology 60 (1998), S. 997-998 
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    Bulletin of mathematical biology 60 (1998), S. 1167-1200 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The interaction of a pair of weakly coupled biological bursters is examined. Bursting refers to oscillations in which an observable slowly alternates between phases of relative quiescence and rapid oscillatory behavior. The motivation for this work is to understand the role of electrical coupling in promoting the synchronization of bursting electrical activity (BEA) observed in the β-cells of the islet of Langerhans, which secrete insulin in response to glucose. By studying the coupled fast subsystem of a model of BEA, we focus on the interaction that occurs during the rapid oscillatory phase. Coupling is weak, diffusive and non-scalar. In addition, non-identical oscillators are permitted. Using perturbation methods with the assumption that the uncoupled oscillators are near a Hopf bifurcation, a reduced system of equations is obtained. A detailed bifurcation study of this reduced system reveals a variety of patterns but suggests that asymmetrically phase-locked solutions are the most typical. Finally, the results are applied to the unreduced full bursting system and used to predict the burst pattern for a pair of cells with a given coupling strength and degree of heterogeneity.
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    Bulletin of mathematical biology 60 (1998), S. 1017-1037 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Hemodynamic forces affect endothelial cell morphology and function. In particular, circumferential cyclic stretch of blood vessels, due to pressure changes during the cardiac cycle, is known to affect the endothelial cell shape, mediating the alignment of the cells in the direction perpendicular to stretch. This change in cell shape proceeds a drastic reorganization at the internal level. The cellular scaffolding, mainly composed of actin filaments, reorganize in the direction which later becomes the cell’s long axis. How this external mechanical stimulus is ’sensed’ and transduced into the cell is still unknown. Here, we develop a mathematical model depicting the dynamics of actin filaments, and the influence of the cyclic stretch of the substratum based on the experimental evidence that external stimuli may be transduced inside the cell via transmembrane proteins which are coupled with actin filaments on the cytoplasmic side. Based on this view, we investigate two approaches describing the formulation of the transduction mechanisms involving the coupling between filaments and the membrane proteins. As a result, we find that the mechanical stimulus could cause the experimentally observed reorganization of the entire cytoskeleton simply by altering the dynamics of the filaments connected with the integral membrane proteins, as described in our model. Comparison of our results with previous studies of cytoskeletal dynamics reveals that the cytoskeleton, which, in the absence of the effect of stretch would maintain its isotropic distribution, slowly aligns with the precise direction set by the external stimulus. It is found that even a feeble stimulus, coupled with a strong internal dynamics, is sufficient to align actin filaments perpendicular to the direction of stretch.
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    Bulletin of mathematical biology 60 (1998), S. 1149-1166 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract We study a general predator—prey system in a spatially heterogeneous environment. The predation process, which occurs on a behavioural time-scale, is much faster than the other processes (reproduction, natural mortality and migrations) occurring on the population dynamics time-scale. We show that, taking account of this difference in time-scales, and assuming that the prey have a refuge, the dynamics of the system on a slow time-scale become donor-controlled. Even though predators may control the prey density locally and on a behavioural fast time-scale, nevertheless, both globally and on a slow time-scale, the prey dynamics are independent of predator density: the presence of predators generates a constant prey mortality. In other words, in heterogeneous environments, the prey population dynamics depend in a switch-like manner on the presence or absence of predators, not on their actual density.
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    The journal of Fourier analysis and applications 4 (1998), S. 283-297 
    ISSN: 1531-5851
    Keywords: Primary 42B25 ; 30D10 ; Secondary 26A16 ; 46B45 ; 47B10 ; 47B35 ; Mean oscillation ; Paley-Wiener space ; Besov spaces ; wavelets ; commutators ; Hankel operators ; Schatten-von Neumann ideals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The oscillatory behavior of functions with compactly supported Fourier transform is characterized in a quantified way using various function spaces. In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points. Several open questions about spaces of sequences are answered and applications in the study of commutator operators on the Paley-Wiener space are shown.
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    The journal of Fourier analysis and applications 4 (1998), S. 329-340 
    ISSN: 1531-5851
    Keywords: 42C15 ; 46E35 ; Wavelets ; function spaces ; fractals
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    Topics: Mathematics
    Notes: Abstract Wavelets on self-similar fractals are introduced. It is shown that for certain totally disconnected fractals, function spaces may be characterized by means of the magnitude of the wavelet coefficients of the functions.
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    The journal of Fourier analysis and applications 4 (1998), S. 357-375 
    ISSN: 1531-5851
    Keywords: 42C15 ; 94A12 ; wavelets ; interpolation ; orthogonal expansions
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    Topics: Mathematics
    Notes: Abstract Gibbs' phenomenon occurs for most orthogonal wavelet expansions. It is also shown to occur with many wavelet interpolating series, and a characterization is given. By introducing modifications in such a series, it can be avoided. However, some series that exhibit Gibbs' phenomenon for orthogonal series do not for the associated sampling series.
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    Transformation groups 2 (1997), S. 225-267 
    ISSN: 1531-586X
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    Topics: Mathematics
    Notes: Abstract We study Edidin and Graham's equivariant Chow groups in the case of torus actions. Our main results are: (i) a presentation of equivariant Chow groups in terms of invariant cycles, which shows how to recover usual Chow groups from equivariant ones; (ii) a precise form of the localization theorem for torus actions on projective, nonsingular varieties; (iii) a construction of equivariant multiplicities, as functionals on equivariant Chow groups; (iv) a construction of the action of operators of divided differences on theT-equivariant Chow group of any scheme with an action of a reductive group with maximal torusT. We apply these results to intersection theory on varieties with group actions, especially to Schubert calculus and its generalizations. In particular, we obtain a presentation of the Chow ring of any smooth, projective spherical variety.
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    Transformation groups 2 (1997), S. 375-390 
    ISSN: 1531-586X
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    Topics: Mathematics
    Notes: Abstract In this paper we explicitly determine the virtual representations of the finite Weyl subgroups of the affine Weyl group on the cohomology of the space of affine flags containing a family of elementsn t in an affine Lie algebra. We also compute the Euler characteristic of the space of partial flags containingn t and give a connection with hyperplane arrangements.
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    Transformation groups 2 (1997), S. 351-374 
    ISSN: 1531-586X
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    Topics: Mathematics
    Notes: Abstract LetG be a connected, simply-connected, real semisimple Lie group andK a maximal compactly embedded subgroup ofG such thatD=G/K is a hermitian symmetric space. Consider the principal fiber bundleM=G/K s →G/K, whereK s is the semisimple part ofK=K s ·Z K 0 andZ K 0 is the connected center ofK. The natural action ofG onM extends to an action ofG 1=G×Z K 0 . We prove as the main result thatM is weakly symmetric with respect toG 1 and complex conjugation. In the case whereD is an irreducible classical bounded symmetric domain andG is a classical matrix Lie group under a suitable quotient, we provide an explicit construction ofM=D×S 1 and determine a one-parameter family of Riemannian metrics Ω onM invariant underG 1. Furthermore,M is irreducible with respect to Ω. As a result, this provides new examples of weakly symmetric spaces that are nonsymmetric, including those already discovered by Selberg (cf. [M]) for the symplectic case and Berndt and Vanhecke [BV1] for the rank-one case.
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    Circuits, systems and signal processing 16 (1997), S. 27-40 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The Wigner bispectrum of multicomponent signals is studied, and its modified and reduced forms are introduced. A generalization of the presented forms to the Wigner higher-order spectra (WHOS), in the case of multicomponent signals, is provided. From our previous work it is known that cross terms removal (reduction) is possible for odd-order spectra with equal numbers of conjugated and nonconjugated terms. Here, we extend the analysis to even-order spectra. The theory is illustrated by examples.
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    Circuits, systems and signal processing 16 (1997), S. 83-89 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We describe methods to establish identifiability and information-regularity of parameters in normal distributions. Parameters are considered identifiable when they are determined uniquely by the probability distribution and they are information-regular when their Fisher information matrix is full rank. In normal distributions, information-regularity implies local identifiability, but the converse is not always true. Using the theory of holomorphic mappings, we show when the converse is true, allowing information-regularity to be established without having to explicitly compute the information matrix. Some examples are given.
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    Circuits, systems and signal processing 16 (1997), S. 141-163 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The extendibility of estimated correlation bisequences from an available sampled data array is described in terms of the generating functions of associated block Toeplitz with Toeplitz block (BTTB) matrices. The periodogram-based correlation bisequences are shown to be extendible. It is shown that the method of resultants and subresultants is convenient for generating the nonlinear constraints in the optimization problem which is solved iteratively for power spectrum estimation. A nontrivial example illustrates the concepts developed.
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    Circuits, systems and signal processing 16 (1997), S. 217-239 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A multiresolutional approach is presented for effectively recognizing three-dimensional (3D) objects. The approach is both pose and scale invariant. A multiresolutional model base is constructed, and multiscale edges of the object are detected using the wavelet transform. The minimum alignment between model base and object is realized by the linear mapping scheme.
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    Circuits, systems and signal processing 16 (1997), S. 59-67 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The potential for data compression in using fractal interpolation functions (FIFs) is realized by the construction of a set of multirate filters. The filter tap weights are determined by optimizing the energy contents of a preselected set of frequency bands. This filter bank implementation of the FIF is successfully used to compress data simulated in a tracking environment.
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    Circuits, systems and signal processing 16 (1997), S. 91-106 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A first-order autoregressive filter is altered by changing the constant gain to two or more gains that cyclically alternate in time. The advantages of this system are shown, and the relation to linear autoregressive moving average difference equations of higher order is derived.
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    Circuits, systems and signal processing 16 (1997), S. 165-195 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper refers to the fast implementation of the positional forward acceleration of the end effector of revolute robotic arms with spherical wrists, using the distributed arithmetic technique. The acceleration of the end effector is calculated by a cascade configuration of two pipelined arrays that calculate the Jacobian matrix and its time derivative, as well as the centrifugal-Coriolis and linear accelerations. These partial accelerations are then added in the adder tree. The building blocks of the arrays are the distributed arithmetic-based circuits that implement the matrix-vector multiplications involved in the calculations. The digit-serial configuration of the proposed implementation of the positional forward acceleration of the end effector is described. The serial and the parallel configurations may result as special cases of the digit-serial configuration. The proposed distributed arithmetic (DA) implementation of the positional forward acceleration may be applied, after appropriate modifications, to the general case of robots having either revolute or prismatic joints, with any type of wrist.
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    Circuits, systems and signal processing 16 (1997), S. 241-245 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper addresses the calculation of the extrema of the sin x/x function. First the Newton-Raphson method is used, which allows us to obtain the extrema locations very fast through the use of a recursion formula. Then a second approach is proposed, which gives the extrema locations and the extrema amplitudes in the form of series expansions. Simple, accurate algebraic expressions are derived.
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    Circuits, systems and signal processing 16 (1997), S. 307-324 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We give some existence results for a resistive network in which the components are neither voltage nor current controlled; that is, they are merely unicursal. In fact we allow coupling. Degree arguments give existence and bounds. We study several ways of avoiding the requirement of eventual passivity. No-gain and passive multiterminal elements are included. The results are extended to infinite networks.
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    Circuits, systems and signal processing 16 (1997), S. 375-386 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Random sampling is one of the methods that can overcome the Nyquist limit when evaluating a frequency spectrum of a signal. However, the computational complexity becomesN 2 as the FFT cannot be used. A new approach, called hybrid additive random sampling, is proposed. This new scheme is devised by concatenating random sampling sequences in such a way that symmetry is created in the transform kernel for reducing the computational effort while the anti-alias property is maintained. A savings of the least 75% in computation is achieved. The sampling scheme is also found to be suitable for parallel implementation. In this paper, the algorithms for generating the sampling sequence and evaluating the spectrum are described in detail. The performances of the scheme in terms of noise, accuracy, etc., are compared with genuine random sampling and another approach proposed previously. The advantages and limitations are included.
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    Circuits, systems and signal processing 17 (1998), S. 85-102 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, we present a hybrid space-time-filtered Viterbi receiver using multiple antennas for co-channel interference (CCI) reduction and intersymbol interference (ISI) equalization in a slow Rayleigh fading channel. In this approach, a space-time filter is first applied at the antenna outputs to maximize the signal-to-interference-plus-noise ratio (SINR), and the scalar output is then sent to a Viterbi equalizer. We propose a closed-form solution to jointly determine the weight vector for the space-time filter and the channel vector for the Viterbi equalizer. We also examine the need for a whitening filter prior to the Viterbi equalizer and show that it only marginally improves the performance. Simulation results are provided to validate our approach and to compare the performance of our receiver with that of different existing receivers.
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    Circuits, systems and signal processing 17 (1998), S. i 
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    Circuits, systems and signal processing 17 (1998), S. 123-136 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Prosthetic heart valves have been responsible for extending the life spans and improving the quality of life of many people with serious heart conditions. Even though the heart valves are extremely reliable, eventually they are susceptible to the long-term fatigue and structural failure effects expected for mechanical devices operating over long periods of time. In [2] a classification procedure was developed using spectral features obtained from acoustic signals to determine the condition of the prosthetic heart valve. Although this classification procedure has produced very encouraging results, this method still lacks a fundamental physical description of the sounds produced by the valve during normal operation. In order to obtain a better understanding of the valve acoustic response, we have performed a set of anechoic tests. In this paper, we describe the anechoic experiment and also present limited transient response results. This transient information will eventually be used to identify and improve the features used to classify the valve condition.
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    Circuits, systems and signal processing 17 (1998), S. 195-218 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this two-part study we present a new design methodology for neural classifiers. The design procedure utilizes a multiclass vector quantization (MVQ) algorithm for information extraction from the training set. The extracted information suffices to specify the hidden layer in a canonical neural network architecture. The extracted information also leads to the specification of neuron inhibition rules and subsequently the design of the hidden layer-to-output map. In Part I of the study we focus attention on the MVQ algorithm and how it is used to extract information from a training set. The extracted information is referred to as thecodebook. The codebook is used to directly specify the hidden layer. This specification can take the form of a perceptron layer, a radial basis layer, or a heterogeneous layer involving a mixture of neuron types. These and otherh-layer specifications are determined directly from the same extracted information. The MVQ codebook also suffices to scale the activation function of each neuron. In Part II we consider the nonsimplistic hidden layer-to-output map design. We note that the MVQ algorithm, as it extracts information, decomposes the design set into disjoint neighborhoods. For each neighborhood we identify subsets of the hidden layer neurons, which are significant sensors for the neighborhood. For each such subset we construct an output map. Inhibition rules are established to ensure that the proper output map is activated. In benchmark simulations the overall design exhibits excellent performance, to the extent that we are hard pressed to identify bounds on performance, if any.
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    Circuits, systems and signal processing 17 (1998), S. 361-389 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A transform domain image tagging orwatermarking method that survives image cropping (and, hence, is “holographic”) was proposed at Bell Labs in September 1994. This report analyzed in detail the various properties of this method and introduces an optimal procedure for watermark recovery.
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    Circuits, systems and signal processing 17 (1998), S. 483-493 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract An algorithm for the exact computation of the frequency responses of linear interval systems is obtained. For the computation a sectoring stage is added to an elimination algorithm to eliminate interior curves. It is shown that the intersection of a ray and the frequency response set is an empty set or a line segment whose endpoints are extrema of the functions defined. Required mathematical analysis tools for the development of the sectoring algorithm and an illustrative example are provided.
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    Circuits, systems and signal processing 17 (1998), S. 559-574 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The geometric theory of the domain of an ordered pair (F, G) of matrices or the geometry associated with matrix pencils provides a unifying framework for the study of algebraic, dynamic and feedback properties of linear singular systems. The key concepts and tools of the geometry are the notions of the (F, G)-, (G, F)-invariance and a set of subspace sequences. In this paper, an alternative characterization of these sequences is given based on the properties of the partitioned null spaces of appropriate sequences of Toeplitz matrices defined by the (F, G) pair. The results provide a simple procedure for the computation of the limit spaces of these sequences and clearly cover corresponding problems of the singular, implicit systems theory.
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    Circuits, systems and signal processing 17 (1998), S. 667-682 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a new concept of narrowband and broadband active noise compression (ANCom) systems which improves the conventional active noise equalization (ANE) technique to meet some practical requirements. By using a variable equalization coefficient, the narrowband ANCom system can automatically switch among the four different operating modes of narrowband ANE, according to the primary noise power. As a result, it can “compress” the narrowband noise into a desired power range when the primary noise power varies drastically. Compared to a conventional broadband ANE system, the novel broadband ANCom system not only has the ability to shape the residual noise power spectrum, but can also compress the residual noise power into a predetermined dynamic range as the narrowband AN-Com does. Theoretical analyses are conducted for both the narrowband ANCom and broadband ANCom systems. Simulation results show that the proposed algorithms work well in both static and dynamic situations.
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    Circuits, systems and signal processing 17 (1998), S. 703-708 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The cornerstone of the theory of discrete-space single-input single-output linear systems is the idea that every such system has an input-output mapH that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight, which, for the case of bounded inputs mapped continuously into bounded outputs, was recently corrected by adding an additional term to the representation. Here we give a more general result that addresses an important larger family of inputs.
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    Circuits, systems and signal processing 17 (1998), S. 737-755 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper the problem of robust stabilizing a linear, time-invariant singular system is studied. The characterization is given in terms ofH ∞-bounded perturbations to the numerator and denominator factors of its normalized left coprime factorization. An optimal stability margin is provided in terms of the definition of the Hankel norm of a singular system. The Hankel norm is computed using two generalized Lyapunov equations.
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    Circuits, systems and signal processing 16 (1997), S. 41-58 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a comparison between the traditional image processing method and the area vector concept as well as the new technique of artificial neural networks. Freeman chain coding is considered in the study, and the principle of segmentation may be based and implemented for further investigations resulting from the proposed work. The pattern recognition concept is analyzed and defined through the sigmoid function and the determination of the threshold of a gray image for an object. The block schemes for the given protocols are summarized in a single scheme for illustration and comparison purposes. The synthetic pictures are generated and investigated regarding the dependence of computer vision on the contents of the artificial neural network. The normalization technique is included to eliminate noise and zooming problems. The minimum computational time for image processing with the generated pictures is also determined. The rate of deflection in the computational time is recommended for sensing the minimum computational time according to the variation of the number of hidden units in the hidden layer. A three-layer neural network has been used. The study of gray binary imaging for color pictures is illustrated to save computational time and effort.
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    Circuits, systems and signal processing 16 (1997), S. 247-270 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Of concern is an environment made up of signals and systems tightly confined both in time and frequency. Such an environment is often encountered in transmission line circuits, radar, sonar, and optical circuits, and when the principal signals are well-defined sharp pulses. It will be seen that once this environment is achieved, the signals and systems possess some attractive properties. A conventional system may preserve the symmetry of a propagating signal or change its symmetry from even to odd or from odd to even. Another system may be used to predict the arrival of an incoming pulse with a high degree of accuracy. Electrical networks may also be associated with these properties. Approximation problems, existence theorems, and realization schemes will be addressed and developed.
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